The dynamics simulation of multibody systems (MBS) using spatial velocities (non-holonomic velocities) requires time integration of the dynamics equations together with the kinematic reconstruction equations (relating time derivatives of configuratio...
We first prove homogenization for the nonlinear Schrödinger equation with sprinkled nonlinearity introduced in [19]. We then investigate how solutions fluctuate about the homogenized solution....
In this article we compute Galois groupoid of discret Painlev{é} equations. Our main tool is a semi-continuity theorem for the Galois groupoid in a confluence situation of a diffrence equation to a differential equation....
In this article, the Galois groupoid of the first Painlevé equation is computed. This computation use E. Cartan's classification of structural equations of pseudogroups acting on $C^2$ and the degeneration of the first Painlevé equation on an ell...
(2.10) Suppose that we have a left handed spinor uL(p) that satisfies the Weyl equation. We can use it to construct a spinor that satisfies the Weyl equation for the right-handed spinor.
We show that one dimensional non-stationary Schrödi-nger equation with a specific choice of potential reduces to the quantum Painlevé II equation and the solution of its Riccati form appears as a dominant term of that potential. Further, we show th...
We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schrödinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude. These pha...
We prove an $L^2$ estimate for the drift heat equation on a complete gradient shrinking Ricci soliton. This estimate has a time-dependent weight which is Gaussian in its spatial asymptotics. When transferred and scaled to an estimate for the heat equ...
We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the $L^2$-norm, and the...
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisf...
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We construct examples and provide a classification of self-similar solutions to the two-dimensional incompressible Euler equations whose pseudo-velocity fields possess more than one stagnation point. These solutions are also homogeneous steady states...
Can you solve the below equation by plotting numbers 1-9 without repeating any number? Note: Only less than 5% of the users can solve this puzzle in less than 10 minutes.
This contribution reviews the present status on the available constraints to the nuclear equation of state (EoS) around saturation density from nuclear structure calculations on ground and collective excited state properties of atomic nuclei. It conc...
In this paper, we are interested in the numerical analysis of blow up for the Chipot-Weissler equation with Dirichlet boundary conditions in bounded domain. To approximate the blow up solution, we construct a finite difference scheme and we prove tha...
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Padé approximants that are known to provide the best approximation for...
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing at $x=0$...
A distributional method to solve the Einstein's field equations for thin shells is formulated. The familiar field equations and jump conditions of Darmois-Israel formalism are derived. A carefull analysis of the Bianchi identities shows that, for c...
We prove that for bounded, divergence-free vector fields in $L^1_{loc}((0,+\infty);BV_{loc}(R^d;R^d))$, regularisation by convolution of the vector field selects a single solution of the transport equation for any integrable initial datum. We recall...
In the article we obtain almost global existence for Dirac Equations with high regularity and small initial datum on Tori. Besides, the global existence with low regularity and small initial datum is gotten. The approaches are mainly Gagliardo-Nirenb...