Power-law falloff in two-dimensional Coulomb gases at inverse temperature β>8π

We consider two-dimensional Coulomb gases (standard or hard-core) with activityz, and prove that for any >8 the two-point external charges correlation function exhibits the power-law falloff characteristic of the Kosterlitz-Thouless phase at sufficiently low activity.     

Wall‐stress boundary conditions for variational‐multiscale LES

Two methods are introduced for the implementation of wall‐stress boundary conditions in variational‐multiscale large‐eddy simulations. In both methods, the boundary conditions are applied weakly using an interior‐penalty approach, where the discretization parameters are determined using information from a wall‐stress model. The performance of the methods is compared with that of hard Dirichlet boundary conditions for turbulent channel flows. A convergence study is performed for the second of the methods, which is found to be the most viable for practical application. Sources of error affecting the convergence study are discussed and quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

Projection‐based variational multiscale method for incompressible Navier–Stokes equations in time‐dependent domains

A variational multiscale method for computations of incompressible Navier–Stokes equations in time‐dependent domains is presented. The proposed scheme is a three‐scale variational multiscale method with a projection‐based scale separation that uses an additional tensor valued space for the large scales. The resolved large and small scales are computed in a coupled way with the effects of unresolved scales confined to the resolved small scales. In particular, the Smagorinsky eddy viscosity model is used to model the effects of unresolved scales. The deforming domain is handled by the arbitrary Lagrangian–Eulerian approach and by using an elastic mesh update technique with a mesh‐dependent stiffness. Further, the choice of orthogonal finite element basis function for the resolved large scale leads to a computationally efficient scheme. Simulations of flow around a static beam attached to a square base, around an oscillating beam and around a plunging aerofoil are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Spectral characteristics of background error covariance and multiscale data assimilation

The spatial resolutions of numerical atmospheric and oceanic circulation models have steadily increased over the past decades. Horizontal grid spacing down to the order of 1 km is now often used to resolve cloud systems in the atmosphere and sub‐mesoscale circulation systems in the ocean. These fine resolution models encompass a wide range of temporal and spatial scales, across which dynamical and statistical properties vary. In particular, dynamic flow systems at small scales can be spatially localized and temporarily intermittent. Difficulties of current data assimilation algorithms for such fine resolution models are numerically and theoretically examined. An analysis shows that the background error correlation length scale is larger than 75 km for streamfunctions and is larger than 25 km for water vapor mixing ratios, even for a 2‐km resolution model. A theoretical analysis suggests that such correlation length scales prevent the currently used data assimilation schemes from constraining spatial scales smaller than 150 km for streamfunctions and 50 km for water vapor mixing ratios. These results highlight the need to fundamentally modify currently used data assimilation algorithms for assimilating high‐resolution observations into the aforementioned fine resolution models. Within the framework of four‐dimensional variational data assimilation, a multiscale methodology based on scale decomposition is suggested and challenges are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupling of two-dimensional atomistic and continuum models for dynamic crack

A concurrent multiscale method of coupling atomistic and continuum models is presented in the two-dimensional system. The atomistic region is governed by molecular dynamics while the continuum region is represented by construct- ing the mass and stiffness matrix dependent on the coarsening of the grids, which ensures that they merge seamlessly. The low-pass phonon filter embedded in the handshaking region is utilized to effectively eliminate the spurious reflection of high-frequency phonons, while keeping the low-frequency phonons transparent. These schemes are demonstrated by numerically calculating the reflection and transmission coefficient, and by the further application of dynamic crack propa- gation subjected to mode-I tensile loading.     

非定常Stokes方程的多级增强Petrov-Galerkin低阶有限元方法

本文对非定常的Stokes方程采用等阶P1/P1元逼近,增强速度有限元空间,应用Petrov-Galerkin途径,根据多级增强空间是否与时间t有关,对时间项采用向后差分,给出了两种全离散的稳定有限元格式.并且证明了这两种格式的稳定性与收敛性.     

Pricing Options on Defaultable Stocks*

? ?. This work was inspired by the SAMSI workshops on Financial Mathematics, Statistics and Econometrics (Fall 2005, Spring 2006 North Carolina). The author wishes to thank the organizers for the travel grant to participate in this stimulating event. I also would like to thank Bo Yang for his research assistance and the two anonymous referees and an anonymous associate editor for their valuable suggestions. Stock option price approximations are developed for a model which takes both the risk of default and the stochastic volatility into account. The intensity of defaults is assumed to be influenced by the volatility. It is shown that it might be possible to infer the risk neutral default intensity from the stock option prices. The proposed option price approximation has a rich implied volatility surface structure and fits the data implied volatility well. A calibration exercise shows that an effective hazard rate from bonds issued by a company can be used to explain the impliedvolatility skew of the option prices issued by the same company. It is also observed that the implied yield spread obtained from calibrating all the model parameters to the option prices matches the observed yield spread.     

PERSPECTIVES IN MECHANICS OF HETEROGENEOUS SOLIDS

The Microand Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives,trends,and directions in mechanics of heterogeneous materials in January 2010.The international journal,Acta Mechanica Solida Sinica,is devoted to all fields of solid mechanics and relevant disciplines in science,technology,and engineering,with a balanced coverage on analytical,experimental,numerical and applied investigations.On the occasion of the 30 th anniversary of Acta Mechanica Solida Sinica,its editor-in-chief,Professor Q.S.Zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids,with a particular emphasis on the recent research development results of Chinese scientists.Their reviews are organized into five research areas as reported in different sections of this paper.§I firstly brings in focus on microand nano-mechanics,with regards to several selective topics,including multiscale coupled models and computational methods,nanocrystal superlattices,surface effects,micromechanical damage mechanics,and microstructural evolution of metals and shape memory alloys.§II shows discussions on multifield coupled mechanical phenomena,e.g.,multi-fields actuations of liquid crystal polymer networks,mechanical behavior of materials under radiations,and micromechanics of heterogeneous materials.In §III,we mainly address the multiscale mechanics of biological nanocomposites,biological adhesive surface mechanics,wetting and dewetting phenomena on microstructured solid surfaces.The phononic crystals and manipulation of elastic waves were elaborated in §IV.Finally,we conclude with a series of perspectives on solid mechanics.This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development.