Parametrically driven dark solitons

We show that unlike the bright solitons, the parametrically driven kinks are immune from instabilities for all dampings and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of stable kinks and their complexes can travel with nonzero velocities.     

A DFT investigation of anthocyanidins

A theoretical analysis of anthocyanidins, a class of natural plant pigments, has been conducted using density functional theory at the B3LYP/6-31G(d) level. It is found that these compounds are non-planar, with the 2-phenyl ring twisted relative to the benzopyrylium rings. TD-DFT calculations reveal a first excited state dominated by two orbital transitions, including the HOMO–LUMO transition. From a comparison of these molecular orbitals with those of related compounds, and from the known chemistry of these compounds, it is suggested that anthocyanidins should be regarded as natural, stable carbocations.     

Canonical Proper-Time Formulation of Relativistic Particle Dynamics. II

Our purpose in this paper is to provide theframework for a generalization of classical mechanicsand electrodynamics, including Maxwell's theory, whichis simple, technically correct, and requires noadditional work for the quantum case. We first show thatthere are two other definitions of proper-time, eachhaving equal status with the Minkowski definition. Weuse the first definition, called the proper-velocity definition, to construct a transformationtheory which fixes the proper-time of a given physicalsystem for all observers. This leads to a new invariancegroup and a generalization of Maxwell's equations left covariant under the action of this group.The second definition, called the canonical variablesdefinition, has the unique property that it isindependent of the number of particles. This definition leads to a general theory of directlyinteracting relativistic particles. We obtain theLorentz force for one particle (using its proper-time),and the Lorentz force for the total system (using theglobal proper-time). Use of the global proper-time tocompute the force on one particle gives the Lorentzforce plus a dissipative term corresponding to thereaction of this particle back on the cause of itsacceleration (Newton's third law). The wave equation derivedfrom Maxwell's equations has an additional term, firstorder in the proper-time. This term arisesinstantaneously with acceleration. This shows explicitly that the longsought origin of radiationreaction is inertial resistance to changes in particlemotion. The field equations carry intrinsic informationabout the velocity and acceleration of the particles in the system. It follows that our theory isnot invariant under time reversal, so that the existenceof radiation introduces an arrow for the (proper-time ofthe) system.     

Temperature dependent deuterium quadrupole coupling constants of short hydrogen bonds

Very short hydrogen bonds universally show large positive dependences of the deuterium NMR quadrupolar coupling constant with temperature. We present temperature dependent NMR data for eight such systems, with OO distances of between 238 and 250 pm, and show we can model the temperature dependences by density functional methods, as long as proper attention is paid to intermolecular effects and intermode couplings.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Smooth curve interpolation

In a recent paper [1] a method was presented for smooth curve interpolation by means of minimising the energy of an idealised elastic beam constrained to pass through given data points. This method of obtaining the curve required an enormous amount of computation, since it involved the repeated solution of a fourth order differential equation and the minimisation of a function of many variables, the number of variables being equal to the number of data points. In this paper a much simpler method is presented for finding the minimum energy curve in which the minimisation procedure is eliminated. An ALGOL procedure to perform the curve fit is supplied.