The Doped Two Chain Hubbard Model

The properties of the two-chain Hubbard Model doped away from half-filling are investigated. The charge gap is found to vanish, but a finite spin gap exists over a range of interchain hopping strength $t_\perp$. In this range, there are modified $d_{x^2-y^2}$--like pairing correlations whose strength is correlated with the size of the spin gap. It is found that the pair field correlations are enhanced by the onsite Coulomb interaction U.Comment: 10 pages and 5 postscript figures, RevTeX 3.0, UCI-CMTHE-94-0

Coarse-grained Interaction Potentials for Anisotropic Molecules

We have proposed an efficient parameterization method for a recent variant of the Gay-Berne potential for dissimilar and biaxial particles and demonstrated it for a set of small organic molecules. Compared to the previously proposed coarse-grained models, the new potential exhibits a superior performance in close contact and large distant interactions. The repercussions of thermal vibrations and elasticity has been studied through a statistical method. The study justifies that the potential of mean force is representable with the same functional form, extending the application of this coarse-grained description to a broader range of molecules. Moreover, the advantage of employing coarse-grained models over truncated atomistic summations with large distance cutoffs has been briefly studied.Comment: 8 pages, 4 tables and 6 figures. To appear in J. Chem. Phy

A model universe with variable dimension: Expansion as decrumpling

We propose a model universe, in which the dimension of the space is a continuous variable, which can take any real positive number. The dynamics leads to a model in which the universe has no singularity. The difference between our model and the standard Friedman-Robertson-Walker models become effective for times much before the presently accepted age of the universe.Comment: 12 pages, emTeX version 3.0, no figure

Cavity driven by a single photon: conditional dynamics and non-linear phase shift

We apply the stochastic master equations (quantum filter) derived by Gough et al. (Proc. 50th IEEE Conference on Decision and Control, 2011) to a system consisting of a cavity driven by a multimode single photon field. In particular, we analyse the conditional dynamics for the problem of cross phase modulation in a doubly resonant cavity. Through the exact integration of the stochastic equations, our results reveal features of the problem unavailable from previous models

Shape Control for Experimental Continuation

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while simultaneously controlling the overall shape using additional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental---as opposed to numerical---continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.Comment: Updated Figure 6 experimental results with correct calibration factor for linear transducer. Updated Figure 6 finite element results with correct load multiplier for half-model. Updated paper text to reflect these changes. 5 pages, 6 figure

Global cross-over dynamics of single semiflexible polymers

We present a mean-field dynamical theory for single semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution. Our approach works globally, covering three decades of strand length and five decades of time: it includes the complex cross-overs occurring between stiffness-dominated and flexible bending modes, along with larger-scale rotational and center-of-mass motion. The accuracy of the theory stems in part from long-range hydrodynamic coupling between the monomers, which makes a mean-field description more realistic. Its validity extends even to short, stiff fragments, where we also test the theory through Brownian hydrodynamics simulations.Comment: 6 pages, 5 figures; updated with minor changes to reflect published versio

A Gelfand-Naimark type theorem

Let $X$ be a completely regular space. For a non-vanishing self-adjoint Banach subalgebra $H$ of $C_B(X)$ which has local units we construct the spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of the Stone-Cech compactification of $X$ which contains $X$ as a dense subspace. The construction of $\mathfrak{sp}(H)$ is simple. This enables us to study certain properties of $\mathfrak{sp}(H)$, among them are various compactness and connectedness properties. In particular, we find necessary and sufficient conditions in terms of either $H$ or $X$ under which $\mathfrak{sp}(H)$ is connected, locally connected and pseudocompact, strongly zero-dimensional, basically disconnected, extremally disconnected, or an $F$-space.Comment: 13 page