1,721,198 research outputs found
Modelling of the convective plasma dynamics in the Sun: anelastic and Boussinesq MHD systems
Full text linkThis work deals with the mathematical modelling and asymptotic analysis of the plasma convective dynamics in the center of the Sun. The heat produced via thermonuclear fusion in the interior of the Sun is transported towards the surface first via radiation, and finally via convection. Convection is thought to be responsible for the generation of magnetic fields and is hence a very important phenomenon to be understood in detail in order to get more insight in the internal structure of the Sun. Anelastic and Boussinesq models are formally derived here from the underlying compressible MHD models and we shall prepare the ground for our future numerical works, based on asymptotic-preserving techniques
Random front propagation in fractional diffusive systems
Full text linkModelling the propagation of interfaces is of interest in several fields of applied sciences, such as those involving chemical reactions where the reacting interface separates two different compounds. When the front propagation occurs in systems characterized by an underlying random motion, the front gets a random character and a tracking method for fronts with a random motion is desired. The Level Set Method, which is a successful front tracking technique widely used for interfaces with deterministic motion, is here randomized assuming that the motion of the interface is characterized by a random diffusive process. In particular, here we consider the case of a motion governed by the time-fractional diffusion equation, leading to a probability density function for the interface particle displacement given by the M-Wright/Mainardi function. Some numerical results are shown and discussed
A Novel ES-BGK Model for Non-polytropic Gases with Internal State Density Independent of the Temperature
Full text linkA novel ES-BGK-based model of non-polytropic rarefied gases in the framework of kinetic theory is presented. Key features of this model are: an internal state density function depending only on the microscopic energy of internal modes (avoiding the dependence on temperature seen in previous reference studies); full compliance with the H-theorem; feasibility of the closure of the system of moment equations based on the maximum entropy principle, following the well-established procedure of rational extended thermodynamics. The structure of planar shock waves in carbon dioxide (CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}) obtained with the present model is in general good agreement with that of previous results, except for the computed internal temperature profile, which is qualitatively different with respect to the results obtained in previous studies, showing here a consistently monotonic behavior across the shock structure, rather than the non monotonic behavior previously found
Shock structure and multiple sub-shocks in binary mixtures of Eulerian fluids
No full textThe problem of sub-shock formation within a shock structure solution of hyperbolic systems of balance laws is investigated for a binary mixture of multi-temperature Eulerian fluids. The main purpose of this work is the analysis of the ranges of Mach numbers characterizing shock-structure solutions with different features, continuous or not, and to show the existence of ranges, below the maximum unperturbed characteristic velocity, for which each constituent of the mixture may develop a sub-shock within a smooth shock structure profile. The theoretical results are supported by numerical calculations
Extended thermodynamics of rarefied polyatomic gases and characteristic velocities
No full textExtended Thermodynamics of rarefied polyatomic gases is characterized by two hi-
erarchies of equations for moments of a suitable distribution function in which the internal degrees
of freedom of a particle is taken into account. To obtain the closed set of the field equations for the
system with many moments and for an arbitrary entropy functional that includes degenerate gases,
the entropy principle and maximum entropy principle are studied and the equivalence of these two
methods is shown as in the well-established case of the monatomic gas. In addition the recent results
of the present theory are summarized. On the basis of physical considerations, the truncation orders
of the two hierarchies are seen to be not independent on each other. The equilibrium characteristic
velocities of the emerging hyperbolic system of partial di¤erential equations are analyzed and com-
pared to those of monatomic gases. Inspection shows that the lower bound estimate of the maximum
equilibrium characteristic velocity valid for monatomic gases, which increases as the truncation
order increases, is valid for any rarefied polyatomic gas
Orbits in a stochastic Schwarzschild geometry
Full text linkWe study geodesics in the Schwarzschild space-time affected by an uncertainty in the mass parameter described by a Gaussian distribution. This study could serve as a first attempt at investigating possible quantum effects of black hole space-times on the motion of matter in their surroundings as well as the role of uncertainties in the measurement of the black hole parameters
Front propagation in anomalous diffusive media governed by time-fractional diffusion
Full text linkIn this paper, a multi-dimensional model is proposed to study the propagation of random fronts in media in which anomalous diffusion takes place. The front position is obtained as the weighted mean of fronts calculated by means of the level set method, using as weight-function the probability density function which characterizes the anomalous diffusion process. Since anomalous diffusion is assumed to be governed by a time-fractional diffusion equation, its fundamental solution is the required probability density function. It is shown that this fundamental solution can be expressed in the multi-dimensional case in terms of the well-known M-Wright/Mainardi function, as in the one-dimensional case. Making use of this representation for the practical purpose of numerical evaluation, the propagation of random fronts in two-dimensional subdiffusive media is discussed and investigated
Modelling and simulation of wildland fire in the framework of the level set method
Full text linkAmong the modelling approaches that have been proposed for the simulation of wildfire propagation, two have gained considerable attention in recent years: the one based on a reaction-diffusion equation, and the one based on the level set method. These two approaches, traditionally seen in competition, do actually lead to similar equation models when the level set method is modified taking into account random effects as those due to turbulent hot air transport and fire spotting phenomena. The connection between these two approaches is here discussed and the application of the modified level set method to test cases of practical interest is shown
On variable-order fractional linear viscoelasticity
Full text linkA generalization of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a variable-order fractional Maxwell model is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions
Alternative formulations of the thermodynamics of scalar-tensor theories
Full text linkWe explore alternative formulations of the analogy between viable Horndeski gravity and Eckart's first-order thermodynamics. We single out a class of identifications for the effective stress-energy tensor of the scalar field fluid that, upon performing the imperfect fluid decomposition, yields constitutive relations that can be mapped onto Eckart's theory. We then investigate how different couplings to Einstein's gravity, at the level of the field equations, can affect the thermodynamic formalism overall. Last, we specialize the discussion to the case of "traditional"scalar-tensor theories and identify a specific choice of the coupling function that leads to a significant simplification of the formalism
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