相关论文: Projections of Patterns and Mode Interactions
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Numerical solution of non-steady problems of supersonic inflow of a binary mixture of a rarefied gas on a normally posed wall with mirror and diffuse reflection laws is obtained on the basis of the kinetic Boltzmann equation for the model…
Interactions between several features sometimes play an important role in prediction tasks. But taking all the interactions into consideration will lead to an extremely heavy computational burden. For categorical features, the situation is…
Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between…
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
A new method for the solution of initial-boundary value problems for evolution PDEs recently introduced by Fokas is generalised to multidimensions. Also the relation of this method with the method of images and with the classical integral…
We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…
We study a message passing model, applicable also to traffic problems. The model is implemented in a discrete lattice, where particles move towards their destination, with fluctuations around the minimal distance path. A repulsive…
The coincidence problem for planar patterns with $N$-fold symmetry is considered. For the N-fold symmetric module with $N<46$, all isometries of the plane are classified that result in coincidences of finite index. This is done by…
We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus $k$. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the…
We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one,…
It is shown that periodic instanton solutions may have bifurcations which qualitatively change the behaviour of the finite temperature transition rate. These bifurcations are studied numerically in a quantum mechanical model and in the…
Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary…
We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanical-like interactions. We find the analytical expression…
Using linear projections one gets new inequalities for the successive minima of the lattice of sections of an hermitian line bundle on an arithmetic surface.
The mode structure of a Bose-Einstein condensate non-adiabatically loaded into a one-dimensional optical lattice is studied by analyzing the visibility of the interference pattern as well as the radial profile of the condensate after a…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…