The equilibrium shapes of biological structures as diverse as plant tendrils and bacterial filaments can be altered by externally imposed stresses of sufficient duration. We study the simplest model for this morphoela...
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The equilibrium shapes of biological structures as diverse as plant tendrils and bacterial filaments can be altered by externally imposed stresses of sufficient duration. We study the simplest model for this morphoelasticity—a filament whose intrinsic curvatures relax to the local curvatures—and illustrate its properties in the context of dynamic Euler buckling and writhing. When a thrust or twist is ramped in time the effective elastic properties of the filament depend on the load rate. Slow ramps interrupted by removal of the external forces can leave in equilibrium any of a whole continuum of buckled shapes. Morphoelastic relaxation can also allow a filament to bypass a bifurcation.
We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observabl...
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We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implement...
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of “traditional” techniques for melting-point calculations, as well as with literature values.
We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experiment...
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We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experimentalists greater and greater control over colloidal interaction potentials, we propose and discuss two computational algorithms that search for optimal potentials for self-assembly of a given target configuration. The first optimizes the potential near the ground state and the second near the melting point. We begin by applying these techniques to assembling open structures in two dimensions (square and honeycomb lattices) using only circularly symmetric pair interaction potentials; we demonstrate that the algorithms do indeed cause self-assembly of the target lattice. Our approach is distinguished from previous work in that we consider (i) lattice sums, (ii) mechanical stability (phonon spectra), and (iii) annealed Monte Carlo simulations. We also devise circularly symmetric potentials that yield chainlike structures as well as systems of clusters.
Recent experiments have shown large-scale dynamic coherence in suspensions of the bacterium B. subtilis, characterized by quorum polarity, collective parallel swimming of cells. To probe mechanisms leading to this, we...
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Recent experiments have shown large-scale dynamic coherence in suspensions of the bacterium B. subtilis, characterized by quorum polarity, collective parallel swimming of cells. To probe mechanisms leading to this, we study the response of individual cells to steric stress, and find that they can reverse swimming direction at spatial constrictions without turning the cell body. The consequences of this propensity to flip the flagella are quantified by measurements of the inward and outward swimming velocities, whose asymptotic values far from the constriction show near perfect symmetry, implying that “forwards” and “backwards” are dynamically indistinguishable, as with E. coli.
In this paper we study convergence of the max-product (MP) algorithm on general graphs with cycles. Our analysis follows analogously to that given for the convergence of the sum-product algorithm. We do not work with ...
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(纸本)142440505X
In this paper we study convergence of the max-product (MP) algorithm on general graphs with cycles. Our analysis follows analogously to that given for the convergence of the sum-product algorithm. We do not work with Gibbs measures but instead we introduce and work with local maxifiers. The contributions of this paper include: reformulation of the MP algorithm on cyclic graphs as max-marginalization on an associated computation tree; existence of local maxifiers and proof that uniqueness of the local maxifier is sufficient for convergence of MP; a Gibbsian theory of local maxifiers and interpretation as operators; an example of non-uniqueness which does not exhibit a phase transition like its Gibbs measure counterpart; and insights into the limitations of Dobrushin-type uniqueness conditions
Previous Monte Carlo investigations by Wojciechowski et al. have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Meth...
Previous Monte Carlo investigations by Wojciechowski et al. have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.
We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted amorphous...
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We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted amorphous glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)].
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