Global stability of an age-structured population model on several temporally variable patches

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number $$R_0$$ R 0 for time-independent and periodical models and establish the permanence dichotomy: if $$R_0\le 1$$ R 0 ≤ 1 , extinction on all patches is imminent, and if $$R_0>1$$ R 0 > 1 , permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.

Stability features of steady-state solutions for a diode with electron and ion counter-streams

Stability features of steady-state solutions for a diode with counter-streaming electron and ion flows are studied. For this purpose, the time-dependent problem for an exponential potential perturbation with complex frequency is considered. By linearization of the Poisson equation and electron and ion densities integrodifferential equation for the potential perturbation amplitude is derived. In the case of uniform unperturbed potential distribution an explicit solution of this equation is obtained. Eigen modes of the perturbation are studied. The limiting value of the diode length above which steady state solutions in question are unstable is found. The obtained analytical Eigen modes coincide with the result of numerical simulation of the potential perturbation evolution.

Design and Analysis of Parison Blow Molding Using Adaptive Mesh

Blow Molding is one of the most versatile and economical process available for molding hollow materials. When polyethylene is stretched, it exhibits strain-hardening properties, which are temperature, pressure, velocity and strain-rate dependent. In this paper, preform is made by extrusion and forced between two halves by pressurization. This process includes isothermal and transient flow of Newtonian fluid in complex geometries simultaneous with structuring and solidification. A time dependent problem is defined and setting material properties and boundaries condition for bottle blow molding. Numerical data available in POLYDATA for a time dependent problem using ANSYS POLYFLOW were applied. Results display in form contours associated with different variables at different time steps and good agreement with the bottle thickness profile is observed. In this paper, the analysis of the stretch-blow molding (SBM) process of polyethylene terephthalate (PET), parison plastic bottles is studied by the finite element method (FEM). A hyper elastic constitutive behavior was calibrated using material data available in literature in variant high temperatures and strain rates and was used in the numerical simulation. Hydrostatic pressure with convention heat transfer has been used instead of a blowing process. Comparisons of numerical results with experimental observations demonstrate that the model can predict an overall trend of thickness distribution. Through the study, it becomes clear that the proposed model is applicable for simulating the stretch-blow molding process of PET bottles, and is capable of offering helpful knowledge in the production of bottles and the design of an optimum preform.

Investigation of instability in ultrasonic welding under parametric excitation

This paper develops a time-varying model for battery tabs based on the parametric excitation of Euler-Bernoulli beams. The instability caused by combination resonance under a high-frequency longitudinal load is considered. A Galerkin procedure is used to discretize the time-dependent problem into the Mathieu equation. The critical axial load is obtained from the transition curve of combination resonance. The effectiveness of the stability analysis was verified by numerical simulations involving longitudinal and bending loads.

STUDY OF THE EIGENVALUE SPECTRA OF THE NEUTRON TRANSPORT PROBLEM IN PN APPROXIMATION

The study of the steady-state solutions of neutron transport equation requires the introduction of appropriate eigenvalues: this can be done in various different ways by changing each of the operators in the transport equation; such modifications can be physically viewed as a variation of the corresponding macroscopic cross sections only, so making the different (generalized) eigenvalue problems non-equivalent. In this paper the eigenvalue problem associated to the time-dependent problem (α eigenvalue), also in the presence of delayed emissions is evaluated. The properties of associated spectra can give different insight into the physics of the problem.

The Time-dependent Problem of the Line Radiation Reflection

We consider the classical time-dependent problem of diffuse reflection of the line-radiation from a semi-infinite absorbing and scattering atmosphere. By the example of the simplest 1D problem it is shown how its solution is constructed in the general case, when both the photon lifetime in the absorbed state and the time of its travel between two consecutive acts of scattering are taken into account. The numerical values of the coefficients in the expansion of the reflection function in the Neumann series are given. The obtained solution is applied to the problem, in which the scattering in both the spectral line and in the continuous spectrum is taken into account.

hp-FEM for the fractional heat equation

We consider a time-dependent problem generated by a nonlocal operator in space. Applying for the spatial discretization a scheme based on $hp$-finite elements and a Caffarelli–Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-discontinuous Galerkin based time stepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the spatial domain $\varOmega $.

The time-dependent Schrödinger equation with piecewise constant potentials

The linear Schrödinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with physically important models. In examples such as ‘particle in a box’ and tunnelling, attention is restricted to the time-independent Schrödinger equation. This paper combines the unified transform method and recent insights for interface problems to present fully explicit solutions for the time-dependent problem.

Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations

In this paper we are concerned with numerical methods for nonlinear time-dependent problem coupled by electron, ion and photon temperatures in two dimensions, which is called the 2D-3T heat conduction equations. We propose discontinuous Galerkin (DG) methods for the discretization of the equations. For solving the resulting discrete system, we employ two domain decomposition (DD) preconditioners, one of which is associated with the non-overlapping DDM and the other is based on DDM with small overlap. The preconditioners are constructed by dropping the couplings between particles and each preconditioner consists of three preconditioners with smaller matrix size. To gauge the efficiency of the preconditioners, we test two examples and make different settings of parameters. Numerical results show that the proposed preconditioners are very effective to the 2D-3T problem.