One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes

We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent $\alpha$ of the power law is taken in the range $0 \le \alpha <1$. The oscillator frequency distribution is symmetric about its mean (taken to be zero), and is non-increasing on $[0,\infty)$. In the continuum limit, the local density of oscillators evolves in time following the continuity equation that expresses the conservation of the number of oscillators of each frequency under the dynamics. This equation admits as a stationary solution the unsynchronized state uniform both in phase and over the space of the lattice. We perform a linear stability analysis of this state to show that when it is unstable, different spatial Fourier modes of fluctuations have different stability thresholds beyond which they grow exponentially in time with rates that depend on the Fourier modes. However, numerical simulations show that at long times, all the non-zero Fourier modes decay in time, while only the zero Fourier mode (i.e., the "mean-field" mode) grows in time, thereby dominating the instability process and driving the system to a synchronized state. Our theoretical analysis is supported by extensive numerical simulations.Comment: 7 pages, 4 figures. v2: new simulation results added, close to the published versio

Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

Using a combination of first-principles theory and experiments, we provide a quantitative explanation for chemical contributions to surface-enhanced Raman spectroscopy for a well-studied organic molecule, benzene thiol, chemisorbed on planar Au(111) surfaces. With density functional theory calculations of the static Raman tensor, we demonstrate and quantify a strong mode-dependent modification of benzene thiol Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential, a well-defined property of each vibrational mode. A straightforward and general analysis is introduced that allows extraction of chemical enhancement from experiments for specific vibrational modes; measured values are in excellent agreement with our calculations.Comment: 5 pages, 4 figures and Supplementary material included as ancillary fil

Scalloped margin domes: What are the processes responsible and how do they operate?

Studies of scalloped margin domes (SMD) indicate the scallops are the result of slope failure. SMD's have similar but smaller average diameters (26.5 km) to unmodified domes (29.8 km), and the majority plot at altitudes ranging from 0.5-4.7 km, relative to the mean planetary diameter. A range of morphological types exist from those least modified to those that show heavy modification. Of the 200 SMD's examined, 33 have clearly discernible debris aprons. Examination and comparison of debris aprons with mass movement features on the Moon, Mars, and in sub-aerial and submarine environments on Earth using H/L against area (km(sup 2)), suggests there are three main types of failure; debris avalanche, slumps, and debris flow. The five examples representing the morphological range within the SMD's, show the different modified forms and the different types of slope failures that have occurred

Synchronization in a System of Globally Coupled Oscillators with Time Delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results

Phase diagram of a generalized Winfree model

We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions and mechanical systems. We let the global coupling k be a function of the Kuramoto order parameter r through an exponent z such that z=1 corresponds to the standard Winfree model, z<1 strengthens the coupling at low r (low amount of synchronization) and, at z>1, the coupling is weakened for low r. Using both analytical and numerical approaches, we find that z controls the size of the incoherent phase region, and one may make the incoherent behavior less typical by choosing z<1. We also find that the original Winfree model is a rather special case, indeed the partial locked behavior disappears for z>1. At fixed k and varying gamma, the stability boundary of the locked phase corresponds to a transition that is continuous for z1. This change in the nature of the transition is in accordance with a previous study on a similarly modified Kuramoto model.Comment: 9 pages, 3 figure

Baboon-to-human liver transplantation

Our ability to control both the cellular and humoral components of xenograft rejection in laboratory experiments, together with an organ shortage that has placed limits on clinical transplantation services, prompted us to undertake a liver transplantation from a baboon to a 35-year-old man with B virus-associated chronic active hepatitis and human immunodeficiency virus infection. Liver replacement was performed according to conventional surgical techniques. Immunosuppression was with the FK 506-prednisone-prostaglandin regimen used routinely for hepatic allotransplantation, to which a daily non-myelotoxic dose of cyclophosphamide was added. During 70 days of survival, there was little evidence of hepatic rejection by biochemical monitoring or histopathological examination. Products of hepatic synthesis, including clotting factors, became those of the baboon liver with no obvious adverse effects. Death followed a cerebral and subarachnoid haemorrhage that was caused by an angioinvasive aspergillus infection. However, the underlying cause of death was widespread biliary sludge that formed in the biliary tree despite a seemingly satisfactory choledochojejunostomy. During life and in necropsy samples, there was evidence of the chimerism that we believe is integral to the acceptance of both xenografts and allografts. Our experience has shown the feasibility of controlling the rejection of the baboon liver xenograft in a human recipient. The biliary stasis that was the beginning of lethal infectious complications may be correctable by modifications of surgical technique. In further trials, the error of over-immunosuppression should be avoidable. © 1993

Cholesteatoma of the concha bullosa: a case report

<p>Abstract</p> <p>Introduction</p> <p>Cholesteatoma is a relatively common disease within the middle ear cavity, but rarely it manifests in the paranasal sinuses. There is, to the best of our knowledge, only one other published case of cholesteatoma inside the concha bullosa in the English language literature.</p> <p>Case presentation</p> <p>An 81-year-old Caucasian woman was admitted to our hospital complaining of nasal obstruction, headache and diplopia. After endoscopic and radiological evaluation a transnasal endoscopic approach was chosen. The diagnosis of cholesteatoma was established by histopathological evaluation of the mass inside the concha bullosa.</p> <p>Conclusion</p> <p>Although it is rarely seen, cholesteatoma should be considered in the differential diagnosis of slow-growing and destructive paranasal masses.</p

Synchronization and resonance in a driven system of coupled oscillators

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective synchronization of the system, is derived; it is found that the total order parameter decreases monotonically with noise, indicating overall suppression of synchronization. Still, for large coupling strengths, there exists an optimal noise level at which the periodic (ac) component of the order parameter reaches its maximum. The response of the phase velocity is also examined and found to display resonance behavior.Comment: 17 pages, 3 figure

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure

Phase synchronization and noise-induced resonance in systems of coupled oscillators

We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is investigated as the noise level and the coupling strength are varied, and hysteretic behavior is manifested. The power spectrum of the phase velocity is also examined and the quality factor as well as the response function is obtained to reveal noise-induced resonance behavior.Comment: to be published in Phys. Rev.