Related papers: A vector field method for massless relativistic tr…
We study the weak convergence behaviour of the Leimkuhler--Matthews method, a non-Markovian Euler-type scheme with the same computational cost as the Euler scheme, for the approximation of the stationary distribution of a one-dimensional…
This paper is concerned with an algorithm for finding a singularity of the nonsmooth vector fields. Firstly, we discuss the main results of the Newton method presented in [1] for solving the aforementioned problem. Combining this method…
In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect…
We apply a new coordinate space method for the evaluation of lattice Feynman diagrams suggested by L\"uscher and Weisz to field theories in two dimensions. Our work is to be presented for the theories with massless propagators. The main…
A geometrically invariant concept of fast-slow vector fields perturbed by transport terms (describing molecular diffusion processes) is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields to…
A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These…
We consider slow motion of a pointlike topological defect (vortex) in the nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field and subject to external uniform magnetic field. It turns out that a formal expansion of…
In this work we develop a well-defined theory of orbit spaces for piecewise smooth vector fields (PSVFs). This approach is inspired by the techniques already used in the study of endomorphisms, namely inverse limit analysis, and has been…
Gravitational scattering of the electromagnetic field from a heavy scalar field provides a fundamental testbed for understanding the deflection of light by massive bodies. In many approaches based on effective field theory, the calculation…
We propose a general method to analytically solve transport equations during a cosmic phase transition without making approximations based on the assumption that any transport coefficient is large. Using the MSSM as an example we derive the…
In a previous paper, we developed a new particle-in-cell method for the Vlasov-Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a…
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu…
We introduce an atomistic approach to the dissipative quantum dynamics of charged or neutral excitations propagating through macromolecular systems. Using the Feynman-Vernon path integral formalism, we analytically trace out from the…
In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…
The Vlasov-Poisson systems of equations (VP) describes the evolution of a distribution of collisionless particles under the effect of a collective-field potential. VP is at the basis of the study of the gravitational instability of…
Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some directions are considered "linear",…
We briefly report on our method [Fiore JPA 2017] of simplifying the equations of motion of charged particles in an electromagnetic field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent…
A covariant relativistic approach based on the Vlasov equation is applied to the study of infinite asymmetric nuclear matter. We use several Walecka-type hadronic models and obtain the dispersion relations for the longitudinal modes. The…
DiPerna-Lions (Invent. Math. 1989) established the existence and uniqueness results for linear transport equations with Sobolev velocity fields. This paper provides mathematical analysis on two simple finite difference methods applied to…
We propose a meshless method to compute pressure fields from image velocimetry data, regardless of whether this is available on a regular grid as in cross-correlation based velocimetry or on scattered points as in tracking velocimetry. The…