Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models

We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function $h_t(x)$ with corner initialization. We prove, with one exception, that the limiting distribution function of $h_t(x)$ (suitably centered and normalized) equals a Fredholm determinant previously encountered in random matrix theory. In particular, in the universal regime of large $x$ and large $t$ the limiting distribution is the Fredholm determinant with Airy kernel. In the exceptional case, called the critical regime, the limiting distribution seems not to have previously occurred. The proofs use the dual RSK algorithm, Gessel's theorem, the Borodin-Okounkov identity and a novel, rigorous saddle point analysis. In the fixed $x$, large $t$ regime, we find a Brownian motion representation. This model is equivalent to the Sepp\"al\"ainen-Johansson model. Hence some of our results are not new, but the proofs are.Comment: 39 pages, 7 figures, 2 tables. The revised version eliminates the simulations and corrects a number of misprints. Version 3 adds a remark about applications to queueing theory and three related references. Version 4 corrects a minor error in Figure

A growth model in a random environment

We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height above $x-1$, if the latter height is larger; otherwise the height above $x$ increases by 1 with probability $p_x$. We assume that $p_x$ are chosen independently at random with a common distribution $F$, and that the initial state is such that the origin is far above the other sites. We explicitly identify the asymptotic shape and prove that, in the pure regime, the fluctuations about that shape, normalized by the square root of time, are asymptotically normal. This contrasts with the quenched version: conditioned on the environment, and normalized by the cube root of time, the fluctuations almost surely approach a distribution known from random matrix theory.Comment: 31 pages, 5 figure

Central venous dialysis : an Australian survey

Aim: To explore the current central venous dialysis catheter (CVDC) nursing care practices in Australia. Method: A survey of dialysis units in Australia. Results: 66% return rate (48/73) Internal jugular is the main insertion site (75%) and the majority are tunneled (85%). Insertion was performed most commonly by radiologists (34%) followed by intensivists (24%) with one center reporting insertion by nursing staff. CVDCs were most commonly inserted in radiology (54%), followed by theatre (33%). Dressings were attended weekly (55%) or on dialysis days (45%). Chlorhexidine was the antiseptic solution of choice (54%) followed by povidine-iodine (37%). In 21% of centres Mupirocin was routinely applied in addition to the antiseptic solution. Transparent dressings were overwhelmingly favoured however most centres recommended alternatives related to patient need. 21% of units reported enrolled nurses undertaking dressings. All units reported the use of sterile gloves and sterile dressing packs. 10% reported different routine care for tunneled and non-tunneled. 40% of the units collected data on infection rates per catheter days. General opinion (39%) was identified as the reason to base CVDC protocols while descriptive studies (25%), RCTs (23%) and guidelines (18%) were also reported. Conclusion: There are significant variations in the Australian nursing practice related to the care of CVDCs. Although there is still practice based on general opinion there is evidence that changes in practice in the past 8 years may be associated with knowledge derived from research.<br /

Phase Fluctuations and Pseudogap Properties: Influence of Nonmagnetic Impurities

The presence of nonmagnetic impurities in a 2D ``bad metal'' depresses the superconducting Berezinskii-Kosterlitz-Thouless transition temperature, while leaving the pairing energy scale unchanged. Thus the region of the pseudogap non-superconducting phase, where the modulus of the order parameter is non-zero but its phase is random, and which opens at the pairing temperature is substantially bigger than for the clean system. This supports the premise that fluctuations in the phase of the order parameter can in principle describe the pseudogap phenomena in high-$T_c$ materials over a rather wide range of temperatures and carrier densities. The temperature dependence of the bare superfluid density is also discussed.Comment: 11 pages, LaTeX, 1 EPS figure; final version to appear in Low.Temp.Phy

Modeling of frictional forces during bare-finger interactions with solid surfaces

Touching an object with our fingers yields frictional forces that allow us to perceive and explore its texture, shape, and other features, facilitating grasping and manipulation. While the relevance of dynamic frictional forces to sensory and motor function in the hand is well established, the way that they reflect the shape, features, and composition of touched objects is poorly understood. Haptic displays -electronic interfaces for stimulating the sense of touch- often aim to elicit the perceptual experience of touching real surfaces by delivering forces to the fingers that mimic those felt when touching real surfaces. However, the design and applications of such displays have been limited by the lack of knowledge about what forces are felt during real touch interactions. This represents a major gap in current knowledge about tactile function and haptic engineering. This dissertation addresses some aspects that would assist in their understanding. The goal of this research was to measure, characterize, and model frictional forces produced by a bare finger sliding over surfaces of multiple shapes. The major contributions of this work are (1) the design and development of a sensing system for capturing fingertip motion and forces during tactile exploration of real surfaces; (2) measurement and characterization of contact forces and the deformation of finger tissues during sliding over relief surfaces; (3) the development of a low order model of frictional force production based on surface specifications; (4) the analysis and modeling of contact geometry, interfacial mechanics, and their effects in frictional force production during tactile exploration of relief surfaces. This research aims to guide the design of algorithms for the haptic rendering of surface textures and shape. Such algorithms can be used to enhance human-machine interfaces, such as touch-screen displays, by (1) enabling users to feel surface characteristics also presented visually; (2) facilitating interaction with these devices; and (3) reducing the need for visual input to interact with them.Ph.D., Electrical Engineering -- Drexel University, 201

Parity Effect in Ground State Energies of Ultrasmall Superconducting Grains

We study the superconductivity in small grains in the regime when the quantum level spacing $\delta\varepsilon$ is comparable to the gap $\Delta$. As $\delta\varepsilon$ is increased, the system crosses over from superconducting to normal state. This crossover is studied by calculating the dependence of the ground state energy of a grain on the parity of the number of electrons. The states with odd numbers of particles carry an additional energy $\Delta_P$, which shows non-monotonic dependence on $\delta\varepsilon$. Our predictions can be tested experimentally by studying the parity-induced alternation of Coulomb blockade peak spacings in grains of different sizes.Comment: 4 pages, revtex, multicol.st

Probing superconducting phase fluctuations from the current noise spectrum of pseudogaped metal-superconductor tunnel junctions

We study the current noise spectra of a tunnel junction of a metal with strong pairing phase fluctuation and a superconductor. It is shown that there is a characteristic peak in the noise spectrum at the intrinsic Josephson frequency $\omega_J=2eV$ when $\omega_J$ is smaller than the pairing gap but larger than the pairing scattering rate. In the presence of an AC voltage, the tunnelling current noise shows a series of characteristic peaks with increasing DC voltage. Experimental observation of these peaks will give direct evidence of the pair fluctuation in the normal state of high-$T_c$ superconductors and from the half width of the peaks the pair decay rate can be estimated.Comment: 4 pages, 3 figure

Sex Steroids Induce Apoptosis of CD8⁺CD4⁺ Double-Positive Thymocytes via TNF-α

T cell production by the thymus, thymic size, cellularity and output all decrease drastically after puberty. Among the candidates that may mediate this decrease are the sex steroids: Hypersecretion or pharmacological administration of these hormones has long been known to induce thymic hypocellularity, and their depletion yields thymic hypercellularity. Here we show that a typical sex steroid, testosterone, specifically targets CD8⁺CD4⁺ double-positive (DP) thymocytes for apoptosis via TNF-α Anti-TNF-α monoclonal antibodies abrogated testosterone-induced DP apoptosis, and TNF-a⁻^/⁻DP thymocytes were largely resistant to testosterone-mediated apoptosis in vivo. Testosterone accomplishes this effect by up-regulating TNF-α production and by simultaneously sensitizing DP thymocytes to TNF-α. Thus, TNF-α is the critical mediator of sex steroid-induced apoptosis in thymocytes, and its manipulation should provide a point of intervention to modulate T cell production in sex hormone disorders

Probing Pseudogap by Josephson Tunneling

We propose here an experiment aimed to determine whether there are superconducting pairing fluctuations in the pseudogap regime of the high-$T_c$ materials. In the experimental setup, two samples above $T_c$ are brought into contact at a single point and the differential AC conductivity in the presence of a constant applied bias voltage between the samples, $V$, should be measured. We argue the the pairing fluctuations will produce randomly fluctuating Josephson current with zero mean, however the current-current correlator will have a characteristic frequency given by Josephson frequency $\omega_J = 2 e V /\hbar$. We predict that the differential AC conductivity should have a peak at the Josephson frequency with the width determined by the phase fluctuations time.Comment: 4 pages, 2 eps figure