English
Related papers

Related papers: Stable Boundary Spike Clusters for the Two-Dimensi…

200 papers

We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…

Statistical Mechanics · Physics 2019-07-29 Nisarga Paul , Ariel Amir

We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin-orbit coupled Bose-Einstein condensates (BECs). The analysis is performed for equal densities of pseudo-spin components. Different combination…

Quantum Gases · Physics 2017-05-22 S. Bhuvaneswari , K. Nithyanandan , P. Muruganandam , K. Porsezian

We investigate the dynamics of a spinor Bose-Einstein condensate inside an optical cavity, driven transversely by a laser with a controllable polarization angle. We focus on a two-component Dicke model with complex light-matter couplings,…

Quantum Gases · Physics 2019-05-21 Ezequiel Rodríguez Chiacchio , Andreas Nunnenkamp

Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau…

Dynamical Systems · Mathematics 2025-06-30 Aric Wheeler , Kevin Zumbrun

In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint…

Analysis of PDEs · Mathematics 2023-05-16 Guodong Wang

In this work, we study the stable determination of four space-dependent coefficients appearing in a coupled semilinear parabolic system with variable diffusion matrices subject to dynamic boundary conditions which couple intern-boundary…

Analysis of PDEs · Mathematics 2022-12-26 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar

Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching…

Soft Condensed Matter · Physics 2015-05-29 Andreas M. Menzel

We consider a 2D infinite channel domain with an incompressible fluid satisfying the so-called dynamic slip boundary condition on the (part of the) boundary. Introducing an exhaustion by a sequence of bounded sub-domains of the whole…

Analysis of PDEs · Mathematics 2024-08-26 Michael Zelina

In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the Euler-Einstein system with a positive cosmological constant in 1 + 3 dimensions. The background…

Mathematical Physics · Physics 2010-08-31 Igor Rodnianski , Jared Speck

The robust stability problem involves designing a controlled system which remains stable in the presence of modeling uncertainty. In this context, results known as small gain theorems are used to quantify the maximum amount of uncertainty…

Optimization and Control · Mathematics 2026-04-01 Gavin Glenn , Emma J. Reid

In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…

chao-dyn · Physics 2007-05-23 R. Vilela Mendes

We demonstrate the occurrence of permanent spikes using the Lemaitre-Tolman-Bondi models, chosen because the solutions are exact and can be analyzed by qualitative dynamical systems methods. Three examples are given and illustrated…

General Relativity and Quantum Cosmology · Physics 2014-05-22 Alan Coley , Woei Chet Lim

We analyze the stability of spin spiral states in the two-dimensional Heisenberg model. Our analysis reveals that the SU(2) symmetric point hosts a dynamic instability that is enabled by the existence of energetically favorable transverse…

Statistical Mechanics · Physics 2022-07-07 Joaquin F. Rodriguez-Nieva , Alexander Schuckert , Dries Sels , Michael Knap , Eugene Demler

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…

Analysis of PDEs · Mathematics 2020-03-09 C. H. S. Hamster , H. J. Hupkes

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system…

Neurons and Cognition · Quantitative Biology 2016-04-19 Henry C. Tuckwell , Susanne Ditlevsen

Spiking Neural Networks are powerful computational modelling tools that have attracted much interest because of the bioinspired modelling of synaptic interactions between neurons. Most of the research employing spiking neurons has been…

Neural and Evolutionary Computing · Computer Science 2019-03-05 Huanneng Qiu , Matthew Garratt , David Howard , Sreenatha Anavatti

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…

Dynamical Systems · Mathematics 2020-12-11 M. Angelova , G. Beliakov , A. Ivanov , S. Shelyag

The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…

Functional Analysis · Mathematics 2019-12-05 Birgit Jacob , Sebastian Möller , Christian Wyss

Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…

Analysis of PDEs · Mathematics 2022-07-01 Szymon Cygan , Anna Marciniak-Czochra , Grzegorz Karch

This paper presents an anti-windup PI controller, using a saturating integrator, for a single-input single-output stable nonlinear plant, whose steady-state input-output map is increasing. We prove that, under reasonable assumptions, there…

Optimization and Control · Mathematics 2021-07-02 Pietro Lorenzetti , George Weiss