Elastic behaviour of matter under very high pressures - Uniform compression

In order to study the elastic behaviour of matter when subjected to very large pressures, such as occur for example in the interior of the earth, and to provide an explanation for phenomena like earthquakes, it is essential to be able to calculate the values of the elastic constants of a substance under a state of large initial stress in terms of the elastic constants of a natural or stress-free state. An attempt has been made in this paper to derive expressions for these quantities for a substance of cubic symmetry on the basis of non-linear theory of elasticity and including up to cubic powers of the strain components in the strain energy function. A simple method of deriving them directly from the energy function itself has been indicated for any general case and the same has been applied to the case of hydrostatic compression. The notion of an effective elastic energy-the energy require to effect an infinitesimal deformation over a state of finite strain-has been introduced, the coefficients in this expression being the effective elastic constants. A separation of this effective energy function into normal co-ordinates has been given for the particular case of cubic symmetry and it has been pointed out, that when any of such coefficients in this normal form becomes negative, elastic instability will set in, with associated release of energy.

Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong-coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime, and then towards and through the quantum phase transition to a charge-ordered ( CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.

Type I seesaw mechanism for quasi-degenerate neutrinos

We discuss symmetries and scenarios leading to quasi-degenerate neutrinos in type I seesaw models. The existence of degeneracy in the present approach is not linked to any specific structure for the Dirac neutrino Yukawa coupling matrix y(D) and holds in general. Basic input is the application of the minimal flavour violation principle to the leptonic sector. Generalizing this principle, we assume that the structure of the right-handed neutrino mass matrix is determined by y(D) and the charged lepton Yukawa coupling matrix y(l) in an effective theory invariant under specific groups G(F) contained in the full symmetry group of the kinetic energy terms. G(F) invariance also leads to specific structure for the departure from degeneracy. The neutrino mass matrix (with degenerate mass m(0)) resulting after seesaw mechanism has a simple form Mv approximate to m(0)(I - py(l)y(l)(T)) in one particular scenario based on supersymmetry. This form is shown tolead to correct description of neutrino masses and mixing angles. The thermal leptogenesis after inclusion of flavour effects can account for the observed baryon asymmetry of the universe within the present scenario. Rates for lepton flavour violating processes can occur at observable levels in the supersymmetric version of the scenario. (c) 2010 Elsevier B.V. All rights reserved.

New Solid State Forms of the Anti-HIV Drug Efavirenz. Conformational Flexibility and High Z ` Issues

Structural information on the solid forms of efavirenz, a non-nucleoside reverse transcriptase inhibitor, is limited, although various polymorphic forms of this drug have been patented. We report here structural studies of four new crystal forms a pure form, a cyclohexane solvate, and cocrystals with 1,4-cyclohexanedione and 4,4'-bipyridine. Temperature dependent single-crystal to single-crystal phase transitions are observed for the pure form and for the cyclohexane solvate with an increase in the number of symmetry independent molecules, Z', upon a lowering of temperature. Other issues related to these solid forms, such as thermal stability, conformational flexibility, and high Z' occurrences, are addressed by using a combined experimental and computational approach.

Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.

Evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source

The present work gives a comprehensive numerical study of the evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source. Using pseudospectral and predictor–corrector implicit finite difference methods, we first reproduced the known analytic results of the plane harmonic problem to a high degree of accuracy. The non-planar harmonic problems, for which the amplitude decay is faster than that for the planar case, are then treated. The results are correlated with the known asymptotic results of Scott (1981) and Enflo (1985). The constant in the old-age formula for the cylindrical canonical problem is found to be 1.85 which is rather close to 2, ‘estimated’ analytically by Enflo. The old-age solutions exhibiting strict symmetry about the maximum are recovered; these provide an excellent analytic check on the numerical solutions. The evolution of the waves for different source geometries is depicted graphically.

Decagonal quasicrystals

Following the discovery of two dimensional quasicrystals in rapidly solidified Al-Mn alloys by us and L. Bendersky in 1985, a number of fascinating studies has been conducted to unravel the atomic configuration of quasicrystals with decagonal symmetry. A comprehensive mapping of the reciprocal space of decagonal quasicrystals is now available. The interpretation of the diffraction patterns brings out the comparative advantages of various indexing schemes. In addition, the nature of the variable periodicity can be addressed as a form of polytypism. The relation between decagonal quasicrystals and their crystalline homologues will be explored with emphasis on Al60Mn11Ni4 and 'Al3Mn'. It will also be shown that decagonal quasicrystals are closely related to icosahedral quasicrystals, icosahedral twins and vacancy ordered phases.

Ultrasonic measurement of the elastic constants of sodium p-nitrophenolate dihydrate single crystals

Sodium p-nitrophenolate dihydrate single crystals possess excellent nonlinear optical properties such that they can be used for optical second-harmonic generation. It belongs to the orthorhombic system with the space group Ima2. Slow evaporation or slow cooling techniques can be used to grow good optical quality single crystals from supersaturated solution. All the nine elastic constants of this crystal have been measured using an ultrasonic technique. Samples for measurements have been cut along desired crystallographic axes and the pulse echo overlap technique has been used to measure longitudinal and shear ultrasonic wave velocities along appropriate symmetry directions in the crystal. The McSkimin Delta t criterion has been applied to determine the round trip travel time accurately, from which the nine elastic constants have been evaluated. Temperature variation of selected elastic constants in a limited range have also been measured and reported.

A density matrix renormalization group study of low-lying excitations of polythiophene within a Pariser-Parr-Pople model

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited C-2 symmetry and spin parity of the system to obtain excited states of experimental interest, and studied the lowest dipole allowed excited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed excited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge excitation gap and the binding energy of the 1(1)B(u)(-) exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium excited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons.

Crystal and molecular structure of the ammonium salt of the dinucleoside monophosphate d(CpG)

The crystal and molecular structure of the ammonium salt of deoxycytidylyl-(3'-5')-deoxyguanosine has been determined from 0.85 A resolution single crystal X-ray diffraction data. The crystals obtained by acetone diffusion technique at -20 degrees C, are orthorhombic, P212121, a = 12.880(2), b = 17444(2) and c = 27.642(2) A. The structure was solved by high resolution Patterson and Fourier methods and refined to R = 0.136. There are two d(CpG) molecules in the asymmetric unit forming a mini left handed Z-DNA helix. This is in contrast to the earlier reported forms of d(CpG) where the molecules form self base paired duplexes. There are two ammonium ions in the asymmetric unit. The major groove NH+4 ion interacts with N7 of guanines through water bridges besides making H-bonded interactions directly with the phosphate oxygen atoms. A second NH+4 ion is found in the minor groove interacting directly with the phosphate oxygen atoms. Symmetry related molecules pack in such a way that the cytosine base stacks on cytosine and guanine base on guanine. Our structure demonstrates that alternating d(CpG) sequences have the ability to adopt the left handed Z-DNA structure even at the dimer level i.e., in a sequence which is only two base pairs long.

Ferroelastic phase transition in CslO4

An optical investigation of the high-temperature structural phase transition in gel-grown single crystals of CslO4 is reported. This crystal undergoes a phase transition from the room-temperature orthorhombic phase of symmetry Pnma to a tetragonal phase at 150°C. The birefringence Δn = |na-nb| falls abruptly at Tc, indicating the first-order nature of the phase transition. Microscopic examination has revealed the existence of ferroelastic domains in the crystal. The domain structure and its dependence on temperature was studied in detail. The experimental results suggest that this crystal can be assigned to the ferroelastic Aizu species 4/mmmFmmm (p).

Freezing of a colloidal liquid subject to shear flow

A nonequilibrium generalization of the density-functional theory of freezing is proposed to investigate the shear-induced first-order phase transition in colloidal suspensions. It is assumed that the main effect of a steady shear is to break the symmetry of the structure factor of the liquid and that for small shear rate, the phenomenon of a shear-induced order-disorder transition may be viewed as an equilibrium phase transition. The theory predicts that the effective density at which freezing takes place increases with shear rate. The solid (which is assumed to be a bcc lattice) formed upon freezing is distorted and specifically there is less order in one plane compared with the order in the other two perpendicular planes. It is shown that there exists a critical shear rate above which the colloidal liquid does not undergo a transition to an ordered (or partially ordered) state no matter how large the density is. Conversely, above the critical shear rate an initially formed bcc solid always melts into an amorphous or liquidlike state. Several of these predictions are in qualitative agreement with the light-scattering experiments of Ackerson and Clark. The limitations as well as possible extensions of the theory are also discussed.

Generalized Burgers equations and Euler–Painlevé transcendents. III

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1

Rapid localization of damage using a circular sensor array and Lamb wave based triangulation

A damage detection and imaging methodology based on symmetry of neighborhood sensor path and similarity of signal patterns with respect to radial paths in a circular array of sensors has been developed It uses information regarding Limb wave propagation along with a triangulation scheme to rapidly locate and quantify the severity of damage without using all of the sensor data. In a plate like structure, such a scheme can be effectively employed besides full field imaging of wave scattering pattern from the damage, if present in the plate. This new scheme is validated experimentally. Hole and corrosion type damages have been detected and quantified using the proposed scheme successfully. A wavelet based cumulative damage index has been studied which shows monotonic sensitivity against the severity of the damage. which is most desired in a Structural Health Monitoring system. (C) 2010 Elsevier Ltd. All rights reserved.