Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-a time scheme and periodic boundary conditions in the material point method(MPM)for the simulation of coseismic site response.The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh.The explicit generalized-a time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations.Firstly,the MPM was verified against finite element method(FEM).Secondly,ability of the MPM in capturing the analytical transfer function was investigated.Thirdly,a symmetric embankment was adopted to investigate the effects of ground motion arias intensity(I_(a)),geometry dimensions,and constitutive models.The results show that the larger the model size,the higher the crest runout and settlement for the same ground motion.When using a Mohr-Coulomb model,the crest runout increases with increasing I_(a).However,if the strain-softening law is activated,the results are less influenced by the ground motion.Finally,the MPM results were compared with the Newmark sliding block solution.The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications,the importance of geometry characterization,and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

Theoretical analysis of the surface temperature regulation of an infrared false target subjected to periodical ambient conditions

Infrared false target is an important mean to induce the infrared-guided weapons,and the key issue is how to keep the surface temperature of the infrared false target to be the same as that of the object to be protected.One-dimensional heat transfer models of a metal plate and imitative material were established to explore the influences of the thermophysical properties of imitative material on the surface temperature difference（STD） between the metal plate and imitative material which were subjected to periodical ambient conditions.It is elucidated that the STD is determined by the imitative material’s dimensionless thickness（dim*,） and the thermal inertia(Pim).When dim* is above 1.0,the STD is invariable as long as Pim is a constant.And if the dimensionless thickness of metal plate（d,m*） is also larger than 1.0,the STD approaches to zero as long as Pimis the same as the thermal inertia of metal plate（Pm）.When dim* is between 0.08 and 1,the STD varies irregularly with Pim and dim*.However,if dm* is also in the range of 0.08-1,the STD approaches to zero on condition that Pim=Pm and dim*= dm*.If dim*,is below 0.08,the STD is unchanged when Pimdim* is a constant.And if dm* is also less than 0.08,the STD approaches to zero as long as Pimdim* = Pmdm*.Furthermore,an applicationoriented discussion indicates that the imitative material can be both light and thin via the application of the phase change material with a preset STD because of its high specific heat capacity during the phase transition process.

Periodic Boundary Conditions for Finite-Differentiation-Method Fast-Fourier-Transform Micromagnetics

We describe an accurate periodic boundary condition （PBC） called the symmetric PBC in the calculation of the magnetostatie interaction field in the finite-differentiation-method fast-Fourier-transform （FDM-FFT） micromagneties. The micromagnetic cells in the regular mesh used by the FDM-FFT method are finite-sized elements, but not geometrical points. Therefore, the key PBC operations for FDM-FFT methods are splitting and relocating the micromagnetic cell surfaces to stay symmetrically inside the box of half-total sizes with respect to the origin. The properties of the demagnetizing matrix of the split micromagnetic cells are discussed, and the sum rules of demagnetizing matrix are fulfilled by the symmetric PBC.

Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin

A moving trapezoidal profiled convective-radiative porous longitudinal fin wetted in a single-phase fluid is considered in the current article.The periodic variation in the fin base temperature is taken into account along with the temperature sensitive thermal conductivity and convective heat transfer coefficients.The modeled problem,which is resolved into a non-linear partial differential equation(PDE),is made dimensionless and solved by employing the finite difference method(FDM).The results are displayed through graphs and discussed.The effects of amplitude,frequency of oscillation,wet nature,Peclet number,and other relevant quantities on the distribution of temperature through the fin length and with the dimensionless time are investigated.It is deciphered that the periodic heat transfer gives rise to the wavy nature of the fin thermal profile against time.The analysis is beneficial in the design of fin structures for applications like solar collectors,space/airborne applications,and refrigeration industries.

Entanglement in an anisotropic spin-1 Heisenberg chain

The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy △ and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearestneighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.

THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.

Stress Analysis of Wire Strands by Mesoscale Mechanics

Steel wire ropes have wide application in a variety of engineering fields such as ocean engineering and civil engineering.The stress calculation for steel wire ropes is of crucial importance when conducting strength and fatigue analyses.In this study,we performed a finite element analysis of single-strand steel wire ropes.For the geometric modeling,we used an analytic geometry of space method.We established helical line equations and used the coordinates of the contact points.The finite-element model was simplified using the periodic law.Periodic boundary conditions were used to simulate a wire strand of infinite length under tensile strain,for which we calculated the cross-sectional stresses and inner forces.The results showed that bending and torsion moments emerged when the wire strand was under tensile load.In some cases,the bending stress reached 18%of the tensile stress,and the torsion stress reached 29%of the tensile stress,which means that the total stress was higher than the nominal stress.Whereas in ear-lier studies,a conservative prediction of nominal stress was not possible,the results of our strength and fatigue analyses were more conservative.

Effects of etching conditions on surface morphology of periodic inverted trapezoidal patterned Si(100) substrate

In this paper,the anisotropic etching process of Si(100) wafers in tetramethyl ammonium hydroxide(TMAH) solution with isopropyl alcohol(IPA) is investigated in detail. An inverted trapezoidal pattern is developed. A series of experiments are performed by changing TMAH concentration,IPA concentration,etching temperature and etching time. The structure of inverted trapezoidal patterns and roughness of the bottom surface are characterized by scanning electron microscopy(SEM) and atomic force microscopy(AFM). The results show that with TMAH concentration increases,the roughness of bottom surface will decrease. The addition of IPA into TMAH solution improves the morphology of the bottom surface significantly. Low temperature is beneficial to get a smooth bottom surface. Furthermore,etching time can change the bottom surface roughness. A model is proposed to explain the etching processes. The hillock area ratio of the bottom surface has the same tendency as the etching area ratio. Finally,smooth silicon inverted trapezoidal patterns are obtained for epitaxial growth of Ga N-based light emitting diode(LED) devices.

Bandgap characteristics of 2D plasma photonic crystal with oblique incidence:TM case

A novel periodic boundary condition （PBC）, that is the constant transverse wavenumber （CTW） method, is introduced to solve the time delay in the transverse plane with oblique incidence. Based on the novel PBC, the FDTD/PBC algorithm is proposed to study periodic structure consisting of plasma and vacuum. Then the reflection coefficient for the plasma slab from the FDTD/PBC algorithm is compared with the analytic results to show the validity of our technique. Finally, the reflection coefficients for the plasma photonic crystals are calculated using the FDTD/PBC algorithm to study the variation of bandgap characteristics with the incident angle and the plasma parameters. Thus it has provided the guiding sense for the actual manufacturing plasma photonic crystal.

A density functional theory study on parameters fitting of ultra long armchair(n,n) single walled boron nitride nanotubes

Armchair （n, n） single walled boron nitride nanotubes with n = 2-17 are studied by the density functional theory at the B3LYP/3-21G（d） level combined with the periodic boundary conditions for simulating the ultra long model. The results show that the structure parameters and the formation energies bear a strong relationship to n. The fitted analytical equations are developed with correlation coefficients larger than 0.999. The energy gaps of （2, 2） and （3, 3） tubes are indirect gaps, and the larger tubes （n = 4-17） have direct energy gaps. Results show that the armchair boron nitride nanotubes （n = 2-17） are insulators with wide energy gaps of between 5.93 eV and 6.23 eV.

The unified transform method to the high-order nonlinear Schrodinger equation with periodic initial condition

In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.

NUMERICAL ANALYSIS OF LONGTIME DYNAMIC BEHAVIOR IN WEAKLY DAMPED FORCED KdV EQUATION

The numerical analysis of the approximate inertial manifold in,weakly damped forced KdV equation is given. The results of numerical analysis under five models is the same as that of nonlinear spectral analysis.

SPECTRAL METHOD FOR ZAKHAROV EQUATION WITH PERIODIC BOUNDARY CONDITIONS

This paper describes the spectral method for numerically solving Zakharov equation with periodicboundary conditions. This method is spectral method for spatial variable and difference method fortime variable. We make error estimation of approximate solution and prove the convergence of spectralmethod. We had given the convergence rate. Also, we prove the stability of approximate method forinitial values.

GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ（（φ（ρ））xxφ′（ρ））x with φ（ρ） = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] （α=1/2） to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI'S EQUATION WITH PERIODIC COEFFICIENTS

In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y^2+b(t)y+c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y^2+b(t)y+c(t)+δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved.

THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE 0F PERIODIC SOLUTIONS OF A TYPE OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL INCLUSION

In this paper,the existence of positive periodic solutions to a second-order differential inclusion is considered.Some existence results are established by the fixed-point theorem for multivalued operators and Sobolev constant.

A LYAPUNOV-TYPE INEQUALITY FOR A PERIODIC BOUNDARY VALUE PROBLEM OF A FRACTIONAL DIFFERENTIAL EQUATION

In this paper, we establish a Lyapunov-type inequality for fractional differential periodic boundary-value problems. As applications, a necessary condition is obtained to ensure the existence and uniqueness of nontrivial solutions to this problem.

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method(DEM)simulation.To avoid the boundary effect,a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing.The shape features of ellipsoids are investigated,including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids.The macroscopic properties of ellipsoidal particle samples,such as the deviatoric stress,volumetric strain,internal friction angle,as well as dilatancy angles are explored.Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips.In addition,it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains.The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.