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Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…
A possible original $SU(2)_{L} \times SU(2)_{R}$ symmetry of the elementary particles and the mechanism of its breaking is discussed. It is concluded that it is the broken symmetry states of the particles which induce the interactions among…
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using…
We consider a version of special relativity assuming that the metric in inertial frames is conformally pseudoeuclidean and depends on some scalar field with zero vacuum average. Applying this modified special relativity to the theory of…
Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and…
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…
In Gurau and Keppler 2022 (arXiv:2207.01993), a relation between orthogonal and symplectic tensor models with quartic interactions was proven. In this paper, we provide an alternative proof that extends to polynomial interactions of…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
The flat anisotropic model of the early Universe is considered. Two interacting scalar fields with special form of potential energy are a source of matter fields. Analytic solutions for inflationary and scalaron stages are found. It is…
We derive exact and closed-form expressions for a large class of two-point and three-point inflation correlators with the tree-level exchange of a single massive particle. The intermediate massive particle is allowed to have arbitrary mass,…
We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
With the great development of parallel computing techniques, the particle-particle (PP) model has been successfully applied in a number of plasma applications. Comparing to particle-mesh (PM) models, for example the widely used…
New representation of the exact Mathisson-Papapetrou-Dixon equations at the Mathisson-Pirani condition in the Kerr metric which does not contain the third-order derivatives of the coordinates of a spinning particle is obtained. For this…
We analyse a two-particle quantum system in $\R^d$ with interaction and in presence of a random external potential field with a continuous argument (an Anderson model in a continuous space). Our aim is to establish the so-called Wegner-type…
We review theoretical ideas, problems and implications of different models for neutrino masses and mixing angles. We give a general discussion of schemes with three or more light neutrinos. Several specific examples are analyzed in some…