Related papers: Discrete spacetime and its applications
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
In this paper, we study the chaotic behavior of a discrete-time linear inclusion.
The model of a geometrically thin gaseous disk in the external gravitational potential is considered. The dinamics of small nonaxisymmetric perturbations in the plane of the accretion disk with dissipative effects is investigated. It is…
A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation…
Non-equilibrium driving systems provide fertile ground for exploring intriguing spontaneous symmetry breaking phenomena. In this study, we report on the intertwined discrete spacetime translational symmetry breaking in a driven-dissipative…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure"…
Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…
This paper investigates the late-time behaviour of certain cosmological models where oscillations play an essential role. Rigorous results are proved on the asymptotics of homogeneous and isotropic spacetimes with a linear massive scalar…
We developed a discrete two-dimensional model of a cantilever which incorporates the effects of inhomogeneity, the geometry of an attached particle, and the influence of external time-dependent forces. We provide a comparison between the…
We consider random walks on quasi one dimensional lattices, as introduced in \cite{FS}. This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general…
As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…
This paper discusses the asymptotic periodic behavior of a class of switched discrete event systems, and shows how to evaluate the asymptotic performance of such systems.
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
The effects of particle discreteness in N-body simulations of Lambda Cold Dark Matter (LambdaCDM) are still an intensively debated issue. In this paper we explore such effects, taking into account the scatter caused by the randomness of the…
We show that airplane boarding can be asymptotically modeled by 2-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are…