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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
- Discipline
- Keyword
-
- Blume-Capel model (1)
- Blume-Emery-Griffiths model (1)
- Bose–Einstein condensates; Periodic potentials; Multiple-scale perturbation theory; Hamiltonian systems (1)
- Brion-Vergne formula (1)
- Coarse graining (1)
-
- Dedekind sums (1)
- Ehrhart polynomial (1)
- Equation-free (1)
- First-order phase transition (1)
- Hecke operators (1)
- Identification (1)
- Lattice polytopes (1)
- Microscopic simulator (1)
- Moderate deviation principle (1)
- Multiscale computation (1)
- Non-linear wave interactions; Klein-Gordon lattices; Ablowitz–Ladik model (1)
- Pseudoholomorphic curves (1)
- Scaling limit (1)
- Second-order phase transition (1)
- Symplectic 4-manifolds (1)
- Toric varieties (1)
- Transformation groups (1)
- Tricritical point (1)
Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
Asymptotic Calculation Of Discrete Non-Linear Wave Interactions, Pg Kevrekidis
Asymptotic Calculation Of Discrete Non-Linear Wave Interactions, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We illustrate how to compute asymptotic interactions between discrete solitary waves of dispersive equations, using the approach proposed by Manton [N.S. Manton, Nucl. Phys. B 150 (1979) 397]. We also discuss the complications arising due to discreteness and showcase the application of the method in non-linear Schrödinger, as well as in Klein-Gordon lattices, finding excellent agreement with direct numerical computations.
Faraday Waves In Bose-Einstein Condensates, Ai Nicolin, R Carretero-Gonzalez, Pg Kevrekidis
Faraday Waves In Bose-Einstein Condensates, Ai Nicolin, R Carretero-Gonzalez, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement. We offer a fully analytical explanation of the observed parametric resonance, based on a Mathieu-type analysis of the non-polynomial Schrödinger equation. The theoretical prediction for the pattern periodicity versus the driving frequency is directly compared to the experimental data, yielding good qualitative and quantitative agreement between the two. These results are corroborated by direct numerical simulations of both the one-dimensional non-polynomial Schrödinger equation and of the fully …
Mobility Of Discrete Solitons In Quadratically Nonlinear Media, H Susanto, Pg Kevrekidis, R Carretero-Gonzalez, Ba Malomed, Dj Frantzeskakis
Mobility Of Discrete Solitons In Quadratically Nonlinear Media, H Susanto, Pg Kevrekidis, R Carretero-Gonzalez, Ba Malomed, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
We study the mobility of solitons in lattices with quadratic (χ(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (χ(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes: staying put, persistent motion, or destruction. On the 2D lattice, the solitons survive the largest kick and attain the largest speed along the diagonal direction.
Solitary Waves Under The Competition Of Linear And Nonlinear Periodic Potentials, Z Rapti, Pg Kevrekidis, Vv Konotop, Ckrt Jones
Solitary Waves Under The Competition Of Linear And Nonlinear Periodic Potentials, Z Rapti, Pg Kevrekidis, Vv Konotop, Ckrt Jones
Mathematics and Statistics Department Faculty Publication Series
In this paper, we study the competition of the linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtain detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of …
Symplectic Symmetries Of 4-Manifolds, Wm Chen, S Kwasik
Symplectic Symmetries Of 4-Manifolds, Wm Chen, S Kwasik
Mathematics and Statistics Department Faculty Publication Series
A study of symplectic actions of a finite group G on smooth 4-manifolds is initiated. The central new idea is the use of G-equivariant Seiberg–Witten–Taubes theory in studying the structure of the fixed-point set of these symmetries. The main result in this paper is a complete description of the fixed-point set structure (and the action around it) of a symplectic cyclic action of prime order on a minimal symplectic 4-manifold with . Comparison of this result with the case of locally linear topological actions is made. As an application of these considerations, the triviality of many such actions on …
Modulational Instability In Nonlinearity-Managed Optical Media, Martin Centurion, Mason Porter, Ye Pu, Pg Kevrekidis
Modulational Instability In Nonlinearity-Managed Optical Media, Martin Centurion, Mason Porter, Ye Pu, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable …
Crossover Dark Soliton Dynamics In Ultracold One-Dimensional Bose Gases, D J. Frantzeskakis, Pg Kevrekidis, N. P. Proukakis
Crossover Dark Soliton Dynamics In Ultracold One-Dimensional Bose Gases, D J. Frantzeskakis, Pg Kevrekidis, N. P. Proukakis
Mathematics and Statistics Department Faculty Publication Series
Ultracold confined one-dimensional atomic gases are predicted to support dark soliton solutions arising from a nonlinear Schrödinger equation of suitable nonlinearity. In weakly-interacting (high density) gases, the nonlinearity is cubic, whereas an approximate model for describing the behavior of strongly-interacting (low density) gases is one characterized by a quintic nonlinearity. We use an approximate analytical expression for the form of the nonlinearity in the intermediate regimes to show that, near the crossover between the two different regimes, the soliton is predicted and numerically confirmed to oscillate at a frequency of View the MathML source, where Ω is the harmonic trap …
Observation Of Dipole-Like Gap Solitons In Self-Defocusing Waveguide Lattices, Lq Tang, Cb Lou, Xs Wang, Dh Song, Xy Chen, Jj Xu, Zg Chen, H Susanto, K Law, Pg Kevrekidis
Observation Of Dipole-Like Gap Solitons In Self-Defocusing Waveguide Lattices, Lq Tang, Cb Lou, Xs Wang, Dh Song, Xy Chen, Jj Xu, Zg Chen, H Susanto, K Law, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We observe dipole-like gap solitons in two-dimensional waveguide lattices optically induced with a self-defocusing nonlinearity. Under appropriate conditions, two mutually coherent input beams excited in neighboring lattice sites evolve into a self-trapped state, whose spatial power spectrum and stability depend strongly on the initial excitation conditions. Our experimental observations are compared with numerical simulations.
Comparative Study Of Different Discretizations Of The Phi(4) Model, I Roy, Sv Dmitriev, Pg Kevrekidis, A Saxena
Comparative Study Of Different Discretizations Of The Phi(4) Model, I Roy, Sv Dmitriev, Pg Kevrekidis, A Saxena
Mathematics and Statistics Department Faculty Publication Series
We examine various recently proposed translationally invariant discretizations of the well-known ϕ4 field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral properties of the linearization around such waves. We study these features as a function of the lattice spacing h, as one deviates from the continuum limit of h→0. We then proceed to a more “stringent” comparison of the models, by discussing the scattering properties of a kink-antikink pair for the different discretizations. These collisions are well known to possess properties that quite sensitively depend on …
Soliton Oscillations In Collisionally Inhomogeneous Attractive Bose-Einstein Condensates, P Niarchou, G Theocharis, Pg Kevrekidis, P Schmelcher, Dj Frantzeskakis
Soliton Oscillations In Collisionally Inhomogeneous Attractive Bose-Einstein Condensates, P Niarchou, G Theocharis, Pg Kevrekidis, P Schmelcher, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and “cigar-shaped” condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis. Numerical results are shown to be in very good agreement with the corresponding analytical predictions.
From Feshbach-Resonance Managed Bose-Einstein Condensates To Anisotropic Universes: Applications Of The Ermakov-Pinney Equation With Time-Dependent Nonlinearity, G Herring, Pg Kevrekidis, F Williams, T Christodoulakis, Dj Frantzeskakis
From Feshbach-Resonance Managed Bose-Einstein Condensates To Anisotropic Universes: Applications Of The Ermakov-Pinney Equation With Time-Dependent Nonlinearity, G Herring, Pg Kevrekidis, F Williams, T Christodoulakis, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
In this work we revisit the topic of two-dimensional Bose–Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov–Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to “engineer” trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how …
Weyl Group Multiple Dirichlet Series Constructed From Quadratic Characters, G Chinta, Pe Gunnells
Weyl Group Multiple Dirichlet Series Constructed From Quadratic Characters, G Chinta, Pe Gunnells
Mathematics and Statistics Department Faculty Publication Series
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are the first examples of an infinite collection of unstable Weyl group multiple Dirichlet series in greater than two variables having the properties predicted in [2].
Nonequilibrium Dynamics And Superfluid Ring Excitations In Binary Bose-Einstein Condensates, Km Mertes, Jw Merrill, R Carretero-Gonzalez, Dj Frantzeskakis, Pg Kevrekidis, Ds Hall
Nonequilibrium Dynamics And Superfluid Ring Excitations In Binary Bose-Einstein Condensates, Km Mertes, Jw Merrill, R Carretero-Gonzalez, Dj Frantzeskakis, Pg Kevrekidis, Ds Hall
Mathematics and Statistics Department Faculty Publication Series
We revisit a classic study [D. S. Hall et al., Phys. Rev. Lett. 81, 1539 (1998)] of interpenetrating Bose-Einstein condensates in the hyperfine states |F=1,mf=-1⟩≡|1⟩ and |F=2,mf=+1⟩≡|2⟩ of 87Rb and observe striking new nonequilibrium component separation dynamics in the form of oscillating ringlike structures. The process of component separation is not significantly damped, a finding that also contrasts sharply with earlier experimental work, allowing a clean first look at a collective excitation of a binary superfluid. We further demonstrate extraordinary quantitative agreement between theoretical and experimental results using a multicomponent mean-field model with key additional features: the inclusion of atomic …
Multiple Critical Behavior Of Probabilistic Limit Theorems In The Neighborhood Of A Tricritical Point, M Costeniuc, Rs Ellis, Pth Otto
Multiple Critical Behavior Of Probabilistic Limit Theorems In The Neighborhood Of A Tricritical Point, M Costeniuc, Rs Ellis, Pth Otto
Mathematics and Statistics Department Faculty Publication Series
We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffiths model [Phys. Rev. A 4 (1971) 1071–1077]. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters n, β, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence of 18 scaling …
Ground-State Properties Of Small-Size Nonlinear Dynamical Lattices, P Buonsante, Pg Kevrekidis
Ground-State Properties Of Small-Size Nonlinear Dynamical Lattices, P Buonsante, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M⩾3 sites, using as a prototypical example the discrete nonlinear Schrödinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground-state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in …
Exact Static Solutions To A Translationally Invariant Discrete Phi4 Model, S V. Dmitriev, Pg Kevrekidis
Exact Static Solutions To A Translationally Invariant Discrete Phi4 Model, S V. Dmitriev, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
For a discrete, translationally invariant phi4 model introduced by Barashenkov et al (2005 Phys. Rev. E 72 35602R), we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a Jacobi elliptic function (JEF) solution. The first integral can be written in the form of a nonlinear map from which the static solution supported by the model can be constructed. A set of JEF solutions, including the staggered ones, is derived. We also report on the stability analysis for the static bounded solutions and exemplify the dynamical …
Schrodinger Maps And Their Associated Frame Systems, Andrea Nahmod, Jalal Shatah, Luis Vega, Chongchun Zeng
Schrodinger Maps And Their Associated Frame Systems, Andrea Nahmod, Jalal Shatah, Luis Vega, Chongchun Zeng
Mathematics and Statistics Department Faculty Publication Series
In this paper we establish the equivalence of solutions between Schr¨odinger maps into S 2 or H 2 and their associated gauge invariant Schr¨odinger equations. We also establish the existence of global weak solutions into H 2 in two space dimensions. We extend these ideas for maps into compact hermitian symmetric manifolds with trivial first cohomology.
Envelopes And Osculates Of Willmore Surfaces, K Leschke, F Pedit
Envelopes And Osculates Of Willmore Surfaces, K Leschke, F Pedit
Mathematics and Statistics Department Faculty Publication Series
We view conformal surfaces in the 4-sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus new conformal surfaces. Applying these constructions to Willmore surfaces, we show that the osculating and enveloping curves of Willmore spheres remain Willmore.
Conformal Maps From A 2-Torus To The 4-Sphere, C Bohle, K Leschke, F Pedit, U Pinkall
Conformal Maps From A 2-Torus To The 4-Sphere, C Bohle, K Leschke, F Pedit, U Pinkall
Mathematics and Statistics Department Faculty Publication Series
We study the space of conformal immersions of a 2-torus into the 4-sphere. The moduli space of generalized Darboux transforms of such an immersed torus has the structure of a Riemann surface, the spectral curve. This Riemann surface arises as the zero locus of the determinant of a holomorphic family of Dirac type operators parameterized over the complexified dual torus. The kernel line bundle of this family over the spectral curve describes the generalized Darboux transforms of the conformally immersed torus. If the spectral curve has finite genus the kernel bundle can be extended to the compactification of the spectral …
Stability Of Waves In Multi-Component Dnls System, V M. Rothos, Pg Kevrekidis
Stability Of Waves In Multi-Component Dnls System, V M. Rothos, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrödinger equation with both nonlinear and linear couplings between the components. The Evans function allows us to qualitatively predict the stability of the nonlinear waves under the relevant perturbations and to quantitatively examine the dependence of the corresponding point spectrum eigenvalues on the system parameters. These analytical predictions are subsequently corroborated by numerical computations.
X, Y, And Z Waves: Extended Structures In Nonlinear Lattices, Pg Kevrekidis
X, Y, And Z Waves: Extended Structures In Nonlinear Lattices, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We propose a new type of waveforms in two-dimensional (2D) and three-dimensional (3D) discrete media-multilegged extended nonlinear structures (ENSs), built as arrays of lattice solitons (tiles and stones, in the 2D and 3D cases, respectively). We study the stability of the tiles and stones analytically, and then extend them numerically to complete ENS forms for both 2D and 3D lattices, aiming to single out stable ENSs. The predicted patterns can be realized in Bose-Einstein condensates trapped in deep optical lattices, crystals built of microresonators, and 2D photonic crystals. In the latter case, the patterns provide for a technique for writing …
Periodic Oscillations Of Dark Solitons In Parabolic Potentials, Dmitry Pelinovsky, Pg Kevrekidis
Periodic Oscillations Of Dark Solitons In Parabolic Potentials, Dmitry Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We reformulate the Gross–Pitaevskii equation with an external parabolic potential as a discrete dynamical system, by using the basis of Hermite functions. We consider small amplitude stationary solutions with a single node, called dark solitons, and examine their existence and linear stability. Furthermore, we prove the persistence of a periodic motion in a neighborhood of such solutions. Our results are corroborated by numerical computations elucidating the existence, linear stability and dynamics of the relevant solutions.
On A Class Of Spatial Discretizations Of Equations Of The Nonlinear Schrödinger Type, Pg Kevrekidis
On A Class Of Spatial Discretizations Of Equations Of The Nonlinear Schrödinger Type, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schrödinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We then focus on the cubic problem and illustrate how our class of models compares with the well-known discretizations such as the standard discrete NLS equation, or the integrable variant thereof. We also discuss the conservation laws of the derived generalizations of the cubic case, such as the lattice momentum or mass and the connection with their corresponding continuum siblings.
Modulated Amplitude Waves In Collisionally Inhomogeneous Bose–Einstein Condensates, Mason A. Porter, Pg Kevrekidis
Modulated Amplitude Waves In Collisionally Inhomogeneous Bose–Einstein Condensates, Mason A. Porter, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate the dynamics of an effectively one-dimensional Bose–Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross–Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization …
Lattice Polytopes, Hecke Operators, And The Ehrhart Polynomial, Pe Gunnells, Fr Villegas
Lattice Polytopes, Hecke Operators, And The Ehrhart Polynomial, Pe Gunnells, Fr Villegas
Mathematics and Statistics Department Faculty Publication Series
Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E(P). We also describe how the Brion–Vergne formula for E(P) transforms under the Hecke operators for nonsingular lattice polytopes P.
Symmetry Breaking In Linearly Coupled Dynamical Lattices, G Herring, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez, Dj Frantzeskakis
Symmetry Breaking In Linearly Coupled Dynamical Lattices, G Herring, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
We examine one- and two-dimensional models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the system with equal powers (norms) in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the total power. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking …
Polarized States And Domain Walls In Spinor Bose-Einstein Condensates, He Nistazakis, Dj Frantzeskakis, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez, Ar Bishop
Polarized States And Domain Walls In Spinor Bose-Einstein Condensates, He Nistazakis, Dj Frantzeskakis, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez, Ar Bishop
Mathematics and Statistics Department Faculty Publication Series
We study spin-polarized states and their stability in the antiferromagnetic phase of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including patterns of the Thomas-Fermi type, structures featuring a pulse in one component inducing a hole in the other components, states with holes in all three components, and domain walls (DWs). The stability analysis based on the Bogoliubov–de Gennes equations reveals intervals of weak oscillatory instability in families of these states, except for the DWs, which are always stable. The development of the instabilities is examined by means of direct …
Dark Matter-Wave Solitons In The Dimensionality Crossover, G Theocharis, Pg Kevrekidis, Mk Oberthaler, Dj Frantzeskakis
Dark Matter-Wave Solitons In The Dimensionality Crossover, G Theocharis, Pg Kevrekidis, Mk Oberthaler, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from three dimensions (3D) to one dimension (1D). There, using the nonpolynomial Schrödinger mean-field model, we find that the anomalous mode of the Bogoliubov spectrum has an eigenfrequency which coincides with the soliton oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that substantial deviations (of the order of 10% or more) from the characteristic frequency ωz∕√2 (ωz being the longitudinal trap frequency) are possible even in the purely 1D regime.
Two-Dimensional Discrete Solitons In Rotating Lattices, J Cuevas, Ba Malomed, Pg Kevrekidis
Two-Dimensional Discrete Solitons In Rotating Lattices, J Cuevas, Ba Malomed, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two types of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance R from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities S=1 and 2. At a fixed value of rotation frequency Ω, a stability interval for the FSs is found in terms of the lattice coupling constant C, 0
Deciding The Nature Of The Coarse Equation Through Microscopic Simulations: The Baby-Bathwater Scheme, J Li, Pg Kevrekidis, Cw Gear, Pg Kevrekidis
Deciding The Nature Of The Coarse Equation Through Microscopic Simulations: The Baby-Bathwater Scheme, J Li, Pg Kevrekidis, Cw Gear, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Recent developments in multiscale computation allow the solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations in closed form. The closure is obtained on demand through appropriately initialized bursts ofmicroscopic simulation. The effective coupling of microscopic simulators with macrosocopic behavior requires certain decisions about the nature of the unavailable coarse equation. Such decisions include (a) the highest spatial derivative active in the coarse equation, (b) whether the equation satisfies certain conservation laws, and (c) whether the coarse dynamics is Hamiltonian. These decisions affect the number and type of boundary conditions …