Cluster expansion in the canonical ensemble

We consider a system of particles confined in a box \La\subset\R^d interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer's virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof

Effective lattice theories for Polyakov loops

We derive effective actions for SU(2) Polyakov loops using inverse Monte Carlo techniques. In a first approach, we determine the effective couplings by requiring that the effective ensemble reproduces the single-site distribution of the Polyakov loops. The latter is flat below the critical temperature implying that the (untraced) Polyakov loop is distributed uniformly over its target space, the SU(2) group manifold. This allows for an analytic determination of the Binder cumulant and the distribution of the mean-field, which turns out to be approximately Gaussian. In a second approach, we employ novel lattice Schwinger-Dyson equations which reflect the SU(2) x SU(2) invariance of the functional Haar measure. Expanding the effective action in terms of SU(2) group characters makes the numerics sufficiently stable so that we are able to extract a total number of 14 couplings. The resulting action is short-ranged and reproduces the Yang-Mills correlators very well.Comment: 27 pages, 8 figures, v2: method refined, chapter and references adde

Multiple bound states in scissor-shaped waveguides

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a tunable $\theta$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $\theta=90^o$ there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of $\theta$ in the interval $(0,90^o)$. Moreover, states which are sufficiently strongly bent exist in pairs with a small energy difference and opposite parities. Finally, we discuss how with increasing $\theta$ the bound states transform into the quasi-bound states with a complex wave vector.Comment: 6 pages, 6 figure

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid Dynamics. Several references have been adde

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.Comment: 41 pages, 13 figures. Accepted for publication in a book: "Tsunami and Nonlinear Waves", Kundu, Anjan (Editor), Springer 2007, Approx. 325 p., 170 illus., Hardcover, ISBN: 978-3-540-71255-8, available: May 200

Linear Wave Interaction with a Vertical Cylinder of Arbitrary Cross Section: An Asymptotic Approach

An asymptotic approach to the linear problem of regular water waves interacting with a vertical cylinder of an arbitrary cross section is presented. The incident regular wave was one-dimensional, water was of finite depth, and the rigid cylinder extended from the bottom to the water surface. The nondimensional maximum deviation of the cylinder cross section from a circular one plays the role of a small parameter of the problem. A fifth-order asymptotic solution of the problem was obtained. The problems at each order were solved by the Fourier method. It is shown that the first-order velocity potential is a linear function of the Fourier coefficients of the shape function of the cylinder, the second-order velocity potential is a quadratic function of these coefficients, and so on. The hydrodynamic forces acting on the cylinder and the water surface elevations on the cylinder are presented. The present asymptotic results show good agreement with numerical and experimental results of previous investigations. Long-wave approximation of the hydrodynamic forces was derived and used for validation of the asymptotic solutions. The obtained values of the forces are exact in the limit of zero wave numbers within the linear wave theory. An advantage of the present approach compared with the numerical solution of the problem by an integral equation method is that it provides the forces and the diffracted wave field in terms of the coefficients of the Fourier series of the deviation of the cylinder shape from the circular one. The resulting asymptotic formula can be used for optimization of the cylinder shape in terms of the wave loads and diffracted wave fields

ATP-Sensitive Potassium Channels Exhibit Variance in the Number of Open Channels below the Limit Predicted for Identical and Independent Gating

In small cells containing small numbers of ion channels, noise due to stochastic channel opening and closing can introduce a substantial level of variability into the cell's membrane potential. Negatively cooperative interactions that couple a channel's gating conformational change to the conformation of its neighbor(s) provide a potential mechanism for mitigating this variability, but such interactions have not previously been directly observed. Here we show that heterologously expressed ATP-sensitive potassium channels generate noise (i.e., variance in the number of open channels) below the level possible for identical and independent channels. Kinetic analysis with single-molecule resolution supports the interpretation that interchannel negative cooperativity (specifically, the presence of an open channel making a closed channel less likely to open) contributes to the decrease in noise. Functional coupling between channels may be important in modulating stochastic fluctuations in cellular signaling pathways

Molecular imaging of glycan chains couples cell-wall polysaccharide architecture to bacterial cell

Biopolymer composite cell walls maintain cell shape and resist forces in plants, fungi and bacteria. Peptidoglycan, a crucial antibiotic target and immunomodulator, performs this role in bacteria. The textbook structural model of peptidoglycan is a highly ordered, crystalline material. Here we use atomic force microscopy (AFM) to image individual glycan chains in peptidoglycan from Escherichia coli in unprecedented detail. We quantify and map the extent to which chains are oriented in a similar direction (orientational order), showing it is much less ordered than previously depicted. Combining AFM with size exclusion chromatography, we reveal glycan chains up to 200 nm long. We show that altered cell shape is associated with substantial changes in peptidoglycan biophysical properties. Glycans from E. coli in its normal rod shape are long and circumferentially oriented, but when a spheroid shape is induced (chemically or genetically) glycans become short and disordered

Edge wave and non-trapped modes of the 25 april 1992 Cape Mendocino tsunami

The 25 April 1992 Cape Mendocino earthquake generated a tsunami characterized by both coastal trapped edge wave and non-trapped tsunami modes that propagated north and south along the U.S. West Coast. Both observed and synthetic time series at Crescent City and North Spit are consistent with the zero-order edge wave mode solution for a semi-infinite sloping beach depth profile. Wave amplitudes at Crescent City were about twice that observed at North Spit, in spite of the fact that the source region was three times farther from Crescent City than North Spit. The largest observed amplitude was due to an edge wave which arrived almost three hours after the initial onset of the tsunami; since such waves are highly localized nearshore, this suggests that the enhanced responsiveness at Crescent City is at least partly due to local dynamic processes. Furthermore, the substantially delayed arrival of this wave, which was generated at the southern end of the Cascadia Subduction Zone, has significant implications for hazard mitigation efforts along the entire U.S. West Coast. Specifically, this study demonstrates that slow-moving but very energetic edge wave modes could be generated by future large tsunamigenic earthquakes in the CSZ, and that these might arrive unexpectedly at coastal communities several hours after the initial tsunami waves have subsided.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43189/1/24_2004_Article_BF00874375.pd