THE LARGE TIME BEHAVIOR OF SPECTRAL APPROXIMATION FOR A CLASS OF PSEUDOPARABOLIC VISCOUS DIFFUSION EQUATION

The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estiation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d(AN,A)→0 are proved.     

Power expansions for the self-similar solutions of the modified Sawada-Kotera equation

The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z ₀ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.      

Potential-dependent structure of the interfacial water on the gold electrode

Doubly tunable sum frequency generation (SFG) spectra demonstrate that the water molecules at gold/electrolyte interface change their orientation with applied potential. At negative potentials, water molecules in the double layer align with their oxygen atom pointing to the solution. As potential became positive to be close to the potential of zero charge (PZC), the SFG signal decreased, suggesting the OH groups of the water molecule are either in random orientation or parallel to the electrode. As potential became more positive than the PZC, the SFG signal increased again with the oxygen-up orientation as same as in the negative potential region, indicating that water molecules interact with the adsorbed sulfate anions. The peak position of the SFG spectra indicates a relatively disordered state of water molecules at the gold electrode surface, in contrast to the previously observed ice-like structure of water at electrolyte/oxide interfaces.     

THE STEP-TRANSITION OPERATORS FOR MULTI-STEP METHODS OF ODE'S

1.'IntroductionThedisad~ageofsymplecticmethodsinusingtheinformationfrompasttimestepsleadstotheirneedingmorefunctionevaluationthannonsymplecticmethods.Thisdisadvantagecanbeovercomeifonecouldconstructsymplecticmulti-stepmethods.But'theaestProblemshouldbesolvedistogiveoutthedefinitionofsymplecticmultistepmethod.Ulltilnow,apopularideaisthatanm-stepmethodonMmaybewrittenasaone-stepmethodonMa.Inpaper12,71,theauthorshaveinvestigatedthecircumstanceunderWhichadifferenceschemecanpreservetheproductsympl…     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

浅议物理实验教学环节改革

为进一步提高大学物理实验的教学质量，本文就实验课的预习、操作、实验报告的撰写及考核方法进行了探讨。     

Computational experience with general equilibrium problems

We report on computational experience with an implementation of three algorithms for the general economic equilibrium problem. As a result we get that the projection algorithm for variational inequalities increases the size of solvable models by a factor of 5–10 in comparison with the classical homotopy method. As a third approach we implemented a simulated annealing heuristic which might be suitable to estimate equilibria for very large models.Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

A 3D-BPP approach for optimising stowage plans and terminal productivity

This paper addresses the problem of determining stowage plans for containers in a ship, that is the so-called master bay plan problem (MBPP).     

The nanogranular nature of C-S-H

Despite its ubiquitous presence as binding phase in all cementitious materials, the mechanical behavior of calcium-silicate-hydrates (C-S-H) is still an enigma that has deceived many decoding attempts from experimental and theoretical sides. In this paper, we propose and validate a new technique and experimental protocol to rationally assess the nanomechanical behavior of C-S-H based on a statistical analysis of hundreds of nanoindentation tests. By means of this grid indentation technique we identify in situ two structurally distinct but compositionally similar C-S-H phases heretofore hypothesized to exist as low density (LD) C-S-H and high density (HD) C-S-H, or outer and inner products. The main finding of this paper is that both phases exhibit a unique nanogranular behavior which is driven by particle-to-particle contact forces rather than by mineral properties. We argue that this nanomechanical blueprint of material invariant behavior of C-S-H is a consequence of the hydration reactions during which precipitating C-S-H nanoparticles percolate generating contact surfaces. As hydration proceeds, these nanoparticles pack closer to center on-average around two characteristic limit packing densities, the random packing limit (η=64%) and the ordered face-centered cubic (fcc) or hexagonal close-packed (hcp) packing limit (η=74%), forming a characteristic LD C-S-H and HD C-S-H phase.     

Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.