[show abstract][hide abstract] ABSTRACT: Self-assembly of a binary monolayer of charged particles is modeled using molecular dynamics and statistical mechanics. The equilibrium phase diagram for the system has three distinct phases: an ionic crystal; a geometrically ordered crystal with disordered charges; and a fluid. We show that self-assembly occurs near the phase transition between the ionic crystal and the fluid, and that the rate of ordering is sensitive to the applied pressure. By assuming an Arrhenius form for the rate of ordering, an optimality condition for the temperature and pressure is derived that maximizes the rate. Using the Clausius-Clapeyron equation, the optimal point on the phase boundary is expressed in terms of the thermodynamic changes in state variables across the boundary. The predicted optimal temperature and pressure conditions are in good agreement with numerical simulations and result in self-organization rates five times that of a simulation without applied pressure.
The Journal of chemical physics 10/2011; 135(15):154501. · 3.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: Reduced-dimensionality, coarse-grained models are commonly employed to describe the structure and dynamics of large molecular systems. In those models, the dynamics is often described by Langevin equations of motion with phenomenological parameters. This paper presents a rigorous coarse-graining method for the dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes.
The Journal of chemical physics 08/2011; 135(5):054107. · 3.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: Recently, self-assembly has emerged as an efficient method to create scale-independent regular structures. A problem commonly encountered in experiment is little or no control over the kinetics of structure formation. In this work, an optimal choice of macroscopic control parameters is identified. Using Molecular Dynamics simulations, kinetics of self-assembly is evaluated in systems proposed by Whitesides et. al.. An idealized model is put forward to explain the results observed in simulations.
[show abstract][hide abstract] ABSTRACT: In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.
[show abstract][hide abstract] ABSTRACT: We present generalizations of Hill's classical results concerned with the macroscopic strain and stress measures. Generalizations involve polynomial boundary conditions and polynomial moments of the microscopic fields. It is shown that for higher-order polynomials certain boundary conditions and moments should be excluded from considerations in order to guarantee unique relationships between boundary data and macroscopic measures. Particularly simple relationships are obtained for spherical specimens, for which higher-order macroscopic measures are defined in terms of spherical harmonics. Also it is demonstrated that higher-order macroscopic measures and constitutive equations can be useful in multi-scale analysis of problems formulated in terms of integral equations.
Journal of the Mechanics and Physics of Solids 01/2007; 55(6):1103-1119. · 3.41 Impact Factor
[show abstract][hide abstract] ABSTRACT: Anti-plane deformation of square lattices containing interphases is analyzed. It is assumed that lattices are linear elastic but not necessarily isotropic, whereas interphases exhibit non-linear elastic behavior. It is demonstrated that such problems can be treated effectively using Green’s functions, which allow to eliminate the degrees of freedom outside of the interphase. Illustrative numerical examples focus on the determination of applied stresses leading to lattice instability.
[show abstract][hide abstract] ABSTRACT: We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each cross-link increases until it ruptures. The stochastic cross-link rupture process is assumed to be governed by first order kinetics with a rate that depends exponentially on the transmitted force. We have performed random searches to identify optimal cross-link configurations whose unfolding requires a large applied force (measure of strength) and/or large dissipated energy (measure of toughness). We found that such optimal chains always involve cross-links arranged to form parallel strands. The location of those optimal strands generally depends on the loading rate. Optimal chains with a small number of cross-links were found to be almost as strong and tough as optimal chains with a large number of cross-links. Furthermore, optimality of chains with a small number of cross-links can be easily destroyed by adding cross-links at random. The present findings are relevant for the interpretation of single molecule force probe spectroscopy studies of the mechanical unfolding of "load-bearing" proteins, whose native topology often involves parallel strand arrangements similar to the optimal configurations identified in the study.
[show abstract][hide abstract] ABSTRACT: We present a fast boundary element method for analyzing three-dimensional linearly elastic solids containing many cracks. The method is constructed in a modular fashion, by combining existing conventional boundary element method, iterative method, and fast summation method for the many-body electrostatics problems. The fast boundary element method preserves the advantageous features of the conventional boundary element method—weakly singular kernel, problem-specific approximations, and effective near-singular integration scheme. Numerical examples confirm the accuracy and efficiency of the new method for problems involving closely spaced cracks and large arrays of cracks imbedded in an infinite solid.
Engineering Analysis with Boundary Elements. 09/2003;
[show abstract][hide abstract] ABSTRACT: Proteins that perform mechanical functions in living organisms often exhibit exceptionally high strength and elasticity. Recent studies of the unfolding of single protein molecules under mechanical loading showed that their strength is mostly determined by their native topology rather than by thermodynamic stability. To identify the topologies of polymer molecules that maximize their resistance to unfolding, we have simulated the response of cross-linked polymer chains under tensile loading and have found that chain configurations that maximize the unfolding work and force involve parallel strands. Chains with such optimal topologies tend to unfold in an all-or-none fashion, in contrast to randomly cross-linked chains, most of which exhibit low mechanical resistance and tend to unfold sequentially. These findings are consistent with AFM studies and molecular mechanics simulations of the unfolding of -sheet proteins. In particular, parallel strands give rise to the high strength of the immunoglobulin-like domains in the muscle protein titin.
The Journal of Physical Chemistry B 08/2003; 107:8730-8733. · 3.61 Impact Factor
[show abstract][hide abstract] ABSTRACT: We discuss the statistical mechanical properties of a single polymer chain that forms cross links among its monomers. Models of this type have served as prototypes in theories of RNA and protein folding. The chain is allowed to form pseudoknots and its monomers can each participate in multiple cross links. We demonstrate that the conformational free energy of such a chain can be estimated by using an algorithm that scales as a power of the number of cross links N(N1-N3, depending on the problem). Straightforward exact evaluation of the chain partition function via multidimensional integration scales exponentially with N and often is computationally prohibitive. Our approach can also be used to compute the "entropic force" generated by a cross-linked chain when it is stretched at its ends. Such forces can be directly measured by atomic force microscopy or by laser optical trap experiments performed on single RNA, DNA, and protein molecules.
[show abstract][hide abstract] ABSTRACT: This work presents regular and singular asymptotic solutions for non-planar quasi-circular cracks. Regular asymptotic solutions, which do not give rise to hyper-singular stresses near the crack tip, are developed in the general three-dimensional setting. Singular asymptotic solutions are considered for axisymmetric problems only, because those problems do not involve hyper-singularity. The validity of asymptotic solutions for planar and non-planar cracks is investigated by comparing them with detailed numerical and analytical solutions. Also asymptotic solutions are applied to analysis of quasi-static crack growth in three dimensions.
International Journal of Fracture 12/2001; 113(1):1-25. · 1.25 Impact Factor
[show abstract][hide abstract] ABSTRACT: The force–velocity relationships for rigid bodies translating through unbounded shear-thinning power-law fluids are analyzed. Numerical solutions are presented for the sphere, finite, and infinite circular cylinders. General properties of the force–velocity relationships and flow and stress patterns in highly non-linear fluids are discussed.
International Journal of Non-linear Mechanics - INT J NON-LINEAR MECH. 01/2001; 36(6):947-953.
[show abstract][hide abstract] ABSTRACT: Fracture toughness testing is prone to exhibit various size effects that have to be understood in order to properly interpret
the results. It is shown that the size effect associated with polycrystalline inhomogeneity is weak. Instead polycrystalline
inhomogeneity induces statistical effects controlled by a small number of grains adjacent to the crack tip.
International Journal of Fracture 01/1998; 93(1):247-259. · 1.25 Impact Factor
[show abstract][hide abstract] ABSTRACT: A simple multiaxial constitutive model for primary creep of S2 fresh-water and saline ice is proposed. This model is applied to available primary creep data for fresh-water, sea, and laboratory-grown saline ice. Results of these comparisons are used to examine microscopic and macroscopic aspects of creep of S2 ice. Also the proposed model provides dimensionless representations that can be useful for design of creep tests and presentation of creep data.
[show abstract][hide abstract] ABSTRACT: An algorithmic closed-form solution is derived for Eshelby's problem for polygonal and polyhedral inclusions. Illustrative calculations are presented for two- and three-dimensional problems. Also it is proven that polyhedra with constant Eshelby's tensor do not exist.
Journal of the Mechanics and Physics of Solids 01/1996; · 3.41 Impact Factor