Related papers: Variational approximations to homoclinic snaking
We study the structure of stationary patterns in bistable lattice dynamical systems posed on rings with a symmetric coupling structure in the regime of small coupling strength. We show that sparse coupling (for instance, nearest-neighbour…
This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local…
We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where the pattern resembles one of the bistable states, while the…
Spatially localised stationary patterns of arbitrary wide spatial extent emerge from subcritical Turing bifurcations in one-dimensional reaction-diffusion systems. They lie on characteristic bifurcation curves that oscillate around a…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
An investigation is undertaken of coupled reaction-diffusion systems in one spatial dimension that are able to support, in different regions of their parameter space, either an isolated spike solution, or stable localized patterns with an…
The classical Cahn-Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale…
We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…
We consider localised states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localised states is made possible by…
We study temporally localized structures in doubly resonant degenerate optical parametric oscillators in the absence of temporal walk-off. We focus on states formed through the locking of domain walls between the zero and a non-zero…
Geometrical disorder is present in many physical situations giving rise to eigenvalue problems. The simplest case of diffusion on a random lattice with fluctuating site connectivities is studied analytically and by exact numerical…
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…
We document a sequence of bifurcations and elastic patterns in sheared bent sheets of intermediate aspect ratio. The sheets undergo inversion of curvature through the passage of localized features, often in S-shaped pairs. Nested…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…
Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
We introduce a new variational approach to the stationary state of kinetic Ising-like models. The approach is based on the cluster expansion of the entropy term appearing in a functional which is minimized by the system history. We rederive…
Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is…