We consider thermal fluid structure interaction to model industrial gas quenching in steel forging, where hot steel is cooled using cold high pressured gas. This allows to define properties of the finished steel part, as for example yield strength, locally at low cost and without environmental problems. For the numerical simulation, a partitioned approach via a Dirichlet-Neumann coupling and a ...

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension ≥ 4, over which every extension of line bundles splits.

We prove that a divergence-free and C1-robustly transitive vector field has no singularities. Moreover, if the vector field is C4 then the linear Poincaré flow associated to it admits a dominated splitting over M . MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Volume-preserving flows; Robust transitivity; Dominated splitting; Ergodicity.

Since the kinetic and potential energy terms of the real-time nonlinear Schrödinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well-known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even ...

A class of splitting iterative methods are considered for solving fuzzy system of linear equations, which covers Jacobi, Gauss Seidel, SOR, SSOR and their block variance proposed. Theoretical analysis showed that for a regular splitting, the corresponding iterative method converge to the unique fuzzy solution for any initial vector and fuzzy right hand side vector. Finally, we illustrate our ap...

A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible, viscous flow around a 2D flapping airfoil. The Newton-Krylov method uses matrix-free GMRES to solve the linear systems of equations that arise in the nonlinear...

A mathematical model of contractile ring-dependent cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical model following the hypothesis in authors knowledge. I consider a hybrid method to model the phenom...

The stochastic volatility jump diffusion model with jumps in both return and volatility leads to a two-dimensional partial integro-differential equation (PIDE). We exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as the action of an exponential of a block Toeplitz matrix on a ...

The Dirac equation serves as the basis for the relativistic description of atoms, nuclei and hadrons. In atoms the relevant potentials felt by the electron are Coulombic vector potentials. A Dirac Hamiltonian with a Coulomb potential exhibits a finestructure spectrum with characteristic two-fold degeneracy. Relativistic mean fields in nuclei generated by meson exchanges , and quark confinement ...

In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with an equation of state of the form p = ργ (where p stands for the pressure and ρ for the density). This scheme is based on Crouzeix-Raviart approximation spaces. The discretization of the momentum balance is obtained by the usual finite element technique. The discrete mass balance is obtained by a ...