Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

A Constitutive Equation for Grain Boundary Sliding: An Experimental Approach

Although grain boundary sliding (GBS) has been recognized as an important process during high-temperature deformation in crystalline materials, there is paucity in experimental data for characterizing a constitutive equation for GBS. High-temperature tensile creep experiments were conducted, together with measurements of GBS at different strains, stresses, grain sizes, and temperatures. Experimental data obtained on a Mg AZ31 alloy demonstrate that, for the first time, dynamic recrystallization during creep does not alter the contribution of GBS to creep during high-temperature deformation. The experimentally observed invariance of the sliding contribution with strain was used together with the creep data for developing a constitutive equation for GBS in a manner similar to the standard creep equation. Using this new approach, it is demonstrated that the stress, grain size, and temperature dependence for creep and GBS are identical. This is rationalized by a model based on GBS controlled by dislocations, within grains or near-grain boundaries. (C) The Minerals, Metals & Materials Society and ASM International 2013

Continuity equation based nonquasi-static charge model for independent double gate MOSFET

Using the numerical device simulation we show that the relationship between the surface potentials along the channel in any double gate (DG) MOSFET remains invariant in QS (quasistatic) and NQS (nonquasi-static) condition for the same terminal voltages. This concept along with the recently proposed `piecewise charge linearization' technique is then used to develop the intrinsic NQS charge model for a Independent DG (IDG) MOSFET by solving the governing continuity equation. It is also demonstrated that unlike the usual MOSFET transcapacitances, the inter-gate transcapacitance of a IDG-MOSFET initially increases with the frequency and then saturates, which might find novel analog circuit application. The proposed NQS model shows good agreement with numerical device simulations and appears to be useful for efficient circuit simulation.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|(n-1)e(beta vertical bar x vertical bar 2)/2, beta >= 0, x is an element of R-n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

An open source massively parallel solver for Richards equation: Mechanistic modelling of water fluxes at the watershed scale

In this paper we present a massively parallel open source solver for Richards equation, named the RichardsFOAM solver. This solver has been developed in the framework of the open source generalist computational fluid dynamics tool box OpenFOAM (R) and is capable to deal with large scale problems in both space and time. The source code for RichardsFOAM may be downloaded from the CPC program library website. It exhibits good parallel performances (up to similar to 90% parallel efficiency with 1024 processors both in strong and weak scaling), and the conditions required for obtaining such performances are analysed and discussed. These performances enable the mechanistic modelling of water fluxes at the scale of experimental watersheds (up to few square kilometres of surface area), and on time scales of decades to a century. Such a solver can be useful in various applications, such as environmental engineering for long term transport of pollutants in soils, water engineering for assessing the impact of land settlement on water resources, or in the study of weathering processes on the watersheds. (C) 2014 Elsevier B.V. All rights reserved.

L-p estimates for the wave equation associated to the Grushin operator

We prove that the solution of the wave equation associated to the Grushin operator G = -Delta -vertical bar x vertical bar(2)partial derivative(2)(t) is bounded on L-P (Rn+1), with 1 < p < infinity, when vertical bar 1/p - 1/2 vertical bar < 1/n+2.

Internal noise-driven generalized Langevin equation from a nonlocal continuum model

Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

HOMOGENIZATION OF A HYPERBOLIC EQUATION WITH HIGHLY CONTRASTING DIFFUSIVITY COEFFICIENTS

We study a hyperbolic problem in the framework of periodic homogenization assuming a high contrast between the diffusivity coefficients of the two components M-epsilon and B-epsilon of the heterogeneous medium. There are three regimes depending on the ratio between the size of the period and the amplitude a, of the diffusivity in B-epsilon. For the critical regime alpha(epsilon) similar or equal to epsilon, the limit problem is a strongly coupled system involving both the macroscopic and the microscopic variables. We also include the results in the non critical case.

HOMOGENIZATION OF A HYPERBOLIC EQUATION WITH HIGHLY CONTRASTING DIFFUSIVITY COEFFICIENTS

We study a hyperbolic problem in the framework of periodic homogenization assuming a high contrast between the diffusivity coefficients of the two components M-epsilon and B-epsilon of the heterogeneous medium. There are three regimes depending on the ratio between the size of the period and the amplitude a, of the diffusivity in B-epsilon. For the critical regime alpha(epsilon) similar or equal to epsilon, the limit problem is a strongly coupled system involving both the macroscopic and the microscopic variables. We also include the results in the non critical case.