Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows

In this article, we shall explore the state of art of stochastic flows to derive an exponential affine form of the bond price when the short rate process is governed by a Markovian regime-switching jump-diffusion version of the Vasicek model. We provide the flexibility that the market parameters, including the mean-reversion level, the volatility rate and the intensity of the jump component switch over time according to a continuous-time, finite-state Markov chain. The states of the chain may be interpreted as different states of an economy or different stages of a business cycle. We shall provide a representation for the exponential affine form of the bond price in terms of fundamental matrix solutions of linear matrix differential equations.     

A low-Mach number model for time-harmonic acoustics in arbitrary flows

This paper concerns the finite element simulation of the diffraction of a time-harmonic acoustic wave in the presence of an arbitrary mean flow. Considering the equation for the perturbation of displacement (due to Galbrun), we derive a low-Mach number formulation of the problem which is proved to be of Fredholm type and is therefore well suited for discretization by classical Lagrange finite elements. Numerical experiments are done in the case of a potential flow for which an exact approach is available, and a good agreement is observed.     

Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

A three-field finite element scheme designed for solving systems of partial differential equations governing time-dependent viscoelastic flows is studied. Once a classical backward Euler time discretization is performed, the resulting three-field system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two- and three- dimensional space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it provides an algorithm for the explicit iterative resolution of system nonlinearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.     

On the Rayleigh-Taylor Instability for Two Uniform Viscous Incompressible Flows

The authors study the Rayleigh-Taylor instability for two incompressible immis- cible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eule- rian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in （unstable） equilibrium is analyzed. By a general method of studying a family of modes, the smooth （when restricted to each fluid domain） solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem. Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.     

Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ? of ? ^d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ? endowed with Riemannian 2-Wasserstein metric.     

Maximum flow problem on dynamic generative network flows with time-varying bounds

This paper considers a new class of network flows, called dynamic generative network flows in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, an efficient algorithm is developed to solve the general form of the dynamic problem as a minimum cost static flow problem.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

Quasi-sure Flows Associated with Vector Fields of Low Regularity

The authors construct a solution Ut（x） associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity, namely one-fold differentiability. Besides, the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.     

NZ‐flows in strong products of graphs

We prove that the strong product G₁? G₂ of G₁ and G₂ is ?₃‐flow contractible if and only if G₁? G₂ is not T? K₂, where T is a tree (we call T? K₂ a K₄‐tree). It follows that G₁? G₂ admits an NZ 3 ‐flow unless G₁? G₂ is a K₄ ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G₁? G₂ is not a K₄ ‐tree, and an NZ 4‐flow otherwise. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010     

A note on anisotropic,inhomogeneous, poro‐elastic media

A modification of the material law associated with the well‐known Biot system as suggested by Murad and Cushman (Int. J. Eng. Sci. 1996; 34(3):313–338) and first investigated by Showalter (J. Math. Anal. Appl. 2000; 251(1):310–340) is reconsidered, generalized and analysed in the light of a new approach to a comprehensive class of evolutionary problems. The framework allows a uniform approach to problems involving general anisotropic, inhomogeneous, non‐smooth media thus covering, for example, transmission problems in layered materials. Copyright © 2009 John Wiley & Sons, Ltd.