Search results for "linear equations"
showing 10 items of 64 documents
Variable time amplitude amplification and quantum algorithms for linear algebra problems
2012
Quantum amplitude amplification is a method of increasing a success probability of an algorithm from a small epsilon>0 to Theta(1) with less repetitions than classically. In this paper, we generalize quantum amplitude amplification to the case when parts of the algorithm that is being amplified stop at different times. We then apply the new variable time amplitude amplification to give two new quantum algorithms for linear algebra problems. Our first algorithm is an improvement of Harrow et al. algorithm for solving systems of linear equations. We improve the running time of the algorithm from O(k^2 log N) to O(k log^3 k log N) where k is the condition number of the system of equations. …
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.
Local behaviour of singular solutions for nonlinear elliptic equations in divergence form
2012
We consider the following class of nonlinear elliptic equations $$\begin{array}{ll}{-}{\rm div}(\mathcal{A}(|x|)\nabla u) +u^q=0\quad {\rm in}\; B_1(0)\setminus\{0\}, \end{array}$$ where q > 1 and $${\mathcal{A}}$$ is a positive C 1(0,1] function which is regularly varying at zero with index $${\vartheta}$$ in (2−N,2). We prove that all isolated singularities at zero for the positive solutions are removable if and only if $${\Phi\not\in L^q(B_1(0))}$$ , where $${\Phi}$$ denotes the fundamental solution of $${-{\rm div}(\mathcal{A}(|x|)\nabla u)=\delta_0}$$ in $${\mathcal D'(B_1(0))}$$ and δ0 is the Dirac mass at 0. Moreover, we give a complete classification of the behaviour near zero of al…
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…
Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type
2014
Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.
Modulational instability and generation of self-induced transparency solitons in resonant optical fibers
2009
International audience; We consider continuous-wave propagation through a fiber doped with two-level resonant atoms, which is described by a system of nonlinear Schrodinger-Maxwell-Bloch (NLS-MB) equations. We identify the modulational instability (MI) conditions required for the generation of ultrashort pulses, in cases of both anomalous and normal GVD (group-velocity dispersion). It is shown that the self-induced transparency (SIT) induces non-conventional MI sidebands. The main result is a prediction of the existence of both bright and dark SIT solitons in the anomalous and normal GVD regimes.
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 …