Impact of Stone-Wales and lattice vacancy defects on the electro-thermal transport of the free standing structure of metallic ZGNR

We report the effect of topological as well as lattice vacancy defects on the electro-thermal transport properties of the metallic zigzag graphene nano ribbons at their ballistic limit. We employ the density function theory-Non equilibrium green's function combination to calculate the transmission details. We then present an elaborated study considering the variation in the electrical current and the heat current transport with the change in temperature as well as the voltage gradient across the nano ribbons. The comparative analysis shows, that in the case of topological defects, such as the Stone-Wales defect, the electrical current transport is minimum. Besides, for the voltage gradient of 0.5 Volt and the temperature gradient of 300 K, the heat current transport reduces by similar to 62 % and similar to 50% for the cases of Stones-Wales defect and lattice vacancy defect respectively, compared to that of the perfect one.

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Orientational relaxation in a random dipolar lattice: Wave-number and frequency dependence

In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

Multiscale modeling of lamellar mesophases

The mesoscale simulation of a lamellar mesophase based on a free energy functional is examined with the objective of determining the relationship between the parameters in the model and molecular parameters. Attention is restricted to a symmetric lamellar phase with equal volumes of hydrophilic and hydrophobic components. Apart from the lamellar spacing, there are two parameters in the free energy functional. One of the parameters, r, determines the sharpness of the interface, and it is shown how this parameter can be obtained from the interface profile in a molecular simulation. The other parameter, A, provides an energy scale. Analytical expressions are derived to relate these parameters to r and A to the bending and compression moduli and the permeation constant in the macroscopic equation to the Onsager coefficient in the concentration diffusion equation. The linear hydrodynamic response predicted by the theory is verified by carrying out a mesoscale simulation using the lattice-Boltzmann technique and verifying that the analytical predictions are in agreement with simulation results. A macroscale model based on the layer thickness field and the layer normal field is proposed, and the relationship between the parameters in the macroscale model from the parameters in the mesoscale free energy functional is obtained.

An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

New Look at Kirchhoff's Theory of Plates

KIRCHHOFF’S theory [1] and the first-order shear deformation theory (FSDT) [2] of plates in bending are simple theories and continuously used to obtain design information. Within the classical small deformation theory of elasticity, the problem consists of determining three displacements, u, v, and w, that satisfy three equilibrium equations in the interior of the plate and three specified surface conditions. FSDT is a sixth-order theory with a provision to satisfy three edge conditions and maintains, unlike in Kirchhoff’s theory, independent linear thicknesswise distribution of tangential displacement even if the lateral deflection, w, is zero along a supported edge. However, each of the in-plane distributions of the transverse shear stresses that are of a lower order is expressed as a sum of higher-order displacement terms. Kirchhoff’s assumption of zero transverse shear strains is, however, not a limitation of the theory as a first approximation to the exact 3-D solution.

Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

On the shear deformation theory for dynamic analysis of beams

Timoshenko's shear deformation theory is widely used for the dynamical analysis of shear-flexible beams. This paper presents a comparative study of the shear deformation theory with a higher order model, of which Timoshenko's shear deformation model is a special case. Results indicate that while Timoshenko's shear deformation theory gives reasonably accurate information regarding the set of bending natural frequencies, there are considerable discrepancies in the information it gives regarding the mode shapes and dynamic response, and so there is a need to consider higher order models for the dynamical analysis of flexure of beams.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Proton spin lattice relaxation in lithium ammonium sulphate LiNH4SO4

Lithium ammonium sulphate (LAS) undergoes a phase transition at TC1=459.5K from a paraelectric phase (phase I) to a ferroelectric phase (phase II) and again at TC2=283K to a polar ferroelastic phase (phase III). Proton spin lattice relaxation time measured at 10 MHz in powdered LAS in the temperature range 480 to 77K shows discontinuous changes at the two transitions.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

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.