Stochastic Process Associated with Traveling Wave Solutions of the Sine-Gordon Equation

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave structure. The derived stochastic processes are analyzed numerically. An interpretation of the behaviors of the stochastic processes is given in terms of the equation of motion.Comment: 12 pages, 9 figures; corrected typo

Exact results on the dynamics of multi-component Bose-Einstein condensate

We study the time-evolution of the two dimensional multi-component Bose-Einstein condensate in an external harmonic trap with arbitrary time-dependent frequency. We show analytically that the time-evolution of the total mean-square radius of the wave-packet is determined in terms of the same solvable equation as in the case of a single-component condensate. The dynamics of the total mean-square radius is also the same for the rotating as well as the non-rotating multi-component condensate. We determine the criteria for the collapse of the condensate at a finite time. Generalizing our previous work on a single-component condensate, we show explosion-implosion duality in the multi-component condensate.Comment: Two-column 6 pages, RevTeX, no figures(v1); Added an important reference, version to appear in Physical Review A (v2

Methylated DNA recognition during the reversal of epigenetic silencing is regulated by cysteine and cerine residues in the Epstein-Barr Virus lytic switch protein

Epstein-Barr virus (EBV) causes infectious mononucleosis and is associated with various malignancies, including Burkitt's lymphoma and nasopharyngeal carcinoma. Like all herpesviruses, the EBV life cycle alternates between latency and lytic replication. During latency, the viral genome is largely silenced by host-driven methylation of CpG motifs and, in the switch to the lytic cycle, this epigenetic silencing is overturned. A key event is the activation of the viral BRLF1 gene by the immediate-early protein Zta. Zta is a bZIP transcription factor that preferentially binds to specific response elements (ZREs) in the BRLF1 promoter (Rp) when these elements are methylated. Zta's ability to trigger lytic cycle activation is severely compromised when a cysteine residue in its bZIP domain is mutated to serine (C189S), but the molecular basis for this effect is unknown. Here we show that the C189S mutant is defective for activating Rp in a Burkitt's lymphoma cell line. The mutant is compromised both in vitro and in vivo for binding two methylated ZREs in Rp (ZRE2 and ZRE3), although the effect is striking only for ZRE3. Molecular modeling of Zta bound to methylated ZRE3, together with biochemical data, indicate that C189 directly contacts one of the two methyl cytosines within a specific CpG motif. The motif's second methyl cytosine (on the complementary DNA strand) is predicted to contact S186, a residue known to regulate methyl-ZRE recognition. Our results suggest that C189 regulates the enhanced interaction of Zta with methylated DNA in overturning the epigenetic control of viral latency. As C189 is conserved in many bZIP proteins, the selectivity of Zta for methylated DNA may be a paradigm for a more general phenomenon

Effects of ac-field amplitude on the dielectric susceptibility of relaxors

The thermally activated flips of the local spontaneous polarization in relaxors were simulated to investigate the effects of the applied-ac-field amplitude on the dielectric susceptibility. It was observed that the susceptibility increases with increasing the amplitude at low temperatures. At high temperatures, the susceptibility experiences a plateau and then drops. The maximum in the temperature dependence of susceptibility shifts to lower temperatures when the amplitude increases. A similarity was found between the effects of the amplitude and frequency on the susceptibility.Comment: 8 pages, 7 figures, Phys. Rev. B (in July 1st

Nonlocal interactions prevent collapse in negative scattering length Bose-Einstein gases

We study the effect of nonlocality on the collapse properties of a self-focusing Nonlinear Schr\"odinger system related to Bose-Einstein condensation problems. Using a combination of moment techniques, time dependent variational methods and numerical simulations we present evidences in support of the hypothesis that nonlocal attractively interacting condensates cannot collapse when the dominant interaction term is due to finite range interactions. Instead there apppear oscillations of the wave packet with a localized component whose size is of the order of the range of interactions. We discuss the implications of the results to collapse phenomena in negative scattering length Bose-Einstein condensates

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure

Nonlinear magnetoinductive transmission lines

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.Comment: 11 pages, 11 figures, submitted to International Journal of Bifurcation and Chao

Solutions of Gross-Pitaevskii equations beyond the hydrodynamic approximation: Application to the vortex problem

We develop the multiscale technique to describe excitations of a Bose-Einstein condensate (BEC) whose characteristic scales are comparable with the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory we derive approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times of the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by the numerical simulations.Comment: To appear in Phys. Rev.

OGLE-2013-BLG-0102LA,B: Microlensing binary with components at star/brown-dwarf and brown-dwarf/planet boundaries

We present the analysis of the gravitational microlensing event OGLE-2013-BLG-0102. The light curve of the event is characterized by a strong short-term anomaly superposed on a smoothly varying lensing curve with a moderate magnification $A_{\rm max}\sim 1.5$. It is found that the event was produced by a binary lens with a mass ratio between the components of $q = 0.13$ and the anomaly was caused by the passage of the source trajectory over a caustic located away from the barycenter of the binary. From the analysis of the effects on the light curve due to the finite size of the source and the parallactic motion of the Earth, the physical parameters of the lens system are determined. The measured masses of the lens components are $M_{1} = 0.096 \pm 0.013~M_{\odot}$ and $M_{2} = 0.012 \pm 0.002~M_{\odot}$, which correspond to near the hydrogen-burning and deuterium-burning mass limits, respectively. The distance to the lens is $3.04 \pm 0.31~{\rm kpc}$ and the projected separation between the lens components is $0.80 \pm 0.08~{\rm AU}$.Comment: 6 figures, 2 tables, ApJ submitte