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

Statistics and Characteristics of Spatio-Temporally Rare Intense Events in Complex Ginzburg-Landau Models

We study the statistics and characteristics of rare intense events in two types of two dimensional Complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapse-like solutions which approach the infinite amplitude solutions of the nonlinear Schr\"{o}dinger (NLS) equation in an appropriate parameter regime. We also determine the probability distribution function (PDF) of the amplitude of the CGL solutions, which is found to be approximately described by a stretched exponential distribution, $P(|A|) \approx e^{-|A|^\eta}$, where $\eta < 1$. This non-Gaussian PDF is explained by the nonlinear characteristics of individual bursts combined with the statistics of bursts. Our results suggest a general picture in which an incoherent background of weakly interacting waves, occasionally, `by chance', initiates intense, coherent, self-reinforcing, highly nonlinear events.Comment: 7 pages, 9 figure

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

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to an amplitude instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength

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

Two and three-dimensional oscillons in nonlinear Faraday resonance

We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

Quasiparticle Inelastic Lifetime from Paramagnons in Disordered Superconductors

The paramagnon contribution to the quasiparticle inelastic scattering rate in disordered superconductors is presented. Using Anderson's exact eigenstate formalism, it is shown that the scattering rate is Stoner enhanced and is further enhanced by the disorder relative to the clean case in a manner similar to the disorder enhancement of the long-range Coulomb contribution. The results are discussed in connection with the possibility of conventional or unconventional superconductivity in the borocarbides. The results are compared to recent tunneling experiments on LuNi$_{2}$B$_{2}$C.Comment: 5 pages, no figure