Extended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method

We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than previous.Comment: 9 page

Theory and simulations of rigid polyelectrolytes

We present theoretical and numerical studies on stiff, linear polyelectrolytes within the framework of the cell model. We first review analytical results obtained on a mean-field Poisson-Boltzmann level, and then use molecular dynamics simulations to show, under which circumstances these fail quantitatively and qualitatively. For the hexagonally packed nematic phase of the polyelectrolytes we compute the osmotic coefficient as a function of density. In the presence of multivalent counterions it can become negative, leading to effective attractions. We show that this results from a reduced contribution of the virial part to the pressure. We compute the osmotic coefficient and ionic distribution functions from Poisson-Boltzmann theory with and without a recently proposed correlation correction, and also simulation results for the case of poly(para-phenylene) and compare it to recently obtained experimental data on this stiff polyelectrolyte. We also investigate ion-ion correlations in the strong coupling regime, and compare them to predictions of the recently advocated Wigner crystal theories.Comment: 32 pages, 15 figures, proceedings of the ASTATPHYS-MEX-2001, to be published in Mol. Phy

Radius of a Photon Beam with Orbital Angular Momentum

We analyze the transverse structure of the Gouy phase shift in light beams carrying orbital angular momentum and show that the Gouy radius $r_G$ characterizing the transverse structure grows as $\sqrt{2p+|\ell|+1}$ with the nodal number $p$ and photon angular momentum number $\ell$. The Gouy radius is shown to be closely related to the root-mean-square radius of the beam, and the divergence of the radius away from the focal plane is determined. Finally, we analyze the rotation of the Poynting vector in the context of the Gouy radius.Comment: 11 page

Non-mean-field theory of anomalously large double-layer capacitance

Mean-field theories claim that the capacitance of the double-layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double-layer capacitor is substantially smaller. We propose an alternate, non-mean-field theory of the ionic double-layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely-charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double-layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions, so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our ``one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudo-capacitance.Comment: 19 pages, 14 figures; some Monte Carlo results and a section about aqueous solutions adde

CD5 expression promotes IL-10 production through activation of the MAPK/Erk pathway and upregulation of TRPC1 channels in B lymphocytes.

CD5 is constitutively expressed on T cells and a subset of mature normal and leukemic B cells in patients with chronic lymphocytic leukemia (CLL). Important functional properties are associated with CD5 expression in B cells, including signal transducer and activator of transcription 3 activation, IL-10 production and the promotion of B-lymphocyte survival and transformation. However, the pathway(s) by which CD5 influences the biology of B cells and its dependence on B-cell receptor (BCR) co-signaling remain unknown. In this study, we show that CD5 expression activates a number of important signaling pathways, including Erk1/2, leading to IL-10 production through a novel pathway independent of BCR engagement. This pathway is dependent on extracellular calcium (Ca2+) entry facilitated by upregulation of the transient receptor potential channel 1 (TRPC1) protein. We also show that Erk1/2 activation in a subgroup of CLL patients is associated with TRPC1 overexpression. In this subgroup of CLL patients, small inhibitory RNA (siRNA) for CD5 reduces TRPC1 expression. Furthermore, siRNAs for CD5 or for TRPC1 inhibit IL-10 production. These findings provide new insights into the role of CD5 in B-cell biology in health and disease and could pave the way for new treatment strategies for patients with B-CLL

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Electrolytic depletion interactions

We consider the interactions between two uncharged planar macroscopic surfaces immersed in an electrolyte solution which are induced by interfacial selectivity. These forces are taken into account by introducing a depletion free-energy density functional, in addition to the usual mean-field Poisson-Boltzmann functional. The minimization of the total free-energy functional yields the density profiles of the microions and the electrostatic potential. The disjoining pressure is obtained by differentiation of the total free energy with respect to the separation of the surfaces, holding the range and strength of the depletion forces constant. We find that the induced interaction between the two surfaces is always repulsive for sufficiently large separations, and becomes attractive at shorter separations. The nature of the induced interactions changes from attractive to repulsive at a distance corresponding to the range of the depletion forces.Comment: 17 pages, 4 Postscript figures, submitted to Physical Review

Axion-like-particle search with high-intensity lasers

We study ALP-photon-conversion within strong inhomogeneous electromagnetic fields as provided by contemporary high-intensity laser systems. We observe that probe photons traversing the focal spot of a superposition of Gaussian beams of a single high-intensity laser at fundamental and frequency-doubled mode can experience a frequency shift due to their intermittent propagation as axion-like-particles. This process is strongly peaked for resonant masses on the order of the involved laser frequencies. Purely laser-based experiments in optical setups are sensitive to ALPs in the $\mathrm{eV}$ mass range and can thus complement ALP searches at dipole magnets.Comment: 25 pages, 2 figure

Genome Trees from Conservation Profiles

The concept of the genome tree depends on the potential evolutionary significance in the clustering of species according to similarities in the gene content of their genomes. In this respect, genome trees have often been identified with species trees. With the rapid expansion of genome sequence data it becomes of increasing importance to develop accurate methods for grasping global trends for the phylogenetic signals that mutually link the various genomes. We therefore derive here the methodological concept of genome trees based on protein conservation profiles in multiple species. The basic idea in this derivation is that the multi-component “presence-absence” protein conservation profiles permit tracking of common evolutionary histories of genes across multiple genomes. We show that a significant reduction in informational redundancy is achieved by considering only the subset of distinct conservation profiles. Beyond these basic ideas, we point out various pitfalls and limitations associated with the data handling, paving the way for further improvements. As an illustration for the methods, we analyze a genome tree based on the above principles, along with a series of other trees derived from the same data and based on pair-wise comparisons (ancestral duplication-conservation and shared orthologs). In all trees we observe a sharp discrimination between the three primary domains of life: Bacteria, Archaea, and Eukarya. The new genome tree, based on conservation profiles, displays a significant correspondence with classically recognized taxonomical groupings, along with a series of departures from such conventional clusterings