Related papers: Solve thermal explosion model by central differenc…
The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction $\a$ of its wall is ideally thermally conducting while the remaining fraction $1-\a$ is thermally isolated. Partial isolation of…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
When a sphere of one reactant is placed in the medium of another reactant with which it is hypergolic, a chemical reaction (modeled here as a zeroth-order one-step irreversible Arrhenius reaction) occurs at the common interface of the two…
We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
A method for integrating the chemical equations associated with nuclear combustion at high temperature is presented and extensively checked. Following the idea of E. M\"uller, the feedback between nuclear rates and temperature was taken…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary…
We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend…
A model in which a projectile like fragment can be simply regarded as a remnant after removal of some part of the projectile leads to an excited fragment. This excitation energy can be calculated with a Hamiltonian that gives correct…
It is seen how to write the standard\^E form of the four partial differential equations in four unknowns of anisotropic thermoelasticity as a single equation in one variable, in terms of isothermal and isentropic wave operators. This…
This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain…
In the paper, we propose a new approach to the mathematical description of the separation of a neutron from the atom's nucleus on the basis of the formalisms of tropical mathematics and nonstandard analysis. In studying the behavior of…
The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…
The paper represents original development of thermodynamic criteria of occurrence conditions of steam-gas explosions in the process of severe accidents. The received results can be used for modelling of processes of severe accidents in…
The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so…
A magnetothermoelastic problem is considered for a nonhomogeneous, isotropic rotating hollow cylinder in the context of three theories of generalized formulations, the classical dynamical coupled (C-D) theory, the Lord and Shulman's (L-S)…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…