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We consider a $d$-dimensional gas in canonical equilibrium under pairwise screened Coulomb repulsion and external confinement, and subject to a volume constraint. We show that its excess free energy displays a generic third-order…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
The union of the particles of a stationary Poisson process of compact (convex) sets in Euclidean space is called Boolean model and is a classical topic of stochastic geometry. In this paper, Boolean models in hyperbolic space are…
Colloid or nanoparticle mobility under confinement is of central importance to a wide range of physical and biological processes. Here, we introduce a minimal model of particles in a hydrodynamic continuum to examine how particle shape and…
The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…
We study numerically and analytically a model of self-propelled polar disks on a substrate in two dimensions. The particles interact via isotropic repulsive forces and are subject to rotational noise, but there is no aligning interaction.…
The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of…
We present a model in which elementary particles and forces are unified in the framework of quantum field theory in higher dimensions. The particles include gauge bosons, quarks and leptons, as well as the Higgs bosons and the forces…
The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…
We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particles distribution over velocities is radially symmetric. Under…
A self-similar formalism for the study of the gravitational collapse of molecular gas provides an important theoretical framework from which to explore the dynamics of star formation. Motivated by the presence of elongated and filamentary…
Recently we studied $N$ run-and-tumble particles in one dimension - which switch with rate $\gamma$ between driving velocities $\pm v_0$ - interacting via the long range 1D Coulomb potential (also called rank interaction), both in the…
We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that…
We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged…
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate…
We investigate dynamics of deformable self-propelled particles with a repulsive interaction whose magnitude depends on the relative direction of elongation of a pair of particles. A collective motion of the particles appears in two…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…