相关论文: Front localization in a ballistic annihilation mod…
We consider a system of annihilating particles where particles start from the points of a Poisson process on the line, move at constant i.i.d. speeds symmetrically distributed in {-1,0,+1} and annihilate upon collision. We prove that…
Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site.…
We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $\phi^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with…
Foundation models are trained on broad data distributions, yielding generalist capabilities that enable many downstream applications but also expand the space of potential misuse and failures. This position paper argues that capability…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…
A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…
Front propagation into unstable states is often determined by the linearization, that is, propagation speeds agree with predictions from the linearized equation at the unstable state. The leading edge behavior is then a Gaussian tail…
Conventional classifiers are trained and evaluated using balanced data sets in which all classes are equally present. Classifiers are now trained on large data sets such as ImageNet, and are now able to classify hundreds (if not thousands)…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
In this paper we formulate and analyze an elementary model for the propagation of advancing autoignition fronts in reactive co-flow fuel/oxidizer jets injected into an aqueous environment at high pressure. This work is motivated by the…
We develop a theory for fluctuations and correlations in a gas evolving under ballistic annihilation dynamics. Starting from the hierarchy of equations governing the evolution of microscopic densities in phase space, we subsequently…
The paper is an attempt to generalize a methodology, which is similar to the bounded-input bounded-output method currently widely used for the system stability studies. The presented earlier methodology allows decomposition of input space…
In coalescing ballistic annihilation, infinitely many particles move with fixed velocities across the real line and, upon colliding, either mutually annihilate or generate a new particle. We compute the critical density in symmetric…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
The current paper is to investigate the numerical approximation of logistic type chemotaxis models in one space dimension with a free boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject…
This paper studies the problem of multi-agent formation maneuver control where both of the centroid and scale of a formation are required to track given velocity references while maintaining the formation shape. Unlike the conventional…
We extend and investigate the spheroidal model of interstellar dust grains used to simultaneously interpret the observed interstellar extinction and polarization curves. We compare our model with similar models recently suggested by other…
We consider a kinetic model for a system of two species of particles interacting through a longrange repulsive potential and a reservoir at given temperature. The model is described by a set of two coupled Vlasov-Fokker-Plank equations. The…