The Transmission Property of the Discrete Heisenberg Ferromagnetic Spin Chain

We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic spin chain (DHF) via a geometric approach. By the aid of a discrete nonlinear Schr\"odinger-like equation which is the discrete gauge equivalent to the DHF, we show that the determination of transmitting coefficients in the transmission problem is always bistable. Thus a definite algorithm and general stochastic algorithms are presented. A new invariant periodic phenomenon of the non-transmitting behavior for the DHF, with a large probability, is revealed by an adoption of various stochastic algorithms.Comment: 16 pages, 7 figure

Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation

Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. In this paper, we use a variable-coefficient Korteweg–de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each. We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train. We find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a pre-factor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave

Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation

We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV equation in the presence of weak dissipative disorder in the linear growth/damping term. With the weak disorder in the system, the amplitude of solitary wave randomly fluctuates during evolution. We demonstrate numerically that the probability density function of a solitary wave parameter $\kappa$ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible $\kappa$ value.Comment: 8 pages, 4 figure

Genotype moderates the impact of food additives on hyperactive behavior in children

Introduction: The claim of a relationship between artificial food color and additive (AFCs) intake and behavior is highly contentious. We have shown in a previous population-based trial with 3yo children adverse effects of food additives on parentally-rated hyperactive behaviour (Bateman et al, 2004). The possible role of genetic polymorphisms in moderating this adverse effect has not been previously examined. Methods A randomised, double blind, placebo-controlled, within subject crossover food challenge was used for 144, 8 to 9 year old children and 153, 3 year old children. Following baseline assessment children were placed on a diet eliminating food additives and a benzoate preservative for 6 weeks during which time they were challenged for weekly periods with either a placebo mix or a drink containing sodium benzoate (45mg daily) and one of two mixes of AFCs.: Results: The T939C and Thr105Ile polymorphisms of the histamine N-methyltransferase gene (HNMT) moderated the adverse effect s of AFCs but the polymorphisms in catecholamine genes COMT Val108Met and ADRA2A C1291G did not. These findings point to a possible role for histamine in mediating the effects of food additives and help to explain why there has been inconsistency between previous studies. Conclusions: Genes influencing a range of neurotransmitter systems and their interplay with environmental factors, such as diet, need to be examined to understand genetic influences on hyperactivity.<br/

Cuspons, peakons and regular gap solitons between three dispersion curves

A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the system contains two waves with a strong linear coupling between them, to which a third wave is then coupled. This model has two gaps in its linear spectrum. Realizations of this model can be made in terms of temporal or spatial evolution of optical fields in, respectively, a planar waveguide or a bulk-layered medium resembling a photonic-crystal fiber. Another physical system described by the same model is a set of three internal wave modes in a density-stratified fluid. A nonlinear analysis is performed for solitons which have zero velocity in the reference frame in which the group velocity of the third wave vanishes. Disregarding the self-phase modulation (SPM) term in the equation for the third wave, we find two coexisting families of solitons: regular ones, which may be regarded as a smooth deformation of the usual gap solitons in a two-wave system, and cuspons with a singularity in the first derivative at their center. Even in the limit when the linear coupling of the third wave to the first two vanishes, the soliton family remains drastically different from that in the linearly uncoupled system; in this limit, regular solitons whose amplitude exceeds a certain critical value are replaced by peakons. While the regular solitons, cuspons, and peakons are found in an exact analytical form, their stability is tested numerically, which shows that they all may be stable. If the SPM terms are retained, we find that there again coexist two different families of generic stable soliton solutions, namely, regular ones and peakons.Comment: a latex file with the text and 10 pdf files with figures. Physical Review E, in pres

A coupled 'AB' system: Rogue waves and modulation instabilities

published_or_final_versio

Strategies for the introduction and implementation of a guideline for the treatment of type 2 diabetics by general practitioners (GPs) of the Lazio region of Italy (IMPLEMEG study): Protocol for a cluster randomised controlled trial [ISRCTN80116232]

BACKGROUND: Despite broad agreement on the necessity to improve quality of diabetic care through implementation of clinical guidelines, in Italy many people with diabetes still lack adequate care in general practice. In addition there is little evidence to support the choice of implementation strategies, especially in the Lazio region (central Italy), where comparative studies among general practitioners (GPs) are uncommon. The primary objective of the study is to assess the effectiveness of different strategies for the implementation of an evidence-based guideline for the management of non-complicated type 2 diabetes mellitus (DM) among GPs of the Lazio region. METHODS/DESIGN: Three-arm cluster-randomised trial (C-RCT). 252 GPs were randomised either to arm 1 (comprising a training module and administration of the guideline), or to arm 2 (administration of guideline without training), or to arm 3 (control arm), continuing current practice. Arm 1 participants attended a two-day course with CME credits. Data collection will be performed using current information systems. Patients' health data was also collected to describe diabetic populations cared for by GP participants. Process outcomes will be measured at the patient level and at the cluster level one year after the intervention. We will assess GPs' adherence to guideline recommendations for diabetes management relative to: 1) pharmacological management of diabetes; 2) pharmacological management of cardiovascular risk factors (hypertension and dislypidaemia); 3) measurement of glycosilated haemoglobin as the principal indicator of glycaemic control; 4) micro- and macrovascular complications assessment tests. Outcomes will be expressed as proportions of patients cared for by GPs who will have prescriptions of drugs, requests for tests and for outpatient appointment visits. To estimate the efficiency of resource use associated with the intervention a cost-effectiveness analysis will be carried out. The design of the study is based on three Cochrane and one Health Technology Assessment systematic reviews of guideline dissemination and implementation strategies

Combined effect of rotation and topography on shoaling oceanic internal solitary waves

Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg-de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth's background rotation is potentially significant. The relevant extension of the Kortweg-de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia-gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal solitary wave. Hence, the combined effects of background rotation and variable topography are examined. Then the Ostrovsky equation is replaced by a variable coefficient Ostrovsky equation whose coefficients depend explicitly on the spatial coordinate. Some numerical simulations of this equation, together with analogous simulations using the Massachusetts Institute of Technology General Circulation Model (MITgcm), for a certain cross section of the South China Sea are presented. These demonstrate that the combined effect of shoaling and rotation is to induce a secondary trailing wave packet, induced by enhanced radiation from the leading wave. © 2014 American Meteorological Society

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure