Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures [M. C. Rec...
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Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures [M. C. Rechtsman et al., Phys. Rev. Lett. 95, 228301 (2005); Phys. Rev. E 73, 011406 (2006)], we present an isotropic pair potential V(r) for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors, and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered-cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.
Real collective density variables C(k) [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor S(k), where k denotes the wave vector. Our...
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Real collective density variables C(k) [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor S(k), where k denotes the wave vector. Our objective is to prescribe C(k) and then to find many-particle configurations that correspond to such a target C(k) using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control S(k) in the neighborhood of ∣k∣=0. The optimization method employed generates multiparticle configurations for which S(k)∝∣k∣α, ∣k∣⩽K, and α=1, 2, 4, 6, 8, and 10. The case α=1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid He4, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground states are configurationally degenerate and disordered.
Robertson and Seymour prove that a set of graphs of bounded tree-width is well-quasi-ordered by the graph minor relation. By extending their methods to matroids, Geelen, Gerards, and Whittle prove that a set of matroi...
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In the context of the recently developed “equation-free” approach to computer-assisted analysis of complex systems, we extract the self-similar solution describing core collapse of a stellar system from numerical ex...
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In the context of the recently developed “equation-free” approach to computer-assisted analysis of complex systems, we extract the self-similar solution describing core collapse of a stellar system from numerical experiments. The technique allows us to sidestep the core “bounce” that occurs in direct N-body simulations due to the small-N correlations that develop in the late stages of collapse, and hence to follow the evolution well into the self-similar regime.
We present a formalism for coupling a density-functional-theory-based quantum simulation to a classical simulation for the treatment of simple metallic systems. The formalism is applicable to multiscale simulations in...
We present a formalism for coupling a density-functional-theory-based quantum simulation to a classical simulation for the treatment of simple metallic systems. The formalism is applicable to multiscale simulations in which the part of the system requiring quantum-mechanical treatment is spatially confined to a small region. Such situations often arise in physical systems where chemical interactions in a small region can affect the macroscopic mechanical properties of a metal. We describe how this coupled treatment can be accomplished efficiently, and we present a coupled simulation for a bulk aluminum system.
In this article, we study a class of numerical ODE schemes that use a time filtering strategy and operate in two time scales. The algorithms follow the framework of the heterogeneous multiscale methods (HMM) [1]. We a...
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ISBN:
(纸本)9783540253358
In this article, we study a class of numerical ODE schemes that use a time filtering strategy and operate in two time scales. The algorithms follow the framework of the heterogeneous multiscale methods (HMM) [1]. We apply the methods to compute the averaged path of the inverted pendulum under a highly oscillatory vertical forcing on the pivot. The averaged equation for related problems has been studied analytically in [9]. We prove and show numerically that the proposed methods approximate the averaged equation and thus compute the average path of the inverted pendulum.
We study the approach to jamming in hard-sphere packings and, in particular, the pair correlation function g2(r) around contact, both theoretically and computationally. Our computational data unambiguously separate th...
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We study the approach to jamming in hard-sphere packings and, in particular, the pair correlation function g2(r) around contact, both theoretically and computationally. Our computational data unambiguously separate the narrowing δ-function contribution to g2 due to emerging interparticle contacts from the background contribution due to near contacts. The data also show with unprecedented accuracy that disordered hard-sphere packings are strictly isostatic: i.e., the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom, once rattlers are removed. For such isostatic packings, we derive a theoretical connection between the probability distribution of interparticle forces Pf(f), which we measure computationally, and the contact contribution to g2. We verify this relation for computationally generated isostatic packings that are representative of the maximally random jammed state. We clearly observe a maximum in Pf and a nonzero probability of zero force, shedding light on long-standing questions in the granular-media literature. We computationally observe an unusual power-law divergence in the near-contact contribution to g2, persistent even in the jamming limit, with exponent −0.4 clearly distinguishable from previously proposed inverse-square-root divergence. Additionally, we present high-quality numerical data on the two discontinuities in the split-second peak of g2 and use a shared-neighbor analysis of the graph representing the contact network to study the local particle clusters responsible for the peculiar features. Finally, we present the computational data on the contact contribution to g2 for vacancy-diluted fcc crystal packings and also investigate partially crystallized packings along the transition from maximally disordered to fully ordered packings. We find that the contact network remains isostatic even when ordering is present. Unlike previous studies, we find that ordering has a significant impact on the sh
We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithm...
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We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k)∼|k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r)∼−r−4, and a long-ranged direct correlation function c(r).
We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disord...
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We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (nondirectional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic band gap properties.
It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal f...
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It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. The multifunctionality of such two-phase systems has been further established by demonstrating that they are also extremal when a competition is set up between the effective bulk modulus and electrical (or thermal) conductivity of the bicontinuous composite. Here we compute the fluid permeabilities of these and other triply periodic bicontinuous structures at a porosity ϕ=1∕2 using the immersed-boundary finite-volume method. The other triply periodic porous media that we study include the Schoen gyroid (G) minimal surface, two different pore-channel models, and an array of spherical obstacles arranged on the sites of a simple cubic lattice. We find that the Schwartz P porous medium has the largest fluid permeability among all of the six triply periodic porous media considered in this paper. The fluid permeabilities are shown to be inversely proportional to the corresponding specific surfaces for these structures. This leads to the conjecture that the maximal fluid permeability for a triply periodic porous medium with a simply connected pore space at a porosity ϕ=1∕2 is achieved by the structure that globally minimizes the specific surface.
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