Related papers: The Specification Property on the Lelek Fan
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
Ferrogels are smart soft materials, consisting of a polymeric network and embedded magnetic particles. Novel phenomena, such as the variation of the overall mechanical properties by external magnetic fields, emerge consequently. However,…
We propose a new and general method for deriving exact density functionals in one dimension for lattice gases with finite-range pairwise interactions. Corresponding continuum functionals are derived by applying a proper limiting procedure.…
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be…
The solutions of traditional fractional differential equations neither satisfy group property nor generate dynamical systems, so the study on hyperbolicity is in blank. Relying on the new proposed conformable fractional derivative, we…
We show that in the presence of a harmonically varying magnetic field the fundamental or $f$-mode in a stratified layer is altered in such a way that it fans out in the diagnostic $k\omega$ diagram, but with mode power also within the fan.…
Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this…
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal,…
A fan is an arcwise-connected continuum, which is hereditarily unicoherent and has exactly one ramification point. Many of the known examples of fans were constructed as 1-dimensional continua that are unions of arcs which intersect in…
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic $\mathbb{Z}$-extensions of expanding interval maps. Our main focus lies in the dimensional analysis of the…
We analyze a quasi-continuous linear chain with self-similar distribution of harmonic interparticle springs as recently introduced for one dimension (Michelitsch et al., Phys. Rev. E 80, 011135 (2009)). We define a continuum limit for one…
A numerical investigation of flat fan sprays is conducted via Direct Numerical Simulations (DNS). Diverging liquid sheets are generated using tailored initial velocity profiles, where the opening angle serves as an explicit control…
In this paper notions of strong specification property and quasi-weak specification property for non-autonomous discrete systems are introduced and studied. It is shown that these properties are dynamical properties and are preserved under…
We introduce and discuss the one-dimensional L\'{e}vy crystal as a probable candidate for an experimentally accessible realization of space fractional quantum mechanics (SFQM) in a condensed matter environment. The discretization of the…
In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both…
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…
We study the one-dimensional discrete $\Phi^4$ model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of local correlation functions. Both properties imply the…
One-dimensional hard rod gases are explicitly constructed as the limits of discrete systems: exclusion processes involving particles of arbitrary length. Those continuum many-body systems in general do not exhibit the same hydrodynamic…
Liquid crystals are materials that experience an intermediate phase where the material can flow like a liquid, but the molecules maintain an orientation order. The Frank-Oseen model is a continuum model of a liquid crystal. The model…