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Inverse design of disordered stealthy hyperuniform spin chains

Physical Review B 2016年第6期93卷 064201-064201页

作者： Eli Chertkov Robert A. DiStasio, Jr. Ge Zhang Roberto Car Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Chemistry and Chemical Biology Cornell University Ithaca New York 14853 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and thermodynamic properties. Such stealthy and hyperuniform states are unique in that they are transparent to radiation for a range of wave numbers around the origin. In this work, we employ recently developed inverse statistical-mechanical methods, which seek to obtain the optimal set of interactions that will spontaneously produce a targeted structure or configuration as a unique ground state, to investigate the spin-spin interaction potentials required to stabilize disordered stealthy hyperuniform one-dimensional (1D) Ising-type spin chains. By performing an exhaustive search over the spin configurations that can be enumerated on periodic 1D integer lattices containing N=2,3,...,36 sites, we were able to identify and structurally characterize all stealthy hyperuniform spin chains in this range of system sizes. Within this pool of stealthy hyperuniform spin configurations, we then utilized such inverse optimization techniques to demonstrate that stealthy hyperuniform spin chains can be realized as either unique or degenerate disordered ground states of radial long-ranged (relative to the spin-chain length) spin-spin interactions. Such exotic ground states appear to be distinctly different from spin glasses in both their inherent structural properties and the nature of the spin-spin interactions required to stabilize them. As such, the implications and significance of the existence of these disordered stealthy hyperuniform ground-state spin systems warrants further study, including whether their bulk physical properties and excited states, like their many-particle system counterparts, are singularly remarkable, and can be experimentally realized.

关键词： Optimization problems Ising model Spin chains

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Wall to wall optimal transport 15

Wall to wall optimal transport

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15th European Turbulence Conference, ETC 2015

作者： Doering, Charles R. Souza, Andre N. Chini, Gregory P. Hassanzadeh, Pedram Department of Physics University of Michigan United States Department of Mathematics University of Michigan United States Center for the Study of Complex Systems University of Michigan United States Department of Mechanical Engineering Program in Integrated Applied Mathematics and Center for Fluid Physics University of New Hampshire United States Centre for the Environment Department of Earth and Planetary Sciences Harvard University United States

The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of the kinetic energy or a fixed value of the enstrophy (the mean square rate of strain in this situation). The optimizing flows realize upper limits on convective transport in this scenario. We interpret the results in the context of buoyancy-driven Rayleigh–Bénard convection problems that satisfy the flow intensity constraints, enabling us to investigate how optimal transport scalings compare with upper bounds on Nu expressed as a function of the Rayleigh number Ra. © TU Delft.

关键词： Kinetic energy

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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Usability of VGI for validation of land cover maps (vol 29, pg 1269, 2015)

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INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2015年第7期29卷 1269-1291页

作者： Fonte, C. C. Lupia, Flavio [a] Department of Mathematics University of Coimbra Coimbra Portugal[b] Institute for Systems Engineering and Computers at Coimbra (INESC Coimbra) Coimbra Portugal[c] School of Engineering and Applied Science Aston University Birmingham UK[d] Ecosystems Services and Management Program International Institute for Applied Systems Analysis (IIASA) Laxenburg Austria[e] School of Geography University of Nottingham Nottingham UK[f] National Institute of Agricultural Economics (INEA) Rome Italy

Volunteered Geographic Information (VGI) represents a growing source of potentially valuable data for many applications, including land cover map validation. It is still an emerging field and many different approaches can be used to take value from VGI, but also many pros and cons are related to its use. Therefore, since it is timely to get an overview of the subject, the aim of this article is to review the use of VGI as reference data for land cover map validation. The main platforms and types of VGI that are used and that are potentially useful are analysed. Since quality is a fundamental issue in map validation, the quality procedures used by the platforms that collect VGI to increase and control data quality are reviewed and a framework for addressing VGI quality assessment is proposed. A review of cases where VGI was used as an additional data source to assist in map validation is made, as well as cases where only VGI was used, indicating the procedures used to assess VGI quality and fitness for use. A discussion and some conclusions are drawn on best practices, future potential and the challenges of the use of VGI for land cover map validation.

关键词： VGI land cover/land use quality validation crowdsourcing

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Confined disordered strictly jammed binary sphere packings

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Physical Review E 2015年第6期92卷 062207-062207页

作者： D. Chen S. Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H, small to large sphere radius ratio α, and small sphere relative concentration x. We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term “confinement frustration.” Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H, though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call “size-disparity” frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance στ2(R) to characterize confined packings and find that these packings possess essentially the same level of

关键词： RESEARCH Combinatorial packing & covering Linear programming Density Powders Sphere packings

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Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases

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Physical Review E 2015年第2期92卷 022120-022120页

作者： G. Zhang F. H. Stillinger S. Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space Rd. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.

关键词： GROUND state (Quantum mechanics) ENERGY levels (Quantum mechanics) EUCLIDEAN domains MOLECULAR dynamics QUANTUM entropy

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Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations

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Physical Review E 2015年第2期92卷 022119-022119页

Systems of particles interacting with “stealthy” pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like “pseudo” disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperatur

关键词： THERMODYNAMIC equilibrium PROBABILITY theory QUANTUM spin models MOLECULAR dynamics QUANTUM entropy

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Covariance estimation using conjugate gradient for 3D classification in CRYO-EM

Covariance estimation using conjugate gradient for 3D classi...

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IEEE International Symposium on Biomedical Imaging

作者： Joakim Andén Eugene Katsevich Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ Department of Statistics Stanford University Stanford CA

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.

关键词： Covariance matrices Eigenvalues and eigenfunctions Microscopy Image reconstruction Biology Image resolution

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Digital Microfluidics: Paper-Based Digital Microfluidic Chip for Multiple Electrochemical Assay Operated by a Wireless Portable Control System (Adv. Mater. Technol. 3/2017)

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Advanced Materials Technologies 2017年第3期2卷

作者： Nipapan Ruecha Jumi Lee Heedo Chae Haena Cheong Veasna Soum Pattarachaya Preechakasedkit Orawon Chailapakul Georgi Tanev Jan Madsen Nadnudda Rodthongkum Oh-Sun Kwon Kwanwoo Shin Program in Macromolecular Science Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Department of Chemistry and Institute of Biological Interfaces Sogang University Seoul 04107 Republic of Korea Program in Biotechnology Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Electrochemistry and Optical Spectroscopy Research Unit (EOSRU) Department of Chemistry Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby 2800 Denmark Metallurgy and Materials Science Research Institute Chulalongkorn University Bangkok 10330 Thailand

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Phenomenological Blasius-type friction equation for turbulent power-law fluid flows

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Physical Review E 2015年第6期92卷 063006-063006页

作者： H. R. Anbarlooei D. O. A. Cruz F. Ramos A. P. Silva Freire Mechanical Engineering Program Federal University of Rio de Janeiro (COPPE/UFRJ) Rio de Janeiro 21941-594 Brazil Department of Applied Mathematics Institute of Mathematics. Federal University of Rio de Janeiro Rio de Janeiro 21941-594 Brazil

We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.

关键词： Blasius equation Friction Turbulent flow Mathematical formulas Newtonian fluids Kolmogorov complexity

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