Dispersion equation

In this work, we design circular lattice photonic crystal fibers using Lumerical Mode Solution software, its hollow core filled with carbon tetrachloride. Optical properties including effective refractive index, chromatic dispersion, nonlinearity, and fiber loss were investigated numerically in detail based on solving Maxwell's wave equations.

14p viambani 18-06-2024 1 1   Download

The Nambu-Goldstone (NG) modes in the system of two segregated Bose-Einstein condensates (BECs) limited by two hard walls are studied by means of the Gross-Pitaevskii (GP) theory. Based on the double-parabola approximation (DPA) combining with the Bogoliubov-de Gennes (BdG) equations we found four NG modes that proves the failure of the Watanabe-Brauner counting rule and, furthermore, their dispersion relations depend explicitly on the geometrical structure.

11p viambani 18-06-2024 1 1   Download

In this paper, we considered the propagation wave in transversely isotropic piezoelastic medium based on the nonlocal strain gradient theory. Two kinds of scale parameters, namely, the nonlocal parameter and the strain gradient parameter are introduced to account for the size effect of mechanical properties of nanostructures.

18p dianmotminh02 03-05-2024 6 2   Download

Part 1 book "Mathematical modeling - A chemical engineer's perspective" by author Rutherford Aris includes content: What is mathematical modeling; manipulation of models; solving the equations; presenting the model and its behavior; maxims for modelers; style, dispersion in flow.

169p muasambanhan10 03-04-2024 5 1   Download

Part 2 book "Engineering electromagnetics" includes content: Time varying fields and Maxwell's equations; the uniform plane wave; plane waves at boundries and in dispersive media; transmission lines; waveguide and antenna fundamentals.

264p muasambanhan06 03-02-2024 4 2   Download

Part 2 book "Engineering electromagnetics" includes content: Magnetic forces, materials, and inductance; time varying fields and Maxwell’s equations; transmission lines; the uniform plane wave; plane wave reflection and dispersion; guided waves; electromagnetic radiation and antennas.

367p muasambanhan06 03-02-2024 2 2   Download

Part 1 of ebook "Physics of oscillations and waves: With use of Matlab and Python" provides readers with contents including: Chapter 1 - Introduction; Chapter 2 - Free and damped oscillations; Chapter 3 - Forced oscillations and resonance; Chapter 4 - Numerical methods; Chapter 5 - Fourier analysis; Chapter 6 - Waves; Chapter 7 - Sound; Chapter 8 - Dispersion and waves on water; Chapter 9 - Electromagnetic waves;...

304p dangsovu 20-10-2023 10 7   Download

In addition, the displacement field of THSDT needs the high continuity in approximated formulation with high-order derivatives for a weak form of fourth order equation. According to IGA formulation based on the generalized THSDT, the shear locking phenomenon is free. The variables of THSDT are less than HSDTs which contain five DOFs per node. The influences of weight fractions, the coefficient porosity, dispersion patterns of GPLs and distribution types of porosity on structure’s natural frequencies are studied through some numerical examples.

16p chauchaungayxua12 09-07-2021 10 2   Download

The existence of shale has a major effect on reservoir quality because it reduces the rock’s both the porosity and permeability. There are several types of shale, and they can be distributed in the sand in four different ways: laminated, structural, dispersed, or any combination of these. Each of them has various features and physical properties. Therefore, shale volume estimation is one ofthemostimportant and challengin tasksto be solved information evaluation.

7p cothumenhmong12 08-07-2021 27 2   Download

This study is devoted to investigate the propagation of Rayleigh-type waves in transversely isotropic nonlocal piezoelastic half-space. When the stress-free boundary is maintained at charge-free condition, the dispersion equation for the propagation of Rayleigh waves at the free surface of transversely isotropic piezoelastic solids has been obtained. Based on the obtained dispersion equation, the effect of the nonlocality on the speed of Rayleigh wave is numerically considered.

9p nguaconbaynhay11 07-04-2021 9 2   Download

The analytical expressions for the wave functions of two-component Bose-Einstein Condensates are derived by means of the Gross-Pitaevskii equations in linear approximation. Based on the Bernoulli equation the shape of the interface and the dispersion relations for both phonon and ripplonare studied.

6p tamynhan5 10-12-2020 12 1   Download

In this paper, we analytically investigated the possibility of parametric resonance of acoustic and optical phonons. We obtained a general dispersion equation for parametric amplification and transformation of phonons.

7p viino2711 08-05-2020 10 2   Download

In this work, we proposed a simple model for control of optical properties via an external magnetic field in a vee-type degenerated atomic medium. By numerically solving the density matrix equations in the steady-state, we show that the absorption and dispersion properties are influenced by the strength of coupling laser and external magnetic fields.

8p vimax2711 27-03-2020 22 1   Download

In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion.

7p trinhthamhodang1 16-11-2019 21 0   Download

In nonlinear optics, the soliton transmission in different forms can be described with the use of nonlinear Schrödinger (NLS) equations. Here, the soliton transmission is investigated by solving the NLS equation with the reciprocal of the group velocity b1ðzÞ, the group velocity dispersion coefficient b2ðzÞ and nonlinear coefficient cðzÞ. Two-soliton solutions for the NLS equation are obtained through the Hirota method. According to the solutions obtained, b1ðzÞ and cðzÞ with different function forms are taken to study the characteristics of solitons.

8p trinhthamhodang1 14-11-2019 23 0   Download

In this study, the generalized nonlinear Schrödinger equation describing nonlinear wave propagation in optical fiber with all higher order effects such as higher order dispersion, self-phase modulation and Raman scattering is considered. Using the numerical method, the effects of the terms third order dispersion, Raman scattering on evolution of ultrashort pulses are investigated in detail.

6p viengland2711 23-07-2019 15 2   Download

In this paper, a modified central finite difference scheme for a three-point nonuniform grid is presented for the one-dimensional homogeneous Helmholtz equation using the Bloch wave property. The modified scheme provides highly accurate solutions at the nodes of the nonuniform grid for very small to very large range of wave numbers irrespective of how the grid is adapted throughout the domain.

10p danhdanh27 07-01-2019 20 1   Download

We derive a model for structured population with a two-phase life cycle. Growth and reproduction occur during the first phase. The first phase is followed by a dispersal phase in which individuals are allowed to move throughout a habitat. Also, we prove the existence of a branch of positive equilibria using bifurcation results of Rabinowitz.

13p danhdanh27 07-01-2019 21 1   Download

This paper is concerned with the blow-up of solutions to some nonlocal inhomogeneous dispersal equations subject to homogeneous Neumann boundary conditions. We establish conditions on nonlinearities sufficient to guarantee that solutions exist for all time as well as blow up at some finite time. Moreover, lower bounds for blow-up time of nonlocal problems are obtained.

17p tuongvidanh 06-01-2019 30 1   Download

In this paper, the secular equation of Rayleigh surface waves propagating in an orthotropic layered half-space is derived by the matrix method. All the layers and the halfspace are assumed to have identical principle axes. The explicit form of the matrizant for each layer is obtained by the Sylvester’s theorem. The derived secular equation takes only real values and depends only on the dimensionless variables and dimensionless material parameters. Hence, it is convenient in numerical calculation.

12p thienthanquydu 23-10-2018 29 0   Download