Air-exposure effect on the resistivity of thin bismuth films

A survey of previous studies on vacuum deposited metal films shows that in high frequency measurements, explicit reference to the effect of air-exposure is not made. The present work on bismuth films (in-situ and air-exposed) at dc and rf frequencies, carried out mainly to study the air-exposure effect, shows that in-situ dc and rf and exposed rf all show nearly the same resistivity for thick continuous films. But air-exposed dc film resistances, when compared to in-situ dc resistances, show that the grain boundary reflection coefficient, R _gin Mayadas-Shatzkes model changes from 0·2 to 0·6. This is shown to be due to the grain boundary oxidation. The result is substantiated by rf measurements.     

Maps Between Deformed and Ordinary Gauge Fields

In this paper, we introduce a map between the q-deformed gauge fields defined on the GL_q(N) -covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing à la BRST is discussed. Another star product defined on the hybrid (q,h) -plane is explicitly constructed.     

Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

Singular Integral Operators,Morrey Spaces and Fine Regularity of Solutions to PDE's

Boundedness in Morrey spaces is studied for singular integral operators with kernels of mixed homogeneity and their commutators with multiplication by a BMO-function. The results are applied in obtaining fine (Morrey and Hölder) regularity of strong solutions to higher-order elliptic and parabolic equations with VMO coefficients.     

Two nontrivial solutions for quasilinear periodic equations

In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem".

     

Korn's inequalities for piecewise vector fields

Korn's inequalities for piecewise vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

     

A relaxation scheme for conservation laws with a discontinuous coefficient

We study a relaxation scheme of the Jin and Xin type for conservation laws with a flux function that depends discontinuously on the spatial location through a coefficient . If , we show that the relaxation scheme produces a sequence of approximate solutions that converge to a weak solution. The Murat-Tartar compensated compactness method is used to establish convergence. We present numerical experiments with the relaxation scheme, and comparisons are made with a front tracking scheme based on an exact Riemann solver.     

Trees, parking functions, syzygies, and deformations of monomial ideals

For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.

     

Diffusion Along Migrating Grain Boundaries

The paper summarizes recent experiments on diffusion at migrating grain boundaries (GBs) occurring during discontinuous reactions, like discontinuous precipitation (DP) and diffusion induced grain boundary migration. Analytical electron microscopy was used for measurements of the solute concentration across individual solute-depleted lamellae. These data combined with information on the growth velocity and the thickness of an individual lamella allowed the determination of the local values of the diffusivities of the moving reaction front of the DP cell in Al–Zn, Ni–Sn, Cu–In and Co–Al alloys. The obtained diffusivities and activation energies are very similar to the relevant parameters of stationary GBs. This allows us to conclude that there is no significant difference in the rates of diffusion along migrating and stationary GBs in the systems investigated. It is therefore believed that the diffusivity values of the moving reaction front of the DP reaction can be a source of reliable information on interfacial diffusion characteristics, especially in systems and/or at temperatures where radiotracer data are not readily available.     

New Deformation of Para-Bose Statistics

We propose commutation relations for a single mode -deformed para-Bose oscillator. In this new deformation of para-Bose statistics the distribution function has the same form as in the para-Bose statistics. Furthermore, we show analogies between the coherent states of -deformed and q-deformed para-Bose statistics.