A time-dependent electromagnetic field creates electron-hole excitations in a Fermi sea at low temperature. We show that the electron-hole pairs can be generated in a controlled way using harmonic and biharmonic time-dependent voltages applied to a quantum contact, and we obtain the probabilities of the pair creations. For a biharmonic voltage drive, we find that the probability of a pair creat...

Abstract. Using Maz’ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in R. For n ≥ 8, combined with a result in [S2], these estimates lead to the solvability of the L Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of p. In the case of convex domains, the estimates allow u...

Abstract: This paper deals with the study of the numerical solution of biharmonic equations in one dimension. Biharmonic equations appear frequently in many areas of engineering and physics representing some phenomena. The solution of such problems have been tackled by many authors. In this paper, a numerical method based on the Adomian decomposition method is introduced for the approximate sol...

We examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads to preconditio...

Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data from the boundary of a planar domain to its interior. Many different recipes for barycentric coordinates exist, some offering the convenience of a closedform expression, some providing other desirable properties at the expen...

The main purpose of this paper is to study biharmonic hypersurface in a quasi-paraSasakian manifold $\mathbb{Q}^{2m+1}$. Biharmonic hypersurfaces are special cases maps and the critical points bienergy functional. condition biharmonicity for non-degenerate $\mathbb{Q}^{2m+1}$ investigated both cases: either characteristic vector field unit normal or it belongs tangent space hypersurface. Some r...

We study the biharmonic stress-energy tensor S2 of Gauss map. Adding few assumptions, the Gauss map with vanishing S2 would be harmonic.