Research on temperature profiles of honeycomb regenerator with asymptotic analysis

An asymptotic semi-analytical method for heat transfer in counter-flow honeycomb regenerator is proposed. By introducing a combined heat-transfer coefficient between the gas and solid phase, a heat transfer model is built based on the thin-walled assumption. The dimensionless thermal equation is deduced by considering solid heat conduction along the passage length. The asymptotic analysis is used for the small parameter of heat conduction term in equation. The first order asymptotic solution to temperature distribution under weak solid heat conduction is achieved after Laplace transformation through the multiple scales method and the symbolic manipulation function in MATLAB. Semi-analytical solutions agree with tests and finite-difference numerical results. It is proved possible for the asymptotic analysis to improve the effectiveness, economics and precision of thermal research on regenerator.

Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlocal Source

In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t>0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f(s) = s^p,h(s) = s^q,0 ≤ p≤1,p + q >1,we obtain the asymptotic behavior of the blow up solution.

Asymptotic analysis of multi-valley dark soliton solutions in defocusing coupled Hirota equations

We construct uniform expressions of such dark soliton solutions encompassing both single-valley and double-valley dark solitons for the defocusing coupled Hirota equation with high-order nonlinear effects utilizing the uniform Darboux transformation,in addition to proposing a sufficient condition for the existence of the above dark soliton solutions.Furthermore,the asymptotic analysis we perform reveals that collisions for single-valley dark solitons typically exhibit elastic behavior;however,collisions for double-valley dark solitons are generally inelastic.In light of this,we further propose a sufficient condition for the elastic collisions of double-valley dark soliton solutions.Our results offer valuable insights into the dynamics of dark soliton solutions in the defocusing coupled Hirota equation and can contribute to the advancement of studies in nonlinear optics.

ASYMPTOTIC ANALYSIS OF DYNAMIC PROBLEMS FOR LINEARLY ELASTIC SHELLS--JUSTIFICATION OF EQUATIONS FOR DYNAMIC FLEXURAL SHELLS

Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.

ASYMPTOTIC ANALYSIS OF DYNAMIC PROBLEMS FOR LINEARLY ELASTIC SHELLS-JUSTIFICATION OF EQUATIONS FOR DYNAMIC KOITER SHELLS

Under certain conditions, the dynamic equations of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.

Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

The Hirota equation can be used to describe the wave propagation of an ultrashort optical field.In this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are explored.We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(i.e.nonlinear combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial degree.For the larger solution parameters,the first m(m<n)components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons,and the last n-m components with zero backgrounds can approach bright-like solitons.Moreover,we analyze the accelerations and curvatures of the quasi-characteristic curves,as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons.We also find the semi-rational rogon-soliton solutions with ultrahigh amplitudes.In particular,we can also deduce vector semi-rational solitons of the ncomponent complex mKdV equation.These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background,and even design the related physical experiments.

Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrodinger equation

In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions.Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula.

Exact Controllability and Asymptotic Analysis for Shallow Shells

The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2ε with controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickhess of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.

ASYMPTOTIC ANALYSIS OF LINEARLY ELASTIC SHALLOW SHELLS WITH VARIABLE THICKNESS

The author considers a linearly elastic shallow shell with variable thickness and shows that, as the thickness of the shell goes to zero, the solution of the three-dimensional equations converges to the solution of the two-dimensional shallow shell equations with variable thickness.

A Two-Scale Asymptotic Analysis of a Time-Harmonic Scattering Problem with a Multi Layered Thin Periodic Domain

The scope of this paper is to show how a two-scale asymptotic analysis,based on a superposition principle,allows us to derive high order approximate boundary conditions for a scattering problem of a time-harmonic wave by a thin and tangentially periodic multi-layered domain.The periods are assumed of the same order of the thickness.New terms like memory effect and variance-covariance ones are observed contrarily to the laminar case.As a result,optimal error estimates are obtained.

Asymptotic Analysis of Lattice Boltzmann Outflow Treatments

We show the methodology and advantages of asymptotic analysis when applied to lattice Boltzmann outflow treatments.On the one hand,one can analyze outflow algorithms formulated directly in terms of the lattice Boltzmann variables,like the extrapolation method,to find the induced outflow conditions in terms of the NavierStokes variables.On the other hand,one can check the consistency and accuracy of lattice Boltzmann outflow treatments to given hydrodynamic outflow conditions like the Neumann or average pressure condition.As example how the gained insight can be used,we propose an improvement of the well known extrapolation method.

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schr?dinger equation

We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.

ASYMPTOTIC THEORY FOR THE CIRCUIT ENVELOPE ANALYSIS

Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.

The asymptotic field of mode Ⅰ quasi-static crack growth on the interface between a rigid and a pressure-sensitive material

A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering hi-materials. In the stable growth stage, stress and strain have the same singularity, ie （σ, ε） ∝ r^-1/（n-1）. The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy＇s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio v of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

Analysis of current induced by long internal solitary waves in stratified ocean

An approximate theoretical expression for the current induced by long internal solitary waves is presented when the ocean is continuously or two-layer stratified. Particular attention is paid to characterizing velocity fields in terms of magnitude, flow components, and their temporal evolution/spatial distribution. For the two-layer case, the effects of the upper/lower layer depths and the relative layer density difference upon the induced current are further studied. The results show that the horizontal components are basically uniform in each layer with a shear at the interface. In contrast, the vertical counterparts vary monotonically in the direction of the water depth in each layer while they change sign across the interface or when the wave peak passes through. In addition, though the vertical components are generally one order of magnitude smaller than the horizontal ones, they can never be neglected in predicting the heave response of floating platforms in gravitationally neutral balance. Comparisons are made between the partial theoretical results and the observational field data. Future research directions regarding the internal wave induced flow field are also indicated.

HIGHER-ORDER ANALYSIS OF NEAR-TIP FIELDS AROUND AN INTERFACIAL CRACK BETWEEN TWO DISSIMILAR POWER LAW HARDENING MATERIALS

By means of an asymptotic expansion method of a regular series, an exact higher-order analysis has been carried out for the near-tip fields of an in- terfacial crack between two different elastic-plastic materials. The condition of plane strain is invoked. Two group of solutions have been obtained for the crack surface conditions: (1) traction free and (2) frictionless contact, respectively. It is found that along the interface ahead of crack tip the stress fields are co-order continuous while the displacement fields are cross-order continuous. The zone of dominance of the asymptotic solutions has been estimated.

Asymptotic Solution for Coupled Heat and Mass Transfer During the Solidification of High Water Content Materials

This paper focuses on obtaining an asymptotic solution for coupled heat and mass transfer problem during the solidification of high water content materials. It is found that a complicated function involved in governing equations can be approached by Taylor polynomials unlimitedly, which leads to the simplification of governing equations. The unknown functions involved in governing equations can then be approximated by Chebyshev polynomials. The coefficients of Chebyshev polynomials are determined and an asymptotic solution is obtained. With the asymptotic solution, the dehydration and freezing fronts of materials are evaluated easily, and are consistent with numerical results obtained by using an explicit finite difference method.

High-Order Two-Scale Asymptotic Paradigm for the Elastodynamic Homogenization of Periodic Composites

The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable,which offers an approximate framework for the asymptotic homogenization analysis of the motion equation.However,in this framework,the growing complexity of the homogenization formulation gradually becomes an obstacle as the asymptotic order increases.In such a context,a compact,fast,and accurate asymptotic paradigm is developed.This work reviews the high-order spatial two-scale asymptotic paradigm with the effective displacement field representation and optimizes the implementation by symmetrizing the tensor to be determined.Remarkably,the modified implementation gets rid of the excessive memory consumption required for computing the high-order tensor,which is demonstrated by representative one-and two-dimensional cases.The numerical results show that(1)the contrast of the material parameters between media in composites directly affects the convergence rate of the asymptotic results for the homogenization of periodic composites,(2)the convergence error of the asymptotic results mainly comes from the truncation error of the modified asymptotic homogenized motion equation,and(3)the excessive norm of the normalized wavenumber vector in the two-dimensional inclusion case may lead to a non-convergence of the asymptotic results.