Related papers: Localized states in coupled Cahn-Hilliard equation…
In this paper we study a nonlocal Cahn-Hilliard model (CHE) in the framework of random walk spaces, which includes as particular cases, the CHE on locally finite weighted connected graphs, the CHE determined by finite Markov chains or the…
We explore topology-localization phase diagram by simulating one-dimensional Su-Schrieffer-Heeger (SSH) model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial…
We analyze the implication of tristability on localization phenomena in one-dimensional extended dissipative systems. In this context, localized states appear due to the interaction and locking of front waves connecting different extended…
We investigate steady-state properties of a two-dimensional incoherent-pumped dissipative Bose-Hubbard model, which describes a photon square lattice. This incoherent pumping exhibits an important environment-induced higher-order…
The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger…
The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and…
We study the existence of one-dimensional localized states supported by linear periodic potentials and a domain-wall-like Kerr nonlinearity. The model gives rise to several new types of asymmetric localized states, including single- and…
Biological active matter is typically tightly coupled to chemical reaction networks affecting its assembly-disassembly dynamics and stress generation. We show that localized states can emerge spontaneously if assembly of active matter is…
We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material ux is imposed. The first instability is localized within a boundary layer at the exposed free surface by…
A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. This dispersion is associated with the continuous spectrum of…
Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyze the basic mechanisms for this scenario by…
Entanglement cohomology assigns a graded cohomology ring to a multipartite pure state, providing homological invariants that are stable under local unitaries and characterize inequivalent patterns of entanglement. In this work we derive…
Axisymmetric and nonaxisymmetric patterns in the cubic-quintic Swift-Hohenberg equation posed on a disk with Neumann boundary conditions are studied via numerical continuation and bifurcation analysis. Axisymmetric localized solutions in…
We discuss the microscopic origin of dynamical instabilities and segregation patterns discovered in granular mixtures under oscillating horizontal shear, by investigating, via molecular dynamics simulations, the effective interaction…
Self-assembly driven by phase separation coupled to Coulombic interactions is fundamental to a wide range of applications, examples of which include soft matter lithography via di-block copolymers, membrane design using polyelectrolytes,…
Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and drastically alters transport properties of the lattice. In the original Anderson model, the addition of a periodic driving increases, in a certain range…
We study the focusing inhomogeneous nonlinear Schr\"odinger equation $$ i\partial_t u + \Delta u = -|x|^b |u|^{p-1}u ,\quad (t,x)\in (0,\infty)\times\mathbb{R}^N, $$ with $b>0$ and $p>1$. Due to the spatial growth of the nonlinearity,…
The coincidence of a pitchfork and Hopf bifurcation at a Takens-Bogdanov (TB) bifurcation occurs in many physical systems such as double-diffusive convection, binary convection and magnetoconvection. Analysis of the associated normal form,…
The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is…
We investigate a model for pattern formation in the presence of Galilean symmetry proposed by Matthews and Cox [Phys.\ Rev.\ E \textbf{62}, R1473 (2000)], which has the form of coupled generalized Burgers and Ginzburg-Landau-type equations.…