{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.

An interior penalty method for a sixth-order elliptic equation

We derive and study a C(0) interior penalty method for a sixth-order elliptic equation on polygonal domains. The method uses the cubic Lagrange finite-element space, which is simple to implement and is readily available in commercial software. After introducing some notation and preliminary results, we provide a detailed derivation of the method. We then prove the well-posedness of the method as well as derive quasi-optimal error estimates in the energy norm. The proof is based on replacing Galerkin orthogonality with a posteriori analysis techniques. Using this approach, we are able to obtain a Cea-like lemma with minimal regularity assumptions on the solution. Numerical experiments are presented that support the theoretical findings.

Exact controllability of generalized Hammerstein type equation

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Analytical Solution of Joule-Heating Equation for Metallic Single-Walled Carbon Nanotube Interconnects

In this paper, we address a closed-form analytical solution of the Joule-heating equation for metallic single-walled carbon nanotubes (SWCNTs). Temperature-dependent thermal conductivity kappa has been considered on the basis of second-order three-phonon Umklapp, mass difference, and boundary scattering phenomena. It is found that kappa, in case of pure SWCNT, leads to a low rising in the temperature profile along the via length. However, in an impure SWCNT, kappa reduces due to the presence of mass difference scattering, which significantly elevates the temperature. With an increase in impurity, there is a significant shift of the hot spot location toward the higher temperature end point contact. Our analytical model, as presented in this study, agrees well with the numerical solution and can be treated as a method for obtaining an accurate analysis of the temperature profile along the CNT-based interconnects.

Transport processes in one component plasmas using Landau equation

A system of transport equations have been obtained for plasma of electrons and having a background of positive ions in the presence of an electric and magnetic field. The starting kinetic equation is the well-known Landau kinetic equation. The distribution function of the kinetic equation has been expanded in powers of generalized Hermite polynomials and following Grad, a consistent set of transport equations have been obtained. The expressions for viscosity and heat conductivity have been deduced from the transport equation.

An inverse problem for Helmholtz equation

This article is concerned with subsurface material identification for the 2-D Helmholtz equation. The algorithm is iterative in nature. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. It linearizes the otherwise nonlinear problem around the background field. The background field is the field variable generated using the guessed value of the unknown function at each iteration. Numerical results indicate that the algorithm can recover a close estimate of the unknown function based on the measurements collected at the boundary.

On the Presumed Kinetic Consequences of Pre-equilibrium. Implications for the Michaelis-Menten Equation

The overall rate equation for a reaction sequence consisting of a pre-equilibrium and rate-determining steps should not be derived on the basis of the concentration of the intermediate product (X). This is apparently indicated by transition state theory (as the path followed to reach the highest energy transition state is irrelevant), but also proved by a straight-forward mathematical approach. The thesis is further supported by the equations of concurrent reactions as applied to the partitioning of X between the two competing routes (reversal of the pre-equilibrium and formation of product). The rate equation may only be derived rigorously on the basis of the law of mass action. It is proposed that the reactants acquire the overall activation energy prior to the pre-equilibrium, thus forming X in a high-energy state en route to the rate-determining transition state. (It is argued that conventional energy profile diagrams are misleading and need to be reinterpreted.) Also, these arguments invalidate the Michaelis-Menten equation of enzyme kinetics, and necessitate a fundamental revision of our present understanding of enzyme catalysis. (The observed ``saturation kinetics'' possibly arises from weak binding of a second molecule of substrate at the active site; analogous conclusions apply to reactions at surfaces).

On the structure of analytic vectors for the Schrodinger representation

This article deals with the structure of analytic and entire vectors for the Schrodinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and their connection with Hermite expansions we obtain very precise representation theorems for analytic and entire vectors.

MODELING HETEROSTRUCTURES WITH SCHRODINGER-POISSON-NAVIER ITERATIVE SCHEMES, EFFECT OF CARRIER CHARGE, AND INFLUENCE OF ELECTROMECHANICAL COUPLING

This paper presents a detailed investigation of the erects of piezoelectricity, spontaneous polarization and charge density on the electronic states and the quasi-Fermi level energy in wurtzite-type semiconductor heterojunctions. This has required a full solution to the coupled Schrodinger-Poisson-Navier model, as a generalization of earlier work on the Schrodinger-Poisson problem. Finite-element-based simulations have been performed on a A1N/GaN quantum well by using both one-step calculation as well as the self-consistent iterative scheme. Results have been provided for field distributions corresponding to cases with zero-displacement boundary conditions and also stress-free boundary conditions. It has been further demonstrated by using four case study examples that a complete self-consistent coupling of electromechanical fields is essential to accurately capture the electromechanical fields and electronic wavefunctions. We have demonstrated that electronic energies can change up to approximately 0.5 eV when comparing partial and complete coupling of electromechanical fields. Similarly, wavefunctions are significantly altered when following a self-consistent procedure as opposed to the partial-coupling case usually considered in literature. Hence, a complete self-consistent procedure is necessary when addressing problems requiring more accurate results on optoelectronic properties of low-dimensional nanostructures compared to those obtainable with conventional methodologies.

Analyticity of the Schrodinger propagator on the Heisenberg group

We discuss the analytic extension property of the Schrodinger propagator for the Heisenberg sublaplacian and some related operators. The result for the sublaplacian is proved by interpreting the sublaplacian as a direct integral of an one parameter family of dilated special Hermite operators.

Calculation of Heat of Adsorption of Gases and Refrigerants on Activated Carbons from Direct Measurements Fitted to the Dubinin-Astakhov Equation

The heat of adsorption of methane, ethane, carbon dioxide, R-507a and R-134a on several specimens of microporous activated carbons is derived from experimental adsorption data fitted to the Dubinin-Astakhov equation. These adsorption results are compared with literature data obtained from calorimetric measurements and from the pressure-temperature relation during isosteric heating/cooling. Because the adsorbed phase volume plays an important role, its dependence on temperature and pressure needs to be correctly assessed. In addition, for super-critical gas adsorption, the evaluation of the pseudo-saturation pressure also needs a judicious treatment. Based on the evaluation of carbon dioxide adsorption, it can be seen that sub-critical and super-critical adsorption show different temperature dependences of the isosteric heat of adsorption. The temperature and loading dependence of this property needs to be taken into account while designing practical systems. Some practical implications of these findings are enumerated.

SOLVING VOLUME INTEGRAL EQUATION USING ScaLAPACK

In this article, we investigate the performance of a volume integral equation code on BlueGene/L system. Volume integral equation (VIE) is solved for homogeneous and inhomogeneous dielectric objects for radar cross section (RCS) calculation in a highly parallel environment. Pulse basis functions and point matching technique is used to convert the volume integral equation into a set of simultaneous linear equations and is solved using parallel numerical library ScaLAPACK on IBM's distributed-memory supercomputer BlueGene/L by different number of processors to compare the speed-up and test the scalability of the code.

Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets

Parabolized stability equation (PSE) models are being deve loped to predict the evolu-tion of low-frequency, large-scale wavepacket structures and their radiated sound in high-speed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer. 1,2 Here we show they also in very good agreement with hot-wire measurements at the jet center line in the potential core,for a different set of experiments. 3 When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large -scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative impor-tance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that n onlinearity has a very limited impact on the evolution of the wavepackets for St≥0. 3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode 4,5 of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.