Analysis of Parameter Values in the van der Waals and Platteeuw Theory for Methane Hydrates Using Monte Carlo Molecular Simulations

The van der Waals and Platteuw (vdVVP) theory has been successfully used to model the thermodynamics of gas hydrates. However, earlier studies have shown that this could be due to the presence of a large number of adjustable parameters whose values are obtained through regression with experimental data. To test this assertion, we carry out a systematic and rigorous study of the performance of various models of vdWP theory that have been proposed over the years. The hydrate phase equilibrium data used for this study is obtained from Monte Carlo molecular simulations of methane hydrates. The parameters of the vdWP theory are regressed from this equilibrium data and compared with their true values obtained directly from simulations. This comparison reveals that (i) methane-water interactions beyond the first cage and methane-methane interactions make a significant contribution to the partition function and thus cannot be neglected, (ii) the rigorous Monte Carlo integration should be used to evaluate the Langmuir constant instead of the spherical smoothed cell approximation, (iii) the parameter values describing the methane-water interactions cannot be correctly regressed from the equilibrium data using the vdVVP theory in its present form, (iv) the regressed empty hydrate property values closely match their true values irrespective of the level of rigor in the theory, and (v) the flexibility of the water lattice forming the hydrate phase needs to be incorporated in the vdWP theory. Since methane is among the simplest of hydrate forming molecules, the conclusions from this study should also hold true for more complicated hydrate guest molecules.

Dynamics of rotating composite beams: A comparative study between CNT reinforced polymer composite beams and laminated composite beams using spectral finite elements

This paper presents a spectral finite element formulation for uniform and tapered rotating CNT embedded polymer composite beams. The exact solution to the governing differential equation of a rotating Euler-Bernoulli beam with maximum centrifugal force is used as an interpolating function for the spectral element formulation. Free vibration and wave propagation analysis is carried out using the formulated spectral element. The present study shows the substantial effect of volume fraction and L/D ratio of CNTs in a beam on the natural frequency, impulse response and wave propagation characteristics of the rotating beam. It is found that the CNTs embedded in the matrix can make the rotating beam non-dispersive in nature at higher rotation speeds. Embedded CNTs can significantly alter the dynamics of polymer-nanocomposite beams. The results are also compared with those obtained for carbon fiber reinforced laminated composite rotating beams. It is observed that CNT reinforced rotating beams are superior in performance compared to laminated composite rotating beams. © 2012 Elsevier Ltd. All rights reserved.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Theory and Algorithms for Hop-Count-Based Localization with Random Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Synthesis, Spectral Characterization, Crystal Structure and Thermal Behavior of Tert-butyl 2,2-bis(2,4-dinitrophenyl)ethanoate

Tert-butyl 2,2-bis(2,4-dinitrophenyl)ethanoate was prepared from the ethanolic solution of 1-chloro-2,4-dinitrobenzene, tert-butyl 3-oxobutanoate and triethylamine. Acetyl group in tert-butyl 3-oxobutanoate has cleaved off during the formation of the title molecule. UV-VIS, IR, 1H NMR, 13C NMR, Proton-Proton COSY data and single crystal XRD results support the proposed structure. Flammability test, impact sensitivity test and TG/DTA studies at different heating rates on the synthesized molecule imply that it is an insensitive high energy density material.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Study of terahertz wave propagation properties in nanoplates with surface and small-scale effects

In macroscopic and even microscopic structural elements, surface effects can be neglected and classical theories are sufficient. As the structural size decreases towards the nanoscale regime, the surface-to-bulk energy ratio increases and surface effects must be taken into account. In the present work, the terahertz wave dispersion characteristics of a nanoplate are studied with consideration of the surface effects as well as the nonlocal small-scale effects. Nonlocal elasticity theory of plate is used to derive the general differential equation based on equilibrium approach to include those scale effects. Scale and surface property dependent wave characteristic equations are obtained via spectral analysis. For the present study the material properties of an anodic alumina with crystallographic of < 111 > direction are considered. The present analysis shows that the effect of surface properties on the flexural waves of nanoplates is more significant. It can be found that the flexural wavenumbers with surface effects are high as compared to that without surface effects. The scale effects show that the wavenumbers of the flexural wave become highly non-linear and tend to infinite at certain frequency. After that frequency the wave will not propagate and the corresponding wave velocities tend to zero at that frequency (escape frequency). The effects of surface stresses on the wave propagation properties of nanoplate are also captured in the present work. (C) 2012 Elsevier Ltd. All rights reserved.

Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two it-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.

Intermolecular charge transfer and vibrational analysis of hydrogen bonding in acetazolamide

In the present work the structural and spectral characteristics of acetazolamide have been studied by methods of infrared, Raman spectroscopy and quantum chemistry. Electrostatic potential surface, optimized geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman scattering were calculated by density functional theory (DFT) employing B3LYP with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. Based on these results, we have discussed the correlation between the vibrational modes and the structure of the dimers of acetazolamide. The calculated vibrational spectra of three dimers of acetazolamide have been compared with observed spectra, and the assignment of observed bands was carried out using potential energy distribution. The observed spectra agree well with the values computed from the OFT. A comparison of observed and calculated vibrational spectra clearly shows the effect of hydrogen bonding. The frequency shifts observed for the different dimers are in accord with the hydrogen bonding in acetazolamide. Natural bond orbital (NBO) analyses reflect the charge transfer interaction in the individual hydrogen bond units and the stability of different dimers of acetazolamide. (C) 2012 Elsevier B.V. All rights reserved.

Spectral analysis on SL(2, R)

Let G be the group . For this group we prove a version of Schwartz's theorem on spectral analysis for the group G. We find the sharp range of Lebesgue spaces L (p) (G) for which a smooth function is not mean periodic unless it is a cusp form. Failure of the Schwartz-like theorem is also proved when C (a)(G) is replaced by L (p) (G) with suitable p. We show that the last result is linked with the failure of the Wiener-tauberian theorem for G.

Quasiuniversal Transient Behavior of a Nonequilibrium Mott Insulator Driven by an Electric Field

We use a self-consistent strong-coupling expansion for the self-energy (perturbation theory in the hopping) to describe the nonequilibrium dynamics of strongly correlated lattice fermions. We study the three-dimensional homogeneous Fermi-Hubbard model driven by an external electric field showing that the damping of the ensuing Bloch oscillations depends on the direction of the field and that for a broad range of field strengths a long-lived transient prethermalized state emerges. This long-lived transient regime implies that thermal equilibrium may be out of reach of the time scales accessible in present cold atom experiments but shows that an interesting new quasiuniversal transient state exists in nonequilibrium governed by a thermalized kinetic energy but not a thermalized potential energy. In addition, when the field strength is equal in magnitude to the interaction between atoms, the system undergoes a rapid thermalization, characterized by a different quasiuniversal behavior of the current and spectral function for different values of the hopping. DOI: 10.1103/PhysRevLett.109.260402

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Pattern clustering using cooperative game theory

In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performance of DRAC with that of well known algorithms. We show an interesting result that four prominent solution concepts, Nucleolus, Shapley value, Gately point and \tau-value coincide for the defined characteristic form game. This vindicates the choice of the characteristic function of the clustering game and also provides strong intuitive foundation for our approach.