On a slender dry patch in a liquid film draining under gravity down an inclined plane

In this paper two similarity solutions describing a steady, slender, symmetric dry patch in an infinitely wide liquid film draining under gravity down an inclined plane are obtained. The first solution, which predicts that the dry patch has a parabolic shape and that the transverse profile of the free surface always has a monotonically increasing shape, is appropriate for weak surface-tension effects and far from the apex of the dry patch. The second solution, which predicts that the dry patch has a quartic shape and that the transverse profile of the free surface has a capillary ridge near the contact line and decays in an oscillatory manner far from it, is appropriate for strong surface-tension effects (in particular, when the plane is nearly vertical) and near (but not too close) to the apex of the dry patch. With the average volume flux per unit width (or equivalently with the uniform height of the layer far from the dry patch) prescribed, both solutions contain a free parameter. For each value of this parameter there is a unique solution in the first case and either no solution or a one-parameter family of solutions in the second case. The solutions capture some of the qualitative features observed in experiments

Coupled Bose-Einstein condensate: Collapse for attractive interaction

We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two or three of the scattering lengths $a_{ij}$ for scattering of boson $i$ with $j$, $i,j = 1, 2$, are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.Comment: 5 pages and 9 figures, small changes mad

Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor

We present a mathematica package that performs the symbolic calculation of integrals of the form \int^{\infty}_0 e^{-x/u} x^n j_{\nu} (x) j_{\mu} (x) dx where $j_{\nu} (x)$ and $j_{\mu} (x)$ denote spherical Bessel functions of integer orders, with $\nu \ge 0$ and $\mu \ge 0$. With the real parameter $u>0$ and the integer $n$, convergence of the integral requires that $n+\nu +\mu \ge 0$. The package provides analytical result for the integral in its most simplified form. The novel symbolic method employed enables the calculation of a large number of integrals of the above form in a fraction of the time required for conventional numerical and Mathematica based brute-force methods. We test the accuracy of such analytical expressions by comparing the results with their numerical counterparts.Comment: 17 pages; updated references for the introductio

Bose-Einstein condensate collapse: a comparison between theory and experiment

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed at JILA with Bose-Einstein condensates of Rb-85, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. Besides the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally. Quantum field effects, such as fragmentation, that might account for these discrepancies are discussed.Comment: 4 pages, 2 figure

Mean-field description of collapsing and exploding Bose-Einstein condensates

We perform numerical simulation based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. on the dynamics of collapsing and exploding Bose-Einstein condensates of $^{85}$Rb atoms. They manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one and vice versa. In the actual experiment they changed suddenly the scattering length of atomic interaction from positive to a large negative value on a pre-formed condensate in an axially symmetric trap. Consequently, the condensate collapses and ejects atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical Review A, minor changes mad

Scaling limit of virtual states of triatomic systems

For a system with three identical atoms, the dependence of the $s-$wave virtual state energy on the weakly bound dimer and trimer binding energies is calculated in a form of a universal scaling function. The scaling function is obtained from a renormalizable three-body model with a pairwise Dirac-delta interaction. It was also discussed the threshold condition for the appearance of the trimer virtual state.Comment: 9 pages, 3 figure

Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field

The effect of a homogeneous magnetic field on surface-tension-driven B\'{e}nard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.Comment: 26 pages, 9 figure

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the molecules $^4$He$_3$, $^4$He$_2-^6$Li, $^4$He$_2-^7$Li and $^4$He$_2-^{23}$Na are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-delta interaction. The root-mean-square distance between two atoms of mass $m_A$ in a triatomic molecule are estimated to be of de order of ${\cal C}\sqrt{\hbar^2/[m_A(E_3-E_2)]}$, where $E_2$ is the dimer and $E_3$ the trimer binding energies, and ${\cal C}$ is a constant (varying from $\sim 0.6$ to $\sim 1$) that depends on the ratio between $E_2$ and $E_3$. Considering previous estimates for the trimer energies, we also predict the sizes of Rubidium and Sodium trimers in atomic traps.Comment: 7 pages, 2 figure

Telomere-based proliferative lifespan barriers in Werner-syndrome fibroblasts involve both p53-dependent and p53-independent mechanisms

Werner-syndrome fibroblasts have a reduced in vitro life span before entering replicative senescence. Although this has been thought to be causal in the accelerated ageing of this disease, controversy remains as to whether Werner syndrome is showing the acceleration of a normal cellular ageing mechanism or the occurrence of a novel Werner-syndrome-specific process. Here, we analyse the signalling pathways responsible for senescence in Werner-syndrome fibroblasts. Cultured Werner-syndrome (AG05229) fibroblasts senesced after approximately 20 population doublings with most of the cells having a 2N content of DNA. This was associated with hypophosphorylated pRb and high levels of p16(Ink4a) and p21(Waf1). Senescent AG05229 cells re-entered the cell cycle following microinjection of a p53-neutralizing antibody. Similarly, production of the human papilloma virus 16 E6 oncoprotein in presenescent AG05229 cells resulted in senescence being bypassed and extended cellular life span. Werner-syndrome fibroblasts expressing E6 did not proliferate indefinitely but reached a second proliferative lifespan barrier, termed M(int), that could be bypassed by forced production of telomerase in post-M1 E6-producing cells. The conclusions from these studies are that: (1) replicative senescence in Werner-syndrome fibroblasts is a telomere-induced p53-dependent event; and (2) the intermediate lifespan barrier M(int) is also a telomere-induced event, although it appears to be independent of p53. Werner-syndrome fibroblasts resemble normal human fibroblasts for both these proliferative lifespan barriers, with the strong similarity between the signalling pathway linking telomeres to cell-cycle arrest in Werner-syndrome and normal fibroblasts providing further support for the defect in Werner syndrome causing the acceleration of a normal ageing mechanism

Infrared optical properties of the spin-1/2 quantum magnet TiOClTiOCl

We report results on the electrodynamic response of $TiOCl$, a low-dimensional spin-1/2 quantum magnet that shows a spin gap formation for T$<T_{c1}$= 67 $K$. The Fano-like shape of a few selected infrared active phonons suggests an interaction between lattice vibrations and a continuum of low frequency (spin) excitations. The temperature dependence of the phonon mode parameters extends over a broad temperature range well above $T_{c1}$, indicating the presence of an extended fluctuation regime. In the temperature interval between 200 $K$ and $T_{c1}$ there is a progressive dimensionality crossover (from two to one), as well as a spectral weight shift from low towards high frequencies. This allows us to identify a characteristic energy scale of about 430 $K$, ascribed to a pseudo spin-gap