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Physical Review E 2019年第4期99卷 042133-042133页

作者： Mobolaji Williams Department of Physics Harvard University Cambridge Massachusetts 02138 USA

In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the statistical physics of self-assembly in a simpler scenario: the formation of dimers from a system of monomers. The properties of the model allow us to frame the microstate counting as a combinatorial problem whose solution leads to an exact partition function. From the associated equilibrium conditions, we find that such dimer systems come in two types: ”search-limited” and ”combinatorics-limited,” only the former of which has states where partial assembly can be dominated by correct contacts. Using estimates of biophysical quantities in systems of single-stranded DNA dimerization, transcription factor and DNA interactions, and protein-protein interactions, we find that all of these systems appear to be of the search-limited type, i.e., their fully correct dimerization regimes are more limited by the ability of monomers to find one another in the constituent volume than by the combinatorial disadvantage of correct dimers. We derive the parameter requirements for fully correct dimerization and find that rather than the ratio of particle number and volume (i.e., number density) being the relevant quantity, it is the product of particle diversity and volume that is constrained. Ultimately, this work contributes to an understanding of self-assembly by using the simple case of a system of dimers to analytically study the combinatorics of assembly.

关键词： Biomolecular self-assembly Classical statistical mechanics DNA-protein interactions Phase diagrams Protein-protein interactions Self-organized systems Biomolecules Combinatorics Exact solutions for many-body systems metropolis algorithm Monte Carlo methods

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Discontinuous evolution of the structure of stretching polycrystalline graphene

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Physical Review B 2019年第16期100卷 161402(R)-161402(R)页

作者： Federico D'Ambrosio Vladimir Juričić Gerard T. Barkema Department of Information and Computing Sciences Utrecht University Princetonplein 5 3584 CC Utrecht The Netherlands Nordita KTH Royal Institute of Technology and Stockholm University Roslagstullsbacken 23 10691 Stockholm Sweden

Polycrystalline graphene has an inherent tendency to buckle, i.e., develop out-of-plane, three-dimensional structure. A force applied to stretch a piece of polycrystalline graphene influences the out-of-plane structure. Even if the graphene is well relaxed, this happens in nonlinear fashion: Occasionally, a tiny increase in stretching force induces a significant displacement, in close analogy to avalanches, which in turn can create vibrations in the surrounding medium. We establish this effect in computer simulations: By continuously changing the strain, we follow the displacements of the carbon atoms that turn out to exhibit a discontinuous evolution. Furthermore, the displacements exhibit a hysteretic behavior upon the change from low to high stress and back. These behaviors open up another direction in studying dynamical elasticity of polycrystalline quasi-two-dimensional systems, and in particular the implications on their mechanical and thermal properties.

关键词： Mechanical deformation Mechanical properties of membranes 2-dimensional systems Graphene metropolis algorithm Molecular dynamics

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Reaching the Continuum Limit in Finite-Temperature Ab Initio Field-Theory Computations in Many-Fermion Systems

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Physical Review Letters 2019年第13期123卷 136402-136402页

作者： Yuan-Yao He Hao Shi Shiwei Zhang Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Physics College of William and Mary Williamsburg Virginia 23187 USA

Finite-temperature grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and the lattice gauge theory. However, these calculations have computational costs scaling as Ns3 with the size of the lattice or basis set, Ns. We report a new approach based on systematically controllable low-rank factorization that reduces the scaling of such computations to NsNe2, where Ne is the average number of fermions in the system. In any realistic calculations aiming to describe the continuum limit, Ns/Ne is large and needs to be extrapolated effectively to infinity for convergence. The method thus fundamentally changes the prospect for finite-temperature many-body computations in correlated fermion systems. Its application, in combination with frameworks to control the sign or phase problem as needed, will provide a powerful tool in ab initio quantum chemistry and correlated electron materials. We demonstrate the method by computing exact properties of the two-dimensional Fermi gas with zero-range attractive interaction as a function of temperature in both the normal and superfluid states.

关键词： Fermi gases Superfluidity Two-dimensional electron gas Computational complexity Finite-size scaling Hubbard model Lattice models in condensed matter metropolis algorithm Path-integral Monte Carlo

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Spirit: Multifunctional framework for atomistic spin simulations

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Physical Review B 2019年第22期99卷 224414-224414页

作者： Gideon P. Müller Markus Hoffmann Constantin Dißelkamp Daniel Schürhoff Stefanos Mavros Moritz Sallermann Nikolai S. Kiselev Hannes Jónsson Stefan Blügel Peter Grünberg Institut and Institute for Advanced Simulation Forschungszentrum Jülich and JARA 52425 Jülich Germany Science Institute and Faculty of Physical Sciences University of Iceland VR-III 107 Reykjavík Iceland Department of Physics RWTH Aachen University 52056 Aachen Germany

The Spirit framework is designed for atomic-scale spin simulations of magnetic systems with arbitrary geometry and magnetic structure, providing a graphical user interface with powerful visualizations and an easy-to-use scripting interface. An extended Heisenberg-type spin-lattice Hamiltonian including competing exchange interactions between neighbors at arbitrary distances, higher-order exchange, Dzyaloshinskii-Moriya and dipole-dipole interactions is used to describe the energetics of a system of classical spins localized at atom positions. A variety of common simulation methods are implemented including Monte Carlo and various time evolution algorithms based on the Landau-Lifshitz-Gilbert (LLG) equation of motion. These methods can be used to determine static ground-state and metastable spin configurations, sample equilibrium and finite-temperature thermodynamical properties of magnetic materials and nanostructures, or calculate dynamical trajectories including spin torques induced by stochastic temperature or electric current. Methods for finding the mechanism and rate of thermally assisted transitions include the geodesic nudged elastic band method, which can be applied when both initial and final states are specified, and the minimum mode-following method when only the initial state is given. The lifetimes of magnetic states and rates of transitions can be evaluated within the harmonic approximation of transition-state theory. The framework offers performant central processing unit (CPU) and graphics processing unit (GPU) parallelizations. All methods are verified and applications to several systems, such as vortices, domain walls, skyrmions, and bobbers are described.

关键词： Dipolar interaction Exchange interaction Frustrated magnetism Magnetic anisotropy Magnetic order Magnetic texture Magnetization dynamics Skyrmions Spintronics Ferrimagnets Magnetic systems Nanostructures Noncollinear magnets Heisenberg model Landau-Lifschitz-Gilbert equation Langevin algorithm metropolis algorithm Monte Carlo methods Spin lattice models

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Influence of finite-size and edge effects on the exchange-bias properties of ferromagnetic/antiferromagnetic nanodots: Granular Monte Carlo investigation

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Physical Review B 2019年第5期99卷 054410-054410页

作者： Haydar Kanso Renaud Patte Vincent Baltz Denis Ledue Normandie Université UNIROUEN INSA Rouen CNRS GPM F-76800 Saint Étienne du Rouvray France Université Grenoble Alpes CNRS CEA Grenoble INP INAC-Spintec F-38000 Grenoble France

In this paper, we investigate exchange-biased square nanodots whose lateral sizes range between 130 and 500 nm, in comparison with continuous films by kinetic Monte Carlo simulations. We use a granular model which takes into account disordered interfacial phases by considering less stable magnetic grains at the interface in the antiferromagnetic (AF) layer. We further model the effect of the nanofabrication process by considering grains with reduced surfaces at the edges, due to grain cutting. Since less stable grains at the nanodot edges in the AF layer have been experimentally evidenced, we assumed a weaker anisotropy for the grains which are in the AF layer at the dot edges. Our results evidence two different mechanisms of the ferromagnetic (F) layer reversal depending on the magnitude of the coupling between F grains. In the weak coupling regime relative to the anisotropy, the exchange field is independent of the coupling and no variability from one nanodot to another is observed. By contrast, in the strong coupling regime, the exchange field depends on the coupling and it shows a high variability from one nanodot to another. Our model also well explain some experimental features observed in NiFe/IrMn nanodots (for various lateral sizes) and continuous films, at various measurement temperatures and various AF thicknesses. Finally, our model explains a long lasting issue about why the exchange field in nanodots can be either smaller or larger than in continuous films.

关键词： Exchange bias Magnetic anisotropy Multilayer thin films metropolis algorithm

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Analytical and numerical investigations of noncollinear magnetic ordering in the frustrated delafossite CuCrO2

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Physical Review B 2019年第10期99卷 104415-104415页

作者： Ahmed Albaalbaky Yaroslav Kvashnin Renaud Patte Denis Ledue Normandie Université UNIROUEN INSA Rouen CNRS GPM F-76800 Saint Étienne du Rouvray France Department of Physics and Astronomy Division of Materials Theory Uppsala University Box 516 SE-75120 Uppsala Sweden

The magnetic propagation vector in delafossite CuCrO2 with classical Heisenberg spins is calculated analytically as a function of exchange interactions up to fourth-nearest neighbors. Exchange interactions are estimated by a series of density functional theory calculations for several values of lattice distortion. Our calculations show that the magnetic propagation vector is directly affected by the considered distortions providing different stable commensurate or incommensurate magnetic configurations. A realistic set of exchange interactions corresponding to a 0.1% lattice distortion yields the experimental ground state with an incommensurate propagation vector q ∼ (0.329, 0.329, 0). We find that a very weak antiferromagnetic interlayer interaction favors an incommensurate ordering even in the absence of lattice distortion. Moreover, the exchange energy of a magnetic configuration of a finite crystal of CuCrO2 with periodic boundary conditions is derived analytically. Based on that, highly accurate Monte Carlo simulations performed on CuCrO2 confirm both the proposed analytical calculations and the density functional theory estimations, where we obtain excellent convergence toward the experimental ground state with a magnetic propagation vector q = (0.3288, 0.3288, 0).

关键词： Exchange interaction Frustrated magnetism Magnetic order Antiferromagnets Density functional theory metropolis algorithm

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Finding minimum node separators: A Markov chain Monte Carlo method

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2018年第Oct.期178卷 225-235页

作者： Lee, Joohyun Kwak, Jaewook Lee, Hyang-Won Shroff, Ness B. Hanyang Univ Div Elect Engn Ansan South Korea Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA Konkuk Univ Dept Software Seoul South Korea Ohio State Univ Dept Comp Sci & Engn Columbus OH 43210 USA 120 Neungdong Ro Seoul 05029 South Korea

In networked systems such as communication networks or power grids, graph separation from node failures can damage the overall operation severely. One of the most important goals of network attackers is thus to separate nodes so that the sizes of connected components become small. In this work, we consider the problem of finding a minimum a-separator, that partitions the graph into connected components of sizes at most an, where n is the number of nodes. To solve the alpha-separator problem, we develop a random walk algorithm based on metropolis chain. We characterize the conditions for the first passage time (to find an optimal solution) of our algorithm. We also find an optimal cooling schedule, under which the random walk converges to an optimal solution almost surely. Furthermore, we generalize our algorithm to non-uniform node weights. We show through extensive simulations that the first passage time is less than O(n(3)), thereby validating our analysis. The solution found by our algorithm allows us to identify the weakest points in the network that need to be strengthened. Simulations in real topologies show that attacking a dense area is often not an efficient solution for partitioning a network into small components.

关键词： Graph separation problem Node attack Markov chain Monte Carlo metropolis algorithm Hierarchical Markov chain

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How to Escape Local Optima in Black Box Optimisation: When Non-elitism Outperforms Elitism

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algorithmICA 2018年第5期80卷 1604-1633页

作者： Oliveto, Pietro S. Paixao, Tiago Heredia, Jorge Perez Sudholt, Dirk Trubenova, Barbora Univ Sheffield Sheffield S1 4DP S Yorkshire England IST Austria Campus 1 A-3400 Klosterneuburg Austria

Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The () EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the () EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and metropolis can also efficiently optimise a rugged function consisting of consecutive valleys.

关键词： Evolutionary algorithms Runtime analysis Population genetics Strong selection weak mutation regime metropolis algorithm Simulated annealing Black box optimisation

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Model-Free Measurement of the Pair Potential in Colloidal Fluids Using Optical Microscopy

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Physical Review Letters 2019年第9期123卷 098002-098002页

作者： Adam Edward Stones Roel P. A. Dullens Dirk G. A. L. Aarts Department of Chemistry Physical & Theoretical Chemistry Laboratory University of Oxford Oxford OX1 3QZ United Kingdom

We report a straightforward, model-free approach for measuring pair potentials from particle-coordinate data, based on enforcing consistency between the pair distribution function measured separately by the distance-histogram and test-particle insertion routes. We demonstrate the method’s accuracy and versatility in simulations of simple fluids, before applying it to an experimental system composed of superparamagnetic colloidal particles. The method will enable experimental investigations into many-body interactions and allow for effective coarse graining of interactions from simulations.

关键词： Structural properties Superparamagnetism Charged colloids Classical fluids Colloids Liquids Magnetic colloids metropolis algorithm Optical microscopy

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Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times

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Physical Review B 2019年第12期100卷 125129-125129页

作者： Corentin Bertrand Olivier Parcollet Antoine Maillard Xavier Waintal Université Grenoble Alpes CEA INAC-PHELIQS GT F-38000 Grenoble France Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New York 10010 USA Institut de Physique Théorique (IPhT) CEA CNRS UMR 3681 91191 Gif-sur-Yvette France Laboratoire de Physique de l'Ecole Normale Supérieure UMR 8550 24 Rue Lhomond 75005 Paris France

We present a quantum Monte Carlo algorithm for computing the perturbative expansion in power of the coupling constant U of the out-of-equilibrium Green's functions of interacting Hamiltonians of fermions. The algorithm extends the one presented in Profumo et al. [Phys. Rev. B 91, 245154 (2015)], and inherits its main property: it can reach the infinite time (steady state) limit since the computational cost to compute order Un is uniform versus time; the computing time increases as 2n. The algorithm is based on the Schwinger-Keldysh formalism and can be used for both equilibrium and out-of-equilibrium calculations. It is stable at both small and long real times including in the stationary regime, because of its automatic cancellation of the disconnected Feynman diagrams. We apply this technique to the Anderson quantum impurity model in the quantum dot geometry to obtain the Green's function and self-energy expansion up to order U10 at very low temperature. We benchmark our results at weak and intermediate coupling with high precision numerical renormalization-group computations as well as analytical results.

关键词： Anderson impurity model Diagrammatic methods metropolis algorithm Nonequilibrium Green's function Quantum Monte Carlo

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