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Articles 1 - 25 of 25
Full-Text Articles in Physical Sciences and Mathematics
Statics And Dynamics Of Atomic Dark-Bright Solitons In The Presence Of Impurities, V. Achilleos, Panos Kevrekidis, V. M. Rothos, D. J. Frantzeskakis
Statics And Dynamics Of Atomic Dark-Bright Solitons In The Presence Of Impurities, V. Achilleos, Panos Kevrekidis, V. M. Rothos, D. J. Frantzeskakis
Panos Kevrekidis
Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with results …
Transfer And Scattering Of Wave Packets By A Nonlinear Trap, Kai Li, Panos Kevrekidis, Boris A. Malomed, D. J. Frantzeskakis
Transfer And Scattering Of Wave Packets By A Nonlinear Trap, Kai Li, Panos Kevrekidis, Boris A. Malomed, D. J. Frantzeskakis
Panos Kevrekidis
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by “nonlinear tweezers,” as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding “radiation.” A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy …
On Hilbert Modular Threefolds Of Discriminant 49, Lev A. Borisov, Paul E. Gunnells
On Hilbert Modular Threefolds Of Discriminant 49, Lev A. Borisov, Paul E. Gunnells
Paul Gunnells
Let K be the totally real cubic field of discriminant 49 , let \fancyscriptO be its ring of integers, and let p⊂\fancyscriptO be the prime over 7 . Let Γ(p)⊂Γ=SL2(\fancyscriptO) be the principal congruence subgroup of level p . This paper investigates the geometry of the Hilbert modular threefold attached to Γ(p) and some related varieties. In particular, we discover an octic in P3 with 84 isolated singular points of type A2 .
Modular Forms And Elliptic Curves Over The Cubic Field Of Discriminant - 23, Paul E. Gunnells, Dan Yasaki
Modular Forms And Elliptic Curves Over The Cubic Field Of Discriminant - 23, Paul E. Gunnells, Dan Yasaki
Paul Gunnells
Let F be the cubic field of discriminant –23 and let O Ϲ F be its ring of integers. By explicitly computing cohomology of congruence subgroups of 〖GL〗_2(O) , we computationally investigate modularity of elliptic curves over F.
Vortex–Bright-Soliton Dipoles: Bifurcations, Symmetry Breaking, And Soliton Tunneling In A Vortex-Induced Double Well, M. Pola, J. Stockhofe, P. Schmelcher, Panos Kevrekidis
Vortex–Bright-Soliton Dipoles: Bifurcations, Symmetry Breaking, And Soliton Tunneling In A Vortex-Induced Double Well, M. Pola, J. Stockhofe, P. Schmelcher, Panos Kevrekidis
Panos Kevrekidis
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the brightwave function between the two vortex “wells.” We interpret this phenomenon by virtue of a vortex-induced double-well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition …
Nonlinear Pt-Symmetric Plaquettes, Kai Li, Panos Kevrekidis, Boris A. Malomed, Uwe Günther
Nonlinear Pt-Symmetric Plaquettes, Kai Li, Panos Kevrekidis, Boris A. Malomed, Uwe Günther
Panos Kevrekidis
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its PT symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient, . Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of …
Hierarchical Fractional-Step Approximations And Parallel Kinetic Monte Carlo Algorithms, Giorgos Arampatzis, Markos Katsoulakis, Petr Plechac, Michela Taufer, Lifan Xu
Hierarchical Fractional-Step Approximations And Parallel Kinetic Monte Carlo Algorithms, Giorgos Arampatzis, Markos Katsoulakis, Petr Plechac, Michela Taufer, Lifan Xu
Markos Katsoulakis
We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition …
There Is No Triangulation Of The Torus With Vertex Degrees 5, 6, . . ., 6, 7 And Related Results: Geometric Proofs For Combinatorial Theorems, Ivan Izmestiev, Robert B. Kusner, Günter Rote, Boris Springborn, John M. Sullivan
There Is No Triangulation Of The Torus With Vertex Degrees 5, 6, . . ., 6, 7 And Related Results: Geometric Proofs For Combinatorial Theorems, Ivan Izmestiev, Robert B. Kusner, Günter Rote, Boris Springborn, John M. Sullivan
Robert Kusner
There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and 7. Similarly, there is no 3,5-quadrangulation. The vertices of a 2,4-hexangulation of the torus cannot be bicolored. Similar statements hold for 4,8-triangulations and 2,6-quadrangulations. We prove these results, of which the first two are known and the others seem to be new, as corollaries of a theorem on the holonomy group of a euclidean cone metric on the torus with just two cone points. We provide two proofs of this theorem: One argument is metric in nature, the other relies …
Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, Y. Shen, Panos Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis
Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, Y. Shen, Panos Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis
Panos Kevrekidis
We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for …
New Bilinear Estimates For Quadratic-Derivative Nonlinear Wave Equations In 2+1 Dimensions, Allison J. Tanguay
New Bilinear Estimates For Quadratic-Derivative Nonlinear Wave Equations In 2+1 Dimensions, Allison J. Tanguay
Open Access Dissertations
This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Lebesgue spaces to bilinear estimates in associated wave Fourier Lebesgue spaces, for which we prove new product estimates. These estimates then allow us to establish local well-posedness in a parameter range that gives improvement over previously known results on the Sobolev scale.
Ultrashort Pulses And Short-Pulse Equations In 2+1 Dimensions, Y. Shen, N. Whitaker, Panos Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis
Ultrashort Pulses And Short-Pulse Equations In 2+1 Dimensions, Y. Shen, N. Whitaker, Panos Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis
Panos Kevrekidis
In this paper, we derive and study two versions of the short pulse equation (SPE) in (2 + 1) dimensions. Using Maxwell’s equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab wave guides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting (2 + 1)-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort one-dimensional breathers appear to be …
Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, V. Achilleos, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez
Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, V. Achilleos, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez
Panos Kevrekidis
We consider nonlinear analogs of parity-time- (PT-) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and odd excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter ɛ controlling the strength of the PT-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as ɛ is further increased, the ground state and first excited state, as well as branches of higher multisoliton (multivortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear PT phase transition—thus …
Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, Andrey Kanshu, Christian E. Rüter, Detlef Kip, Jesús Cuevas, Panos Kevrekidis
Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, Andrey Kanshu, Christian E. Rüter, Detlef Kip, Jesús Cuevas, Panos Kevrekidis
Panos Kevrekidis
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they may also feature both prototypical types of instabilities, namely exponential and oscillatory ones, for …
Local Torsion On Abelian Surfaces, Adam Gamzon
Local Torsion On Abelian Surfaces, Adam Gamzon
Open Access Dissertations
Fix an integer d > 0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of degree at most d for only finitely many primes p. This dissertation is an extension of that work, investigating the frequency with which a principally polarized abelian surface A over Q with real multiplication by Q adjoin a squared-root of 5 has a nontrivial p-torsion point defined over K. Averaging by height, the main result shows that A …
Dark-Bright Solitons In Bose–Einstein Condensates At Finite Temperatures, V. Achilleos, D. Yan, Panos Kevrekidis, D. J. Frantzeskakis
Dark-Bright Solitons In Bose–Einstein Condensates At Finite Temperatures, V. Achilleos, D. Yan, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while …
Dynamics Of Bright Solitons And Soliton Arrays In The Nonlinear Schrödinger Equation With A Combination Of Random And Harmonic Potentials, Qian-Yong Chen, Panos Kevrekidis, Boris A. Malomed
Dynamics Of Bright Solitons And Soliton Arrays In The Nonlinear Schrödinger Equation With A Combination Of Random And Harmonic Potentials, Qian-Yong Chen, Panos Kevrekidis, Boris A. Malomed
Panos Kevrekidis
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation, which includes the harmonic oscillator potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose–Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in a BEC. The basic characteristics of the …
Defect Modes In One-Dimensional Granular Crystals, Y. Man, N. Boechler, G. Theocharis, Panos Kevrekidis, C. Daraio
Defect Modes In One-Dimensional Granular Crystals, Y. Man, N. Boechler, G. Theocharis, Panos Kevrekidis, C. Daraio
Panos Kevrekidis
We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined …
Generalised Burnside Rings, G-Categories And Module Categories, Paul E. Gunnells, Andrew Rose, Dmitriy Rumynin
Generalised Burnside Rings, G-Categories And Module Categories, Paul E. Gunnells, Andrew Rose, Dmitriy Rumynin
Paul Gunnells
This note describes an application of the theory of generalised Burnside rings to algebraic representation theory. Tables of marks are given explicitly for the groups S4 and S5 which are of particular interest in the context of reductive algebraic groups. As an application, the base sets for the nilpotent element F4(a3) are computed.
Spatial Solitons Under Competing Linear And Nonlinear Diffractions, Y. Shen, Panos Kevrekidis, N. Whitaker
Spatial Solitons Under Competing Linear And Nonlinear Diffractions, Y. Shen, Panos Kevrekidis, N. Whitaker
Panos Kevrekidis
We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, …
Escape Dynamics In The Discrete Repulsive Model, V. Achilleos, A. Alvarez, J. Cuevas, D. J. Frantzeskakis, N. I. Karachalios, Panos Kevrekidis, B. Sanchez-Rey
Escape Dynamics In The Discrete Repulsive Model, V. Achilleos, A. Alvarez, J. Cuevas, D. J. Frantzeskakis, N. I. Karachalios, Panos Kevrekidis, B. Sanchez-Rey
Panos Kevrekidis
We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the Hamiltonian and the linearly damped versions of the system and showcase different potential fates of the single-site excitation, such as the possibility to be “pulled back” from outside the well or to “drive over” the barrier some of its neighbors. Next, we study the evolution of a uniform (small) segment of the chain …
A Relative Entropy Rate Method For Path Space Sensitivity Analysis Of Stationary Complex Stochastic Dynamics, Yannis Pantazis, Markos Katsoulakis
A Relative Entropy Rate Method For Path Space Sensitivity Analysis Of Stationary Complex Stochastic Dynamics, Yannis Pantazis, Markos Katsoulakis
Markos Katsoulakis
We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the relative entropy rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the relative entropy rate and the corresponding Fisher information matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-Gaussian stationary probability …
Symmetry-Breaking Effects For Polariton Condensates In Double-Well Potentials, A. S. Rodrigues, Panos Kevrekidis, J. Cuevas, R. Carretero-Gonzalez, D. J. Frantzeskakis
Symmetry-Breaking Effects For Polariton Condensates In Double-Well Potentials, A. S. Rodrigues, Panos Kevrekidis, J. Cuevas, R. Carretero-Gonzalez, D. J. Frantzeskakis
Panos Kevrekidis
We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in the …
Breathers For The Discrete Nonlinear Schrödinger Equation With Nonlinear Hopping, N. I. Karachalios, B. Sánchez-Rey, Panos Kevrekidis, J. Cuevas
Breathers For The Discrete Nonlinear Schrödinger Equation With Nonlinear Hopping, N. I. Karachalios, B. Sánchez-Rey, Panos Kevrekidis, J. Cuevas
Panos Kevrekidis
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below the prescribed lower bounds of the power which depend on the dimension, the parameters of the lattice as well as of the frequency of breathers. In the case of supercritical power nonlinearities we investigate the interplay of these estimates with the optimal …
Multilevel Coarse Graining And Nano-Pattern Discovery In Many Particle Stochastic Systems, Evangelia Kalligiannski, Markos Katsoulakis, Petr Plechac, Dion Vlachos
Multilevel Coarse Graining And Nano-Pattern Discovery In Many Particle Stochastic Systems, Evangelia Kalligiannski, Markos Katsoulakis, Petr Plechac, Dion Vlachos
Markos Katsoulakis
In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition …
Characteristics Of Two-Dimensional Quantum Turbulence In A Compressible Superfluid, T. W. Neely, A. S. Bradley, E. C. Samson, S. J. Rooney, E. M. Wright, K. J. H. Law, R. Carretero-Gonz´Alez, Panos Kevrekidis, M. J. Davis, B. P. Anderson
Characteristics Of Two-Dimensional Quantum Turbulence In A Compressible Superfluid, T. W. Neely, A. S. Bradley, E. C. Samson, S. J. Rooney, E. M. Wright, K. J. H. Law, R. Carretero-Gonz´Alez, Panos Kevrekidis, M. J. Davis, B. P. Anderson
Panos Kevrekidis
Under suitable forcing a fluid exhibits turbulence, with characteristics strongly aected by the fluid’s confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap. As a compressible quantum fluid, this system aords a rich phenomenology, allowing coupling between vortex and acoustic energy. Small-scale stirring generates an experimentally observed disordered vortex distribution that evolves into large-scale flow in the form of a persistent current. Numerical simulation of the experiment reveals additional characteristics of two-dimensional quantum turbulence: spontaneous clustering of same-circulation vortices, and an incompressible energy spectrum with k5=3 dependence for low wavenumbers k …