Perturbative spectrum of Trapped Weakly Interacting Bosons in Two Dimensions

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-N expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.Comment: Revtex, 10 pages, 1 table, to appear in Phys. Rev.

Infinite-dimensional diffusions as limits of random walks on partitions

The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group. This problem leads to a family {P_z} of probability measures, the z-measures, which depend on the complex parameter z. The z-measures live on the Thoma simplex, an infinite-dimensional compact space which is a kind of dual object to the infinite symmetric group. The aim of the paper is to introduce stochastic dynamics related to the z-measures. Namely, we construct a family of diffusion processes in the Toma simplex indexed by the same parameter z. Our diffusions are obtained from certain Markov chains on partitions of natural numbers n in a scaling limit as n goes to infinity. These Markov chains arise in a natural way, due to the approximation of the infinite symmetric group by the increasing chain of the finite symmetric groups. Each z-measure P_z serves as a unique invariant distribution for the corresponding diffusion process, and the process is ergodic with respect to P_z. Moreover, P_z is a symmetrizing measure, so that the process is reversible. We describe the spectrum of its generator and compute the associated (pre)Dirichlet form.Comment: AMSTex, 33 pages. Version 2: minor changes, typos corrected, to appear in Prob. Theor. Rel. Field

Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial text overlap with arXiv:0712.105

Does modafinil enhance activity of patients with myotonic dystrophy?: A double-blind placebo-controlled crossover study

We performed a double-blind placebo-controlled crossover study in 13 patients with myotonic dystrophy to address the question whether modafinil, known to improve hypersomnolence in myotonic dystrophy, may improve levels of activity as well. We used the Epworth Sleepiness Scale as a measure of hypersomnolence and a structured interview of the patient and the partner or housemate as a measure of activity. We additionally used a restricted form of the RAND-36 to relate a possible improvement of activity to perceived general health. We confirmed earlier positive findings of modafinil regarding reduced somnolence (p = 0.015), but no significant effects were seen regarding activity levels (p = 0.2 for patients’ self-reports and 0.5 for partners’ reports)

Connecting Numerical Relativity and Data Analysis of Gravitational Wave Detectors

Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict gravitational wave signals from likely sources are crucial for the success of this endeavor. Modeling binary black hole sources of gravitational radiation requires solving the Eintein equations of General Relativity using powerful computer hardware and sophisticated numerical algorithms. This proceeding presents where we are in understanding ground-based gravitational waves resulting from the merger of black holes and the implications of these sources for the advent of gravitational-wave astronomy.Comment: Appeared in the Proceedings of 2014 Sant Cugat Forum on Astrophysics. Astrophysics and Space Science Proceedings, ed. C.Sopuerta (Berlin: Springer-Verlag

Generalized Green Functions and current correlations in the TASEP

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the ${Airy}_2$ process.Comment: 46 pages, 3 figure

Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited

This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.Comment: 30 pages, 7 figures, corrected typo

Carbon nanotubes in TiO₂ nanofiber photoelectrodes for high-performance perovskite solar cells

1D semiconducting oxides are unique structures that have been widely used for photovoltaic (PV) devices due to their capability to provide a direct pathway for charge transport. In addition, carbon nanotubes (CNTs) have played multifunctional roles in a range of PV cells because of their fascinating properties. Herein, the influence of CNTs on the PV performance of 1D titanium dioxide nanofiber (TiO2 NF) photoelectrode perovskite solar cells (PSCs) is systematically explored. Among the different types of CNTs, single-walled CNTs (SWCNTs) incorporated in the TiO2 NF photoelectrode PSCs show a significant enhancement (≈40%) in the power conversion efficiency (PCE) as compared to control cells. SWCNTs incorporated in TiO2 NFs provide a fast electron transfer within the photoelectrode, resulting in an increase in the short-circuit current (J sc) value. On the basis of our theoretical calculations, the improved open-circuit voltage (V oc) of the cells can be attributed to a shift in energy level of the photoelectrodes after the introduction of SWCNTs. Furthermore, it is found that the incorporation of SWCNTs into TiO2 NFs reduces the hysteresis effect and improves the stability of the PSC devices. In this study, the best performing PSC device constructed with SWCNT structures achieves a PCE of 14.03%

Understanding Hematopoietic Stem Cell Development through Functional Correlation of Their Proliferative Status with the Intra-aortic Cluster Architecture

During development, hematopoietic stem cells (HSCs) emerge in the aorta-gonad-mesonephros (AGM) region through a process of multi-step maturation and expansion. While proliferation of adult HSCs is implicated in the balance between self-renewal and differentiation, very little is known about the proliferation status of nascent HSCs in the AGM region. Using Fucci reporter mice that enable in vivo visualization of cell-cycle status, we detect increased proliferation during pre-HSC expansion followed by a slowing down of cycling once cells start to acquire a definitive HSC state, similar to fetal liver HSCs. We observe time-specific changes in intra-aortic hematopoietic clusters corresponding to HSC maturation stages. The proliferative architecture of the clusters is maintained in an orderly anatomical manner with slowly cycling cells at the base and more actively proliferating cells at the more apical part of the cluster, which correlates with c-KIT expression levels, thus providing an anatomical basis for the role of SCF in HSC maturation

Negatively Charged Excitons and Photoluminescence in Asymmetric Quantum Well

We study photoluminescence (PL) of charged excitons ($X^-$) in narrow asymmetric quantum wells in high magnetic fields B. The binding of all $X^-$ states strongly depends on the separation $\delta$ of electron and hole layers. The most sensitive is the ``bright'' singlet, whose binding energy decreases quickly with increasing $\delta$ even at relatively small B. As a result, the value of B at which the singlet--triplet crossing occurs in the $X^-$ spectrum also depends on $\delta$ and decreases from 35 T in a symmetric 10 nm GaAs well to 16 T for $\delta=0.5$ nm. Since the critical values of $\delta$ at which different $X^-$ states unbind are surprisingly small compared to the well width, the observation of strongly bound $X^-$ states in an experimental PL spectrum implies virtually no layer displacement in the sample. This casts doubt on the interpretation of PL spectra of heterojunctions in terms of $X^-$ recombination