Search results for "Mathematical analysis"
showing 10 items of 2409 documents
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
2014
Let $\mathcal{M}_{n,2n+2}$ be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of $\mathbb{P}^n$ branched along $2n+2$ hyperplanes in general position. We show that the monodromy group of a good family for $\mathcal{M}_{n,2n+2}$ is Zariski dense in the corresponding symplectic or orthogonal group if $n\geq 3$. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever $n\geq 3$. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of $m$ ordered points in $\mathbb{P}^n$ is shown to be large once it is not…
High-order regularization in lattice-Boltzmann equations
2017
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained afte…
Numerical approach for signal delay in general distributed networks
2003
The authors consider a general network with telegraph equations modelling distributed elements and having, additionally, nonlinear capacitors. A global asymptotic exponential stability of the solution is given. A simple computable upper bound of the delay time is given. Numerical examples illustrate the usefulness of the results. >
Compact-like pulse signals in a new nonlinear electrical transmission line
2013
International audience; A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers' equations. This equation admits compact pulse solutions and shares some symmetry properties with the Rosenau-Hyman K(2,2) equation. An exact discrete compactly- supported signal voltage is found for the network and the dissipative effects on the pulse motion analytically studied. Numerical simulations confirm the validity of analytical results and the robustness of these …
Pattern dynamics in a nonlinear electrical lattice
2003
International audience; In this paper, we present experiments using a nonlinear electrical line, modeling the FitzHugh-Nagumo equation, without recovery term. Different patterns are studied according to the para meters of this medium and initial conditions. We then propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, two kinds,of binarization-one depending on an amplitude threshold, the other on an energetical threshold-and nonlinear filtering allowing noise removal can be obtained in the same medium.
Generalized singly-implicit Runge-Kutta methods with arbitrary knots
1985
The aim of this paper is to derive Butcher's generalization of singly-implicit methods without restrictions on the knots. Our analysis yields explicit computable expressions for the similarity transformations involved which allow the efficient implementation of the first phase of the method, i.e. the solution of the nonlinear equations. Furthermore, simple formulas for the second phase of the method, i.e. computation of the approximations at the next nodal point, are established. Finally, the matrix which governs the stability of the method is studied.
Harmonic maps and singularities of period mappings
2015
We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem. MSC Classification 14M27, 58E20
Gradient with respect to nodes for non-isoparametric finite elements
2006
We consider the problem of controlling the solution of a finite element model using the nodal co-ordinates as control variables. The main emphasis is on the study of the applicability of the domain deformation method for different element types. The results are applied to a simple problem of finite element grid optimization.
Multidomain spectral method for the Gauss hypergeometric function
2018
International audience; We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞, except for the singular points and cuts of the Rie…
Smooth Feshbach map and operator-theoretic renormalization group methods
2003
Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.