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We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…
Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as $\ell$, is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of…
Within the framework of random multiplicative energy cascade models of fully developed turbulence, expressions for two-point correlators and cumulants are derived, taking into account a proper conversion from an ultrametric to an Euclidean…
One of the most important problems in Geometric Tomography is to establish properties of a given convex body if we know some properties over its sections or its projections. There are many interesting and deep results that provide…
We present a theory and computation method of radiation pressure from partially coherent light by establishing a coherent mode representation of the radiation forces. This is illustrated with the near field emitted from a Gaussian Schell…
The Dedekind tessellation -- the regular tessellation of the upper half-plane by the Mobius action of the modular group -- is usually viewed as a system of ideal triangles. We change the focus from triangles to circles and give their…
We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We present a new model of a non-Euclidean plane, in which angles in a triangle sum up to $\pi$. It is a subspace of the Cartesian plane over the field of hyperreal numbers $\mathbb{R}^*$. The model enables one to represent the negation of…
Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $\alpha$-stable L\'evy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo…
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…
Heavy ion collisions at ultrarelativistic energies offer the opportunity to study the irreversibility of multiparticle processes. Together with the many-body decays of resonances, the multiparticle processes cause the system to evolve…
The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long range correlations, which behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We calculate the…
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…
It is argued that continuum realisations of distributions of collisionless charged particles should accommodate a dynamically evolving number of electric currents even if the continuum is composed of only one species of particle, such as…
Excitons, i.e. the bound states of an electron and a positively charged hole are the solid state analogue of the hydrogen atom. As such they exhibit a Rydberg series, which in cuprous oxide has been observed up to high principal quantum…
The gauge coupling constants in the electroweak standard model can be written as mass ratios, e.g. the coupling constant for isospin interactions $g_2^2=2{m_W^2\over m^2}\sim 2({80\over169})^2\sim{1\over 2.3}$ with the mass of the charged…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
The transport of heavy, neutral or charged, point-like particles by incompressible, resistive magnetohydrodynamic (MHD) turbulence is investigated by means of high-resolution numerical simulations. The spatial distribution of such…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…