Complete derivation of 2D shallow-water model from the primitive equations governing geophysical flows

The fact that the 2D shallow-water model has been used for decades is such a long time that a complete reference on how to derive it from the primitive equations either has likely to become a very rare article or written in a way that is very complicated for the newcomers. Certain physical assumptions and mathematical theorem should be acquired in order to fully understand how the complete 2D shallow-water model is derived which are often being skipped in many recent ocean modelling text books. In this paper, full derivation of the model that consist of momentum conversation in Cartesian coordinates and the continuity equations will be shown in the simplest way to satisfy the curiosity of fresh physical oceanographers

Compactons in Interspecies Spin–Orbit-Coupled Nonlinear Schrodinger Lattices Under Strong Nonlinearity Management

This study shows the existence of special matter waves, known as compactons, in binary discrete nonlinear Schr¨odinger (DNLS) equations with equal distributions of interspecies Rashba and Dresselhaus spin-orbit coupling (SOC) in the presence of fast periodic time modulations of the interspecies scattering length. However, the existence is limited to only of one-site compacton type, which means the absence of larger size compactons such as the two- and three-site. Further, the dynamical stability of the compactons is predicted by using linear stability analysis method and verified through the direct numerical integrations of the equations. We find that the stability of the compactons has strong dependence on the strength of SOC term

Double microring resonators polymer waveguide for optical biosensing

The potential of double microring resonator polymer waveguide as an optical biosensor was demonstrated. Visible wavelength region at 632 nm is used as a centre wavelength because it is commonly used in biological and chemical sensing for both label and label-free sensing. The double microring resonator waveguide structure is simulated using COMSOL Multiphysics optical design and analysis software. The results show that there is a transmission drop with a 3 dB bandwidth of 631.4 nm when the surrounding refractive index is 1.33. The specific wavelength (output transmission) is shifted to 674.6 nm when the surrounding medium into 1.43, in order to imitate the bioanalytes solution. According to simulation result, the wavelength shift was approximately 43.2 nm for 0.1 increasing of surrounding refractive index. The double microring resonator polymer waveguide was fabricated by using electron beam lithography. Then, the fabricated devices were integrated into microfluidic systems in order to validate the wavelength shift. From the experiments, the wavelength shift occurred approximately 32.3 nm over 0.1 increment of refractive index. Thus both simulation and experimental results strongly indicate that double microring resonator polymer waveguide structure at visible wavelength region have a potential for label or label-free optical biosensing applications

Modelling transmission dynamics of covid-19 during Pre-vaccination period in Malaysia: a predictive guiseird model using streamlit

Coronavirus disease (COVID-19) is a major health threat worldwide pandemic, first identified in Malaysia on 25 January 2020. This outbreak can be represented in the mathematical expressions of a non-linear system of ordinary differential equations (ODEs). With the lack of a predictive SEIRD model in terms of Graphical Users Interface (GUI) in Malaysia, this paper aims to model the COVID-19 outbreak in Malaysia during the pre-vaccination period using the Susceptible-Exposed-Infected-Recovered-Death (SEIRD) model with time-varying parameters, then develop a GUI-SEIRD predictive model using Streamlit Python library. This GUI-SEIRD predictive model considers different values of the proportion of the quarantine-abiding population (r) and three different decisions of MCO lifted date to forecast the number of active cases (I) on 15 October 2020 that gives insightful information to government agencies. The mathematical model is solved using Scipy odeint function, which uses Livermore Solver for Ordinary Differential Equations with an Automatic method switching (LSODA) algorithm. The time-varying coefficients of SEIRD model that best fit the real data of COVID-19 cases are obtained using the Nelder-Mead optimization algorithm. This an extended SIRD model with exposed (E) compartment becoming SEIRD, leads to a robust model. It adequately fitted two datasets of Malaysian COVID-19 indicated by the slightest average values of root mean square error (RMSE) as compared to other existing models. The results highlight that the larger the values of the proportion of the quarantine-abiding population (r) and the later the date of the lifted MCO, the faster Malaysia reaches disease free equilibrium

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested

COMPLETE DERIVATION OF 2D SHALLOW-WATER MODEL FROM THE PRIMITIVE EQUATIONS GOVERNING GEOPHYSICAL FLOWS

ABSTRACT The fact that the 2D shallow-water model has been used for decades is such a long time that a complete reference on how to derive it from the primitive equations either has likely to become a very rare article or written in a way that is very complicated for the newcomers. Certain physical assumptions and mathematical theorem should be acquired in order to fully understand how the complete 2D shallow-water model is derived which are often being skipped in many recent ocean modelling text books. In this paper, full derivation of the model that consist of momentum conversation in Cartesian coordinates and the continuity equations will be shown in the simplest way to satisfy the curiosity of fresh physical oceanographers

Dark compactons in nonlinear Schrödinger Lattices with strong nonlinearity management

The existence of dark compacton solution of discrete nonlinear Schrödinger (DNLS) equation with strong nonlinearity management (SNLM) is investigated. The stability analysis was carry out using standard linearization stability procedure.Even though the stability regime is not so wide but evidently some stable dark compactons can exist in the SNLM DNLS system. Surprisingly, even within the confirmed stability regime from the analysis, the time evolution of the dark compacton solution exhibits small bounded ripples

Plane wave solution of extended discrete nonlinear Schrödinger equation

In this paper, we considered the extended discrete nonlinear Schrödinger equation (EDNLSE) which includes the nearest neighbour nonlinear interaction in addition to the on-site cubic and quintic nonlinearities. The objective of this study is to investigate the modulational instability of plane matterwave solution in dipolar Bose-Einstein Condensates (BEC) in a periodic optical lattice and to compare the analytical results with numerical. Analytically, the problem is solved by using perturbed solution of the plane wave where the instability of the gain can be obtained. The conditions of the stability of the plane wave had been analysed and confirmed numerically, by applications of Runge- Kutta method. Three specific cases were studied where only cubic-quintic nonlinearity(q = 0) is considered, only quintic-dipolar (alpha = 0) is considered and lastly non-zero for all terms. The numerical results are aligned with the analytical results

Scattering of the vector soliton in coupled nonlinear Schrödinger equation with Gaussian potential

Nonlinear Schrodinger equation (NLSE) is the fundamental equation which describes the wave field envelope dynamics in a nonlinear and dispersive medium. However, if the fields have many components, one should consider the Coupled Nonlinear Schrodinger equation (CNLSE). We considered the interactions of orthogonally polarized and equal-amplitude vector solitons with two polarization directions. In this paper, we focused on the effect of Gaussian potential on the scattering of the vector soliton in CNLSE. The scattering process was investigated by the variational approximation method and direct numerical solution of CNLSE. Analytically, we analyzed the dynamics of the width and center of mass position of a soliton by the variational approximation method. Soliton may be reflected from each other or transmitted through or trapped. Initially, uncoupled solitons may form the coupled state if the kinetic energy of solitons less than the potential of attractive interaction between solitons but when its’ velocity above the critical velocity, the soliton will pass through each other easily. Meanwhile, a direct numerical simulation of CNLSE had been run to check the accuracy of the approximation. The result of the variational model gives a slightly similar pattern with direct numerical simulation of CNLSE by fixing the parameters for both solutions with the same value. The interaction of the vector soliton with Gaussian potential depends on the initial velocity and amplitude of the soliton and the strength of the external potential