Related papers: Balanced flux formulations for multidimensional Ev…
We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in $D$ dimensions coupled to a $q$-form field and positive cosmological constant. We show that…
Classical tools of nonlinear dynamics are used to study the highly excited vibrations of small molecules. For effective Hamiltonians with one polyad number (approximate constant of motion), previously developed methods locate new anharmonic…
In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of $L^2$-flow. This flow is also a distributional BV-solution for a short time, when the…
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow…
Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this…
Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions.…
We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics)…
We present a Green's function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in a mesoscopic system of N Fermi particles moving independently in a linear potential. The…
Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance in glaciology, where they arise in the study of grounding…
Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
The probability distribution for vacuum fluctuations of the energy flux in two dimensions will be constructed, along with the joint distribution of energy flux and energy density. Our approach will be based on previous work on probability…
The well-known analytical solution of Burgers' equation is extended to curvilinear coordinate systems in three-dimensions by a method which is much simpler and more suitable to practical applications than that previously used. The results…
In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…
We show how to compute vacuum expectation values from derivative expansions of the vacuum wave functional. Such expansions appear to be valid only for slowly varying fields, but by exploiting analyticity in a complex scale parameter we can…
We study nonlinear time-asymptotic stability of small--amplitude planar Lax shocks in a model consisting of a system of multi--dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics…
Understanding the flow dynamics of non-Newtonian fluids is crucial in various engineering, industrial, and biomedical applications. However, the existing generalized Reynolds number formulations for non-Newtonian fluids have limited…
In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the…
A firm understanding and control of viscous fingering (VF) and miscible displacement will be vital to a wide range of industrial, environmental, and pharmaceutical applications, such as geological carbon-dioxide sequestration, enhanced oil…
In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this…