Search results for "Numerical Analysis"
showing 10 items of 883 documents
A Comparison and Survey of Finite Difference Methods for Pricing American Options Under Finite Activity Jump-Diffusion Models
2012
Partial-integro differential formulations are often used for pricing American options under jump-diffusion models. A survey on such formulations and numerical methods for them is presented. A detailed description of six efficient methods based on a linear complementarity formulation and finite difference discretizations is given. Numerical experiments compare the performance of these methods for pricing American put options under finite activity jump models.
Lattices of Jordan algebras
2010
AbstractCommutative Jordan algebras play a central part in orthogonal models. The generations of these algebras is studied and applied in deriving lattices of such algebras. These lattices constitute the natural framework for deriving new orthogonal models through factor aggregation and disaggregation.
A Numerical Method for the Analysis of Plane-Strain Forming Processes with Unilateral Constraints
1983
The Authors propose a numerical model for the solution of plane-strain forming processes, based on the linearization of the yield surface. This allows to employ the linear programming technique for the solution of the variational problem derived from the application of the upper-bound theorem. Such a model permits to take into account the unilateral constraints in a very simple way. Therefore it is well suited to solve a large class of problems, such as sheet forming, in which the unilateral constraints are often present.
Particle transport in recirculated liquid metal flows
2008
PurposeAims to present recent activities in numerical modeling of turbulent transport processes in induction crucible furnace.Design/methodology/approach3D large eddy simulation (LES) method was applied for fluid flow modeling in a cylindrical container and transport of 30,000 particles was investigated with Lagrangian approach.FindingsParticle accumulation near the side crucible boundary is determined mainly by the ρp/ρ ratio and according to the presented results. Particle settling velocity is of the same order as characteristic melt flow velocity. Particle concentration homogenization time depends on the internal flow regime. Separate particle tracks introduce very intensive mass exchang…
The Lyapunov dimension formula for the global attractor of the Lorenz system
2015
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the …
Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimensi…
2018
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rossler system. Using the example of the Vallis system describing the El…
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
2015
The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a {hidden attractor} in the case of multistability as well as a classical {self-excited attractor}. The hidden attractor in this system can be localized by analytical-numerical methods based on the {continuation} and {perpetual points}. For numerical study of the attractors' dimension the concept of {finite-time Lyapunov dimension} is developed. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of {exact Lyapunov dimension} are discussed. A comparative survey on the computation of the finite-time Lyapunov expon…
Optimal measurement setup for damage detection in piezoelectric plates
2009
[EN] An optimization of the excitation-measurement configuration is proposed for the characterization of damage in PZT-4 piezoelectric plates, from a numerical point of view. To perform such an optimization, a numerical method to determine the location and extent of defects in piezoelectric plates is developed by combining the solution of an identification inverse problem, using genetic algorithms and gradient-based methods to minimize a cost functional, and using an optimized finite element code and meshing algorithm. In addition, a semianalytical estimate of the probability of detection is developed and validated, which provides a flexible criterion to optimize the experimental design. Th…
Empirical measures and Vlasov hierarchies
2013
The present note reviews some aspects of the mean field limit for Vlasov type equations with Lipschitz continuous interaction kernel. We discuss in particular the connection between the approach involving the N-particle empirical measure and the formulation based on the BBGKY hierarchy. This leads to a more direct proof of the quantitative estimates on the propagation of chaos obtained on a more general class of interacting systems in [S.Mischler, C. Mouhot, B. Wennberg, arXiv:1101.4727]. Our main result is a stability estimate on the BBGKY hierarchy uniform in the number of particles, which implies a stability estimate in the sense of the Monge-Kantorovich distance with exponent 1 on the i…
Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents.
2017
In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution…