On solving the nonlinear Biswas-Milovic equation with dual-power law nonlinearity using the extended tanh-function method

In this article, we apply the extended tanh-function method to find the exact traveling wave solutions of the nonlinear Biswas-Milovic equation (BME), which describes the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances. This equation is a generalized version of the nonlinear Schrödinger equation with dual-power law nonlinearity. With the aid of computer algebraic system Maple, both constant and time-dependent coefficients of BME are discussed. Comparison between our new results and the well-known results is given. The given method in this article is straightforward, concise and can be applied to other nonlinear partial differential equations (PDEs) in mathematical physics

Melting and Solidification Study of As-Deposited and Recrystallized Bi Thin Films

Melting and solidification of as-deposited and recrystallized Bi crystallites, deposited on highly oriented 002-graphite at 423 K, were studied using reflection high-energy electron diffraction (RHEED). Films with mean thickness between 1.5 and 33 ML (monolayers) were studied. Ex situ atomic force microscopy was used to study the morphology and the size distribution of the formed nanocrystals. The as-deposited films grew in the form of three-dimensional crystallites with different shapes and sizes, while those recrystallized from the melt were formed in nearly similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting and solidification of the crystallites. Melting started at temperatures below the bulk melting point of Bi, T0=544.5 K, and extended over a temperature range that depended on the size distribution of the crystallites. The as-deposited 1.5 ML film started to melt at T0-50 K and melted completely at T0-20 K. For films with higher coverage, the size distribution was observed to spread over a wider range with a larger mean value, resulting in a shift in the melting temperature range towards higher temperatures. Due to the shift in size distribution to higher values upon recrystallization, the recrystallized Bi crystallites showed a melting temperature range higher than that of the as-deposited crystallites. For the investigated conditions, all films were completely melted below or at T 0 of Bi. The characteristic film melting point, defined as the temperature at which the film melting rate with temperature is the fastest, showed a linear dependence on the reciprocal of the average crystallite radius, consistent with theoretical models. Of these models, the surface-phonon instability model best fits the obtained results. During solidification, the Bi films showed high amount of supercooling relative to T0 of Bi. The amount of liquid supercooling was found to decrease linearly with the reciprocal of the average crystallite size. © 2006 American Institute of Physics. [DOI: 10.1063/1.2208551

Condensation on (002) Graphite of Liquid Bismuth Far Below Its Bulk Melting Point

Condensation of thermally evaporated Bi on (002) graphite, at temperatures of 300-523K, was studied using in situ reflection high-energy electron diffraction (RHEED) and room temperature ex situ atomic force microscopy (AFM). For deposition at temperatures below 415±5K, transmission RHEED patterns of Bi appeared at an average thickness of ∼0.5 monolayer (ML). AFM images showed that the film consisted of crystallites in the shape of triangular step pyramids with step heights corresponding to single and double Bi layers in the [111] direction. This morphology indicates crystallization from the vapor. For deposition at higher temperatures, diffuse RHEED patterns appeared independent of the deposited thickness. When these films were cooled, clear transmission patterns of crystalline Bi appeared. After cooling to near room temperature, the melting and solidification behaviors of these films were investigated with RHEED. Upon subsequent heating, the topmost layers of the probed Bi crystallites started to lose long-range order at ∼10-15K below the Bi bulk melting point, T0=544.52K. When crystallized from the melt, supercooling by ∼125K below T0 was observed. These results indicate that Bi condensed on graphite in the form of supercooled liquid droplets when the graphite temperature was above 419K (T0-125). Below that temperature, Bi condensed in the solid phase. Bi films crystallized by cooling the liquid had crystal morphologies that depended on the degree of liquid supercooling. © 2005 The American Physical Society

The development and validation of a scoring tool to predict the operative duration of elective laparoscopic cholecystectomy

Background: The ability to accurately predict operative duration has the potential to optimise theatre efficiency and utilisation, thus reducing costs and increasing staff and patient satisfaction. With laparoscopic cholecystectomy being one of the most commonly performed procedures worldwide, a tool to predict operative duration could be extremely beneficial to healthcare organisations. Methods: Data collected from the CholeS study on patients undergoing cholecystectomy in UK and Irish hospitals between 04/2014 and 05/2014 were used to study operative duration. A multivariable binary logistic regression model was produced in order to identify significant independent predictors of long (> 90 min) operations. The resulting model was converted to a risk score, which was subsequently validated on second cohort of patients using ROC curves. Results: After exclusions, data were available for 7227 patients in the derivation (CholeS) cohort. The median operative duration was 60 min (interquartile range 45–85), with 17.7% of operations lasting longer than 90 min. Ten factors were found to be significant independent predictors of operative durations > 90 min, including ASA, age, previous surgical admissions, BMI, gallbladder wall thickness and CBD diameter. A risk score was then produced from these factors, and applied to a cohort of 2405 patients from a tertiary centre for external validation. This returned an area under the ROC curve of 0.708 (SE = 0.013, p  90 min increasing more than eightfold from 5.1 to 41.8% in the extremes of the score. Conclusion: The scoring tool produced in this study was found to be significantly predictive of long operative durations on validation in an external cohort. As such, the tool may have the potential to enable organisations to better organise theatre lists and deliver greater efficiencies in care

Highly Dispersive Optical Solitons in Birefringent Fibers of Complex Ginzburg–Landau Equation of Sixth Order with Kerr Law Nonlinear Refractive Index

In this paper, we derived optical soliton solutions with a highly dispersive nonlinear complex Ginzburg–Landau (CGL) equation in birefringent fibers that have Kerr law nonlinearity. We applied two mathematical methods, namely the addendum Kudryashov’s method and the unified Riccati equation expansion method. Straddled solitary solutions, bright soliton, dark soliton and singular soliton solutions were obtained.This model represents the propagation of a dispersive optical soliton through a birefringent fiber. This happens when pulses propagating through an optical fiber split into two pulses

)- expansion Method

Abstract: In this paper, a variable- coefficient generalized dispersive water-wave system which can model the propagation of the long weakly nonlinear and weakly dispersive surface waves of variable depth in shallow water is presented. With the aid of symbolic computation and using the generalized ( G′ G)-expansion method, the exact traveling wave solutions of this system are obtained. It is shown that the proposed method provides a more general powerful mathematical tool for finding the exact solutions of nonlinear evolution equations in mathematical physics

The traveling wave solutions for nonlinear partial differential equations using the (G ′ G )-expansion method.

Abstract: In the present paper, we construct the traveling wave solutions involving parameters for some nonlinear evolution equations in mathematical physics via th

The Extended Tanh-Method For Finding Traveling Wave Solutions Of Nonlinear Evolution Equations, Applied Mathematics E-Notes

Abstract In this article, we find traveling wave solutions of the coupled (2+1)-dimensional Nizhnik-Novikov-Veselov and the (1+1)-dimensional Jaulent-Miodek (JM) equations. Based on the extended tanh method, an efficient method is proposed to obtain the exact solutions to the coupled nonlinear evolution equations. The extended tanh method presents a wider applicability for handling nonlinear wave equations