Search results for "Applied Mathematics"

Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects

2016

We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion free sheaves. For a very general such cubic fourfold, we show that $Z$ is isomorphic to a connected component of a moduli space of tilt-stable objects in the derived category and to a moduli space of Bridgeland stable objects in the Kuznetsov component. Moreover, the contraction between $Z'$ and $Z$ i…

The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Mean ergodicity of weighted composition operators on spaces of holomorphic functions

2016

[EN] Let phi be a self-map of the unit disc D of the complex plane C and let psi be a holomorphic function on D. We investigate the mean ergodicity and power boundedness of the weighted composition operator C-phi,C-psi(f) = psi(f o phi) with symbol phi and multiplier psi on the space H(D). We obtain necessary and sufficient conditions on the symbol phi and on the multiplier psi which characterize when the weighted composition operator is power bounded and (uniformly) mean ergodic. One necessary condition is that the symbol phi has a fixed point in D. If phi is not a rational rotation, the sufficient conditions are related to the modulus of the multiplier on the fixed point of phi. Some of o…

2014

This paper investigates the finite-time distributedL2–L∞consensus control problem of multiagent systems with parameter uncertainties. The relative states of neighboring agents are used to construct the control law and some agents know their own states. By substituting the control input into multiagent systems, an augmented closed-loop system is obtained. Then, we analyze its finite-time boundedness (FTB) and finite-timeL2–L∞performance. A sufficient condition for the existence of the designed controller is given with the form of linear matrix inequalities (LMIs). Finally, simulation results are described.

Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions

2019

We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a natural geometric condition.

Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation

2012

The sedimentation of a polydisperse suspension with particles belonging to N size classes (species) can be described by a system of N nonlinear, strongly coupled scalar first-order conservation laws. Its solutions usually exhibit kinematic shocks separating areas of different composition. Based on the so-called secular equation [J. Anderson, Lin. Alg. Appl. 246, 49–70 (1996)], which provides access to the spectral decomposition of the Jacobian of the flux vector for this class of models, Burger et al. [J. Comput. Phys. 230, 2322–2344 (2011)] proposed a spectral weighted essentially non-oscillatory (WENO) scheme for the numerical solution of the model. It is demonstrated that the efficiency …

Adaptive mesh reconstruction for hyperbolic conservation laws with total variation bound

2012

We consider 3-point numerical schemes, that resolve scalar conservation laws, that are oscillatory either to their dispersive or anti-diffusive nature. The spatial discretization is performed over non-uniform adaptively redefined meshes. We provide a model for studying the evolution of the extremes of the oscillations. We prove that proper mesh reconstruction is able to control the oscillations; we provide bounds for the Total Variation (TV) of the numerical solution. We, moreover, prove under more strict assumptions that the increase of the TV, due to the oscillatory behavior of the numerical schemes, decreases with time; hence proving that the overall scheme is TV Increase-Decreasing (TVI…

Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme

2001

The numerical simulation of physical problems modeled by systems of conservation laws can be difficult due to the occurrence of discontinuities and other non-smooth features in the solution.

Conservation Laws and Asymptotic Behavior of a Model of Social Dynamics

2008

Abstract A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061–1084]. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The asymptotic trend of their solutions…

High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles

2017

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.