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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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- Solitons (14)
- Pattern Formation and Solitons (5)
- Bose-Einstein condensation (4)
- Cohomology of arithmetic groups (4)
- Hecke operators (4)
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- Large deviation principle (4)
- Pattern Formation (4)
- Stability (4)
- Bifurcation (3)
- Equivalence of ensembles (3)
- First-order phase transition (3)
- Microcanonical entropy (3)
- Nonlinear Schrödinger equation (3)
- Nonlinear optics (3)
- Second-order phase transition (3)
- Vortices (3)
- Automorphic forms (2)
- Bilinear operator (2)
- Blume-Capel model (2)
- Bose-Einstein condensates (2)
- Canonical ensemble (2)
- Discrete nonlinear Schrodinger equation (2)
- Eisenstein cohomology (2)
- Equilibrium macrostates (2)
- Existence (2)
- Generalized canonical ensemble (2)
- Gibbs measures (2)
- Gross-Pitaevskii equation (2)
- Microcanonical ensemble (2)
- Modulational instability (2)
Articles 31 - 60 of 351
Full-Text Articles in Physical Sciences and Mathematics
Robust Optimization Of Biological Protocols, Patrick Flaherty, Ronald W. Davis
Robust Optimization Of Biological Protocols, Patrick Flaherty, Ronald W. Davis
Mathematics and Statistics Department Faculty Publication Series
When conducting high-throughput biological experiments, it is often necessary to develop a protocol that is both inexpensive and robust. Standard approaches are either not cost-effective or arrive at an optimized protocol that is sensitive to experimental variations. Here, we describe a novel approach that directly minimizes the cost of the protocol while ensuring the protocol is robust to experimental variation. Our approach uses a risk-averse conditional value-at-risk criterion in a robust parameter design framework. We demonstrate this approach on a polymerase chain reaction protocol and show that our improved protocol is less expensive than the standard protocol and more robust …
Stability Of Solitary Waves And Vortices In A 2d Nonlinear Dirac Model, Jesús Cuevas–Maraver, P. G. Kevrekidis, Avadh Saxena, Andrew Comech, Ruomeng Lan
Stability Of Solitary Waves And Vortices In A 2d Nonlinear Dirac Model, Jesús Cuevas–Maraver, P. G. Kevrekidis, Avadh Saxena, Andrew Comech, Ruomeng Lan
Mathematics and Statistics Department Faculty Publication Series
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions consisting of a soliton in one component and a vortex in the other to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These results pave the way for a systematic stability and dynamics analysis of higher dimensional waveforms …
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, C. Chong, E. Kim, E. G. Charalampidis, H. Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, C. Daraio, J. Yang
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, C. Chong, E. Kim, E. G. Charalampidis, H. Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, C. Daraio, J. Yang
Mathematics and Statistics Department Faculty Publication Series
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schrodinger (NLS) equation predicts the corresponding ¨ modes fairly well. We propose that nonlinear …
Vortex–Soliton Complexes In Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, Panayotis G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed
Vortex–Soliton Complexes In Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, Panayotis G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed
Mathematics and Statistics Department Faculty Publication Series
We consider a two-component, two-dimensional nonlinear Schr¨odinger system with unequal dispersion coefficients and self-defocusing nonlinearities. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component. We show that the potential well may support not only the fundamental bound state, which forms a vortex–bright (VB) soliton, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states …
Solitons In Multi-Component Nonlinear Schrödinger Models: A Survey Of Recent Developments, P. G. Kevrekidis, D. J. Frantzeskakis
Solitons In Multi-Component Nonlinear Schrödinger Models: A Survey Of Recent Developments, P. G. Kevrekidis, D. J. Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
In this review we try to capture some of the recent excitement induced by experimental developments, but also by a large volume of theoretical and computational studies addressing multi-component nonlinear Schrödinger models and the localized structures that they support. We focus on some prototypical structures, namely the dark-bright and dark-dark solitons. Although our focus will be on one-dimensional, two-component Hamiltonian models, we also discuss variants, including three (or more)-component models, higher-dimensional states, as well as dissipative settings. We also offer an outlook on interesting possibilities for future work on this theme.
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Positive And Negative Mass Solitons In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D.J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, J. Stockhofe
Mathematics and Statistics Department Faculty Publication Series
We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals “negative mass” regimes, where corresponding “negative mass” bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity …
Traveling Waves For The Mass In Mass Model Of Granular Chains, Panayotis G. Kevrekidis, Atanas G. Stefanov, Haitao Xu
Traveling Waves For The Mass In Mass Model Of Granular Chains, Panayotis G. Kevrekidis, Atanas G. Stefanov, Haitao Xu
Mathematics and Statistics Department Faculty Publication Series
In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves …
Nonlinear Resonances And Antiresonances Of A Forced Sonic Vacuum, D. Pozharskiy, Y. Zhang, M. O. Williams, D. M. Mcfarland, P. G. Kevrekidis, A. F. Vakakis, I. G. Kevrekidis
Nonlinear Resonances And Antiresonances Of A Forced Sonic Vacuum, D. Pozharskiy, Y. Zhang, M. O. Williams, D. M. Mcfarland, P. G. Kevrekidis, A. F. Vakakis, I. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of …
Conical Wave Propagation And Diffraction In 2d Hexagonally Packed Granular Lattices, C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi-Ping Ma
Conical Wave Propagation And Diffraction In 2d Hexagonally Packed Granular Lattices, C. Chong, P. G. Kevrekidis, M. J. Ablowitz, Yi-Ping Ma
Mathematics and Statistics Department Faculty Publication Series
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wavepacket, as well as via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression i.e., near the linear regime. …
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Mathematics and Statistics Department Faculty Publication Series
For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one dimensional amplitude equation that describes the slow …
Generating And Manipulating Quantized Vortices On-Demand In A Bose-Einstein Condensate: A Numerical Study, B. Gertjerenken, P. G. Kevrekidis, R. Carretero-González, B. P. Anderson
Generating And Manipulating Quantized Vortices On-Demand In A Bose-Einstein Condensate: A Numerical Study, B. Gertjerenken, P. G. Kevrekidis, R. Carretero-González, B. P. Anderson
Mathematics and Statistics Department Faculty Publication Series
We numerically investigate an experimentally viable method, that we will refer to as the “chopsticks method”, for generating and manipulating on-demand several vortices in a highly oblate atomic Bose-Einstein condensate (BEC) in order to initialize complex vortex distributions for studies of vortex dynamics. The method utilizes moving laser beams (the “chopsticks”) to generate, capture and transport vortices inside and outside the BEC. We examine in detail this methodology and show a wide parameter range of applicability for the prototypical two-vortex case, and show case examples of producing and manipulating several vortices for which there is no net circulation, equal numbers …
Pt Meets Supersymmetry And Nonlinearity: An Analytically Tractable Case Example, P. G. Kevrekidis, Jesús Cuevas–Maraver, Avadh Saxena, Fred Cooper, Avinash Khare
Pt Meets Supersymmetry And Nonlinearity: An Analytically Tractable Case Example, P. G. Kevrekidis, Jesús Cuevas–Maraver, Avadh Saxena, Fred Cooper, Avinash Khare
Mathematics and Statistics Department Faculty Publication Series
In the present work, we combine the notion of PT -symmetry with that of super-symmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which the corresponding solution of the regular …
Bright Discrete Solitons In Spatially Modulated Dnls Systems, Panayotis G. Kevrekidis, R. L. Horne, N. Whitaker, Q. E. Hoq, D. Kip
Bright Discrete Solitons In Spatially Modulated Dnls Systems, Panayotis G. Kevrekidis, R. L. Horne, N. Whitaker, Q. E. Hoq, D. Kip
Mathematics and Statistics Department Faculty Publication Series
In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the “extended” solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Finally, …
Staggered Parity-Time-Symmetric Ladders With Cubic Nonlinearity, Jennie D'Ambroise, Panayotis G. Kevrekidis, B. A. Malomed
Staggered Parity-Time-Symmetric Ladders With Cubic Nonlinearity, Jennie D'Ambroise, Panayotis G. Kevrekidis, B. A. Malomed
Mathematics and Statistics Department Faculty Publication Series
We introduce a ladder-shaped chain with each rung carrying a parity-time- (PT -) symmetric gain-loss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gain-loss and loss-gain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system PT -symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from ¨ the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton’s method for continuation of …
Bifurcation And Stability Of Single And Multiple Vortex Rings In Three-Dimensional Bose-Einstein Condensates, R. N. Bisset, Wenlong Wang, C. Ticknor, R. Carretero-González, D. J. Frantzeskakis, L. A. Collins, P. G. Kevrekidis
Bifurcation And Stability Of Single And Multiple Vortex Rings In Three-Dimensional Bose-Einstein Condensates, R. N. Bisset, Wenlong Wang, C. Ticknor, R. Carretero-González, D. J. Frantzeskakis, L. A. Collins, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach and find good qualitative and quantitative agreement with our Bogoliubov–de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortexring states. We systematically capture these as stationary states of the …
Vortex Nucleation In A Dissipative Variant Of The Nonlinear Schrödinger Equation Under Rotation, R. Carretero-González, Panayotis G. Kevrekidis, T. Kolokolnikov
Vortex Nucleation In A Dissipative Variant Of The Nonlinear Schrödinger Equation Under Rotation, R. Carretero-González, Panayotis G. Kevrekidis, T. Kolokolnikov
Mathematics and Statistics Department Faculty Publication Series
In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μ of the system, increasing proportionally toμ2/3. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We …
Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis
Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis
Mathematics and Statistics Department Faculty Publication Series
We explore the form of rogue waves solution sin a select set of case examples of non linear Schrodinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue waves solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations …
Time- And Space-Variant Wave Transmission In Helicoidal Phononic Crystals, F. Li, C. Chong, Panayotis G. Kevrekidis, C Daraio
Time- And Space-Variant Wave Transmission In Helicoidal Phononic Crystals, F. Li, C. Chong, Panayotis G. Kevrekidis, C Daraio
Mathematics and Statistics Department Faculty Publication Series
We present a dynamically tunable mechanism of wave transmission in 1D helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylindrical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in cross-talking between in-plane torsional and out-of-plane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion towards an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on/off through …
Interaction Of Sine-Gordon Kinks And Breathers With A Parity-Time-Symmetric Defect, Danial Saadatmand, Sergey V. Dmitriev, Denis I. Borisov, Panayotis G. Kevrekidis
Interaction Of Sine-Gordon Kinks And Breathers With A Parity-Time-Symmetric Defect, Danial Saadatmand, Sergey V. Dmitriev, Denis I. Borisov, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. …
Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis
Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
In this work, we consider the dynamics of vector rogue waves and ark bright solitons in two component nonlinear Schrodinger equations with various physically motivated time dependent non linearity coefficients, as well as spatio temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark bright boomeron like soliton solutions of the latter are converted back into ones of the original non autonomous model. Using direct numerical simulations we find that, in most cases, the rogue waves formation is rapidly followed by a modulational instability that leads …
Lattice Three Dimensional Skyrmions Revisited, E. G. Charalampidis, T. A. I, P. G. Kevrekidis
Lattice Three Dimensional Skyrmions Revisited, E. G. Charalampidis, T. A. I, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, an a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed: and their stability under small perturbation sis explored by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, …
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one …
Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers, Daniel Law, Jennie D’Ambroise, Panayotis G. Kevrekidis, Detlef Kip
Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers, Daniel Law, Jennie D’Ambroise, Panayotis G. Kevrekidis, Detlef Kip
Mathematics and Statistics Department Faculty Publication Series
In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant …
Wormholes Threaded By Chiral Fields, Efstathios Charalampidis, Theodora Ioannidou, Burkhard Kleihaus, Jutta Kunz
Wormholes Threaded By Chiral Fields, Efstathios Charalampidis, Theodora Ioannidou, Burkhard Kleihaus, Jutta Kunz
Mathematics and Statistics Department Faculty Publication Series
We consider Lorentzian wormholes with a phantom field and chiral matter fields. The chiral fields are described by the non linear sigma model with or without a Skyrme term. When the gravitational coupling of the chiral fields is increased, the wormhole geometry changes. The single throat is replaced by a double throat with a belly inbetween. For a maximal value of the coupling, the radii of both throats reach zero. Then the interior part pinches off, leaving a closed universe and two (asympotically) flat spaces. A stability analysis shows that all wormholes threaded by chiral fields inherit the instability of …
On The Orders Of Periodic Diffeomorphisms Of 4-Manifolds, Wm Chen
On The Orders Of Periodic Diffeomorphisms Of 4-Manifolds, Wm Chen
Mathematics and Statistics Department Faculty Publication Series
This paper initiated an investigation on the following question: Suppose that a smooth 4 -manifold does not admit any smooth circle actions. Does there exist a constant C>0 such that the manifold supports no smooth Zp -actions of prime order for p>C ? We gave affirmative results to this question for the case of holomorphic and symplectic actions, with an interesting finding that the constant C in the holomorphic case is topological in nature, while in the symplectic case it involves also the smooth structure of the manifold.
Entropic Fluctuations In Statistical Mechanics: I. Classical Dynamical Systems, V Jakšić, C-A Pillet, L Rey-Bellet
Entropic Fluctuations In Statistical Mechanics: I. Classical Dynamical Systems, V Jakšić, C-A Pillet, L Rey-Bellet
Mathematics and Statistics Department Faculty Publication Series
Within the abstract framework of dynamical system theory we describe a general approach to the transient (or Evans–Searles) and steady state (or Gallavotti–Cohen) fluctuation theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. In addition to its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.
Representations Of Semi-Simple Lie Algebras In Prime Characteristic And Noncommutative Springer Resolution, R Bezrukavnikov, I Mirkovic
Representations Of Semi-Simple Lie Algebras In Prime Characteristic And Noncommutative Springer Resolution, R Bezrukavnikov, I Mirkovic
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Symmetric Symplectic Homotopy K3 Surfaces, Wm Chen, S Kwasik
Symmetric Symplectic Homotopy K3 Surfaces, Wm Chen, S Kwasik
Mathematics and Statistics Department Faculty Publication Series
A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is shown that an effective action by various maximal symplectic K3 groups forces the corresponding homotopy K3 surface to be minimally exotic with respect to our measure. (However, the standard K3 is the only known example of such minimally exotic homotopy K3 surfaces.) The possible structure of a finite group …
Effects Of Long-Range Nonlinear Interactions In Double-Well Potentials, C Wang, Pg Kevrekidis
Effects Of Long-Range Nonlinear Interactions In Double-Well Potentials, C Wang, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider the interplay of linear double-well-potential (DWP) structures and nonlinear longrange interactions of different types, motivated by applications to nonlinear optics and matter waves. We find that, while the basic spontaneous-symmetry-breaking (SSB) bifurcation structure in the DWP persists in the presence of the long-range interactions, the critical points at which the SSB emerges are sensitive to the range of the nonlocal interaction. We quantify the dynamics by developing a few-mode approximation corresponding to the DWP structure, and analyze the resulting system of ordinary differential equations and its bifurcations in detail. We compare results of this analysis with those produced …
Nonlinear Waves In Disordered Diatomic Granular Chains, Laurent Ponson, Nicholas Boechler, Yi M. Lai, Mason A. Porter, Pg Kevrekidis
Nonlinear Waves In Disordered Diatomic Granular Chains, Laurent Ponson, Nicholas Boechler, Yi M. Lai, Mason A. Porter, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a “spin,” so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of …