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Comprehensive analysis of compositional interface fluctuations in planar lipid bilayer membranes

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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Parsimonious reconstruction of network evolution

Parsimonious reconstruction of network evolution

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Lecture Notes in Computer science

作者： Patro, Rob Sefer, Emre Malin, Justin Marçais, Guillaume Navlakha, Saket Kingsford, Carl Center for Bioinformatics and Computational Biology University of Maryland College Park MD 20742 United States Department of Computer Science University of Maryland College Park MD 20742 United States Computational Biology Bioinformatics and Genomics Concentration Biological Sciences Graduate Program University of Maryland College Park MD 20742 United States Program in Applied Mathematics Statistics and Scientific Computation University of Maryland College Park MD 20742 United States School of Computer Science Carnegie Mellon University Pittsburgh PA 15213 United States

ISBN: (纸本)9783642230370

We consider the problem of reconstructing a maximally parsimonious history of network evolution under models that support gene duplication and loss and independent interaction gain and loss. We introduce a combinatorial framework for encoding network histories, and we give a fast procedure that, given a set of duplication histories, in practice finds network histories with close to the minimum number of interaction gain or loss events. In contrast to previous studies, our method does not require knowing the relative ordering of unrelated duplication events. Results on simulated histories suggest that common ancestral networks can be accurately reconstructed using this parsimony approach. © 2011 Springer-Verlag.

关键词： Genes

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Berry phase and Hannay angle of an interacting boson system

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Physical Review A 2011年第4期83卷 042107-042107页

作者： S. C. Li J. Liu L. B. Fu Science and Technology Computation Physics Laboratory Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Applied Physics and Technology Peking University Beijing 100084 China

In the present paper, we investigate the Berry phase and the Hannay angle of an interacting two-mode boson system and obtain their analytic expressions in explicit forms. The relation between the Berry phase and the Hannay angle is discussed. We find that, in the large-particle-number limit, the classical Hannay angle equals the particle number derivative of the quantum Berry phase except for a sign. This relationship is applicable to other many-body boson systems where the coherent-state description is available and the total particle number is conserved. The measurement of the classical Hannay angle in the many-body systems is briefly discussed as well.

关键词： GEOMETRIC quantum phases ANGLE modulation INTERACTING boson models MANY-body problem COHERENT states QUANTUM interference HARMONIC oscillators

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Quantum phase transition from mixed atom-molecule phase to pure molecule phase: Characteristic scaling laws and Berry-curvature signature

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Physical Review A 2011年第2期84卷 023605-023605页

作者： Sheng-Chang Li Li-Bin Fu Science and Technology Computation Physics Laboratory Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Applied Physics and Technology Peking University Beijing 100084 China

We investigate the quantum phase transition in an ultracold atom-molecule conversion system. It is found that the system undergoes a phase transition from a mixed atom-molecule phase to a pure molecule phase when the energy bias exceeds a critical value. By constructing a coherent state as variational state, we get a good approximation of the quantum ground state of the system. Using this variational state, we deduce the critical point analytically. We then discuss the scaling laws characterizing the transition and obtain the corresponding critical exponents. Furthermore, the Berry curvature signature of the transition is studied. In particular, we find that the derivatives of the Berry curvature with respect to total particle number intersect at the critical point. The underlying mechanism of this finding is discussed as well.

关键词： ATOMS PHASE transformations (Physics) SCALING laws (Nuclear physics) QUANTUM theory PARTICLES (Nuclear physics) QUANTUM Hall effect

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Adiabatic geometric phase for a Bose-Einstein condensate coupled to a cavity

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Physical Review A 2011年第5期84卷 053610-053610页

作者： Sheng-Chang Li Li-Bin Fu Jie Liu National Key Laboratory of Science and Technology on Computation Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Applied Physics and Technology Peking University Beijing 100084 China

We investigate the geometric phase in a model of a Bose-Einstein condensate coupled to an optical cavity in which both the condensate and the cavity are described with coherent states. When the argument of the atom-cavity coupling term varies in time slowly from zero to 2π, we calculate the geometric phase accumulated by the ground state and obtain its analytic expression in explicit form. We find that the adiabatic geometric phase jumps from zero to nontrivial π at a critical value that corresponds to the normal-superradiant phase-transition point. The magneticlike flux interpretation of the geometric phase is also discussed.

关键词： BOSE-Einstein condensation PHASE transformations (Physics) COUPLINGS (Gearing) SUPERRADIANCE MOLECULAR emission cavity analysis

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Continuum model of irradiation-induced spinodal decomposition in the presence of dislocations

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Physical Review B 2011年第17期83卷 174106-174106页

作者： J. J. Hoyt M. Haataja Department of Materials Science and Engineering McMaster University Hamilton Ontario Canada L8S4L7 Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544

A model of phase-separation kinetics in systems exposed to energetic particle irradiation has been extended to include the effects of mobile dislocations. It is shown that when dislocations are allowed to participate in the decomposition reaction, phase separation can occur at temperatures above the coherent spinodal, which is in agreement with several experiments on irradiated alloys. A linear stability analysis of the governing kinetic equations is performed and three regimes of microstructural evolution are identified within the parameter space of damage cascade size vs incident flux: complete phase separation, solid-solution behavior, and compositional patterning. In addition, numerical simulations of the evolving dislocation density and composition fields are performed. The numerical results provide the amplitude and wavelength of the stable patterns that can form under irradiation and elucidate the role of misfit dislocations in reducing the coherency strain due to atomic size mismatch.

关键词： PHASE transformations (Physics) THERMODYNAMICS PARTICLES (Nuclear physics) ALLOYS IRRADIATION STRAINS & stresses (Mechanics)

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Phase Diagram and Structural Diversity of the Densest Binary Sphere Packings

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Physical Review Letters 2011年第12期107卷 125501-125501页

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

The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the α−x plane of sphere radius ratio α and relative concentration x are at the Kepler limit α=1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (α,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings.

关键词： SPHERE packings PHASE diagrams SOLID geometry KEPLER'S laws CRYSTALLOGRAPHY CELLS

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Improved reconstructions of random media using dilation and erosion processes

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Physical Review E 2011年第5期84卷 056102-056102页

作者： Chase E. Zachary Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. The aforementioned correlation functions are special cases of the so-called canonical n-point correlation function Hn and generalize the ones that have been recently employed to advance our ability to reconstruct complex microstructures [Y. Jiao, F. H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. 106, 17634 (2009)]. The use of these generalized correlation functions is tantamount to dilating or eroding a reference phase of the target medium and incorporating the additional topological information of the modified media, thereby providing more accurate reconstructions of percolating, filamentary, and other topologically complex microstructures. We apply our methods to a multiply connected “donut” medium and a dilute distribution of “cracks” (a set of essentially zero measure), demonstrating improved accuracy in both cases with implications for higher-dimensional and biconnected two-phase systems. The high information content of the generalized two-point correlation functions suggests that it would be profitable to explore their use to characterize the structural and physical properties of not only random media, but also molecular systems, including structural glasses.

关键词： FUNCTIONS (mathematics) MICROSTRUCTURE TOPOLOGY COMPOSITE materials PROBABILITY theory STATISTICS

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Single-scattering optical tomography: Simultaneous reconstruction of scattering and absorption

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Physical Review E 2010年第1期81卷 016602-016602页

作者： Lucia Florescu Vadim A. Markel John C. Schotland Department of Bioengineering and Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia Pennsylvania 19104 USA

We report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured. That is, no physical mechanism for separating single-scattered photons from the rest of the multiply-scattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering.

关键词： Image reconstruction

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Why Gabor frames? Two fundamental measures of coherence and their role in model selection

Why Gabor frames? Two fundamental measures of coherence and ...

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作者： Bajwa, Waheed U. Calderbank, Robert Jafarpour, Sina Department of Electrical Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Computer Science Princeton University Princeton NJ 08544 United States

The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence- termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carr

关键词： Recovery

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