Related papers: Surface in statistical ensembles
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define some kind of approximation of main quantities, which describe…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
When two spherical particles submerged in a viscous fluid are subjected to an oscillatory flow, they align themselves perpendicular to the direction of the flow leaving a small gap between them. The formation of this compact structure is…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure,…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations…
In this work, we study a particular system of coagulation equations characterized by two values, namely volume $v$ and surface area $a$. Compared to the standard one-dimensional models, this model incorporates additional information about…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive…
Within the theory of statistical ensemble, the so-called $\mu PT$ ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number…
We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface…