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.

Interaction of metal ions with 6-oxopurine nucleotides. Part 1. X-Ray structures of ternary cobalt(III) complexes with inosine 5'-monophosphate or guanosine 5'-monophosphate

The crystal structures of two ternary metal nucleotide complexes of cobalt, [Co(en)2(H2O)2]-[Co(5?-IMP)2(H2O)4]Cl2·4H2O (1) and [Co(en)2(H2O)2][Co(5?-GMP)2(H2O)4]Cl2·4H2O (2), have been analysed by X-ray diffraction (en = ethylenediamine, 5?-IMP = inosine 5?-monophosphate, and 5?-GMP = guanosine 5?-monophosphate). Both complexes crystallize in the orthorhombic space group C2221 with a= 8.725(1), b= 25.891(5), c= 21.212(5)Å, Z= 4 for (1) and a= 8.733(2), b= 26.169(4), c= 21.288(4)Å, Z= 4 for (2). The structure of (1) was solved by the heavy-atom method, while that of (2) was deduced from (1). The structures were refined to R values of 0.09 and 0.10 for 1 546 and 1 572 reflections for (1) and (2) respectively. The two structures are isomorphous. A novel feature is that the chelate ligand en and the nucleotide are not co-ordinated to the same metal ion. One of the metal ions lying on the two-fold a axis is octahedrally co-ordinated by two chelating en molecules and two water oxygens, while the other on the two-fold b axis is octahedrally co-ordinated by two N(7) atoms of symmetry-related nucleotides in a cis position and four water oxygens. The conformations of the nucleotides are C(2?)-endo, anti, and gauche�gauche. In both (1) and (2) the charge-neutralising chloride ions are disordered in the vacant space between the molecules. These structures bear similarities to the mode of nucleotide co-ordination to PtII complexes of 6-oxopurine nucleotides, which are the proposed models for intrastrand cross-linking in DNA by a metal complex.

Partially conserved axial-vector current inS-matrix theory

Mandelstam�s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm ? andm ? as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionm?2?m?2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

A.C. electrical conductivity of pure and doped potassium perchlorate

A.C. electrical conductivity of potassium perchlorate (KP) has been measured in the temperature range 25�325°C at frequencies ranging from 50�500 Hz using an automated technique. The results are interpreted in terms of a novel mechanism involving Schottky defects in the anion sublattice and Frenkel defects in the cation sublattice. Theconductivity behavior of KP is compared with literature data on similar low-symmetry systems containing polyatomic ions.

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosm

Studies on the phase transitions in thiourea

Thiourea (CS(NH2)2) is one of the few examples of molecular crystals exhibiting ferroelectric properties. The dielectric constant along the ferroelectric axis [100] shows maxima at 169, 177 and 202 K. An inflection point occurs at 170.5 KZ Following Goldsmith and White the phases are named as I (F.E. below 169 K), II (A.F.E. 169 Ksymmetry, though the overall structure is Pnma. Thiourea also exhibits thermoluminescence after being irradiated with x-rays which is accounted for by defects like NH3+ and NH- formed by the breaking of hydrogen bonds.

First-principles analysis of electron correlation, spin ordering and phonons in the normal state of FeSe1-x

We present first-principles density-functional-theory-based calculations to determine the effects of the strength of on-site electron correlation, magnetic ordering, pressure and Se vacancies on phonon frequencies and electronic structure of FeSe1-x. The theoretical equilibrium structure (lattice parameters) of FeSe depends sensitively on the value of the Hubbard parameter U of on-site correlation and magnetic ordering. Our results suggest that there is a competition between different antiferromagnetic states due to comparable magnetic exchange couplings between first- and second-neighbor Fe sites. As a result, a short range order of stripe antiferromagnetic type is shown to be relevant to the normal state of FeSe at low temperature. We show that there is a strong spin-phonon coupling in FeSe (comparable to its superconducting transition temperature) as reflected in large changes in the frequencies of certain phonons with different magnetic ordering, which is used to explain the observed hardening of a Raman-active phonon at temperatures (similar to 100 K) where magnetic ordering sets in. The symmetry of the stripe antiferromagnetic phase permits an induced stress with orthorhombic symmetry, leading to orthorhombic strain as a secondary order parameter at the temperature of magnetic ordering. The presence of Se vacancies in FeSe gives rise to a large peak in the density of states near the Fermi energy, which could enhance the superconducting transition temperature within the BCS-like picture.