35 research outputs found
Numerical instability of the Akhmediev breather and a finite-gap model of it
In this paper we study the numerical instabilities of the NLS Akhmediev
breather, the simplest space periodic, one-mode perturbation of the unstable
background, limiting our considerations to the simplest case of one unstable
mode. In agreement with recent theoretical findings of the authors, in the
situation in which the round-off errors are negligible with respect to the
perturbations due to the discrete scheme used in the numerical experiments, the
split-step Fourier method (SSFM), the numerical output is well-described by a
suitable genus 2 finite-gap solution of NLS. This solution can be written in
terms of different elementary functions in different time regions and,
ultimately, it shows an exact recurrence of rogue waves described, at each
appearance, by the Akhmediev breather. We discover a remarkable empirical
formula connecting the recurrence time with the number of time steps used in
the SSFM and, via our recent theoretical findings, we establish that the SSFM
opens up a vertical unstable gap whose length can be computed with high
accuracy, and is proportional to the inverse of the square of the number of
time steps used in the SSFM. This neat picture essentially changes when the
round-off error is sufficiently large. Indeed experiments in standard double
precision show serious instabilities in both the periods and phases of the
recurrence. In contrast with it, as predicted by the theory, replacing the
exact Akhmediev Cauchy datum by its first harmonic approximation, we only
slightly modify the numerical output. Let us also remark, that the first rogue
wave appearance is completely stable in all experiments and is in perfect
agreement with the Akhmediev formula and with the theoretical prediction in
terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv
admin note: text overlap with arXiv:1707.0565
Effect of Carnitine and herbal mixture extract on obesity induced by high fat diet in rats
<p>Abstract</p> <p>Background</p> <p>Obesity-associated type 2 diabetes is rapidly increasing throughout the world. It is generally recognized that natural products with a long history of safety can modulate obesity.</p> <p>Aim</p> <p>To investigate the development of obesity in response to a high fat diet (HFD) and to estimate the effect of L-carnitine and an Egyptian Herbal mixture formulation (HMF) (consisting of T. chebula, Senae, rhubarb, black cumin, aniseed, fennel and licorice) on bodyweight, food intake, lipid profiles, renal, hepatic, cardiac function markers, lipid Peroxidation, and the glucose and insulin levels in blood and liver tissue in rats.</p> <p>Method</p> <p>White male albino rats weighing 80-90 gm, 60 days old. 10 rats were fed a normal basal diet (Cr), 30 rats fed a high-fat diet (HFD) for 14 weeks during the entire study. Rats of the HFD group were equally divided into 3 subgroups each one include 10 rats. The first group received HFD with no supplement (HFD), the 2<sup>nd </sup>group HFD+L-carnitine and the third group received HFD+HMF. Carnitine and HMF were administered at 10<sup>th </sup>week (start time for treatments) for 4 weeks.</p> <p>Body weight, lipid profile & renal function (urea, uric acid creatinine) ALT & AST activities, cardiac markers, (LDH, C.K-NAC and MB) the oxidative stress marker reduced glutathione (GSH), and Malondialdehyde (MDA) catalase activity, in addition to glucose, insulin, and insulin resistance in serum & tissues were analyzed.</p> <p>Results</p> <p>Data showed that feeding HFD diet significantly increased final body weight, triglycerides (TG), total cholesterol, & LDL concentration compared with controls, while significantly decreasing HDL; meanwhile treatment with L-carnitine, or HMF significantly normalized the lipid profile.</p> <p>Serum ALT, urea, uric acid, creatinine, LDH, CK-NAC, CK-MB were significantly higher in the high fat group compared with normal controls; and administration of L-carnitine or herbal extract significantly lessened the effect of the HFD. Hyperglycemia, hyperinsulinemia, and high insulin resistance (IR) significantly increased in HFD in comparison with the control group. The treatment with L-carnitine or HMF improved the condition. HFD elevated hepatic MDA and lipid peroxidation associated with reduction in hepatic GSH and catalase activity; whereas administration of L-carnitine or herbal extract significantly ameliorated these hepatic alterations.</p> <p>Conclusion</p> <p>HFD induced obesity associated with a disturbed lipid profile, defective antioxidant stability, and high values of IR parameters; this may have implications for the progress of obesity related problems. Treatment with L-carnitine, or HMF extract improved obesity and its associated metabolic problems in different degrees. Also HMF has antioxidant, hypolipidaemic insulin sensitizing effects. Moreover HMF might be a safe combination on the organs whose functions were examined, as a way to surmount the obesity state; and it has a distinct anti-obesity effect.</p
Lead effects on cereal roots in terms of cell growth, root architecture and metal accumulation
MBE of GaN with DC-plasma source for nitrogen activation
In this paper we report on the first results of epitaxial growth of GaN layers on GaAs (100) substrates using a modified MBE system, equipped with a DC-plasma source for nitrogen activation in configuration of reverse magnetron at ultra-low pressures