A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Contribution from normal and starburst galaxies to the extragalactic gamma-ray background (EGRB)

The extragalactic diffuse emission at gamma-ray energies has interesting cosmological implications since these photons suffer little or no attenuation during their propagation from the site of origin. The emission could originate from either truly diffuse processes or from unresolved point sources such as AGNs, normal galaxies and starburst galaxies. Here, we examine the unresolved point source origin of the extragalactic gamma-ray background emission from normal galaxies and starburst galaxies. gamma-ray emission from normal galaxies is primarily coming from cosmic-ray interactions with interstellar matter and radiation (similar to 90%) along with a small contribution from discrete point sources (similar to 10%). Starburst galaxies are expected to have enhanced supernovae activity which leads to higher cosmic-ray densities, making starburst galaxies sufficiently luminous at gamma-ray energies to be detected by the current gamma-ray mission(Fermi Gamma-ray Space Telescope).

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Solid-State Acyl Migration In Salicylamides - An X-Ray Study Of The Ortho-Propionyl And Normal-Propionyl Derivatives

In recent years there has been an upsurge of interest in the study of organic reactions in the solid state. It is now realised that the crystalline matrix provides an extra-ordinary spatial control on the initiation and progress of these reactions. Electronic and dipolar effects which are important in solution are replaced by structural and geometric effects in solids. These 'spatial' or 'topochemical' aspects are important in understanding the mechanistic details of the reaction. In our laboratory, the thermally induced acyl migration in salicylamides from 0- to N- position in the solid state has been under study (Scheme 1). The structures of the acetyl and benzoyl derivatives (Ia,IIa, Ib and IIb) have been reported.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Small local variations in B-form DNA lead to a large variety of global geometries which can accommodate most DNA-binding protein motifs

An important question of biological relevance is the polymorphism of the double-helical DNA structure in its free form, and the changes that it undergoes upon protein-binding. We have analysed a database of free DNA crystal structures to assess the inherent variability of the free DNA structure and have compared it with a database of protein-bound DNA crystal structures to ascertain the protein-induced variations.

Normal-mode sound propagation in an ocean with sinusoidal surface waves

The normal-mode solution to the problem of acoustic wave propagation in an isovelocity ocean with a wavy surface is considered. The surface wave amplitude is assumed to be small compared to the acoustic wavelength, and the method of multiple scales is employed to study the interaction between normal-mode acoustic waves and the surface waves. A nonresonant interaction causes small fluctuations of the amplitude and phase of the acoustic wave at a rate dependent on the frequency of the surface wave. Backscatter occurs if the wavenumber of the surface wave is larger than that of the acoustic wave. The interaction becomes resonant if appropriate phase-matching conditions are satisfied. In this case, two acoustic normal modes get coupled, resulting in a large-scale periodic exchange of energy from one mode to another.

Flexure of composite plates

A new higher order shear deformation theory of laminated composite plates is developed. The basic displacement variables in this theory are two partial normal displacements and two in-plane displacement parameters. The governing equations are presented in the form of four simultaneous partial differential equations. The shear deformation theories of Bhimareddy and Stevens, and of Reddy are special cases of this formulation. In their models, transverse shear strains will become zero at points in the plate where displacements are constrained to be zero such as those on fixed edges. This limitation has been overcome in the present formulation.

3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Absence of reptation in highly confined polymers

We present results of mechanical stress relaxation measurements on polymers confined at the air-water interface in the form of a monolayer. Systematic measurements allow, to our knowledge, for the first time, observation of the scaling of the stress relaxation time of the highly confined polymers as a function of both surface concentration and molecular weight. The observed scaling is found to be very close to that expected for motion of unentangled polymer solutions with hydrodynamic interactions. Our experimental observations thus clearly rule out the possibility of entanglement and hence reptation as a mode of relaxation in such highly confined polymeric systems.

X-ray studies on crystalline complexes involving amino acids and peptides. Part XIV: Closed conformation and head-to-tail arrangement in a new crystal form of L-histidine L-aspartate monohydrate

A new form of L-histidine L-aspartate monohydrate crystallizes in space group P22 witha = 5.131(1),b = 6.881(1),c= 18.277(2) Å,β= 97.26(1)° and Z = 2. The structure has been solved by the direct methods and refined to anR value of 0.044 for 1377 observed reflections. Both the amino acid molecules in the complex assume the energetically least favourable allowed conformation with the side chains staggered between the α-amino and α-scarboxylate groups. This results in characteristic distortions in some bond angles. The unlike molecules aggregate into alternating double layers with water molecules sandwiched between the two layers in the aspartate double layer. The molecules in each layer are arranged in a head-to-tail fashion. The aggregation pattern in the complex is fundamentally similar to that in other binary complexes involving commonly occurring L amino acids, although the molecules aggregate into single layers in them. The distribution of crystallographic (and local) symmetry elements in the old form of the complex is very different from that in the new form. So is the conformation of half the histidine molecules. Yet, the basic features of molecular aggregation, particularly the nature and the orientation of head-to-tail sequences, remain the same in both the forms. This supports the thesis that the characteristic aggregation patterns observed in crystal structures represent an intrinsic property of amino acid aggregation.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.