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Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

Physical Review Letters 2012年第11期109卷 114302-114302页

作者： Zi Chen Qiaohang Guo Carmel Majidi Wenzhe Chen David J. Srolovitz Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08544 USA Department of Biomedical Engineering Washington University St. Louis Missouri 63130 USA College of Materials Science and Engineering Fuzhou University Fuzhou Fujian 350108 China Department of Mathematics and Physics Fujian University of Technology Fuzhou Fujian 350108 China Department of Mechanical Engineering Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA Department of Materials Science and Engineering Fujian University of Technology Fuzhou Fujian 350108 China Institute for High Performance Computing 1 Fusionopolis Way Singapore 138632 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Mathematics Institute for Advanced Study Princeton New Jersey 08540 USA

Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.

关键词： NONLINEAR theories DEFORMATIONS (Mechanics) PARAMETER estimation OPTICAL bistability STRUCTURAL shells PLATES (Engineering) CRYSTAL structure

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Fast wavelet-based single-particle reconstruction in Cryo-EM

Fast wavelet-based single-particle reconstruction in Cryo-EM

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IEEE International Symposium on Biomedical Imaging

作者： Cédric Vonesch Lanhui Wang Yoel Shkolnisky Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Applied Mathematics Tel-Aviv University Tel-Aviv Israel

This paper presents a novel algorithm for the 3D tomographic inversion problem that arises in single-particle electron cryomicroscopy (Cryo-EM). It is based on two key components: 1) a variational formulation that promotes sparsity in the wavelet domain and 2) the Toeplitz structure of the combined projection/back-projection operator. The first idea has proven to be very effective for the recovery of piecewise-smooth signals, which is confirmed by our numerical experiments. The second idea allows for a computationally efficient implementation of the reconstruction procedure, using only one circulant convolution per iteration.

关键词： Image reconstruction Signal to noise ratio Three dimensional displays Fourier transforms Kernel Tomography

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Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

Strong and weak divergence in finite time of Euler's method ...

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作者： Hutzenthaler, Martin Jentzen, Arnulf Kloeden, Peter E. LMU Biozentrum Department Biologie II University of Munich 82152 Planegg-Martinsried Germany Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544-1000 United States Institute for Mathematics Goethe University Frankfurt am Main 60054 Frankfurt am Main Germany

The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz continuous coefficients, that Euler's approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point. Even worse, the difference of the exact solution and of the numerical approximation at a finite time point diverges to infinity in the strong mean-square sense and in the numerically weak sense. © 2010 The Royal Society.

关键词： Stochastic systems

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Comprehensive analysis of compositional interface fluctuations in planar lipid bilayer membranes

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Physical Review E 2011年第5期84卷 051903-051903页

作者： Tao Han Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

In this paper we present a comprehensive analysis of line tension-driven compositional interface fluctuations in planar lipid bilayer membranes. Our starting point is the advective Cahn-Hilliard equation for the local lipid composition in symmetric membranes, which explicitly incorporates both advective and diffusive lipid transport processes, and which is coupled to the continuum hydrodynamic equations governing the flow behavior of the membrane and surrounding solvent with finite subphase thickness. In order to extract the interface dynamics from the continuum phase-field formalism, we first derive the appropriate sharp-interface limit equations. We then carry out a linear perturbation analysis for the relaxational dynamics of small-amplitude sinusoidal interface fluctuations to yield the general dispersion relation ωk as a function of perturbation wave number k. The resulting expression incorporates the effects of diffusive and advective lipid transport processes within the membrane, viscous or viscoelastic membrane properties, coupling between membrane and solvent, and inertial effects within the membrane and solvent. It is shown that previously considered scenarios naturally emerge as limiting cases of the general result. Furthermore, we discuss two additional scenarios amenable to analysis, one in which the inertia of the solvent is relevant, and another one in which the membrane displays significant viscoelastic properties. Finally, we numerically evaluate the general dispersion relation for three representative model membrane systems.

关键词： BILAYER lipid membranes FLUCTUATIONS (Physics) PERTURBATION (mathematics) VISCOELASTICITY HYDRODYNAMICS

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Coarse graining the dynamics of heterogeneous oscillators in networks with spectral gaps

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Physical Review E 2011年第3期84卷 036708-036708页

作者： Karthikeyan Rajendran Ioannis G. Kevrekidis Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

We present a computer-assisted approach to coarse graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low dimensional. Our first choice of coarse variables consists of the components of the oscillator states—their (complex) phase angles—along the leading eigenvectors of this Laplacian. We then use the equation-free framework, circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed-point, and coarse limit-cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fast-developing correlations between oscillator state and oscillator intrinsic properties and establishes a connection with tools developed in the context of uncertainty quantification.

关键词： GRAINING COMPUTER-aided design LAPLACIAN operator EIGENVECTORS HARMONIC oscillators

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Direct minimization of the optimized effective problem based on efficient finite differences

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Physical Review B 2011年第16期84卷 165122-165122页

作者： Chen Huang Emily A. Carter Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and the Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

To avoid the difficult-to-solve optimized effective potential (OEP) integral equation, we introduce an efficient direct minimization scheme for performing OEP calculations within Kohn–Sham density functional theory (KS-DFT). We reformulated the functional derivative of the total energy with respect to the KS effective potential in terms of efficient finite differences. Our method only uses the orbitals involved in the construction of the KS exchange-correlation functionals. We demonstrate our scheme by performing exact-exchange OEP for sodium clusters, in which only occupied KS orbitals are needed to obtain the OEP. Our efficient direct minimization scheme should aid future development of orbital-dependent density functionals and render OEP to be a practical choice for various applications.

关键词： INTEGRAL equations DENSITY functionals TOTAL energy systems (On-site electric power production) FINITE differences PHYSICS

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Anatomically adapted wavelets for integrated statistical analysis of fMRI data

Anatomically adapted wavelets for integrated statistical ana...

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2011 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI'11

作者： Özkaya, S. Görkem Van De Ville, Dimitri Program in Applied and Computational Mathematics Princeton University Princeton NJ United States Medical Image Processing Lab Ecole Polytechnique Fédérale de Lausanne Switzerland Medical Image Processing Lab. Université de Genëve Genëve Switzerland

ISBN: (纸本)9781424441280

Wavelets have been successfully used in statistical analysis of fMRI data as a spatial transform providing a compact representation of brain activation maps. However, conventional (tensor-product) wavelet transforms assume a rectangular domain, while the essential brain activity takes place in the convoluted gray-matter layer. We use the lifting scheme to design wavelet bases for more arbitrary domains which do not have a group structure. In particular, we have considered the grey-matter cortical layer as the domain. We then applied the new transform to fMRI data using the wavelet-based SPM (WSPM) framework. Preliminary results show that the adapted wavelets have superior performance in terms of sensitivity than the standard tensor-product wavelets, while having the same control over type-I error rate (specificity). © 2011 IEEE.

关键词： Wavelet transforms

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Densest local sphere-packing diversity. II. Application to three dimensions

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Physical Review E 2011年第1期83卷 011304-011304页

作者： Adam B. Hopkins Frank H. Stillinger Salvatore Torquato Department of Chemistry and Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N=1054. In the predecessor to this paper [A. B. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of N up to N=348. Here we analyze the properties and characteristics of the densest local packings in R3 and employ knowledge of the Rmin(N), using methods applicable in any d, to construct both a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In R3, we find wide variability in the densest local packings, including a multitude of packing symmetries such as perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest local packings of N spheres near a central sphere to minimal-energy configurations of N+1 points interacting with short-range repulsive and long-range attractive pair potentials, e.g., 12–6 Lennard-Jones, and find that they are in general completely different, a result that has possible implications for nucleation theory. We also compare the densest local packings to finite subsets of stacking variants of the densest infinite packings in R3 (the Barlow packings) and find that the densest local packings are almost always most similar as measured by a similarity metric, to the subsets of Barlow packings with the smallest number of coordination shells measured about a single central sphere, e.g., a subset of the fcc Barlow packing. Additionally, we observe that the densest local packings are dominated by the dense arrangement of spheres with centers at distance Rmin(N). In particular, we find two “maracas” packings at N=77 and N=93, each consisting of a few unjammed sphere

关键词： DENSITY functionals SPHERES MATHEMATICAL models EUCLIDEAN metric CORRELATION (Statistics) SYMMETRY

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Frame coherence and sparse signal processing

Frame coherence and sparse signal processing

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IEEE International Symposium on Information Theory

作者： Dustin G. Mixon Waheed U. Bajwa Robert Calderbank Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Electrical and Computer Engineering Duke University Durham NC USA

The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate whether an arbitrary matrix, or frame, is suitable for sensing sparse signals. To this end, the present paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first provide several examples of frames that have small spectral norm, worst-case coherence, and average coherence. Next, we present a new lower bound on worst-case coherence and compare it to the Welch bound. Later, we propose an algorithm that decreases the average coherence of a frame without changing its spectral norm or worst-case coherence. Finally, we use worst-case and average coherence, as opposed to the Restricted Isometry Property, to garner near-optimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. This contrasts with recent results that only guarantee noiseless signal recovery from arbitrary frames, and which further assume independence across the nonzero entries of the signal-in a sense, requiring small average coherence replaces the need for such an assumption.

关键词： Coherence Signal processing algorithms Noise Harmonic analysis Noise measurement Geometry

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Structure and dynamics of highly charged heavy ions studied with the electron beam ion trap in Tokyo

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Hyperfine Interactions 2011年第1期199卷 123-130页

作者： Nakamura, Nobuyuki Hu, Zhimin Watanabe, Hirofumi Li, Yueming Kato, Daiji Currell, Fred J. Tong, Xiao-Min Watanabe, Tsutomu Ohtani, Shunsuke Institute for Laser Science The University of Electro-Communications 1-5-1 Chofugaoka Chofu Tokyo 182-8585 Japan Chubu University 1200 Matsumoto-cho Kasugai-shi Aichi 487-8501 Japan Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 China National Institute for Fusion Science 322-6 Oroshi-cho Toki Gifu 509-5292 Japan Centre for Plasma Physics School of Mathematics and Physics Queen's University Belfast Belfast BT7 1NN United Kingdom Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki 305-8573 Japan

In this paper, we present the structure and the dynamics of highly charged heavy ions studied through dielectronic recombination (DR) observations performed with the Tokyo electron beam ion trap. By measuring the energy dependence of the ion abundance ratio in the trap at equilibrium, we have observed DR processes for open shell systems very clearly. Remarkable relativistic effects due to the generalized Breit interaction have been clearly shown in DR for highly charged heavy ions. We also present the first result for the coincidence measurement of two photons emitted from a single DR event. © 2011 Springer Science+Business Media B.V.

关键词： Heavy ions

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