Showing 1–50 of 74 results for author: Cross, M

A multi-agent system for spine MRI report generation from multi-sequence imaging

Authors: Zhiping Xiao, Junwei Yang, Gongbo Sun, Han Zhang, Hanwen Xu, Yi Yao, Zachary D. Miller, William E. King III, Mohammed M. Kanani, Jalal B. Andre, Sammy Chu, Ming Zhang, Paul E. Kinahan, Nathan M. Cross, Sheng Wang

Abstract: Spinal pathology is a leading cause of pain and disability worldwide. Spine MRI is central to clinical evaluation, yet its interpretation remains complex and time-consuming, requiring integration of information across multiple imaging sequences and anatomical regions. Despite recent advances in automated MRI analysis, effectively combining multi-sequence data while preserving sequence-specific dia… ▽ More Spinal pathology is a leading cause of pain and disability worldwide. Spine MRI is central to clinical evaluation, yet its interpretation remains complex and time-consuming, requiring integration of information across multiple imaging sequences and anatomical regions. Despite recent advances in automated MRI analysis, effectively combining multi-sequence data while preserving sequence-specific diagnostic information remains an open challenge. Here we present SpineAgent, a multi-agent framework for spine MRI report generation built upon a multi-sequence foundation model trained on routine clinical data from 32,047 patients and 453,683 MRI series, comprising a total of 13,441,191 MRI slices. To accommodate diverse modalities of sequences, we first pre-train two DINOv3-based encoders separately on T1- and T2-weighted sequences. We then introduce a continual training strategy that learns a synthesizer to embed images of other sequences using the T1 and T2 encoders, producing patient-level embedding that integrates various signals across MRI sequences. Using these embeddings, SpineAgent achieves state-of-the-art performance, and demonstrates strong generalizability under cross-manufacturer and cross-cohort evaluation. Beyond classification, SpineAgent enables pathology localization by identifying findings-relevant slices and segmenting pathological regions. It also supports multimodal image-report retrieval, providing a solid foundation for scalable and explainable MRI report generation. We further integrate these validated capabilities of SpineAgent into 37 specialized agents. Finally, we incorporate their outputs as structured tokens within a Medical Report Agent trained end-to-end for report generation. Through both automated metrics and expert evaluation by five radiologists, SpineAgent achieves leading performance in spine MRI report generation. △ Less

Submitted 7 June, 2026; originally announced June 2026.

MSC Class: 68T07 ACM Class: J.3; I.2.1

Terahertz field-induced giant symmetry modulations in a van der Waals antiferromagnet

Authors: Sheikh Rubaiat Ul Haque, Martin J. Cross, Sangeeta Rajpurohit, Jonah B. Haber, Christopher J. Ciccarino, Alexandra C. Zimmerman, Isabelle J. Sealey, Vadym Kulichenko, Monique Tie, Huaiyu Wang, Sharon S. Philip, Choongwon Seo, Jake D. Koralek, Luis Balicas, Mykhaylo Ozerov, Dmitry Smirnov, Liang Z. Tan, Felipe H. da Jornada, Tadashi Ogitsu, Matthias C. Hoffmann, Tony F. Heinz, Aaron M. Lindenberg

Abstract: Strong-field terahertz (THz) excitations enable dynamic control over electronic, lattice and symmetry degrees of freedom in quantum materials. Here, we uncover pronounced terahertz-induced symmetry modulations and coherent phonon dynamics in the van der Waals antiferromagnet MnPS3, in which inversion symmetry is broken by its antiferromagnetic spin configuration. Time-resolved second harmonic gene… ▽ More Strong-field terahertz (THz) excitations enable dynamic control over electronic, lattice and symmetry degrees of freedom in quantum materials. Here, we uncover pronounced terahertz-induced symmetry modulations and coherent phonon dynamics in the van der Waals antiferromagnet MnPS3, in which inversion symmetry is broken by its antiferromagnetic spin configuration. Time-resolved second harmonic generation measurements reveal long-lived giant oscillations in the antiferromagnetic phase, with amplitudes comparable to the equilibrium signal, driven by phonons involving percent-level atomic displacements relative to the equilibrium bond lengths. The temporal evolution of the rotational anisotropy patterns indicate a dynamic breaking of mirror symmetry, modulated by two vibrational modes at 1.7 THz and 4.5 THz, with the former corresponding to a hidden mode not observed in equilibrium spectroscopy. We show that these effects arise in part from a field-induced charge rearrangement mechanism that lowers the local crystal symmetry, and couples to the phonon modes. A long-lived field-driven response was uncovered with a complex THz polarization dependence which, in comparison to theory, indicates evidence for an antiferromagnetic-to-ferrimagnetic transition. Our results establish an effective field-tunable pathway for driving excitations otherwise weak in equilibrium, and for manipulating magnetism in low-dimensional materials via dynamical modulation of symmetry. △ Less

Submitted 1 October, 2025; originally announced October 2025.

Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement

Authors: Mattias Cross, Anton Ragni

Abstract: Current flow-based generative speech enhancement methods learn curved probability paths which model a mapping between clean and noisy speech. Despite impressive performance, the implications of curved probability paths are unknown. Methods such as Schrodinger bridges focus on curved paths, where time-dependent gradients and variance do not promote straight paths. Findings in machine learning resea… ▽ More Current flow-based generative speech enhancement methods learn curved probability paths which model a mapping between clean and noisy speech. Despite impressive performance, the implications of curved probability paths are unknown. Methods such as Schrodinger bridges focus on curved paths, where time-dependent gradients and variance do not promote straight paths. Findings in machine learning research suggest that straight paths, such as conditional flow matching, are easier to train and offer better generalisation. In this paper we quantify the effect of path straightness on speech enhancement quality. We report experiments with the Schrodinger bridge, where we show that certain configurations lead to straighter paths. Conversely, we propose independent conditional flow-matching for speech enhancement, which models straight paths between noisy and clean speech. We demonstrate empirically that a time-independent variance has a greater effect on sample quality than the gradient. Although conditional flow matching improves several speech quality metrics, it requires multiple inference steps. We rectify this with a one-step solution by inferring the trained flow-based model as if it was directly predictive. Our work suggests that straighter time-independent probability paths improve generative speech enhancement over curved time-dependent paths. △ Less

Submitted 28 August, 2025; originally announced August 2025.

Comments: preprint, accepted

Ultrafast control of coherent acoustic lattice dynamics in the transition metal dichalcogenide alloy WSSe

Authors: Sergio I. Rey, Martin J. Cross, Malte L. Welsch, Frederik Schröder, Binbin Zhou, Nicolas Stenger, Peter U. Jepsen, Edmund J. R. Kelleher

Abstract: Coherent acoustic phonons (CAPs)$-$propagating strain waves that can dynamically modify the structure and symmetry of a crystal$-$offer unique opportunities for controlling material properties. We investigate CAP generation in the Janus-like layered alloy tungsten sulfide selenide (WS$_x$Se$_{1-x}$, hereafter WSSe). Employing high-fluence photoexcitation at 400 nm combined with ultrafast transient… ▽ More Coherent acoustic phonons (CAPs)$-$propagating strain waves that can dynamically modify the structure and symmetry of a crystal$-$offer unique opportunities for controlling material properties. We investigate CAP generation in the Janus-like layered alloy tungsten sulfide selenide (WS$_x$Se$_{1-x}$, hereafter WSSe). Employing high-fluence photoexcitation at 400 nm combined with ultrafast transient reflection spectroscopy, we capture the carrier-lattice dynamics governed by a cascade of processes including rapid exciton formation, phonon recycling, and thermoelastic deformation. These phenomena precede the emergence of a robust CAP mode at 27 GHz. Notably, the CAP amplitude in WSSe substantially exceeds that observed in the symmetric parent crystals WS$_2$ and WSe$_2$, which we attribute to an enhanced coupling mediated by a built-in out-of-plane electric field arising from the inversion asymmetry of the WSSe alloy. Furthermore, the implementation of a tailored two-pulse excitation sequence enables optical control of the CAP, underscoring the potential of WSSe and related Janus-like layered alloys as versatile building blocks in optomechanical and nanoacoustic device applications. △ Less

Submitted 27 March, 2025; originally announced March 2025.

Terahertz-driven parametric excitation of Raman-active phonons in LaAlO$_{3}$

Authors: M. Basini, V. Unikandanunni, F. Gabriele, M. Cross, A. M. Derrico, A. X. Gray, M. C. Hoffmann, F. Forte, M. Cuoco, S. Bonetti

Abstract: Achieving parametric excitation in an oscillating physical system involves periodically adjusting one of its parameters to modulate the oscillator's natural frequency. This phenomenon has been observed in numerous systems within physics and engineering, profoundly transforming modern science and technology. Despite rapid progress, the parametric control of collective excitations, such as phonons,… ▽ More Achieving parametric excitation in an oscillating physical system involves periodically adjusting one of its parameters to modulate the oscillator's natural frequency. This phenomenon has been observed in numerous systems within physics and engineering, profoundly transforming modern science and technology. Despite rapid progress, the parametric control of collective excitations, such as phonons, remains a challenge while promising to generate novel and intriguing effects in a largely unexplored field. Here, we investigate the terahertz (THz) field-induced dynamics of Raman-active phonons in the perovskite structure of LaAlO$_3$ (LAO). Utilizing intense THz pulses, we demonstrate a novel mechanism of parametric phonon excitation marked by substantial subharmonic components. Theoretical analysis can successfully capture the hallmarks of the observed phenomena in a physical scenario with the THz field inducing a parametric coupling between the Raman mode and pairs of acoustic phonon excitations. △ Less

Submitted 26 January, 2026; v1 submitted 9 October, 2024; originally announced October 2024.

Comments: Main text: 12 pages, 3 figures. Supplementary Information: 5 figures

Journal ref: Phys. Rev. Lett. 136, 156902 (2026)

Identifying a severity measure for head acceleration events associated with suspected concussions

Authors: Gregory Tierney, Ross Tucker, James Tooby, Lindsay Starling, Eanna Falvey, Danielle Salmon, James Brown, Sam Hudson, Keith Stokes, Ben Jones, Simon Kemp, Patrick OHalloran, Matt Cross, Melanie Bussey, David Allan

Abstract: Objectives: To identify a head acceleration event (HAE) severity measure associated with HIA1 removals in elite level rugby union. Methods: HAEs were recorded from 215 men and 325 women with 30 and 28 HIA1 removals from men and women, respectively. Logistical regression were calculated to identify if peak power, maximum principal strain (MPS) and or Head Acceleration Response Metric (HARM) were… ▽ More Objectives: To identify a head acceleration event (HAE) severity measure associated with HIA1 removals in elite level rugby union. Methods: HAEs were recorded from 215 men and 325 women with 30 and 28 HIA1 removals from men and women, respectively. Logistical regression were calculated to identify if peak power, maximum principal strain (MPS) and or Head Acceleration Response Metric (HARM) were associated with HIA1 events compared to non-cases. Optimal threshold values were determined using the Youden Index. Area under the curve (AUC) were compared using a paired sample approach. Significant differences were set at p<0.05. Results: All three severity measures were associated with HIA1 removals in both the mens and womens game. Power performed greatest for HIA1 removals in both the mens and womens games, based on overall AUC, sensitivity, and specificity values. HARM and MPS were found to perform lower than PLA in the womens game based on AUC comparisons (p=0.006 and 0.001, respectively), with MPS performing lower than PAA (p=0.001). Conclusion: The findings progress our understanding of HAE measures associated with HIA1 removals. Peak power, a measure based on fundamental mechanics and commonly used in sports performance, may be a suitable HAE severity measure. △ Less

Submitted 2 October, 2024; originally announced October 2024.

Comments: 4 Tables, 2 Figures

What happens to diffusion model likelihood when your model is conditional?

Authors: Mattias Cross, Anton Ragni

Abstract: Diffusion Models (DMs) iteratively denoise random samples to produce high-quality data. The iterative sampling process is derived from Stochastic Differential Equations (SDEs), allowing a speed-quality trade-off chosen at inference. Another advantage of sampling with differential equations is exact likelihood computation. These likelihoods have been used to rank unconditional DMs and for out-of-do… ▽ More Diffusion Models (DMs) iteratively denoise random samples to produce high-quality data. The iterative sampling process is derived from Stochastic Differential Equations (SDEs), allowing a speed-quality trade-off chosen at inference. Another advantage of sampling with differential equations is exact likelihood computation. These likelihoods have been used to rank unconditional DMs and for out-of-domain classification. Despite the many existing and possible uses of DM likelihoods, the distinct properties captured are unknown, especially in conditional contexts such as Text-To-Image (TTI) or Text-To-Speech synthesis (TTS). Surprisingly, we find that TTS DM likelihoods are agnostic to the text input. TTI likelihood is more expressive but cannot discern confounding prompts. Our results show that applying DMs to conditional tasks reveals inconsistencies and strengthens claims that the properties of DM likelihood are unknown. This impact sheds light on the previously unknown nature of DM likelihoods. Although conditional DMs maximise likelihood, the likelihood in question is not as sensitive to the conditioning input as one expects. This investigation provides a new point-of-view on diffusion likelihoods. △ Less

Submitted 26 September, 2024; v1 submitted 10 September, 2024; originally announced September 2024.

Canceled: A New Reliability Incentive for Energy-Only Electricity Markets

Authors: Devin Mounts, Robin M. Cross

Abstract: This paper considers the reliability problem in energy-only markets. Following widespread blackouts in 2011, Texas introduced a reliability price incentive to attract two GW of net additional natural gas-generating capacity. The incentive is unusual because energy buyers pay the incentive directly to producers in a real-time spot market. The program has created $13 billion in direct payments to ge… ▽ More This paper considers the reliability problem in energy-only markets. Following widespread blackouts in 2011, Texas introduced a reliability price incentive to attract two GW of net additional natural gas-generating capacity. The incentive is unusual because energy buyers pay the incentive directly to producers in a real-time spot market. The program has created $13 billion in direct payments to generators annually since 2015 and is now being implemented or considered in several major energy markets in the US and abroad. We assess the incentive's impact on the Texas market from three perspectives: First, we derive the incentive's equilibrium effect on the electricity price in a monopolistic market from first principles using a standard partial equilibrium economic model. We then empirically test whether the incentive encouraged net entry into the market or the generating applicant pool, controlling for market and climatic conditions using monthly capacity data. Finally, we look for direct evidence of an incentive response among active traders using real-time market trading data. The three approaches suggest buyers and producers cancel out the incentive, and the price-only program does not encourage new generation capacity to enter the market. △ Less

Submitted 21 June, 2024; originally announced June 2024.

Training Data Augmentation for Dysarthric Automatic Speech Recognition by Text-to-Dysarthric-Speech Synthesis

Authors: Wing-Zin Leung, Mattias Cross, Anton Ragni, Stefan Goetze

Abstract: Automatic speech recognition (ASR) research has achieved impressive performance in recent years and has significant potential for enabling access for people with dysarthria (PwD) in augmentative and alternative communication (AAC) and home environment systems. However, progress in dysarthric ASR (DASR) has been limited by high variability in dysarthric speech and limited public availability of dys… ▽ More Automatic speech recognition (ASR) research has achieved impressive performance in recent years and has significant potential for enabling access for people with dysarthria (PwD) in augmentative and alternative communication (AAC) and home environment systems. However, progress in dysarthric ASR (DASR) has been limited by high variability in dysarthric speech and limited public availability of dysarthric training data. This paper demonstrates that data augmentation using text-to-dysarthic-speech (TTDS) synthesis for finetuning large ASR models is effective for DASR. Specifically, diffusion-based text-to-speech (TTS) models can produce speech samples similar to dysarthric speech that can be used as additional training data for fine-tuning ASR foundation models, in this case Whisper. Results show improved synthesis metrics and ASR performance for the proposed multi-speaker diffusion-based TTDS data augmentation for ASR fine-tuning compared to current DASR baselines. △ Less

Submitted 12 June, 2024; originally announced June 2024.

Comments: Accepted for Interspeech 2024

Gendered Inequalities in Online Harms: Fear, Safety Work, and Online Participation

Authors: Florence E. Enock, Francesca Stevens, Tvesha Sippy, Jonathan Bright, Miranda Cross, Pica Johansson, Judy Wajcman, Helen Z. Margetts

Abstract: Online harms, such as hate speech, trolling and self-harm promotion, continue to be widespread. There are growing concerns that these harms may disproportionately affect women, reflecting and reproducing existing structural inequalities within digital spaces. Using a nationally representative survey of UK adults (N=1992), we examine how gender shapes exposure to a variety of online harms, fears su… ▽ More Online harms, such as hate speech, trolling and self-harm promotion, continue to be widespread. There are growing concerns that these harms may disproportionately affect women, reflecting and reproducing existing structural inequalities within digital spaces. Using a nationally representative survey of UK adults (N=1992), we examine how gender shapes exposure to a variety of online harms, fears surrounding being targeted, the psychological impact of online experiences, the use of safety tools, and comfort with various forms of online participation. We find that while men and women report roughly similar levels of absolute exposure to harmful content online, women are more often targeted by contact-based harms including image-based abuse, cyberstalking and cyberflashing. Women report heightened fears about being targeted by online harms, more negative psychological impact in response to online experiences, and increased use of safety tools, reflecting more engagement with personal safety work. Importantly, women also say they are significantly less comfortable with several forms of online participation, for example just 23% of women are comfortable expressing political views online compared to 40% of men. Explanatory models show direct associations between fears surrounding harms and comfort with particular online behaviours. Our findings show how online harms reinforce gender inequality by placing disproportionate psychological burden and participation constraints on women. These results are important because with much public discourse happening online, we must ensure all members of society feel safe and able to participate in online spaces. △ Less

Submitted 2 October, 2025; v1 submitted 27 March, 2024; originally announced March 2024.

Modelling Triatomic Biosignatures: Ozone and Isotopomers

Authors: Thomas M. Cross, David M. Benoit, Marco Pignatari, Brad K. Gibson

Abstract: In this work we present a new approach to produce spectroscopic constants and model first-principles synthetic spectra for all molecules of astrophysical interest. We have generalized our previous diatomic molecule simulation framework, employing Transition-Optimised Shifted Hermite (TOSH) theory, thereby enabling the modelling of polyatomic rotational constants for molecules with three or more at… ▽ More In this work we present a new approach to produce spectroscopic constants and model first-principles synthetic spectra for all molecules of astrophysical interest. We have generalized our previous diatomic molecule simulation framework, employing Transition-Optimised Shifted Hermite (TOSH) theory, thereby enabling the modelling of polyatomic rotational constants for molecules with three or more atoms. These capabilities, are now provided by our new code Epimetheus. As a first validation of our approach, we confront our predictions and assess their accuracy against the well-studied triatomic molecule, ozone 666 ($^{16}$O$_3$), in addition to eight of its potential isotopomers: ozone 668 ($^{16}$O$^{16}$O$^{18}$O), 686 ($^{16}$O$^{18}$O$^{16}$O), 667 ($^{16}$O$^{16}$O$^{17}$O), 676 ($^{16}$O$^{17}$O$^{16}$O), 688 ($^{16}$O$^{18}$O$^{18}$O), 868 ($^{18}$O$^{16}$O$^{18}$O), 888 ($^{18}$O$_3$), and 777 ($^{17}$O$_3$). We then assess the accuracy of these rotational constants using the Epimetheus data in our code Pandora, and generate synthetic molecular spectra. The ozone spectra presented here are purely infrared and not Raman. Epimetheus builds upon the work from our previous code Prometheus, which used the TOSH theory to account for anharmonicity for the fundamental $ν=0 \rightarrow ν=1$ band, going further to now account for triatomic molecules. This is combined with thermal profile modeling for the rotational transitions. We have found that this extended method performs promisingly, typically approximating the spectroscopic constants and spectra well. Some issues do arise depending on the symmetry group of the ozone isotopomer. In general, we show that Epimetheus can provide the data to produce appreciable molecular spectra, to help drive future high-resolution studies. △ Less

Submitted 8 March, 2024; originally announced March 2024.

Comments: 26 pages, 6 figure, 10 tables -- Submitted to ApJ; comments from the community welcomed!

Treatment effects without multicollinearity? Temporal order and the Gram-Schmidt process in causal inference

Authors: Robin M. Cross, Steven T. Buccola

Abstract: This paper incorporates information about the temporal order of regressors to estimate orthogonal and economically interpretable regression coefficients. We establish new finite sample properties for the Gram-Schmidt orthogonalization process. Coefficients are unbiased and stable with lower standard errors than those from Ordinary Least Squares. We provide conditions under which coefficients repre… ▽ More This paper incorporates information about the temporal order of regressors to estimate orthogonal and economically interpretable regression coefficients. We establish new finite sample properties for the Gram-Schmidt orthogonalization process. Coefficients are unbiased and stable with lower standard errors than those from Ordinary Least Squares. We provide conditions under which coefficients represent average total treatment effects on the treated and extend the model to groups of ordered and simultaneous regressors. Finally, we reanalyze two studies that controlled for temporally ordered and collinear characteristics, including race, education, and income. The new approach expands Bohren et al.'s decomposition of systemic discrimination into channel-specific effects and improves significance levels. △ Less

Submitted 9 January, 2025; v1 submitted 26 February, 2024; originally announced February 2024.

MSC Class: 62-08; 91-10 ACM Class: I.1.2; I.2.1

Understanding gender differences in experiences and concerns surrounding online harms: A short report on a nationally representative survey of UK adults

Authors: Florence E. Enock, Francesca Stevens, Jonathan Bright, Miranda Cross, Pica Johansson, Judy Wajcman, Helen Z. Margetts

Abstract: Online harms, such as hate speech, misinformation, harassment and self-harm promotion, continue to be widespread. While some work suggests that women are disproportionately affected by such harms, other studies find little evidence for gender differences in overall exposure. Here, we present preliminary results from a large, nationally representative survey of UK adults (N = 2000). We asked about… ▽ More Online harms, such as hate speech, misinformation, harassment and self-harm promotion, continue to be widespread. While some work suggests that women are disproportionately affected by such harms, other studies find little evidence for gender differences in overall exposure. Here, we present preliminary results from a large, nationally representative survey of UK adults (N = 2000). We asked about exposure to 15 specific harms, along with fears surrounding exposure and comfort engaging in certain online behaviours. While men and women report seeing online harms to a roughly equal extent overall, we find that women are significantly more fearful of experiencing every type of harm that we asked about, and are significantly less comfortable partaking in several online behaviours. Strikingly, just 24% of women report being comfortable expressing political opinions online compared with almost 40% of men, with similar overall proportions for challenging certain content. Our work suggests that women may suffer an additional psychological burden in response to the proliferation of harmful online content, doing more 'safety work' to protect themselves. With much public discourse happening online, gender inequality in public voice is likely to be perpetuated if women feel too fearful to participate. Our results are important because to establish greater equality in society, we must take measures to ensure all members feel safe and able to participate in the online space. △ Less

Submitted 1 February, 2024; originally announced February 2024.

The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package

Authors: The Astropy Collaboration, Adrian M. Price-Whelan, Pey Lian Lim, Nicholas Earl, Nathaniel Starkman, Larry Bradley, David L. Shupe, Aarya A. Patil, Lia Corrales, C. E. Brasseur, Maximilian Nöthe, Axel Donath, Erik Tollerud, Brett M. Morris, Adam Ginsburg, Eero Vaher, Benjamin A. Weaver, James Tocknell, William Jamieson, Marten H. van Kerkwijk, Thomas P. Robitaille, Bruce Merry, Matteo Bachetti, H. Moritz Günther, Thomas L. Aldcroft , et al. (111 additional authors not shown)

Abstract: The Astropy Project supports and fosters the development of open-source and openly-developed Python packages that provide commonly needed functionality to the astronomical community. A key element of the Astropy Project is the core package $\texttt{astropy}$, which serves as the foundation for more specialized projects and packages. In this article, we summarize key features in the core package as… ▽ More The Astropy Project supports and fosters the development of open-source and openly-developed Python packages that provide commonly needed functionality to the astronomical community. A key element of the Astropy Project is the core package $\texttt{astropy}$, which serves as the foundation for more specialized projects and packages. In this article, we summarize key features in the core package as of the recent major release, version 5.0, and provide major updates for the Project. We then discuss supporting a broader ecosystem of interoperable packages, including connections with several astronomical observatories and missions. We also revisit the future outlook of the Astropy Project and the current status of Learn Astropy. We conclude by raising and discussing the current and future challenges facing the Project. △ Less

Submitted 28 June, 2022; originally announced June 2022.

Comments: 43 pages, 5 figures. To appear in ApJ. The author list has two parts: the authors that made significant contributions to the writing and/or coordination of the paper, followed by maintainers of and contributors to the Astropy Project. The position in the author list does not correspond to contributions to the Astropy Project as a whole

A Large-scale Approach to Modelling Molecular Biosignatures: The Diatomics

Authors: Thomas M. Cross, David M. Benoit, Marco Pignatari, Brad K. Gibson

Abstract: This work presents the first steps to modelling synthetic rovibrational spectra for all molecules of astrophysical interest using a new approach implemented in the Prometheus code. The goal is to create a new comprehensive source of first-principles molecular spectra, thus bridging the gap for missing data to help drive future high-resolution studies. Our primary application domain is for molecule… ▽ More This work presents the first steps to modelling synthetic rovibrational spectra for all molecules of astrophysical interest using a new approach implemented in the Prometheus code. The goal is to create a new comprehensive source of first-principles molecular spectra, thus bridging the gap for missing data to help drive future high-resolution studies. Our primary application domain is for molecules identified as signatures of life in planetary atmospheres (biosignatures), but our approach is general and can be applied to other systems. In this work we evaluate the accuracy of our method by studying four diatomic molecules H$_2$, O$_2$, N$_2$ and CO, all of which have well-known spectra. Prometheus uses the Transition-Optimised Shifted Hermite (TOSH) theory to account for anharmonicity for the fundamental $ν=0 \rightarrow ν=1$ band, along with thermal profile modeling for the rotational transitions. To this end, we expand TOSH theory to enable the modeling of rotational constants. We show that our simple model achieves results that are a better approximation of the real spectra than those produced through a harmonic approach. We compare our results with high-resolution HITRAN and ExoMol spectral data. We find that modelling accuracy tends to diminish for rovibrational transition away from the band origin, thus highlighting the need for the theory to be further adapted. △ Less

Submitted 15 November, 2021; v1 submitted 14 June, 2021; originally announced June 2021.

Comments: 29 pages, 9 figures, 1 table, accepted for publication in The Astrophysical Journal

Quantum limit-cycles and the Rayleigh and van der Pol oscillators

Authors: Lior Ben Arosh, M. C. Cross, Ron Lifshitz

Abstract: Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems, and as key elements in quantum technology. We consider a family of models that interpolates between the classical textbook examples of the Rayleigh and the van der Pol oscillators, and follow their transition from the classical to t… ▽ More Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems, and as key elements in quantum technology. We consider a family of models that interpolates between the classical textbook examples of the Rayleigh and the van der Pol oscillators, and follow their transition from the classical to the quantum domain, while properly formulating their corresponding quantum descriptions. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models, applicable to any bosonic system---whether mechanical, optical, or otherwise---that is coupled to its environment via single-boson and double-boson emission and absorption. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature, often misattributed to the quantum van der Pol oscillator. We closely explore the classical to quantum transition of the bifurcation to self-oscillations of this oscillator, while noting changes in the dynamics and identifying features that are uniquely quantum. △ Less

Submitted 5 November, 2020; originally announced November 2020.

Journal ref: Phys. Rev. Research 3, 013130 (2021)

Frequency Precision of Oscillators Based on High-Q Resonators

Authors: Eyal Kenig, M. C. Cross

Abstract: We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a slow time scale corresponding physically to the long relaxation time of the resonator. We derive general expressions for the phase drift generated by noise source… ▽ More We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a slow time scale corresponding physically to the long relaxation time of the resonator. We derive general expressions for the phase drift generated by noise sources in the electronic feedback loop of the oscillator. These are mixed with the signal through the nonlinear amplifier, which makes them {cyclostationary}. We also consider noise sources acting directly on the resonator. The expressions allow us to investigate reducing the oscillator phase noise thereby improving the frequency precision using resonator nonlinearity by tuning to special operating points. We illustrate the approach giving explicit results for a phenomenological amplifier model. We also propose a scheme for measuring the slow feedback noise generated by the feedback components in an open-loop driven configuration in experiment or using circuit simulators, which enables the calculation of the closed-loop oscillator phase noise in practical systems. △ Less

Submitted 26 October, 2015; v1 submitted 25 October, 2015; originally announced October 2015.

Hanbury Brown and Twiss Interferometry with Twisted Light

Authors: Omar S. Magana-Loaiza, Mohammad Mirhosseini, Robert M. Cross, Seyed Mohammad Hashemi Rafsanjani, Robert W. Boyd

Abstract: The rich physics exhibited by random optical wave fields permitted Hanbury Brown and Twiss to unveil fundamental aspects of light. Furthermore, it has been recognized that optical vortices are ubiquitous in random light and that the phase distribution around these optical singularities inprints a spectrum of orbital angular momentum onto a light field. We demonstrate that random fluctuations of li… ▽ More The rich physics exhibited by random optical wave fields permitted Hanbury Brown and Twiss to unveil fundamental aspects of light. Furthermore, it has been recognized that optical vortices are ubiquitous in random light and that the phase distribution around these optical singularities inprints a spectrum of orbital angular momentum onto a light field. We demonstrate that random fluctuations of light give rise to the formation of correlations in the orbital angular momentum components and angular positions of pseudothermal light. The presence of these correlations is manisfested through distinct interference structures in the orbital angular momentum-mode distribution of random light. These novel forms of interference correspond to the azimuthal analog of the Hanbury Brown and Twiss effect. This family of effects can be of fundamental importance in applications where entanglement is not required and where correlations in angular position and orbital angular momentum suffice. We also suggest that the azimuthal Hanbury Brown and Twiss effect can be useful in the exploration of novel phenomena in other branches of physics and astrophysics. △ Less

Submitted 8 April, 2016; v1 submitted 6 February, 2015; originally announced February 2015.

Comments: Science Advances

Journal ref: Sci. Adv. 2, e1501143 (2016)

Phase noise of oscillators with unsaturated amplifiers

Authors: Eyal Kenig, M. C. Cross, Jeff Moehlis, Kurt Wiesenfeld

Abstract: We study the role of amplifier saturation in eliminating feedback noise in self-sustained oscillators. We extend previous works that use a saturated amplifier to quench fluctuations in the feedback magnitude, while simultaneously tuning the oscillator to an operational point at which the resonator nonlinearity cancels fluctuations in the feedback phase. We consider a generalized model which featur… ▽ More We study the role of amplifier saturation in eliminating feedback noise in self-sustained oscillators. We extend previous works that use a saturated amplifier to quench fluctuations in the feedback magnitude, while simultaneously tuning the oscillator to an operational point at which the resonator nonlinearity cancels fluctuations in the feedback phase. We consider a generalized model which features an amplitude-dependent amplifier gain function. This allows us to determine the total oscillator phase noise in realistic configurations due to noise in both quadratures of the feedback, and to show that it is not necessary to drive the resonator to large oscillation amplitudes in order to eliminate noise in the phase of the feedback. △ Less

Submitted 28 October, 2013; originally announced October 2013.

Synchronization of two anharmonic nanomechanical oscillators

Authors: M. H. Matheny, M. Grau, L. G. Villanueva, R. B. Karabalin, M. C. Cross, M. L. Roukes

Abstract: We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In… ▽ More We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization given their high-quality factors, small footprint, and ease of co-integration with modern electronic signal processing technologies. △ Less

Submitted 3 May, 2013; originally announced May 2013.

Comments: 34 pages, 8 figures

Journal ref: Phys. Rev. Lett. 112, 014101 (2014)

Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs

Authors: Bryan T. Gard, Jonathan P. Olson, Robert M. Cross, Moochan B. Kim, Hwang Lee, Jonathan P. Dowling

Abstract: Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the H… ▽ More Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schrödinger and Heisenberg pictures of quantum theory, while mathematically equivalent, are not in general computationally equivalent. Finally, we conclude our argument by comparing the symmetry requirements of multiparticle bosonic to fermionic interferometers and, using simple physical reasoning, connect the nonsimulatability of the bosonic device to the complexity of computing the permanent of a large matrix. △ Less

Submitted 18 February, 2014; v1 submitted 15 April, 2013; originally announced April 2013.

Comments: 7 pages, 1 figure Published in PRA Phys. Rev. A 89, 022328 (2014)

Journal ref: Phys. Rev. A 89, 022328 (2014)

Frequency Precision of Two-Dimensional Lattices of Coupled Oscillators with Spiral Patterns

Authors: John-Mark A. Allen, M. C. Cross

Abstract: Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of N for large N, unlike the case of purely dissipative coupling where the improvement is proportional to N, but instead depends on just those oscillators… ▽ More Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of N for large N, unlike the case of purely dissipative coupling where the improvement is proportional to N, but instead depends on just those oscillators in the core of the spiral that acts as the source region of the waves. Our conclusions are based on numerical simulations of up to N=29929 oscillators, and analytic results for a continuum approximation to the lattice in an infinite system. We derive an expression for the dependence of the frequency precision on the reactive component of the coupling constant, depending on a single parameter given by fitting the frequency of the spiral waves to the numerical simulations. △ Less

Submitted 8 May, 2013; v1 submitted 6 March, 2013; originally announced March 2013.

Comments: 7 pages, 6 figures

Journal ref: Phys. Rev. E 87, 052902 (2013)

Optimal operating points of oscillators using nonlinear resonators

Authors: Eyal Kenig, M. C. Cross, L. G. Villanueva, R. B. Karabalin, M. H. Matheny, Ron Lifshitz, M. L. Roukes

Abstract: We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter val… ▽ More We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources. △ Less

Submitted 5 November, 2012; originally announced November 2012.

Journal ref: Phys. Rev. E 86 (2012) 056207

A Nanoscale Parametric Feedback Oscillator

Authors: L. Guillermo Villanueva, Rassul B. Karabalin, Matthew H. Matheny, Eyal Kenig, Michael C. Cross, Michael L. Roukes

Abstract: We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices, and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, like such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry, and reduction in cost and syste… ▽ More We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices, and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, like such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry, and reduction in cost and system size reduction. We show that the PFO topology can also improve nanoscale oscillator performance by circumventing detrimental effects that are otherwise imposed by the strong device nonlinearity in this size regime. △ Less

Submitted 1 November, 2012; originally announced November 2012.

Comments: 17 pages, 3 figures

Journal ref: Nano Letters, 2011, 11 (11), pp 5054_5059

Surpassing fundamental limits of oscillators using nonlinear resonators

Authors: L. G. Villanueva, E. Kenig, R. B. Karabalin, M. H. Matheny, R. Lifshitz, M. C. Cross, M. L. Roukes

Abstract: Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the am… ▽ More Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonators anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system (NEMS)-based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables a significant reduction of the oscillators phase noise, as predicted by our model. △ Less

Submitted 30 October, 2012; originally announced October 2012.

Comments: 14 pages, 2 figures, 1 table

Journal ref: Phys. Rev. Lett. 110 (2013) 177208

Quantum-classical transition of correlations of two coupled cavities

Authors: Tony E. Lee, M. C. Cross

Abstract: We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates periodically in time. Coupling between the cavities leads to synchronization of the oscillations and classical correlations between the cavities. In the quantum limit,… ▽ More We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates periodically in time. Coupling between the cavities leads to synchronization of the oscillations and classical correlations between the cavities. In the quantum limit, there are quantum correlations due to entanglement. The quantum correlations persist even when the cavities are far off resonance with each other, in stark contrast with the classical case. We also find that the quantum and classical limits are connected by an intermediate regime of almost no correlations. Our results can be extended to a wide variety of quantum models. △ Less

Submitted 3 September, 2013; v1 submitted 4 September, 2012; originally announced September 2012.

Comments: 6 pages, 7 figures

Journal ref: Phys. Rev. A 88, 013834 (2013)

A Passive Phase Noise Cancellation Element

Authors: Eyal Kenig, M. C. Cross, Ron Lifshitz, R. B. Karabalin, L. G. Villanueva, M. H. Matheny, M. L. Roukes

Abstract: We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the output of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resona… ▽ More We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the output of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators exhibit self-oscillation at an inherent frequency. We find operating points of the device for which this periodic signal is immune to frequency noise in the driving oscillator, providing a way to clean its phase noise. We present results for the effect of thermal noise to advance a broader understanding of the overall noise sensitivity and the fundamental operating limits. △ Less

Submitted 12 March, 2012; originally announced March 2012.

Journal ref: Phys. Rev. Lett. 108 (2012) 264102

Spatiotemporal dynamics of quantum jumps with Rydberg atoms

Authors: Tony E. Lee, M. C. Cross

Abstract: We study the nonequilibrium dynamics of quantum jumps in a one-dimensional chain of atoms. Each atom is driven on a strong transition to a short-lived state and on a weak transition to a metastable state. We choose the metastable state to be a Rydberg state so that when an atom jumps to the Rydberg state, it inhibits or enhances jumps in the neighboring atoms. This leads to rich spatiotemporal dyn… ▽ More We study the nonequilibrium dynamics of quantum jumps in a one-dimensional chain of atoms. Each atom is driven on a strong transition to a short-lived state and on a weak transition to a metastable state. We choose the metastable state to be a Rydberg state so that when an atom jumps to the Rydberg state, it inhibits or enhances jumps in the neighboring atoms. This leads to rich spatiotemporal dynamics that are visible in the fluorescence of the strong transition. △ Less

Submitted 24 May, 2012; v1 submitted 7 February, 2012; originally announced February 2012.

Comments: 10 pages

Journal ref: Phys. Rev. A 85, 063822 (2012)

Quantum random walks with multiphoton interference and high order correlation functions

Authors: Bryan T Gard, Robert M Cross, Petr M Anisimov, Hwang Lee, Jonathan P Dowling

Abstract: We show a simulation of quantum random walks with multiple photons using a staggered array of 50/50 beam splitters with a bank of detectors at any desired level. We discuss the multiphoton interference effects that are inherent to this setup, and introduce one, two, and threefold coincidence detection schemes. The use of Feynman diagrams are used to intuitively explain the unique multiphoton inter… ▽ More We show a simulation of quantum random walks with multiple photons using a staggered array of 50/50 beam splitters with a bank of detectors at any desired level. We discuss the multiphoton interference effects that are inherent to this setup, and introduce one, two, and threefold coincidence detection schemes. The use of Feynman diagrams are used to intuitively explain the unique multiphoton interference effects of these quantum random walks. △ Less

Submitted 11 April, 2013; v1 submitted 16 December, 2011; originally announced December 2011.

Comments: 15 pages, 7 figures

Collective Dynamics in Arrays of Coupled Nonlinear Resonators

Authors: Ron Lifshitz, Eyal Kenig, M. C. Cross

Abstract: The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We review a wide range of collective dynamical phenomena, while highlighting the common concepts and theoretical tools that we have developed for treating them. We p… ▽ More The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We review a wide range of collective dynamical phenomena, while highlighting the common concepts and theoretical tools that we have developed for treating them. We provide detailed derivations of amplitude equations, which allow us to obtain reduced descriptions for the relevant dynamics of our complex systems. We apply these amplitude equations to study (a) resonant response to parametric excitation; (b) pattern selection, or the nonlinear competition between extended modes in situations of multistability; (c) formation and dynamics of intrinsically localized modes (ILM); and (d) spontaneous synchronization of oscillators with differing frequencies. All the predictions obtained from analyzing the different amplitude equations are in excellent agreement with numerical solutions of the underlying equations of motion, suggesting that the predicted effects can be observed in arrays of real micromechanical or nanomechanical resonators, thus motivating new experiments in these systems. △ Less

Submitted 12 November, 2011; originally announced November 2011.

Comments: To appear in "Fluctuating nonlinear oscillators", Ed. Mark I. Dykman (Oxford University Press, Oxford, 2012)

Journal ref: In Fluctuating Nonlinear Oscillators, Ed. M.I. Dykman (Oxford University Press, Oxford, 2012), ch. 11

Collective quantum jumps of Rydberg atoms

Authors: Tony E. Lee, H. Häffner, M. C. Cross

Abstract: We study an open quantum system of atoms with long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps are inherently collective and in fact exist only for a large number of atoms. We explain how entanglement and quantum measurement enable the jumps,… ▽ More We study an open quantum system of atoms with long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps are inherently collective and in fact exist only for a large number of atoms. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden. △ Less

Submitted 29 September, 2011; originally announced September 2011.

Comments: 4 pages

Journal ref: Phys. Rev. Lett. 108, 023602 (2012)

Improving the Frequency Precision of Oscillators by Synchronization

Authors: M. C. Cross

Abstract: Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency precision of N oscillators perturbed by independent noise sources is improved by a factor N as expected from simple averaging arguments. In the presence of react… ▽ More Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency precision of N oscillators perturbed by independent noise sources is improved by a factor N as expected from simple averaging arguments. In the presence of reactive coupling, such as will typically be the case for non-dissipatively coupled oscillators based on high-Q resonators, the synchronized state consists of target like waves radiating from a local source which is a region of higher frequency oscillators. In this state all the oscillators evolve with the same frequency, however I show that the improvement of the frequency precision is independent of N for large N, but instead depends on the disorder and reflects the dependence of the frequency of the synchronized state on just those oscillators in the source region of the waves. △ Less

Submitted 21 September, 2011; v1 submitted 16 September, 2011; originally announced September 2011.

Comments: 18 pages, 8 figures; clarified wording of text and added references

Antiferromagnetic phase transition in a nonequilibrium lattice of Rydberg atoms

Authors: Tony E. Lee, H. Häffner, M. C. Cross

Abstract: We study a driven-dissipative system of atoms in the presence of laser excitation to a Rydberg state and spontaneous emission. The atoms interact via the blockade effect, whereby an atom in the Rydberg state shifts the Rydberg level of neighboring atoms. We use mean-field theory to study how the Rydberg population varies in space. As the laser frequency changes, there is a continuous transition be… ▽ More We study a driven-dissipative system of atoms in the presence of laser excitation to a Rydberg state and spontaneous emission. The atoms interact via the blockade effect, whereby an atom in the Rydberg state shifts the Rydberg level of neighboring atoms. We use mean-field theory to study how the Rydberg population varies in space. As the laser frequency changes, there is a continuous transition between the uniform and antiferromagnetic phases. The nonequilibrium nature also leads to a novel oscillatory phase and bistability between the uniform and antiferromagnetic phases. △ Less

Submitted 10 August, 2011; v1 submitted 5 April, 2011; originally announced April 2011.

Comments: 4 pages + appendix

Journal ref: Phys. Rev. A 84, 031402(R) (2011)

Pattern formation with trapped ions

Authors: Tony E. Lee, M. C. Cross

Abstract: Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and cooling, while nonlinearity is provided by trap anharmonicity and beam shaping. The collective dynamics are governed by an equation similar to the complex Ginzburg… ▽ More Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and cooling, while nonlinearity is provided by trap anharmonicity and beam shaping. The collective dynamics are governed by an equation similar to the complex Ginzburg-Landau equation, except that the reactive nature of the coupling leads to qualitatively different behavior. The system has the unusual feature of being both oscillatory and excitable at the same time. We account for noise from spontaneous emission and find that the patterns are observable for realistic experimental parameters. Our scheme also allows controllable experiments with noise and quenched disorder. △ Less

Submitted 26 January, 2011; v1 submitted 15 November, 2010; originally announced November 2010.

Comments: 4 pages + appendix

Journal ref: Phys. Rev. Lett. 106, 143001 (2011)

Vortices and the entrainment transition in the 2D Kuramoto model

Authors: Tony E. Lee, Heywood Tam, G. Refael, Jeffrey L. Rogers, M. C. Cross

Abstract: We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We explain why the macroscopic cluster disappears at $K_E$. We view the system in terms of vortices, since cluster boundaries are delineated by the motion… ▽ More We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We explain why the macroscopic cluster disappears at $K_E$. We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase ($K>K_E$), vortices move in fixed paths around clusters, while in the unentrained phase ($K<K_E$), vortices sometimes wander off. These deviant vortices are responsible for the disappearance of the macroscopic cluster. The regularity of vortex motion is determined by whether clusters behave as single effective oscillators. The unentrained phase is also characterized by time-dependent cluster structure and the presence of chaos. Thus, the entrainment transition is actually an order-chaos transition. We present an analytical argument for the scaling $K_E\sim K_L$ for small lattices, where $K_L$ is the threshold for phase-locking. By also deriving the scaling $K_L\sim\log N$, we thus show that $K_E\sim\log N$ for small $N$, in agreement with numerics. In addition, we show how to use the linearized model to predict where vortices are generated. △ Less

Submitted 24 June, 2010; v1 submitted 17 June, 2010; originally announced June 2010.

Comments: 11 pages, 8 figures

Journal ref: Phys. Rev. E 82, 036202 (2010)

Synchronization of oscillators with long range power law interactions

Authors: Debanjan Chowdhury, M. C. Cross

Abstract: We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law exponent $α_c$ across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the la… ▽ More We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law exponent $α_c$ across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find $α_c=3/2$. Frequency entrainment and phase ordering are discussed as a function of $α\geq 1$. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the {\it d}-dimensional problem. △ Less

Submitted 31 July, 2010; v1 submitted 7 March, 2010; originally announced March 2010.

Comments: Final published version

Journal ref: Physical Review E, vol. 82, 016205 (2010)

Universality in the one-dimensional chain of phase-coupled oscillators

Authors: Tony E. Lee, G. Refael, M. C. Cross, Oleg Kogan, Jeffrey L. Rogers

Abstract: We apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e. for distributions with long t… ▽ More We apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e. for distributions with long tails, we find good agreement with numerical simulations even in the regime of weak randomness. We use the RG flow to derive how the correlation length scales with the width of the coupling distribution in the limit of large coupling. This leads to the identification of a universality class of distributions with the same critical exponent $ν$. We also find universal scaling for small coupling. Finally, we show that the RG flow is characterized by a universal approach to the unsynchronized fixed point, which provides physical insight into low-frequency clusters. △ Less

Submitted 16 September, 2009; v1 submitted 3 July, 2009; originally announced July 2009.

Comments: 14 pages, 10 figures

Journal ref: Phys. Rev. E 80, 046210 (2009)

Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators

Authors: Eyal Kenig, Boris A. Malomed, M. C. Cross, Ron Lifshitz

Abstract: We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schroedinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-L… ▽ More We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schroedinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory. △ Less

Submitted 13 August, 2009; v1 submitted 8 April, 2009; originally announced April 2009.

Comments: New version contains a new section discussing the dynamical formation of solitons and the stability of non-zero uniform states

Journal ref: Phys. Rev. E 80 (2009) 046202.

Nonlinear Dynamics and Chaos in Two Coupled Nanomechanical Resonators

Authors: R. B. Karabalin, M. C. Cross, M. L. Roukes

Abstract: Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes the system develops spontaneous oscillations of amplitude modulation that also show period doubling transitions… ▽ More Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes the system develops spontaneous oscillations of amplitude modulation that also show period doubling transitions and chaos. The complex nonlinear dynamics are quantitatively predicted by a simple theoretical model. △ Less

Submitted 17 November, 2008; v1 submitted 6 November, 2008; originally announced November 2008.

Comments: Acknowledgment and references added. Slightly shortened to fit journal requirements

Renormalization Group Approach to Oscillator Synchronization

Authors: Oleg Kogan, Jeffrey L. Rogers, M. C. Cross, G. Refael

Abstract: We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling strengths. The results are compared with numerical simulations of the chain dynamics and good agreement in several characteristics is found. W… ▽ More We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling strengths. The results are compared with numerical simulations of the chain dynamics and good agreement in several characteristics is found. We apply the renormalization group and simulations to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies, as well as the dependence of the characteristic cluster length upon parameters of these Lorentzian distributions. △ Less

Submitted 9 December, 2008; v1 submitted 17 October, 2008; originally announced October 2008.

Comments: 13 pages, 7 figures: 8 figure files in *.eps format and one *.tex file

Journal ref: Phys. Rev. E 80, 036206 (2009)

Pattern selection in parametrically-driven arrays of nonlinear resonators

Authors: Eyal Kenig, Ron Lifshitz, M. C. Cross

Abstract: We study the problem of pattern selection in an array of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS & NEMS), using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [PRE 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive ampli… ▽ More We study the problem of pattern selection in an array of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS & NEMS), using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [PRE 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive amplitude is varied either quasistatically, abruptly, or as a linear ramp in time. We find novel hysteretic effects, which are confirmed by numerical integration of the original equations of motion of the interacting nonlinear resonators. △ Less

Submitted 26 August, 2008; originally announced August 2008.

Journal ref: Phys. Rev. E 79 (2009) 026203.

The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation

Authors: M. R. Paul, M. T. Clark, M. C. Cross

Abstract: The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the… ▽ More The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the autocorrelation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers. △ Less

Submitted 1 May, 2006; originally announced May 2006.

Comments: Submitted to Nanotechnology April 26, 2006

Effect of the Centrifugal Force on Domain Chaos in Rayleigh-Bénard convection

Authors: Nathan Becker, J. D. Scheel, M. C. Cross, Guenter Ahlers

Abstract: Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly-stationary nearly-radial rolls populated by occasional defects reminiscent of undulat… ▽ More Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly-stationary nearly-radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency $f\simε^μ$ with $μ\simeq1$ as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, $μ$ and the domain size closely agreed with experiment. △ Less

Submitted 14 November, 2005; originally announced November 2005.

Comments: 8 pages, 11 figures

Synchronization by Reactive Coupling and Nonlinear Frequency Pulling

Authors: M. C. Cross, J. L. Rogers, Ron Lifshitz, A. Zumdieck

Abstract: We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the initial onset of synchronization as the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state when all the… ▽ More We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the initial onset of synchronization as the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state when all the oscillators evolve with the same frequency. Explicit results are derived for Lorentzian, triangular, and top-hat distributions of oscillator frequencies. Numerical simulations are used to construct complete phase diagrams for these distributions. △ Less

Submitted 3 October, 2005; originally announced October 2005.

Journal ref: Physical Review E 73, 036205 (2006)

Perturbation of magnetostatic modes observed by FMRFM

Authors: R. Urban, A. Putilin, P. E. Wigen, S. -H. Liou, M. C. Cross, P. C. Hammel, M. L. Roukes

Abstract: Magnetostatic modes of Yttrium Iron Garnet (YIG) films are investigated by ferromagnetic resonance force microscopy (FMRFM). A thin film ``probe'' magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the… ▽ More Magnetostatic modes of Yttrium Iron Garnet (YIG) films are investigated by ferromagnetic resonance force microscopy (FMRFM). A thin film ``probe'' magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the cantilever. We present a theoretical model that explains these observations; it shows that tip-induced variation of the internal field creates either a local ``potential barrier'' or ``potential well'' for the magnetostatic waves. The data and model together indicate that local magnetic imaging of ferromagnets is possible, even in the presence of long-range spin coupling, through the induction of localized magnetostatic modes predicted to arise from sufficiently strong tip fields. △ Less

Submitted 22 April, 2005; originally announced April 2005.

Comments: 5 pages, 4 figures, 1 table, 15 references

Response of discrete nonlinear systems with many degrees of freedom

Authors: Yaron Bromberg, M. C. Cross, Ron Lifshitz

Abstract: We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillat… ▽ More We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wavenumber dependent bifurcation similar in character to the behavior known to exist in fluids undergoing the Faraday wave instability. We confirm this behavior numerically and make suggestions for testing it experimentally with MEMS and NEMS resonators. △ Less

Submitted 16 August, 2005; v1 submitted 30 October, 2004; originally announced November 2004.

Comments: Version 2 is an expanded version of the article, containing detailed steps of the derivation that were left out in version 1, but no additional results

Journal ref: Phys. Rev. E 73, 016214 (2006)

Enhanced tracer transport by the spiral defect chaos state of a convecting fluid

Authors: K. -H. Chiam, M. C. Cross, H. S. Greenside, P. F. Fischer

Abstract: To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhanc… ▽ More To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhancement in tracer diffusivity follows two regimes. For large Peclet numbers (that is, small molecular diffusivities of the tracer), we find that the enhancement is proportional to the Peclet number. For small Peclet numbers, the enhancement is proportional to the square root of the Peclet number. We explain the presence of these two regimes in terms of how the local transport depends on the local wave numbers of the convection rolls. For large Peclet numbers, we further find that defects cause the tracer diffusivity to be enhanced locally in the direction orthogonal to the local wave vector but suppressed in the direction of the local wave vector. △ Less

Submitted 23 September, 2004; originally announced September 2004.

Comments: 11 pages, 12 figures

Synchronization by Nonlinear Frequency Pulling

Authors: M. C. Cross, A. Zumdieck, Ron Lifshitz, J. L. Rogers

Abstract: We analyze a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling motivated by the physics of arrays of nanoscale oscillators. We study the model for the mean field case of all-to-all coupling, deriving results for the onset of synchronization as the coupling or nonlinearity increase, and the fully locked state when all the oscillators e… ▽ More We analyze a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling motivated by the physics of arrays of nanoscale oscillators. We study the model for the mean field case of all-to-all coupling, deriving results for the onset of synchronization as the coupling or nonlinearity increase, and the fully locked state when all the oscillators evolve with the same frequency. △ Less

Submitted 28 June, 2004; originally announced June 2004.

Journal ref: Phys. Rev. Lett. 93 (2004) 224101.

Rayleigh-Benard Convection in Large-Aspect-Ratio Domains

Authors: M. R. Paul, K-H. Chiam, M. C. Cross, P. F. Fischer

Abstract: The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coars… ▽ More The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as $t^{0.12}$, the orientational correlation length scales as $t^{0.54}$, and the density of defects scale as $t^{-0.45}$. The final pattern evolves toward the wavenumber where isolated dislocations become motionless, suggesting a possible wavenumber selection mechanism for large-aspect-ratio convection. △ Less

Submitted 8 March, 2004; originally announced March 2004.

Comments: 5 pages, 6 figures

The stochastic dynamics of nanoscale mechanical oscillators immersed in a viscous fluid

Authors: M. R. Paul, M. C. Cross

Abstract: The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in experiment. We use this approach to investigat… ▽ More The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in experiment. We use this approach to investigate the fluid coupled motion of single and multiple cantilevers with experimentally motivated geometries. △ Less

Submitted 3 March, 2004; originally announced March 2004.

Comments: 5 pages, 5 figures