A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

Crystal structures of open and closed forms of D-serine deaminase from Salmonella typhimurium - implications on substrate specificity and catalysis

Metabolism of D-amino acids is of considerable interest due to their key importance in cell structure and function. Salmonella typhimurium D-serine deaminase (StDSD) is a pyridoxal 5' phosphate (PLP) dependent enzyme that catalyses degradation of D-Ser to pyruvate and ammonia. The first crystal structure of D-serine deaminase described here reveals a typical Foldtype II or tryptophan synthase beta subunit fold of PLP-dependent enzymes. Although holoenzyme was used for crystallization of both wild-type StDSD (WtDSD) and selenomethionine labelled StDSD (SeMetDSD), significant electron density was not observed for the cofactor, indicating that the enzyme has a low affinity for the cofactor under crystallization conditions. Interestingly, unexpected conformational differences were observed between the two structures. The WtDSD was in an open conformation while SeMetDSD, crystallized in the presence of isoserine, was in a closed conformation suggesting that the enzyme is likely to undergo conformational changes upon binding of substrate as observed in other Foldtype II PLP-dependent enzymes. Electron density corresponding to a plausible sodium ion was found near the active site of the closed but not in the open state of the enzyme. Examination of the active site and substrate modelling suggests that Thr166 may be involved in abstraction of proton from the C alpha atom of the substrate. Apart from the physiological reaction, StDSD catalyses a, b elimination of D-Thr, D-Allothr and L-Ser to the corresponding alpha-keto acids and ammonia. The structure of StDSD provides a molecular framework necessary for understanding differences in the rate of reaction with these substrates.

{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.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), non-orthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the OAF and NAF protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. In the two-relay case, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known static protocol for higher values of multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays.

High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

A decidable temporal logic with repeating values

Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this paper, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets. This is a surprising result since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier.