Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation

We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV equation in the presence of weak dissipative disorder in the linear growth/damping term. With the weak disorder in the system, the amplitude of solitary wave randomly fluctuates during evolution. We demonstrate numerically that the probability density function of a solitary wave parameter $\kappa$ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible $\kappa$ value.Comment: 8 pages, 4 figure

Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier

In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is completely random, or unbiased. For N-level systems, the 6-level ones are the smallest for which a tomographically efficient set of N+1 mutually unbiased bases (MUBs) has not been found. To facilitate the search, we numerically extend the classification of unbiased bases, or Hadamards, by incrementally adjusting relative phases in a standard basis. We consider the non-unitarity caused by small adjustments with a second order Taylor expansion, and choose incremental steps within the 4-dimensional nullspace of the curvature. In this way we prescribe a numerical integration of a 4-parameter set of Hadamards of order 6.Comment: 5 pages, 2 figure

Mapping the Evolution of Optically-Generated Rotational Wavepackets in a Room Temperature Ensemble of D2_2

A coherent superposition of rotational states in D$_2$ has been excited by nonresonant ultrafast (12 femtosecond) intense (2 $\times$ 10$^{14}$ Wcm$^{-2}$) 800 nm laser pulses leading to impulsive dynamic alignment. Field-free evolution of this rotational wavepacket has been mapped to high temporal resolution by a time-delayed pulse, initiating rapid double ionization, which is highly sensitive to the angle of orientation of the molecular axis with respect to the polarization direction, $\theta$. The detailed fractional revivals of the neutral D$_2$ wavepacket as a function of $\theta$ and evolution time have been observed and modelled theoretically.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. A. Full reference to follow.

Hopf algebras and characters of classical groups

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 200

Zeros of Rydberg-Rydberg Foster Interactions

Rydberg states of atoms are of great current interest for quantum manipulation of mesoscopic samples of atoms. Long-range Rydberg-Rydberg interactions can inhibit multiple excitations of atoms under the appropriate conditions. These interactions are strongest when resonant collisional processes give rise to long-range C_3/R^3 interactions. We show in this paper that even under resonant conditions C_3 often vanishes so that care is required to realize full dipole blockade in micron-sized atom samples.Comment: 10 pages, 4 figures, submitted to J. Phys.

Solitary vortex couples in viscoelastic Couette flow

We report experimental observation of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex couple ("diwhirl") in Couette flow with highly elastic polymer solutions. A unique property of the diwhirls is that they are stationary, in contrast to the usual localized wave structures in both Hamiltonian and dissipative systems which are stabilized by wave dispersion. It is also a new object in fluid dynamics - a couple of vortices that build a single entity somewhat similar to a magnetic dipole. The diwhirls arise as a result of a purely elastic instability through a hysteretic transition at negligible Reynolds numbers. It is suggested that the vortex flow is driven by the same forces that cause the Weissenberg effect. The diwhirls have a striking asymmetry between the inflow and outflow, which is also an essential feature of the suggested elastic instability mechanism.Comment: 9 pages (LaTeX), 5 Postscript figures, submitte

The quantitative significance of dissolved and particulate organic matter released during fragmentation of kelp in coastal waters

There are definite differences in the rate of utilisation of the components of the complex substrate represented by kelp debris. The primary photosynthate D-mannitol is used most rapidly, followed by sugars and finally alginates which comprise as much as 45% of the particulate debris. There are also seasonal differences in the efficiency of conversion of these components into bacterial biomass. During the summer months the gross conversion of carbon to bacterial biomass in the dissolved fraction of detritus is as high as 30% and may reach 66% when associated with particles ( = carbon: carbon conversion efficiency of 33%) whilst the value for the particulate fraction is approximately 11% . Because of the lower conversion efficiencies in the winter, annual conversion of carbon from kelp production to bacterial biomass through the first step in the decomposer food chain is approximately 14% but this value is as high as 22% in the summer months (= carbon: carbon conversion efficiency of 11%). The results suggest that annual bacterial production in the water column based solely on the degradation of kelp is approximately 11.5 g m-3 and could rise to as much as 18.1 g m-3 during the summer months. These values agree well with estimates of bacterial production based on the biomass of bacteria measured in the water column near to kelp beds

Linear Superposition in Nonlinear Equations

Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the elliptic functions.Comment: 7 pages, 1 figur