An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

Evolution and properties of antiphase boundaries in silicate minerals

Experimental and observational evidence is reviewed for the mechanisms and kinetics of antiphase domain coarsening in silicate minerals. The expected rate law has the form (domain size)ⁿ ≈ annealing time, but the ideal value of n=2 has been observed in only one of three cases. Values of n≈8 or 10 are interpreted as implying adsorption of impurity atoms onto the antiphase boundaries. Diffusion of these impurities can then provide the rate determining step for boundary migration. Local ordering at the boundaries can also provide some stabilising influence, though this does not appear to affect the coarsening rate law. If the stabilisation is sufficient it might result in the development of an incommensurate superstructure, either as a stable phase or as a metastable phase under non-equilibrium conditions. The effective width of these boundaries appears to be ～ 25°, or approximately two unit cells, and their maximum effective interaction length appears to be ～ 4 times this width.     

Structural evolution of cylindrical‐phase diblock copolymer thin films

We have measured the time evolution of the self‐assembly process in perpendicular‐oriented cylindrical‐phase diblock copolymer thin films using statistical analysis of high‐resolution scanning electron microscope (SEM) images. Within minutes of annealing above the polymer glass‐transition temperature, microphase separation between polymer blocks results in formation of uniform nanometer‐scale domains whose relative position is initially largely uncorrelated. On further annealing, the cylindrical polymer domains organize into a two‐dimensional hexagonal lattice whose characteristic grain size increases slowly with time (～t^1/4). © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1970–1975, 2004     

Evolution of helium bubbles in nickel-based alloy by post-implantation annealing

Nickel-based alloys have been considered as candidate structural materials used in generation IV nuclear reactors serving at high temperatures. In the present study, alloy 617 was irradiated with 180-keV helium ions to a fluence of 3.6×10¹⁷ ions/cm² at room temperature. Throughout the cross-section transmission electron microscopy (TEM) image, numerous over-pressurized helium bubbles in spherical shape are observed with the actual concentration profile a little deeper than the SRIM predicted result. Post-implantation annealing was conducted at 700 ℃ for 2 h to investigate the bubble evolution. The long-range migration of helium bubbles occurred during the annealing process, which makes the bubbles of the peak region transform into a faceted shape as well. Then the coarsening mechanism of helium bubbles at different depths is discussed and related to the migration and coalescence (MC) mechanism. With the diffusion of nickel atoms slowed down by the alloy elements, the migration and coalescence of bubbles are suppressed in alloy 617, leading to a better helium irradiation resistance.     

Commuting projections on graphs

Motivated by the increasing importance of large‐scale networks typically modeled by graphs, this paper is concerned with the development of mathematical tools for solving problems associated with the popular graph Laplacian. We exploit its mixed formulation based on its natural factorization as product of two operators. The goal is to construct a coarse version of the mixed graph Laplacian operator with the purpose to construct two‐level, and by recursion, a multilevel hierarchy of graphs and associated operators. In many situations in practice, having a coarse (i.e., reduced dimension) model that maintains some inherent features of the original large‐scale graph and respective graph Laplacian offers potential to develop efficient algorithms to analyze the underlined network modeled by this large‐scale graph. One possible application of such a hierarchy is to develop multilevel methods that have the potential to be of optimal complexity. In this paper, we consider general (connected) graphs and function spaces defined on its edges and its vertices. These two spaces are related by a discrete gradient operator, ‘Grad’ and its adjoint, ‘ ? Div’, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then, a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ?₂‐projection Q_H onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π_H from the original edge‐space onto a properly constructed coarse edge‐space associated with the edges of the coarse graph. The projections π_H and Q_H commute with the discrete divergence operator, that is, we have Div π_H = Q_H div. The respective pair of coarse edge‐space and coarse vertex‐space offer the potential to construct two‐level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian, which utilizes the discrete divergence operator. The performance of one two‐level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples. Copyright © 2013 John Wiley & Sons, Ltd.     

The Becker–Döring Equations and the Lifshitz–Slyozov Theory of Coarsening

In this paper the relation between the kinetic set of Becker–Döring (BD) equations and the classical Lifshitz–Slyozov (LS) theory of coarsening is studied. A model that resembles the LS theory but keeps some of the nucleation effects is derived. For this model a solution is described that shows how the kinetic effects explain the particular solution selected in the LS theory. By means of a renormalization procedure, a discrete group of transformations is shown to play an important role in describing the structure of the solution near the critical size of the LS theory.     

2008年欧洲足球锦标赛攻击性进攻技术统计分析

采用专家调查、录像观察和数理统计等研究方法,从训练学角度探讨2008年欧锦赛攻击性进攻的现状。每个国家都适当选择了运球突破,每场突破的次数主要集中在15-18之间,并且P值显示出明显的差异性;西班牙、荷兰、德国和葡萄牙表现突出,多采用中距离传球;比赛成绩(排名)与进球的相关系数为-0.597,且其差异性显著;角球攻击的区域90%集中在1区和2区,而且1区的攻击多于2区;长传279次、短传37次,T=9.76、P=0.00(?)0.01,二者之间存在明显的差异性;运用内弧线球和外弧线球平均次数之间差异不具有显著性。研究认为:运球突破的实效性、传球的成功率、射门的准确性和攻击性控球的把握是决定比赛胜利的关键。     

Friction and energy dissipation mechanisms in adsorbed molecules and molecularly thin films

This review provides an overview of recent advances that have been achieved in understanding the basic physics of friction and energy dissipation in molecularly thin adsorbed films and the associated impact on friction at microscopic and macroscopic length scales. Topics covered include a historical overview of the fundamental understanding of macroscopic friction, theoretical treatments of phononic and electronic energy dissipation mechanisms in thin films, and current experimental methods capable of probing such phenomena. Measurements performed on adsorbates sliding in unconfined geometries with the quartz crystal microbalance technique receive particular attention. The final sections review the experimental literature of how measurements of sliding friction in thin films reveal energy dissipation mechanisms and how the results can be linked to film-spreading behavior, lubrication, film phase transitions, superconductivity-dependent friction, and microelectromechanical systems applications. Materials systems reported on include adsorbed films comprised of helium, neon, argon, krypton, xenon, water, oxygen, nitrogen, carbon monoxide, ethane, ethanol, trifluoroethanol, methanol, cyclohexane, ethylene, pentanol, toluene, tricresylphosphate, t-butylphenyl phosphate, benzene, and iodobenzene. Substrates reported on include silver, gold, aluminum, copper, nickel, lead, silicon, graphite, graphene, fullerenes, C60, diamond, carbon, diamond-like carbon, and YBa₂Cu₃O₇, and self-assembled monolayers consisting of tethered polymeric molecules.