Related papers: Surface in statistical ensembles
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
Galaxy surveys provide finite catalogs of objects observed within bounded volumes, yet clustering statistics are often interpreted using theoretical frameworks developed for infinite point processes. In this work, we formulate key…
The connection between fundamental interactions acting in molecules in a fluid and macroscopically measured properties, such as the viscosity between colloidal particles coated with polymers, is studied here. The role that hydrodynamic and…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
In this book, we study Statistical Physics under conditions of thermodynamic equilibrium, starting from the definition of statistical ensembles. The book is divided into five chapters: First, a brief introduction to statistical methods.…
Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic…
We discuss different definitions of pressure for a system of active spherical particles driven by a non-thermal coloured noise. We show that mechanical, kinetic and free-energy based approaches lead to the same result up to first order in…
The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of…
We generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface $\Sigma$ and introduce the number $C_{\Sigma}(n)$ of non-crossing partitions of a set of $n$ points laying on…
The motion of one-hundred point vortices in a circular cylinder is simulated numerically and compared with theoretical predictions based on statistical mechanics. The novel aspect considered here is that the vortices have greatly different…
We show that the partition function of the Ponzano-Regge quantum gravity model can be written as a sum over surfaces in a $(2+1)$ dimensional space-time. We suggest a geometrical meaning, in terms of surfaces, for the (regulated)…
Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a…
The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of…
The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…