Related papers: Tridiagonal Matrices and Boundary Conditions
We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…
We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of…
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…
We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The asymptotic behavior of three-body scattering wave functions in configuration space is studied by considering a model equation that has the same asymptotic form as the Faddeev equations. Boundary conditions for the wave function are…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…
We propose a stationary system that might be regarded as a migration model of some population abandoning their original place of abode and becoming part of another population, once they reach the interface boundary. To do so, we show a…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type equations in a bounded domain with periodic boundary conditions. The system is motivated by our study of grain boundary dynamics, especially under…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
Social networks exhibit scaling-laws for several structural characteristics, such as the degree distribution, the scaling of the attachment kernel, and the clustering coefficients as a function of node degree. A detailed understanding if…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…
A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed in the previous paper, are solved and a new determinant…
We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to…