Pseudospectral reduction of incompressible two-dimensional turbulence

Spectral reduction was originally formulated entirely in the wavenumber domain as a coarse-grained wavenumber convolution in which bins of modes interact with enhanced coupling coefficients. A Liouville theorem leads to inviscid equipartition solutions when each bin contains the same number of modes. A pseudospectral implementation of spectral reduction which enjoys the efficiency of the fast Fourier transform is described. The model compares well with full pseudospectral simulations of the two-dimensional forced-dissipative energy and enstrophy cascades.     

Coarse Baum-Connes conjecture

In this paper, we shall prove the coarse Baum-Connes conjecture for metric spaces with Lipschitz good covers. This class of metric spaces includes trees and simply connected nonpositively curved manifolds.Supported by DMS8505550 through a MSRI Postdoctoral Fellowship.     

Hypercyclicity and unimodular point spectrum

We show that an operator on a separable complex Banach space with sufficiently many eigenvectors associated to eigenvalues of modulus 1 is hypercyclic. We apply this result to construct hypercyclic operators with prescribed K_σ unimodular point spectrum. We show how eigenvectors associated to unimodular eigenvalues can be used to exhibit common hypercyclic vectors for uncountable families of operators, and prove that the family of composition operators C_? on H²(D), where ? is a disk automorphism having +1 as attractive fixed point, has a residual set of common hypercyclic vectors.     

Coarsely embeddable metric spaces without Property A

We study Guoliang Yu's Property A and construct metric spaces which do not satisfy Property A but embed coarsely into the Hilbert space.     

Efficient sampling of random permutations

We show how to uniformly distribute data at random (not to be confounded with permutation routing) in two settings that are able to deal with massive data: coarse grained parallelism and external memory. In contrast to previously known work for parallel setups, our method is able to fulfill the three criteria of uniformity, work-optimality and balance among the processors simultaneously. To guarantee the uniformity we investigate the matrix of communication requests between the processors. We show that its distribution is a generalization of the multivariate hypergeometric distribution and we give algorithms to sample it efficiently in the two settings.     

A non-equilibrium multiscale simulation of shock wave propagation

A novel non-equilibrium multiscale dynamics (NEMSD) is proposed to simulate non-equilibrium thermal–mechanical processes. The model couples coarse-grain thermodynamics with a fine scale molecular dynamics. A Distributed Nośe-Hoover Thermostat Network is used, which regulates the temperature in each coarse scale Voronoi cell according to the finite element (FE) nodal temperature. The atoms in each element-cell, namely Voronoi cell-ensemble, are assumed to be in a local equilibrium state within one coarse scale time step. The change of FE nodal temperature provides a source of random forces, which drive the system out of equilibrium. The proposed NEMSD can successfully simulate shock wave propagation in a cubic lattice.     

水田污染区稻壳与糙米中铬元素的LIBS分析可行性

为验证激光诱导击穿光谱(LIBS)对江西省环鄱阳湖水田污染区稻谷中铬元素的分析可行性,本试验以在该区收集的稻壳、糙米和白米作为研究对象,分别对所有样品进行LIBS测试,并利用火焰原子吸收法(AAS)对铬元素进行真实浓度检测。LIBS图谱显示稻壳中明显地检测到了铬元素的特征谱线,而糙米和白米则检测不到。AAS结果显示稻壳中Cr浓度远高于糙米,而白米中Cr未超标,同时,稻壳与糙米Cr浓度比率具有一定的梯度关系。结果说明,Cr在稻壳中的富集量高于糙米和白米,利用LIBS技术对稻壳中Cr进行检测具有一定的可行性,最终有望实现通过采集稻壳LIBS光谱信号,预测出糙米中重金属元素的分布规律,进而采用类似的方法获取大米中重金属元素含量。     

Modeling ssDNA electrophoretic migration with band broadening in an entangled or cross-linked network

We use a coarse-grained model proposed by Graham and Larson based on the temporary network model by Schieber et al.. [1] to simulate the electrophoretic motion of ssDNA and corresponding band broadening due to dispersion. With dimensionless numbers reflecting the experimental physical properties, we are able to simulate ssDNA behavior under weak to moderate electric field strengths for chains with 8-50 entanglements per chain ( approximately 1000-8500 base pairs), and model smoothly the transition from reptation to oriented reptation. These results are fitted with an interpolation equation, which allows the user to calculate dimensionless mobilities easily from input parameters characterizing the gel matrix, DNA molecules, and field strengths. Dimensionless peak widths are predicted from mobility fluctuations using the central limit theorem and the assumption that the mobility fluctuations are Gaussian. Using results from previous studies of ssDNA physical properties (effective charge xiq and Kuhn step length b(K)) and sieving matrix properties (pore size or tube diameter a), we give scaling factors to convert the dimensionless values to "real" experimental values, including the mobility, migration distance, and time. We find that the interpolation equation fits well the experimental data of ssDNA mobilities and peak widths, supporting the validity of the coarse-grained model. The model does not account for constraint release and hernia formation, and assumes that the sieving network is a homogeneous microstructure with no temperature gradients and no peak width due to injection. These assumptions can be relaxed in future work for more accurate prediction.     

A modified alignment method based on four-quadrant-grating moiré for proximity lithography

In this paper, we demonstrate a modified coarse-fine alignment scheme designed for proximity lithography. Both wafer alignment mark and mask alignment mark consists of linear grating arrays and “+” bar. Coarse alignment and fine alignment could work together to achieve the perfect alignment. Thereinto, coarse alignment, measured from two superposed “+” bars, guarantees the misalignment across wafer and mask within the measurement range of fine alignment, which is based on moiré fringes formed by the superposition of linear grating arrays. Then we conduct the experiments using a nanometer actuator to drive the wafer alignment mark meanwhile keeping the mask alignment mark motionless, which validates the feasibility and rationality of our designed scheme.