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Multiple Magnetic Pole Reversals and Mössbauer Studies in Molecular-based Mixed Valency Ferrimagnet {[N(n-C4H9)4][MIIFeIII(C2O4)3]}n (M=Zn, Fe)

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Physics Procedia 2012年 25卷 375-381页

作者： Qing Lin Chenglong Lei Guodong Tang Qingmei Zhang Xinlong Dong Fupei Liang Ruijun Wang Siliang Zeng Yun He College of Physics and Technology Guangxi Normal University Guilin 541004 China Department of Information Technology Hainan Medical College Haikou 571101 China College of Chemistry and Chemical Engineering Guangxi Normal University Guilin 541004China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The Molecule magnets Materials {[N(n-C4H9)4][MIIFeIII(C2O4)3]}n (M=Zn Fe) were investigated by magnetic measurements and Mössbauer spectroscopy .In the complex {[N(n-C4H9)4][ZnII0.03FeII0.97 FeIII(C2O4)3]}n detailed investigation of the ferromagnetism behaviour, and a compensation temperature has found with the field being less than 1KOe. And the 57Fe Mössbauer measurements had been carried out in {[N(n-C4H9)4][FeIIFeIII(C2O4)3]}n to investigate the mixed valency character and antiferromagnetic coupling. Some ferrimagnets consisting of magnetic anisotropy ions and two or more types of antiferromagnetically ordered magnetic ions exhibit this behavior. As the temperature was lowered to 40 K, the FeIII doublet subspectrum almost completely turns into a sextet subspectrum. The hyperfine magnetic field increases as the temperature decreasing.

关键词： Molecule-based magnet Oxalate Mössbauer spectroscopy spin glass

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Magnetic Studies in Rare Earth-iron Oxalate-bridged Complexes MFe(C2O4)3·9H2O (M=Ce, Pr)

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Physics Procedia 2012年 25卷 369-374页

作者： Qing Lin Chenglong Lei Hui Zhang Xuehui Long Jianmei Xu Fupei Liang Ruijun Wang Siliang Zeng Yun He College of Physics and Technology Guangxi Normal University Guilin 541004 China Department of Information Technology Hainan Medical College Haikou 571101 China College of Chemistry and Chemical Engineering Guangxi Normal University Guilin 541004China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The rare earth-iron oxalate-bridged complexes CeFe(C2O4)3·9H2O and PrFe(C2O4)3·9H2O have been synthesized. In the sample CeFe(C2O4)3·9H2O, the magnetic susceptibilities of the compound can be fit to the Curie-Weiss law and Weiss paramagnetic Curie temperature of θ=-*** hyperfine field parameters show that the dependent of the hyperfine field and the spontaneous magnetization and that of the spontaneous magnetization and temperature in the latticed FeII and *** are a clear bifurcation phenomenon of the field-cooled (MFC) and Zero-field-cooled (MZFC) magnetization curves at the Néel temperature (4 K).In the sample PrFe(C2O4)3·9H2O,the Weiss paramagnetic Curie temperature θ=-2.7 K,There are a bifurcation of the ZFC and FC plots at the Néel temperature (6 K).The negative Weiss constant indicates an intramolecular antiferromagnetic coupling interaction between the adjacent Fe(II) and Fe(III) ions through the oxalate *** oxalate group has been shown to be an excellent bridging ligand in supporting the magnetic exchange interaction.

关键词： Oxalate rare earth materials susceptibility magnetic interaction

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Microstructural degeneracy associated with a two-point correlation function and its information content

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Physical Review E 2012年第5期85卷 051140-051140页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège Liège 4000 Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the

关键词： MICROSTRUCTURE CORRELATION (Statistics) INFORMATION theory ENTROPY (Information theory) GROUND state (Quantum mechanics) MONTE Carlo method POISSON processes

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Optimal Filling of Shapes

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Physical Review Letters 2012年第19期108卷 198304-198304页

作者： Carolyn L. Phillips Joshua A. Anderson Greg Huber Sharon C. Glotzer Applied Physics Program University of Michigan Ann Arbor Michigan 48109 USA Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 USA Center for Cell Analysis and Modeling University of Connecticut Health Center Farmington Connecticut 06032 USA Department of Cell Biology University of Connecticut Health Center Farmington Connecticut 06032 USA Department of Mathematics University of Connecticut Storrs Connecticut 06032 USA Department of Materials Science and Engineering University of Michigan Ann Arbor Michigan 48109 USA

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N→∞. We note an analogy with energy landscapes.

关键词： SHAPES FORCE & energy COMBINATORIAL packing & covering ANALOGY HEURISTIC THEORY of distributions (Functional analysis)

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Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

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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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Manifold learning techniques and model reduction for dissipative dynamics

Manifold learning techniques and model reduction for dissipa...

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Computing and Systems Technology Division - Core programming Topic at the 2011 AIChE Annual Meeting

作者： Sonday, Benjamin Rajendran, Karthikeyan Gear, William Singer, Amit Kevrekidis, Ioannis G. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Chemical and Biological Engineering Princeton University PrincetonNJ United States Mathematics and PACM Princeton University PrincetonNJ United States

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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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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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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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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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