Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor

Evolution of a Network of Vortex Loops in HeII. Exact Solution of the "Rate Equation"

Evolution of a network of vortex loops in HeII due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function $n(l)$ of number of loops of length $l$ proposed by Copeland with coauthors. By using the special ansatz in the ''collision'' integral we have found the exact power-like solution of ''kinetic equation'' in stationary case. That solution is the famous equilibrium distribution $n(l)\varpropto l^{-5/2}$ obtained earlier in numerical calculations. Our result, however, is not equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of the vortex loop sizes. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of order of interline space. We also obtain that the decay of the vortex tangle obeys the Vinen equation, obtained earlier phenomenologically. We evaluate also the full rate of reconnection events. PACS-number 67.40Comment: 4 pages, submitted to PR

Gravitational effects on defect formation in melt grown photorefractive materials : bismuth silicate

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003.Includes bibliographical references (leaves 206-213).Photorefractivity is the modulation of index of refraction due to nonuniform illumination, and numerous applications have been demonstrated utilizing this nonlinear optical property. However, commercial production is seriously impeded by the inability to produce bulk material with the homogeneity of opto-electronic properties that is required for device applications. Bismuth Silicate, Bi12SiO20, (BSO) is a photorefractive material with outstanding properties including a fast response time and high sensitivity is studied. Its photorefractivity is due to a native defect whose exact nature and origin have not been unambiguously determined. Motivation for current research arose from unexplained optical variations observed in BSO that implicate convective interference as playing a role in native defect formation. Microgravity growth experiments are proposed in order to establish a controlled, convection-free environment to study the origin and nature of the critical native defect. This work aims at resolving critical aspects of performing quantitative microgravity growth experiments that include the interaction of BSO melts with its confinement material; development and characterization of a vertical Bridgman-Stockbarger growth system with a quantifiable, reproducible, and controllable thermal environment; and Bridgman-Stockbarger growth experiments. A comparative analysis of crystals was done in order to establish the relationship between variations in opto-electronic properties as a function of changes in growth conditions. Wetting experiments revealed the sessile drop method to be inappropriate for the BSO-platinum system due to grain boundary pinning. No fundamental difference between the wetting behavior in a terrestrial and a low gravity environment was observed.(cont.) Results from the comparative analysis indicate a lower defect concentration in Bridgman-Stockbarger material as compared to Czochralski material. The ambient atmosphere during processing and high temperature annealing was found affect material response, including removal of the photochromic response and decrease of carrier lifetime. The lack of the critical defect in hydrothermal BSO, and its existence in all melt grown material indicates that the melt plays a fundamental role in its formation. Clustering in the melt is implicated in the literature from nonlinear melt properties. It is therefore hypothesized that these clusters in the melt act as precursors for native defect formation and subject to gravitationally induced convection. The support of the National Aeronautics and Space Administration is gratefully acknowledged.by Michaela E.K. Wiegel.Ph.D

Diffusion of Inhomogeneous Vortex Tangle and Decay of Superfluid Turbulence

The theory describing the evolution of inhomogeneous vortex tangle at zero temperature is developed on the bases of kinetics of merging and splitting vortex loops. Vortex loops composing the vortex tangle can move as a whole with some drift velocity depending on their structure and their length. The flux of length, energy, momentum etc. executed by the moving vortex loops takes a place. Situation here is exactly the same as in usual classical kinetic theory with the difference that the "carriers" of various physical quantities are not the point particles, but extended objects (vortex loops), which possess an infinite number of degrees of freedom with very involved dynamics. We offer to fulfill investigation basing on supposition that vortex loops have a Brownian structure with the only degree of freedom, namely, lengths of loops $l$. This conception allows us to study dynamics of the vortex tangle on the basis of the kinetic equation for the distribution function $n(l,t)$ of the density of a loop in the space of their lengths. Imposing the coordinate dependence on the distribution function n(l,\mathbf{% r},t) and modifying the "kinetic" equation with regard to inhomogeneous situation, we are able to investigate various problem on the transport processes in superfluid turbulence. In this paper we derive relation for the flux of the vortex line density $\mathcal{L}(x,t)$. The correspoding evolution of quantity $\mathcal{L}(x,t)$ obeys the diffusion type equation as it can be expected from dimensional analysis. The according diffusion coefficient is evaluated from calculation of the (size dependent) free path of the vortex loops. We use this equation to describe the decay of the vortex tangle at very low temperature. We compare that solution with recent experiments on decay of the superfluid turbulence.Comment: 7 pages, 6 figure

Mol Cell Proteomics

Protein biochips have a great potential in future parallel processing of complex samples as a research tool and in diagnostics. For the generation of protein biochips, highly automated technologies have been developed for cDNA expression library production, high throughput protein expression, large scale analysis of proteins, and protein microarray generation. Using this technology, we present here a strategy to identify potential autoantigens involved in the pathogenesis of alopecia areata, an often chronic disease leading to the rapid loss of scalp hair. Only little is known about the putative autoantigen(s) involved in this process. By combining protein microarray technology with the use of large cDNA expression libraries, we profiled the autoantibody repertoire of sera from alopecia areata patients against a human protein array consisting of 37,200 redundant, recombinant human proteins. The data sets obtained from incubations with patient sera were compared with control sera from clinically healthy persons and to background incubations with anti-human IgG antibodies. From these results, a smaller protein subset was generated and subjected to qualitative and quantitative validation on highly sensitive protein microarrays to identify novel alopecia areata-associated autoantigens. Eight autoantigens were identified by protein chip technology and were successfully confirmed by Western blot analysis. These autoantigens were arrayed on protein microarrays to generate a disease-associated protein chip. To confirm the specificity of the results obtained, sera from patients with psoriasis or hand and foot eczema as well as skin allergy were additionally examined on the disease-associated protein chip. By using alopecia areata as a model for an autoimmune disease, our investigations show that the protein microarray technology has potential for the identification and evaluation of autoantigens as well as in diagnosis such as to differentiate alopecia areata from other skin diseases

Brownian Motion and Polymer Statistics on Certain Curved Manifolds

We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (function of opening angle and R') contraction of the chain for all lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to appear in Phys. Rev

Entangled Polymer Rings in 2D and Confinement

The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$.Comment: 17 pages of Latex, 1 ps figure now available upon request, accepted for J.Phys.A:Math.Ge