In this paper, we introduce new curl conforming elements of higher order (k ≥ 1) on parallelepiped. This element has smaller number of degrees of freedom than the well knownNedelec spaces do, however, one can still obtain the same convergence order. To prove error estimate for curl conforming finite element methods, we also define the corresponding divergence conforming elements. Some efficient...

Abstract. Accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus provide reliable finite difference methods for approximating the solutions to a wide class of partial differential equations. These methods mimic many fundamental properties of the underlying physical problem including conservation laws, symmetries in the solution...

We investigate the influence of the small-world topology on the composition of information flow on networks. By appealing to the combinatorial Hodge theory, we decompose information flow generated by random threshold networks on the Watts-Strogatz model into three components: gradient, harmonic and curl flows. The harmonic and curl flows represent globally circular and locally circular componen...

In this paper, we consider an approximation to the Maxwell’s eigenvalue problem based on a very weak formulation of two div-curl systems with complementary boundary conditions. We formulate each of these div-curl systems as a general variational problem with different test and trial spaces as done in [12], i.e., the solution space is L(Ω) ≡ (L(Ω)) and components in the test spaces are in subspa...

Physical-field inspired methodology has become a new branch in image processing techniques. In this paper, a novel image transform is proposed imitating the source reverse of magneto-static field. The image is taken as a vertical magnetic field, and its curl is estimated as the virtual source of the field for image structure representation and analysis. The restoration from the virtual source t...

Biological and molecular properties of Tomato leaf curl Madagascar virus isolates from Morondova and Toliary (ToLCMGV-[Tol], -[Mor]), Tomato leaf curl Mayotte virus isolates from Dembeni and Kahani (ToLCYTV-[Dem], -[Kah]) and a Tomato yellow leaf curl virus isolate from Reunion (TYLCV-Mld[RE]) were determined. Full-length DNA components of the five isolates from Madagascar, Mayotte and Reunion ...

It is well known that any given density ρ(x) can be realized by a determinantal wave function for N particles. The question addressed here is whether any given density ρ(x) and current density j(x) can be simultaneously realized by a (finite kinetic energy) determinantal wave function. In case the velocity field v(x) = j(x)/ρ(x) is curlfree, we provide a solution for all N , and we provide an e...

Numerical examples demonstrated that a prescribed positive Jacobian determinant alone can not uniquely determine a diffeomorphism. It is conjectured that the uniqueness of a transformation can be assured by its Jacobian determinant and the curl-vector. In this work, we study the uniqueness problem analytically and propose an approach to the proof of the uniqueness of a transformation with presc...

This article deals with the links between compensated compactness and two-scale convergence. More precisely, we ask the following question: Is the div-curl compactness assumption sufficient to pass to the limit in a product of two sequences which two-scale converge with respect to the pair of variables (x, x/ε)? We reply in the negative. Indeed, the div-curl assumption allows us to control osci...