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Articles 181 - 210 of 210
Full-Text Articles in Entire DC Network
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.
On The Stabilization Of Ion Sputtered Surfaces, B Davidovitch
On The Stabilization Of Ion Sputtered Surfaces, B Davidovitch
Physics Department Faculty Publication Series
The classical theory of ion beam sputtering predicts the instability of a flat surface to uniform ion irradiation at any incidence angle. We relax the assumption of the classical theory that the average surface erosion rate is determined by a Gaussian response function representing the effect of the collision cascade, and consider the surface dynamics for other physically motivated response functions. We show that although instability of flat surfaces at any beam angle results from all Gaussian and a wide class of non-Gaussian erosive response functions, there exist classes of modifications to the response that can have a dramatic effect. …
Critical Behavior Of The Chayes–Machta–Swendsen–Wang Dynamics, Y Deng, T Garoni, J Machta, G Ossola, M Polin, A Sokal
Critical Behavior Of The Chayes–Machta–Swendsen–Wang Dynamics, Y Deng, T Garoni, J Machta, G Ossola, M Polin, A Sokal
Physics Department Faculty Publication Series
We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z≥α/ν is close to but probably not sharp in d=2 and is far from sharp in d=3, for all q. The conjecture z≥β/ν is false (for some values of q) in both d=2 and d=3.
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.
What Makes A Crystal Supersolid?, Nikolai Prokof'ev
What Makes A Crystal Supersolid?, Nikolai Prokof'ev
Physics Department Faculty Publication Series
For nearly half a century the supersolid phase of matter has remained mysterious, not only eluding experimental observation, but also generating a great deal of controversy among theorists. The recent discovery of what is interpreted as a non-classical moment of inertia at low temperature in solid 4He [E. Kim and M.H.W. Chan, Nature 427 225 (2004a); E. Kim and M.H.W. Chan, Science 305 1941 (2004b); E. Kim and M.H.W. Chan, Phys. Rev. Lett. 97 115302 (2006); A.C. Clark and M.H.W. Chan, J. Low Temp. Phys. 138 853 (2005)] has elicited much excitement as a possible first observation of a supersolid …
Superfluid-Insulator And Roughening Transitions In Domain Walls, S Söyler, Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov
Superfluid-Insulator And Roughening Transitions In Domain Walls, S Söyler, Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov
Physics Department Faculty Publication Series
We have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-1∕2 quasiparticles; (iii) in two dimensions, the transition belongs to the three-dimensional …
Phase Diagram And Thermodynamics Of The Three-Dimensional Bose-Hubbard Model, B Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov
Phase Diagram And Thermodynamics Of The Three-Dimensional Bose-Hubbard Model, B Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov
Physics Department Faculty Publication Series
We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than has been done in the past. In particular, the position of the critical point at filling factor n=1 is found to be at (U∕t)c=29.34(2), and the insulating gap Δ is measured with accuracy of a few percent of the hopping amplitude t. We obtain the effective mass of particle and hole excitations in the insulating state—with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip—along with …
Do Killing–Yano Tensors Form A Lie Algebra?, David Kastor, Sourya Ray, Jennie Traschen
Do Killing–Yano Tensors Form A Lie Algebra?, David Kastor, Sourya Ray, Jennie Traschen
Physics Department Faculty Publication Series
Killing–Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing–Yano tensors form a graded Lie algebra with respect to the Schouten–Nijenhuis bracket. We find that this proposition does not hold in general, but that it does hold for constant curvature spacetimes. We also show that Minkowski and (anti)-deSitter spacetimes have the maximal number of Killing–Yano tensors of each rank and that the algebras of these tensors under the SN bracket are relatively simple extensions of the Poincaré and (A)dS symmetry algebras.
Unsupervised Joint Alignment Of Complex Images, Gary B. Huang
Unsupervised Joint Alignment Of Complex Images, Gary B. Huang
Computer Science Department Faculty Publication Series
Many recognition algorithms depend on careful positioning of an object into a canonical pose, so the position of features relative to a fixed coordinate system can be examined. Currently, this positioning is done either manually or by training a class-specialized learning algorithm with samples of the class that have been hand-labeled with parts or poses. In this paper, we describe a novel method to achieve this positioning using poorly aligned examples of a class with no additional labeling. Given a set of unaligned examplars of a class, such as faces, we automatically build an alignment mechanism, without any additional labeling …
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 …
Discrete Surface Solitons In Two Dimensions, H Susanto, Pg Kevrekidis
Discrete Surface Solitons In Two Dimensions, H Susanto, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate fundamental localized modes in two-dimensional lattices with an edge (surface). The interaction with the edge expands the stability area for fundamental solitons, and induces a difference between dipoles oriented perpendicular and parallel to the surface. On the contrary, lattice vortex solitons cannot exist too close to the border. We also show, analytically and numerically, that the edge supports a species of localized patterns, which exists too but is unstable in the uniform lattice, namely, a horseshoe-shaped soliton, whose “skeleton” consists of three lattice sites. Unstable horseshoes transform themselves into a pair of ordinary solitons.
Dark Solitons In Discrete Lattices: Saturable Versus Cubic Nonlinearities, E P. Fitrakis, Pg Kevrekidis
Dark Solitons In Discrete Lattices: Saturable Versus Cubic Nonlinearities, E P. Fitrakis, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them to those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both onsite and intersite modes, are examined analytically and corroborated by numerical results. Our findings indicate that for both models onsite solutions are stable for sufficiently small values of the coupling between adjacent nodes, while intersite solutions are always unstable. The nature of the instability (which is oscillatory for onsite …
Čerenkov-Like Radiation In A Binary Superfluid Flow Past An Obstacle, H Susanto, Pg Kevrekidis
Čerenkov-Like Radiation In A Binary Superfluid Flow Past An Obstacle, H Susanto, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components are subcritical, we do not observe nucleation of coherent structures; when both components are supercritical they both form dark solitons in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions; in the intermediate regime, we observe the nucleation of a structure in the form of a dark-antidark soliton in 1D; the 2D analog of such a structure, a vortex-lump, is also observed.
Weyl Group Multiple Dirichlet Series Of Type A2, G Chinta, Pe Gunnells
Weyl Group Multiple Dirichlet Series Of Type A2, G Chinta, Pe Gunnells
Mathematics and Statistics Department Faculty Publication Series
A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system . The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of . In this paper we construct a Weyl group multiple Dirichlet series over
the rational function field using nth order Gauss sums attached to the root system of type A2. The basic technique is that of [8, 9]; namely, we construct a rational function in r variables invariant under a certain action …
Eflux: A Language And Runtime System For Perpetual Systems, Jacob Sorber
Eflux: A Language And Runtime System For Perpetual Systems, Jacob Sorber
Computer Science Department Faculty Publication Series
A key goal of mobile computing is untethering devices from wires, making them truly portable. While mobile devices can make use of wireless communication for network connectivity, they are still dependent on an electrical connection for continued operation. This need for tethering to available electricity significantly limits their range, usefulness, and manageability. Environmental energy harvesting—collecting energy from the sun, wind, heat differentials, and motion—offers the prospect of unprecedented, large-scale deployments of perpetual mobile systems that never need to be recharged. However, programming these systems presents new challenges: perpetual systems must adapt dynamically to available energy, delivering higher service levels when …
Adaptive Control Of Duty Cycling In Energy-Harvesting Wireless Sensor Networks, Christopher M. Vigorito
Adaptive Control Of Duty Cycling In Energy-Harvesting Wireless Sensor Networks, Christopher M. Vigorito
Computer Science Department Faculty Publication Series
Increasingly many wireless sensor network deployments are using harvested environmental energy to extend system lifetime. Because the temporal profiles of such energy sources exhibit great variability due to dynamic weather patterns, an important problem is designing an adaptive duty-cycling mechanism that allows sensor nodes to maintain their power supply at sufficient levels (energy neutral operation) by adapting to changing environmental conditions. Existing techniques to address this problem are minimally adaptive and assume a priori knowledge of the energy profile. While such approaches are reasonable in environments that exhibit low variance, we find that it is highly inefficient in more variable …
Mixtures Of Hierarchical Topics With Pachinko Allocation, David Mimno
Mixtures Of Hierarchical Topics With Pachinko Allocation, David Mimno
Computer Science Department Faculty Publication Series
The four-level pachinko allocation model (PAM) (Li & McCallum, 2006) represents correlations among topics using a DAG structure. It does not, however, represent a nested hierarchy of topics, with some topical word distributions representing the vocabulary that is shared among several more specific topics. This paper presents hierarchical PAM---an enhancement that explicitly represents a topic hierarchy. This model can be seen as combining the advantages of hLDA's topical hierarchy representation with PAM's ability to mix multiple leaves of the topic hierarchy. Experimental results show improvements in likelihood of held-out documents, as well as mutual information between automatically-discovered topics and humangenerated …
Phytoextraction Of Arsenic From Soil By Leersia Orywides, Rj Ampiah-Bonney, Jf Tyson, Gr Lanza
Phytoextraction Of Arsenic From Soil By Leersia Orywides, Rj Ampiah-Bonney, Jf Tyson, Gr Lanza
Chemistry Department Faculty Publication Series
No abstract provided.
The Fine-Tuning Problems Of Particle Physics And Anthropic Mechanisms, John Donoghue
The Fine-Tuning Problems Of Particle Physics And Anthropic Mechanisms, John Donoghue
Physics Department Faculty Publication Series
Many of the classic problems of particle physics appear in a very different light when viewed from the perspective of the multiverse. Most importantly the two great ``fine tuning'' problems that motivate the field are far less serious when one accounts for the required anthropic constraints which exist in a multiverse. However, the challenge then becomes to construct a realistic physical theory of the multiverse and test it. I describe some phenomenology of the quark and lepton masses that may provide a window to the theory that underlies the multiverse.