(2E)-1-(5-Chlorothiophen-2-yl)-3-(2,3-dimethoxyphenyl)prop-2-en-1-one

In the title compound, C(15)H(13)ClO(3)S, the chlorothiophene and dimethoxyphenyl groups are linked by a prop-2-en-1-one group. The C=C double bond exhibits an E conformation. The molecule is non-planar, with a dihedral angle of 31.12 (5)degrees between the chlorothiophene and dimethoxyphenyl rings. The methoxy group at position 3 is coplanar with the benzene ring to which it is attached, with a C-O-C-C torsion angle of -3.8 (3)degrees. The methoxy group attached at position 2 of the benzene ring is in a (+)synclinal conformation, as indicated by the C-O-C-C torsion angle of -73.6 (2)degrees. In the crystal, two different C-H center dot center dot center dot O intermolecular interactions generate chains of molecules extending along the b axis.

Authors reply to "On uniqueness, transfer and combination of acoustic sources in one-dimensional systems"

The use of electroacoustic analogies suggests that a source of acoustical energy (such as an engine, compressor, blower, turbine, loudspeaker, etc.) can be characterized by an acoustic source pressure ps and internal source impedance Zs, analogous to the open-circuit voltage and internal impedance of an electrical source. The present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected; that is, the evaluated values of ps and Zs are unique, and that the results of the different methods (including the direct method) are identical. In addition, general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements, and also for combining several sources into a single equivalent source. Finally, all the conclusions are extended to the case of a uniformly moving medium, incorporating the convective as well as dissipative effects of the mean flow.

Analysis of a linear one-dimensional active noise control system by means of block diagrams and transfer functions

In arriving at the ideal filter transfer function for an active noise control system in a duct, the effect of the auxiliary sources (generally loudspeakers) on the waves generated by the primary source has invariably been neglected in the existing literature, implying a rigid wall or infinite impedance. The present paper presents a fairly general analysis of a linear one-dimensional noise control system by means of block diagrams and transfer functions. It takes into account the passive as well as active role of a terminal primary source, wall-mounted auxiliary source, open duct radiation impedance, and the effects of mean flow and damping. It is proved that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against an anechoic termination and the other by reflecting the rearward wave (incident on the source) off the passive source impedance. Application of this concept is illustrated for both the types of sources. A concise closed-form expression for the ideal filter transfer function is thus derived and discussed. Finally, the dynamics of an adaptive noise control system is discussed briefly, relating its standing-wave variables and transfer functions with those of the progressive-wave model presented here.

Symmetry of one-dimensional dynamical systems in terms of transfer matrix parameters

The concept of symmetry for passive, one-dimensional dynamical systems is well understood in terms of the impedance matrix, or alternatively, the mobility matrix. In the past two decades, however, it has been established that the transfer matrix method is ideally suited for the analysis and synthesis of such systems. In this paper an investigatiob is described of what symmetry means in terms of the transfer matrix parameters of an passive element or a set of elements. One-dimensional flexural systems with 4 × 4 transfer matrices as well as acoustical and mechanical systems characterized by 2 × 2 transfer matrices are considered. It is shown that the transfer matrix of a symmetrical system, defined with respect to symmetrically oriented state variables, is involutory, and that a physically symmetrical system may not necessarily be functionally or dynamically symmetrical.

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.

Molecular Dynamics of Thermotropic Liquid Crystals: Anomalous relaxation dynamics of calamitic and discotic liquid crystals

Recent optical kerr effect (OKE) studies have demonstrated that orientational relaxation of rod-like nematogens exhibits temporal power law decay at intermediate times not only near the isotropic–nematic (I–N) phase boundary but also in the nematic phase. Such behaviour has drawn an intriguing analogy with supercooled liquids. We have investigated both collective and single-particle orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I–N phase boundary, the system behaves remarkably like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system. A model liquid crystal, consisting of disk-like molecules, has also been investigated in molecular dynamics simulations for orientational relaxation along two isobars starting from the high temperature isotropic phase. The isobars have been so chosen that the phase sequence isotropic (I)–nematic (N)–columnar (C) appears upon cooling along one of them and the sequence isotropic (I)–columnar(C) along the other. While the orientational relaxation in the isotropic phase near the I–N phase transition shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I–C phase boundary. The origin of the power law decay in the single-particle second-rank orientational time correlation function (OTCF) is traced to the growth of the orientational pair distribution functions near the I–N phase boundary. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational OTCF follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary

Gap model of one-way cyclic lateral load on vertical files in soft clay

For the analysis and design of pile foundation used for coastal structures the prediction of cyclic response, which is influenced by the nonlinear behavior, gap (pile soil separation) and degradation (reduction in strength) of soil becomes necessary. To study the effect of the above parameters a nonlinear cyclic load analysis program using finite element method is developed, incorporating the proposed gap and degradation model and adopting an incremental-iterative procedure. The pile is idealized using beam elements and the soil by number of elastoplastic sub-element springs at each node. The effect of gap and degradation on the load-deflection behavior. elasto-plastic sub-element and resistance of the soil at ground-line have been clearly depicted in this paper.

Synthesis, growth, and characterization of a new NLO material 3-(2,3-dimethoxyphenyl)-1-(pyridin-2-yl)prop-2-en-1-one

3-(2,3-Dimethoxyphenyl)-1-(pyridin-2-yl)prop-2-en-1-one (DMPP) a potential second harmonic generating (SHG) has been synthesized and grown as a single crystal by the slow evaporation technique at ambient temperature. The structure determination of the grown crystal was done by single crystal X-ray diffraction study. DMPP crystallizes with orthorhombic system with cell parameters a = 20.3106(8)angstrom, b = 4.9574(2)angstrom, c = 13.4863(5)angstrom, alpha = 90 degrees, beta = 90 degrees, gamma = 90 degrees and space group Pca2(1). The crystals were characterized by FT-IR, thermal analysis, UV-vis-NIR spectroscopy and SHG measurements. Various functional groups present in DMPP were ascertained by FTIR analysis. DMPP is thermally stable up to 80 degrees C and optically transparent in the visible region. The crystal exhibits SHG efficiency comparable to that of KDP. (C) 2011 Elsevier B.V. All rights reserved.

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Unitary invariants for Hilbert modules of finite rank

We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady's privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.

Partition function for hindered, one-and multi-dimensional rotors

Writing the hindered rotor (hr) partition function as the trace of (rho) over cap = e(-beta(H) over cap hr), we approximate it by the sum of contributions from a set of points in position space. The contribution of the density matrix from each point is approximated by performing a local harmonic expansion around it. The highlight of this method is that it can be easily extended to multidimensional systems. Local harmonic expansion leads to a breakdown of the method a low temperatures. In order to calculate the partition function at low temperatures, we suggest a matrix multiplication procedure. The results obtained using these methods closely agree with the exact partition function at all temperature ranges. Our method bypasses the evaluation of eigenvalues and eigenfunctions and evaluates the density matrix for internal rotation directly. We also suggest a procedure to account for the antisymmetry of the total wavefunction in the same. (C) 2012 Elsevier B.V. All rights reserved.

Enantiospecific total synthesis of 15-hydroxy-5-(methoxymethoxy)crinipellin-9-one

Enantiospecific total synthesis of the crinipellin mentioned in the title was accomplished. In the present synthesis cyclopentane ring in campholenaldehyde was identified as the B-ring, two intramolecular rhodium carbenoid CH insertion reactions were employed for the construction of the A and C rings, and an intramolecular Michael addition reaction was utilized for the construction of the D-ring of crinipellin. (C) 2012 Elsevier Ltd. All rights reserved.