Search results for "determinant"

On lacunary Toeplitz determinants

2014

By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ generated by holomorhpic symbols, where $\ell_a=a$ (resp. $m_b=b$) except for a finite subset of indices $a=h_1,\dots, h_n$ (resp. $b=t_1,\dots, t_r$). In addition to the usual Szeg\"{o} asymptotics, our answer involves a determinant of size $n+r$.

Rational solutions to the KPI equation from particular polynomials

2022

Abstract We construct solutions to the Kadomtsev–Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second spatial derivative of a logarithm of a determinant of order n . We obtain with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.

A secular equation for the Jacobian matrix of certain multispecies kinematic flow models

2010

Small Clusters Made of Helium Atoms

2003

Helium atoms interact very weakly through a van der Waals potential. Nevertheless, they are able to form aggregates or drops with a small number of atoms. This work analyzes the stability of clusters made of 4He atoms, of bosonic nature, clusters made of 3He atoms, of fermionic nature and also mixed aggregates with both kinds of constituents. Some of these drops are predicted to be unstable.

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 …

On the hyperbolicity of certain models of polydisperse sedimentation

2012

The sedimentation of a polydisperse suspension of small spherical particles dispersed in a viscous fluid, where particles belong to N species differing in size, can be described by a strongly coupled system of N scalar, nonlinear first-order conservation laws for the evolution of the volume fractions. The hyperbolicity of this system is a property of theoretical importance because it limits the range of validity of the model and is of practical interest for the implementation of numerical methods. The present work, which extends the results of R. Burger, R. Donat, P. Mulet, and C.A. Vega (SIAM Journal on Applied Mathematics 2010; 70:2186–2213), is focused on the fluxes corresponding to the …

Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes

2009

Abstract We present an extension of Marquina’s flux formula, as introduced in Fedkiw et al. [Fedkiw RP, Merriman B, Donat R, Osher S. The penultimate scheme for systems of conservation laws: finite difference ENO with Marquina’s flux splitting. In: Hafez M, editor. Progress in numerical solutions of partial differential equations, Arcachon, France; July 1998], for the shallow water system. We show that the use of two different Jacobians at cell interfaces prevents the scheme from satisfying the exact C -property [Bermudez A, Vazquez ME. Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 1994;23(8):1049–71] while the approximate C -property is satisfied for high…

Numerical decomposition of geometric constraints

2005

Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of inci…

Evolución de los riesgos ambientales en el contexto de la crisis económica. Informe SESPAS 2014

2014

ResumenNuestro objetivo es analizar el impacto de la crisis económica-financiera en los determinantes ambientales de la salud. La Organización Mundial de la Salud estima que entre un 13% y un 27% de la carga de enfermedad de los países podría prevenirse mejorando el medio ambiente. Los efectos son de mayor magnitud en poblaciones más vulnerables, en especial entre los más pobres. En la última década, la contaminación atmosférica exterior (el riesgo ambiental más relevante, en términos de salud, para la mayoría de los países europeos) se ha reducido moderadamente, sobre todo por las políticas europeas de reducción de emisiones y por la disminución de la actividad con la crisis económica. En …

On the Extension of the DIRECT Algorithm to Multiple Objectives

2020

AbstractDeterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce r…