Search results for "System of linear equations"
showing 10 items of 53 documents
A multilayer model for self-propagating high-temperature synthesis of inter-metallic compounds
2007
International audience; Self-propagating high-temperature synthesis of intermetallic compounds is of wide interest. We consider reactions in a binary system in which the rise and fall of the temperature during the reaction is such that one of the reacting metals melts but not the other. For such a system, using the phase diagram of the binary system, we present a general theory that describes the reaction taking place in a single solid particle of one component surrounded by the melt of the second component. The theory gives us a set of kinetic equations that describe the propagation of the phase interfaces in the solid particle and the change in composition of the melt that surrounds it. I…
Direct analysis of power-split CVTs: A unified method
2018
Abstract This paper provides a fast kinematic analysis method for compound power-split CVTs, which consents to identify their functional parameters. Such parameters permit the assessment of power flows, torques and efficiency, and the design of equivalent transmissions by the use of a recently published mathematical model. The same method can easily address either simpler or more complex transmissions by mean of kinematic equivalent parameters, without the need to arrange separate systems of equations. As a case study, we performed the kinematic analysis of the “Voltec” multi-mode GM transmission.
Free-surface flows solved by means of SPH schemes with numerical diffusive terms
2010
A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …
Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms II: Charge Exchange
2019
International audience; We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry, and temperature. We evaluate the role of statistical errors related to the uncertainties of the coupling constants of the Skyrme functional and thus determine the confidence interval of the resulting response functi…
The effects of convolution and gradient dependence on a parametric Dirichlet problem
2020
Our objective is to study a new type of Dirichlet boundary value problem consisting of a system of equations with parameters, where the reaction terms depend on both the solution and its gradient (i.e., they are convection terms) and incorporate the effects of convolutions. We present results on existence, uniqueness and dependence of solutions with respect to the parameters involving convolutions.
New Developments in Quantum Algorithms
2010
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum speedups for any problem that can be expressed via Boolean formulas. This result can be also extended to span problems, a generalization of Boolean formulas. This provides an optimal quantum algorithm for any Boolean function in the black-box query model. The second new development is a quantum algorithm for solving systems of linear equations. In contrast with traditional algorithms that run in time O(N^{2.37...}) where N is the size of the system, the …
An efficient analytical approach for obtaining a five parameters model of photovoltaic modules using only reference data
2013
Exploiting the equivalent one-diode circuit of a photovoltaic (PV) module, this paper proposes a novel and fully analytical model to predict the electrical performance upon solar irradiance intensity and PV module temperature. The model refers essentially to an equivalent circuit governed by five parameters and the extraction of them permits to describe the current–voltage curve of the PV panel and consequently permits to assess the energy output of PV modules. The proposed model extracts the five characteristic parameters using only exact analytical relationship and tabular data always available such as short-circuit current, open circuit voltage and the Maximum Power Point (MPP). The diff…
Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere
2006
We consider the system of equations of viscous gas motion whose pressure is related to the density by the law $p = h \varrho^\gamma$ with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15
Beyond second-order convergence in simulations of binary neutron stars in full general relativity
2014
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions,…
An HLLC Riemann solver for resistive relativistic magnetohydrodynamics
2017
We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through one- and two-dimensional test problems.