This paper analyzes the convergence of discrete approximations to the linearized equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. A simple modified Lax–Friedrichs discretization is used on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It ...

We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if L ⊂ X is an exact Lagrangian submanifold of an exact symplectic manifold with convex end Λ ⊂ Y , where Y is a contact manifold and Λ is a Legendrian submanifold, and if L has empty concave end, then the linearized Legendrian ...

The numerical simulation of the dynamics of the molecular beam epitaxy (MBE) growth is considered in this article. The governing equation is a nonlinear evolutionary equation that is of linear fourth order derivative term and nonlinear second order derivative term in space. The main purpose of this work is to construct and analyze two linearized finite difference schemes for solving the MBE mod...

in this contribution, linearized dynamic model of cumulative mass fraction (cmf) of potassium nitrate-water seeded continues mixed suspension mixed product removal (cmsmpr) crystallizer is approximated by a simplified model in frequency domain. frequency domain model simplification is performed heuristically using the frequency response of the derived linearized models data. however, the cmf fr...

We develope the analogue of S-duality for linearized gravity in (3+1)-dimensions. Our basic idea is to consider the self-dual (anti-self-dual) curvature tensor for linearized gravity in the context of the Macdowell-Mansouri formalism. We find that the strong-weak coupling duality for linearized gravity is an exact symmetry and implies small-large duality for the cosmological constant. Pacs numb...

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are boundary versions of Caffarelli and Gutiérrez’s interior Harnack inequality for the linearized Monge-Ampère equations. As an application, we obtain sharp upp...

The objective of seismic imaging is to obtain an image of the subsurface reflectors, which is very important for estimating whether a reservoir is beneficial for oil/gas exploration or not. It can also provide the relative changes or absolute values of three elastic parameters: compressional wave velocity Vp, shear wave velocity Vs , and density ρ. Two ways can achieve the objectives. In approa...

This article reviews various results on the compactness of the linearized Boltzmann operator and of its generalization to mixtures of non-reactive monatomic gases.

We use the Israel condition to treat carefully the weak-field perturbations due to the presence of matter on a 3-brane embedded between two regions of antide Sitter (AdS) space with different curvature lengths. A four dimensional Newton’s Law only emerges at distances that are large compared to the AdS lengths. When a scalar curvature is included in the brane action, however, it is possible to ...

In this paper, we describe progress on the development of algorithms for triangular decomposition of approximate systems. We begin with the treatment of linear, homogeneous systems with positive-dimensional solution spaces, and approximate coefficients. We use the Singular Value Decomposition to decompose such systems into a stable form, and discuss condition numbers for approximate triangular ...