{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.

Channel Precoding for STBCs from Generalized Pseudo Orthogonal Designs

Statistical information about the wireless channel can be used at the transmitter side to enhance the performance of MIMO systems. This paper addresses how the concept of channel precoding can be used to enhance the performance of STBCs from Generalized Pseudo Orthogonal Designs which were first introduced by Zhu and Jafarkhani. Such designs include some important classes of STBCs that are directly derivable from Quasi-Orthogonal Designs and Co-ordinate Interleaved Orthogonal Designs.

Multi-physics self-consistent modeling in nanotechnological applications: quantum dots and quantum-well lasers

This paper reports a self-consistent Poisson-Schr¨odinger scheme including the effects of the piezoelectricity, the spontaneous polarization and the charge density on the electronic states and the quasi-Fermi level energy in wurtzite type semiconductor heterojunction and quantum-laser.

Multigroup-Decodable STBCs from Clifford Algebras

A Space-Time Block Code (STBC) in K symbols (variables) is called g-group decodable STBC if its maximum-likelihood decoding metric can be written as a sum of g terms such that each term is a function of a subset of the K variables and each variable appears in only one term. In this paper we provide a general structure of the weight matrices of multi-group decodable codes using Clifford algebras. Without assuming that the number of variables in each group to be the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal g-group decodable codes is presented for arbitrary number of antennas. For the special case of Nt=2a we construct two subclass of codes: (i) A class of 2a-group decodable codes with rate a2(a−1), which is, equivalently, a class of Single-Symbol Decodable codes, (ii) A class of (2a−2)-group decodable with rate (a−1)2(a−2), i.e., a class of Double-Symbol Decodable codes. Simulation results show that the DSD codes of this paper perform better than previously known Quasi-Orthogonal Designs.

Achieving the D-MG and DMD Tradeoffs of MIMO fading channels

An overview of our recent results relating to the explicit construction of space-time block codes achieving the DMG tradeoff of the quasi-static fading channel is presented. The results include the explicit construction of D-MG optimal codes,generalization of perfect codes to any number of transmit antennas as well as optimal diversity-multiplexing-delay constructions for the MIMO ARQ Channel.

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.

Synthesis and Characterization of Carbon Nanotube-Polymer Multilayer Structures

We develop lightweight, multilayer materials composed of alternating layers of poly dimethyl siloxane (PDMS) polymer and vertically aligned carbon nanotube (CNT) arrays, and characterize their mechanical response in compression. The CNT arrays used In the assembly are synthesized with graded mechanical properties along their thickness, and their use enables the creation of multilayer structures with low density (0.12-0.28 g/cm(3)). We test the mechanical response of structures composed of different numbers of CNT layers partially embedded in PDMS polymer, under quasi-static and dynamic loading. The resulting materials exhibit a hierarchical, fibrous structure with unique mechanical properties: They can sustain large compressive deformations (up to similar to 0.8 strain) with a nearly complete recovery and present strain localization in selected sections of the materials. Energy absorption, as determined by the hysteresis observed In stress-strain curves, is found to be at least 3 orders of magnitude larger than that of natural and synthetic cellular materials of comparable density. Conductive bucky paper Is Included within the polymer interlayers. This allows the measurement of resistance variation as a function of applied stress, showing strong correlation with the observed strain localization In compression.

Thermodynamic study of oxygen in liquid lead tin alloys

The activity coefficients of oxygen in liquid lead-tin alloys have been measured between 550 and 1100°C by use of solid oxide galvanic cells Pt, Ni-NiO I Zr02 Solid electrolyte I 0 (Pb + Sn), Cermet, Pt Pt, Fe-FeO I Zr02 Solid electrolyte I O(Pb + Sn), Cermet, Pt Alcock and Richardson's quasi-chemical equation, with the coordination number of atoms set to 2, is found to predict successfully the activity coefficients of oxygen in these alloys.The relative partial molar enthalpy and entropy of oxygen ?t 1 atom per cent in the alloys have been calculated from ttva variation of the activity coefficient with temperature. The addition of tin to an unsaturated solution of oxygen in lead is shown to decrease significantly both the partial molar enthalpy and entropy of oxygen. As the measurements were restricted to a narrow range between 750-1100'C in lead-rich alloys, however, the pronounced variation of the partial molar enthalpy of oxygen with temperature at constant alloy composition predicted by the quasi-chemical model could not be verified.

Solute solute and solvent solute interactions in solid solutions of Cu+Sn, Au+Sn and Cu+Au+Sn alloys

The chemical potentials of tin in its α-solid solutions with Cu, Au and Cu + Au alloys have been measured using a gas-solid equilibration technique. The variation of the excess chemical potential of tin with its composition in the alloy is related to the solute-solute repulsive interaction, while the excess chemical potential at infinite dilution of the solute is a measure of solvent-solute interaction energies. It is shown that solute-solute interaction is primarily determined by the concentration of (s + p) electrons in the conduction band, although the interaction energies are smaller than those predicted by either the rigid band model or calculation based on Friedel oscillations in the potential function. Finally, the variation of the solvent-solute interaction with solvent composition in the ternary system can be accounted for in terms of a quasi-chemical treatment which takes into account the clustering of the solvent atoms around the solute.

Impact of metal on the DNA photocleavage activity and cytotoxicity of ferrocenyl terpyridine 3d metal complexes

Ferrocenyl terpyridine 3d metal complexes and their analogues, viz. [M(Fc-tpy)(2)](ClO(4))(2) (1-4), [Zn(Ph-tpy)(2)](ClO(4))(2) (5) and [Zn(Fc-dpa)(2)]X(2) (X = ClO(4), 6; PF6, 6a), where M = Fe(II) in 1, Co(II) in 2, Cu(II) in 3 and Zn(II) in 4, Fc-tpy is 4'-ferrocenyl-2,2': 6', 2 `'-terpyridine, Ph-tpy is 4'-phenyl-2,2': 6', 2 `'-terpyridine and Fc-dpa is ferrocenyl-N,N-dipicolylmethanamine, are prepared and their DNA binding and photocleavage activity in visible light studied. Complexes 2, 4, 5 and 6a that are structurally characterized by X-ray crystallography show distorted octahedral geometry with the terpyridyl ligands binding to the metal in a meridional fashion, with Fc-dpa in 6a showing a facial binding mode. The Fc-tpy complexes display a charge transfer band in the visible region. The ferrocenyl (Fc) complexes show a quasi-reversible Fc(+)-Fc redox couple within 0.48 to 0.66 V vs. SCE in DMF-0.1 M TBAP. The DNA binding constants of the complexes are similar to 10(4) M(-1). Thermal denaturation and viscometric data suggest DNA surface binding through electrostatic interaction by the positively charged complexes. Barring the Cu(II) complex 3, the complexes do not show any chemical nuclease activity in the presence of glutathione. Complexes 1-4 exhibit significant plasmid DNA photocleavage activity in visible light via a photoredox pathway. Complex 5, without the Fc moiety, does not show any DNA photocleavage activity. The Zn(II) complex 4 shows a significant PDT effect in HeLa cancer cells giving an IC(50) value of 7.5 mu M in visible light, while being less toxic in the dark (IC(50) = 49 mu M).

Dynamic Multiscaling in Two-Dimensional Fluid Turbulence

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that different ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold.

Fracture analysis of concrete using singular fractal functions with lattice beam network and confirmation with acoustic emission study

In the present study singular fractal functions (SFF) were used to generate stress-strain plots for quasibrittle material like concrete and cement mortar and subsequently stress-strain plot of cement mortar obtained using SFF was used for modeling fracture process in concrete. The fracture surface of concrete is rough and irregular. The fracture surface of concrete is affected by the concrete's microstructure that is influenced by water cement ratio, grade of cement and type of aggregate 11-41. Also the macrostructural properties such as the size and shape of the specimen, the initial notch length and the rate of loading contribute to the shape of the fracture surface of concrete. It is known that concrete is a heterogeneous and quasi-brittle material containing micro-defects and its mechanical properties strongly relate to the presence of micro-pores and micro-cracks in concrete 11-41. The damage in concrete is believed to be mainly due to initiation and development of micro-defects with irregularity and fractal characteristics. However, repeated observations at various magnifications also reveal a variety of additional structures that fall between the `micro' and the `macro' and have not yet been described satisfactorily in a systematic manner [1-11,15-17]. The concept of singular fractal functions by Mosolov was used to generate stress-strain plot of cement concrete, cement mortar and subsequently the stress-strain plot of cement mortar was used in two-dimensional lattice model [28]. A two-dimensional lattice model was used to study concrete fracture by considering softening of matrix (cement mortar). The results obtained from simulations with lattice model show softening behavior of concrete and fairly agrees with the experimental results. The number of fractured elements are compared with the acoustic emission (AE) hits. The trend in the cumulative fractured beam elements in the lattice fracture simulation reasonably reflected the trend in the recorded AE measurements. In other words, the pattern in which AE hits were distributed around the notch has the same trend as that of the fractured elements around the notch which is in support of lattice model. (C) 2011 Elsevier Ltd. All rights reserved.

Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs

It is well known that the space-time block codes (STBCs) from complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the unitary matrix representations of Clifford Algebras when the number of transmit antennas n is a power of 2. The rate of the square CODs for n = 2(a) has been shown to be a+1/2(a) complex symbols per channel use. However, SSD codes having unitary-weight matrices need not be CODs, an example being the minimum-decoding-complexity STBCs from quasi-orthogonal designs. In this paper, an achievable upper bound on the rate of any unitary-weight SSD code is derived to be a/2(a)-1 complex symbols per channel use for 2(a) antennas, and this upper bound is larger than that of the CODs. By way of code construction, the interrelationship between the weight matrices of unitary-weight SSD codes is studied. Also, the coding gain of all unitary-weight SSD codes is proved to be the same for QAM constellations and conditions that are necessary for unitary-weight SSD codes to achieve full transmit diversity and optimum coding gain are presented.

Theoretical gain optimization studies in 10.6 μm CO2–N2 gasdynamic lasers. IV. Further results of parametric study

Based on a method proposed by Reddy and Shanmugasundaram, similar solutions have been obtained for the steady inviscid quasi‐one‐dimensional nonreacting flow in the supersonic nozzle of CO2–N2–H2O and CO2–N2–He gasdynamic laser systems. Instead of using the correlations of a nonsimilar function NS for pure N2 gas, as is done in previous publications, the NS correlations are computed here for the actual gas mixtures used in the gasdynamic lasers. Optimum small‐signal optical gain and the corresponding optimum values of the operating parameters like reservoir pressure and temperature and nozzle area ratio are computed using these correlations. The present results are compared with the previous results and the main differences are discussed.

Real-time density matrix renormalization group dynamics of spin and charge transport in push-pull polyenes and related systems

In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)(x)-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)(x)-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)(x)-A, systems in which besides electron affinities, the nature of p(z) orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a ``quasi-static'' state.