Related papers: An explicit example for the high temperature convo…
Here we summarize the results from our direct numerical simulations (DNS) and experimental measurements on rotating Rayleigh-B\'enard (RB) convection. Our experiments and simulations are performed in cylindrical samples with an aspect ratio…
In this work, a general definition of Convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e…
Rayleigh-B\'enard cells are one of the simplest systems to explore the laws of natural convection in the highly turbulent limit. However, at very high Rayleigh numbers (Ra > 1E12) and for Prandtl numbers of order one, experiments fall into…
We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…
Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation…
A detailed description of the statistical distribution of thermal vacancies near the melting point is presented, using copper as an example. As the temperature is increased, the average number of thermal vacancies generated by atoms…
Besides the dynamical slowing down signaled by an enormous increase of the viscosity approaching the glass transition, structural glasses show interesting anomalous thermodynamic features at low temperatures that hint at peculiar deviations…
We establish the strong law of large numbers for Betti numbers of random \v{C}ech complexes built on $\mathbb R^N$-valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the…
In this paper we focus on continuous univariate probability distributions, like McKay distributions, $K$-distribution, generalized inverse Gaussian distribution and generalised McKay distributions, with support $[0,\infty),$ which are…
We first established the dynamic equations to describe the noisy circling motion of a single particle and the corresponding probability conservation equation in both two dimensions and three dimensions, and then developed the evolution…
We present a new approach to modeling the future development of extreme temperatures globally and on a long time-scale by using non-stationary generalized extreme value distributions in combination with logistic functions. This approach is…
We study Bessel and Dunkl processes $(X_{t,k})_{t\ge0}$ on $\mathbb R^N$ with possibly multivariate coupling constants $k\ge0$. These processes describe interacting particle systems of Calogero-Moser-Sutherland type with $N$ particles. For…
Employing Monte-Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing…
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-B\'enard convection is theoretically analysed. The force and thermal balance on a single plume detached from the thermal…
We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse…
It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating…
We show how some attractive information--theoretic properties of Gaussians pass over to more general families of stable densities. We define a new score function for symmetric stable laws, and use it to give a stable version of the heat…
The deconfining transition in non-Abelian gauge theory is known to occur by a condensation of Wilson lines. By expanding around an appropriate Wilson line background, it is possible at large $N$ to analytically continue the confining phase…