Effect of ion hydration on the first-order transition in the sequential wetting of hexane on brine

In recent experiments, a sequence of changes in the wetting state (`wetting transitions') has been observed upon increasing the temperature in systems consisting of pentane on pure water and of hexane on brine. This sequence of two transitions is brought about by an interplay of short-range and long-range interactions between substrate and adsorbate. In this work, we argue that the short-range interaction (contact energy) between hexane and pure water remains unchanged due to the formation of a depletion layer (a thin `layer' of pure water which is completely devoid of ions) at the surface of the electrolyte and that the presence of the salt manifests itself only in a modification of the long-range interaction between substrate and adsorbate. In a five-layer calculation considering brine, water, the first layer of adsorbed hexane molecules, liquid hexane, and vapor, we determine the new long-range interaction of brine with the adsorbate {\em across} the water `layer'. According to the recent theory of the excess surface tension of an electrolyte by Levin and Flores-Mena, this water `layer' is of constant, i.e.\ salt-concentration independent, thickness $\delta$, with $\delta$ being the hydrodynamic radius of the ions in water. Our results are in good agreement with the experimental ones.Comment: 27 pages, 2 tables, 4 figure

Effective coupling between two Brownian particles

We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is non-linear in the variables of interest and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method and besides recovering all the local dynamical properties for each particle we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms.Comment: 4 pages, 1 figur

Distances and classification of amino acids for different protein secondary structures

Window profiles of amino acids in protein sequences are taken as a description of the amino acid environment. The relative entropy or Kullback-Leibler distance derived from profiles is used as a measure of dissimilarity for comparison of amino acids and secondary structure conformations. Distance matrices of amino acid pairs at different conformations are obtained, which display a non-negligible dependence of amino acid similarity on conformations. Based on the conformation specific distances clustering analysis for amino acids is conducted.Comment: 15 pages, 8 figure

Spatial Resonator Solitons

Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons and phase solitons have been experimentally shown to exist. Many links appear to exist to fields different from optics, such as fluids, phase transitions or particle physics. These spatial resonator solitons are bistable and due to their mobility suggest schemes of information processing not possible with the fixed bistable elements forming the basic ingredient of traditional electronic processing. The recent demonstration of existence and manipulation of spatial solitons in emiconductor microresonators represents a step in the direction of such optical parallel processing applications. We review pattern formation and solitons in a general context, show some proof of principle soliton experiments on slow systems, and describe in more detail the experiments on semiconductor resonator solitons which are aimed at applications.Comment: 15 pages, 32 figure

The twist-2 Compton operator and its hidden Wandzura-Wilczek and Callan-Gross relations

Power corrections for virtual Compton scattering at leading twist are etermined at operator level. From the complete off-cone representation of the twist-2 Compton operator integral representations for the trace, antisymmetric and symmetric part of that operator are derived. The operator valued invariant functions are written in terms of iterated operators and may lead to interrelations. For matrix elements they go over into relations for generalized parton distributions. -- Reducing to the s-channel relevant part one gets operator pre-forms of the Wandzura-Wilczek and the (target mass corrected) Callan-Gross relations whose structure is exactly the same as known from the case of deep inelastic scattering; taking non-forward matrix elements one reproduces earlier results [B. Geyer, D. Robaschik and J. Eilers, Nucl. Phys. B 704 (2005) 279] for the absorptive part of the virtual Compton amplitude. -- All these relations, obtained without any approximation or using equations of motion, are determined solely by the twist-2 structure of the underlying operator and, therefore, are purely of geometric origin.Comment: 13 pages, Latex 2e, Introduction shortend, Section Prerequisites added, more obvious formulations used, some formulas rewritten as well as added, conclusions extended, references added. Final version as appearing in PR

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio

Thermal equilibrium of two quantum Brownian particles

The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the conventional Brownian motion when the two particles are far apart and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.Comment: 8 pages, 1 figur