Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Properties of the SR Ca-ATPase in an Open Microsomal Membrane Preparation

SR vesicles isolated from rabbit muscle were treated by a SDS incubation and subsequent dialysis to obtain open membrane fragments that allow a direct access to the luminal membrane surface and especially to the ion-binding sites in the P-E2 conformation of the Ca-ATPase. The open membrane fragments showed about 80% of the enzyme activity in the untreated membranes. Pump function was investigated by using electrochromic styryl dyes. The kinetic properties of cytoplasmic ion binding showed no significant differences between the Ca-ATPases in SR vesicles and in membrane fragments. From pH-dependent Ca2+ binding it could be deduced that due to the SDS treatment the density of negatively charged lipid was increased by one elementary charge per 12 lipid molecules. Major differences between Ca-ATPase from SR vesicles and membrane fragments were the respective fluorescence amplitudes. This effect is, however, produced by dye-lipid interaction and not by pump function. It was demonstrated that time-resolved kinetics may be study by the use of caged compounds such as caged ATP or caged calcium also in the case of the membrane fragments

Interaction between habitat limitation and dispersal limitation is modulated by species life history and external conditions: a stochastic matrix model approach

Traditionally, species absence in a community is ascribed either to dispersal limitation (i.e., the inability of propagules of a species to reach a site) or to habitat limitation (abiotic or biotic conditions of a site prevent species from forming a viable population); sowing experiments can then distinguish between these two mechanisms. In our view, the situation is even more complicated. To demonstrate the complexity of the problem, we designed and applied simulations based on an extension of matrix models covering effects of propagule pressure and habitat limitation, and reflecting various characteristics of a species and of a habitat. These included life history, fecundity, seed bank viability of a species, habitat carrying capacity and disturbances. All the investigated factors affected proportion of occupied habitats. Whereas they can, to a large extent, compensate for each other, simultaneous decrease of habitat suitability and propagule input can be detrimental to the survival of a population. Our model demonstrated that in many cases, the absence of a species in a community is of stochastic nature, and result of interaction of species life history and various external conditions, and thus cannot be simply attributed to a single cause. The model results are supported with examples of case studies. The results also explain some well-known ecological phenomena, as decrease of niche breadth from the center to the margins of area of distribution. Finally, the model also suggests some caveats in interpretation of the results of sowing experiments. | Supporting Information Supporting Information </supplementary-material

Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium

Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders, as exact solutions of Maxwell's equations in the presence of vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2+1)-D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one fourth of the wavelength.Comment: 4 pages, 4 figure

Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index

We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out-of-phase the competition between both effects results in remarkable shape transformations of the solitons which profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth.Comment: 11 pages, 3 figures, to appear in Optics Letter

Finite-Band-width Effects on the Transition Temperature and NMR Relaxation Rate of Impure Superconductors

We study the thermodynamic properties of impure superconductors by explicitly taking into consideration the finiteness of electronic bandwidths within the phonon-mediated Eliashberg formalism. For a finite electronic bandwidth, the superconducting transition temperature, $T_c$, is suppressed by nonmagnetic impurity scatterings. This is a consequence of a reduction in the effective electron-phonon coupling, $\lambda_{eff}$. The reduced $\lambda_{eff}$ is reflected in the observation that the coherence peak in $1/(T_1 T)$, where $T_1$ is the nuclear spin-lattice relaxation time and $T$ is the temperature, is enhanced by impurity scatterings for a finite bandwidth. Calculations are presented for $T_c$ and $1/(T_1 T)$ as bandwidths and impurity scattering rates are varied. Implications for doped C$_{60}$ superconductors are discussed in connection with $T_c$ and $1/T_1$ measurements.Comment: 10 pages. REVTeX. 5 postscript figures. Scheduled to be published in Physical Review B, March 1. The previous submission is revised and two figures are adde

Stable two-dimensional solitons in nonlinear lattices

We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into a linear material. We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solitons are also supported by the nonlinear lattices, provided that the nonlinearity exhibits saturation.Comment: 12 pages, 3 figures, to appear in Optics Letter

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation,without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.Comment: 7 figure

Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

Three Dimensional Simulation of Jet Formation in Collapsing Condensates

We numerically study the behavior of collapsing and exploding condensates using the parameters of the experiments by E.A. Donley et al. [Nature, 412, 295, (2001)]. Our studies are based on a full three-dimensional numerical solution of the Gross-Pitaevskii equation (GPE) including three body loss. We determine the three body loss rate from the number of remnant condensate atoms and collapse times and obtain only one possible value which fits with the experimental results. We then study the formation of jet atoms by interrupting the collapse and find very good agreement with the experiment. Furthermore we investigate the sensitivity of the jets to the initial conditions. According to our analysis the dynamics of the burst atoms is not described by the GPE with three body loss incorporated.Comment: 9 pages, 10 figure