First Passage Distributions in a Collective Model of Anomalous Diffusion with Tunable Exponent

We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes whose friction coefficients scale as wavenumber to the power $2-z$. A single (tagged) monomer then executes subdiffusion over a broad range of time scales, and its mean square displacement increases as $t^\alpha$ with $\alpha=1/z$. To demonstrate non-trivial aspects of the model, we numerically study the absorption of the tagged particle in one dimension near an absorbing boundary or in the interval between two such boundaries. We obtain absorption probability densities as a function of time, as well as the position-dependent distribution for unabsorbed particles, at several values of $\alpha$. Each of these properties has features characterized by exponents that depend on $\alpha$. Characteristic distributions found for different values of $\alpha$ have similar qualitative features, but are not simply related quantitatively. Comparison of the motion of translocation coordinate of a polymer moving through a pore in a membrane with the diffusing tagged monomer with identical $\alpha$ also reveals quantitative differences.Comment: LaTeX, 10 pages, 8 eps figure

Measurements of Grain Motion in a Dense, Three-Dimensional Granular Fluid

We have used an NMR technique to measure the short-time, three-dimensional displacement of grains in a system of mustard seeds vibrated vertically at 15g. The technique averages over a time interval in which the grains move ballistically, giving a direct measurement of the granular temperature profile. The dense, lower portion of the sample is well described by a recent hydrodynamic theory for inelastic hard spheres. Near the free upper surface the mean free path is longer than the particle diameter and the hydrodynamic description fails.Comment: 4 pages, 4 figure

Improving the discovery potential of charged Higgs bosons at Tevatron Run 2

By exploiting the full process $p\bar p\to t\bar b H^-$, in place of the standard Monte Carlo procedure of factorising production and decay, $p\bar p\to t\bar t$ followed by $\bar t\to\bar b H^-$, we show how to improve the discovery reach of the Tevatron (Run 2) in charged Higgs boson searches, in the large $\tan\beta$ region. This is achieved in conjunction with dedicated cuts on a `transverse mass' distribution sensitive to the Higgs boson mass and to `polarisation' effects in the $H^-\to\tau^-\bar\nu_\tau$ decay channel.Comment: 12 pages, LaTeX, 5 figures (one figure added, discussion slightly changed: version to appear in JHEP

NLO Higgs boson production via vector-boson fusion matched with shower in POWHEG

We present a next-to-leading order calculation of Higgs boson production in vector-boson fusion processes interfaced to shower Monte Carlo programs, implemented according to the POWHEG method.Comment: 16 pages, 9 figures. A few references and a new figure adde

Using competition assays to quantitatively model cooperative binding by transcription factors and other ligands.

BACKGROUND: The affinities of DNA binding proteins for target sites can be used to model the regulation of gene expression. These proteins can bind to DNA cooperatively, strongly impacting their affinity and specificity. However, current methods for measuring cooperativity do not provide the means to accurately predict binding behavior over a wide range of concentrations. METHODS: We use standard computational and mathematical methods, and develop novel methods as described in Results. RESULTS: We explore some complexities of cooperative binding, and develop an improved method for relating in vitro measurements to in vivo function, based on ternary complex formation. We derive expressions for the equilibria among the various complexes, and explore the limitations of binding experiments that model the system using a single parameter. We describe how to use single-ligand binding and ternary complex formation in tandem to determine parameters that have thermodynamic relevance. We develop an improved method for finding both single-ligand dissociation constants and concentrations simultaneously. We show how the cooperativity factor can be found when only one of the single-ligand dissociation constants can be measured. CONCLUSIONS: The methods that we develop constitute an optimized approach to accurately model cooperative binding. GENERAL SIGNIFICANCE: The expressions and methods we develop for modeling and analyzing DNA binding and cooperativity are applicable to most cases where multiple ligands bind to distinct sites on a common substrate. The parameters determined using these methods can be fed into models of higher-order cooperativity to increase their predictive power

Fluorescence visualization of a convective instability which modulates the spreading of volatile surface films

The spontaneous spreading of a thin liquid film along the surface of a deep liquid layer of higher surface tension is a ubiquitous process which provides rapid and efficient surface transport of organic or biological material. For a source of constant concentration, the leading edge of a nonvolatile, immiscible film driven to spread by gradients in surface tension is known to advance as t^3/4 in time. Recent experiments using laser shadowgraphy to detect the advancing front of spreading films indicate, however, that immiscible but volatile sources of constant concentration spread with a reduced exponent according to t^1/2. Using a novel technique whereby fluorescent lines are inscribed in water, we have detected the evolution of a thermal instability beneath the leading edge of volatile films which strongly resembles a Rayleigh-Bénard roll. We propose that the increased dissipation from this rotational flow structure is likely responsible for the reduction in spreading exponent. This observation suggests a conceptual framework for coupling the effects of evaporation to the dynamics of spreading

Supermarket Model on Graphs

We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson processes with rate $\lambda$, and each task is irrevocably assigned to the shortest queue among the one it first appears and its $d-1$ randomly selected neighbors. This model has been extensively studied when the underlying graph is a clique in which case it reduces to the well known power-of-$d$ scheme. In particular, results of Mitzenmacher (1996) and Vvedenskaya et al. (1996) show that as the size of the clique gets large, the occupancy process associated with the queue-lengths at the various servers converges to a deterministic limit described by an infinite system of ordinary differential equations (ODE). In this work, we consider settings where the underlying graph need not be a clique and is allowed to be suitably sparse. We show that if the minimum degree approaches infinity (however slowly) as the number of servers $N$ approaches infinity, and the ratio between the maximum degree and the minimum degree in each connected component approaches 1 uniformly, the occupancy process converges to the same system of ODE as the classical supermarket model. In particular, the asymptotic behavior of the occupancy process is insensitive to the precise network topology. We also study the case where the graph sequence is random, with the $N$-th graph given as an Erd\H{o}s-R\'enyi random graph on $N$ vertices with average degree $c(N)$. Annealed convergence of the occupancy process to the same deterministic limit is established under the condition $c(N)\to\infty$, and under a stronger condition $c(N)/\ln N\to\infty$, convergence (in probability) is shown for almost every realization of the random graph.Comment: 32 page