# Browsing by Subject "Statistical mechanics"

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Item Efficient computational strategies for predicting homogeneous fluid structure(2014-08) Hollingshead, Kyle Brady; Truskett, Thomas Michael, 1973-Show more A common challenge in materials science is the "inverse design problem," wherein one seeks to use theoretical models to discover the microscopic characteristics (e.g., interparticle interactions) of a system which, if fabricated or synthesized, would yield a targeted material property. Inverse design problems are commonly addressed by stochastic optimization strategies like simulated annealing. Such approaches have the advantage of being general and easy to apply, and they can be effective as long as material properties required for evaluating the objective function of the optimization are feasible to accurately compute for thousands to millions of different trial interactions. This requirement typically means that "exact" yet computationally intensive methods for property predictions (e.g., molecular simulations) are impractical for use within such calculations. Approximate theories with analytical or simple numerical solutions are attractive alternatives, provided that they can make sufficiently accurate predictions for a wide range of microscopic interaction types. We propose a new approach, based on the fine discretization (i.e., terracing) of continuous pair interactions, that allows first-order mean-spherical approximation theory to predict the equilibrium structure and thermodynamics of a wide class of complex fluid pair interactions. We use this approach to predict the radial distribution functions and potential energies for systems with screened electrostatic repulsions, solute-mediated depletion interactions, and ramp-shaped repulsions. We create a web applet for introductory statistical mechanics courses using this approach to quickly estimate the equilibrium structure and thermodynamics of a fluid from its pair interaction. We use the applet to illustrate two fundamental fluid phenomena: the transition from ideal gas-like behavior to correlated-liquid behavior with increasing density in a system of hard spheres, and the water-like tradeoff between dominant length scales with changing temperature in a system with ramp-shaped repulsions. Finally, we test the accuracy of our approach and several other integral equation theories by comparing their predictions to simulated data for a series of different pair interactions. We introduce a simple cumulative structural error metric to quantify the comparison to simulation, and find that according to this metric, the reference hypernetted chain closure with a semi-empirical bridge function is the most accurate of the tested approximations.Show more Item Inverse design methods for targeted self-assembly(2014-12) Jain, Avni; Truskett, Thomas Michael, 1973-Show more In this thesis, we study the problem of what microscopic thermodynamic driving forces can stabilize target macroscopic structures. First, we demonstrate that inverse statistical mechanical optimization can be used to rationally design inter-particle interactions that display target open structures as ground states over a wide range of thermodynamic conditions. We focus on designing simple interactions (e.g., isotropic, convex-repulsive) that drive the spontaneous assembly of material constituents to low-coordinated ground states of diamond and simple cubic lattices. This is significant because these types of phases are typically accessible given more complex systems (e.g., particles with orientation-dependent attractive interactions) and for a narrow range of conditions. We subject the optimal interactions to stringent stability tests and also observe assembly of the target structures from disordered fluid states. We then use extensive free energy based Monte Carlo simulation techniques to construct the equilibrium phase diagrams for the model materials with interactions designed to feature diamond and simple cubic ground states, i.e., at zero temperatures. We find that both model materials, despite the largely featureless interaction form, display rich polymorphic phase behavior featuring not only thermally stable target ground state structures, but also a variety of other crystalline (e.g., hexagonal and body-centered cubic) phases. Next, we investigate whether isotropic interactions designed to stabilize given two-dimensional (2D) lattices (e.g., honeycomb or square) will favor their analogous three-dimensional (3D) structures (e.g., diamond or simple cubic), and vice versa. We find a remarkable transferability of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that computationally inexpensive 2D material optimizations can assist in isolating rare isotropic interactions that drive the assembly of materials into 3D open lattice structures.Show more Item Mecanique statistique(1952-07) Rosenfeld, LeonShow more Item Modeling the interaction and energetics of biological molecules with a polarizable force field(2013-05) Shi, Yue, active 21st century; Ren, PengyuShow more Accurate prediction of protein-ligand binding affinity is essential to computational drug discovery. Current approaches are limited by the accuracy of the underlying potential energy model that describes atomic interactions. A more rigorous physical model is critical for evaluating molecular interactions to chemical accuracy. The objective of this thesis research is to develop a polarizable force field with an accurate representation of electrostatic interactions, and apply this model to protein-ligand recognition and to ultimately solve practical problems in computer aided drug discovery. By calculating the hydration free energies of a series of organic small molecules, an optimal protocol is established to develop the electrostatic parameters from quantum mechanics calculations. Next, the systematical development and parameterization procedure of AMOEBA protein force field is presented. The derived force field has gone through extensive validations in both gas phase and condensed phase. The last part of the thesis involves the application of AMOEBA to study protein-ligand interactions. The binding free energies of benzamidine analogs to trypsin using molecular dynamics alchemical perturbation are calculated with encouraging accuracy. AMOEBA is also used to study the thermodynamic effect of constraining and hydrophobicity on binding energetics between phosphotyrosine(pY)-containing tripeptides and the SH2 domain of growth receptor binding protein 2 (Grb2). The underlying mechanism of an "entropic paradox" associated with ligand preorganization is explored.Show more Item Ordering in dense packings(2011-05) Aristoff, David Gregory; Radin, Charles, 1945-; Koch, Hans; de la Llave, Rafael; Gamba, Irene; Gonzalez, Oscar; Raizen, MarkShow more We examine various models of soft matter, and one model of quasicrystals, focusing on abrupt changes as density is varied. We consider in detail two models, one of granular matter and another of confined wires, showing that the models become ordered as density is increased, with crystalline order observed in the former and nematic order observed in the latter. We associate the phenomenon of random close packing with the onset of crystalline order in our granular model, and we conjecture that crumpled wires should exhibit a nematic transition with increasing compaction. We also consider two other models of granular matter: one which describes dilatancy onset as a second order phase transition, and one which describes random loose packing as a precise, well- defined density. Finally, we examine an equilibrium model of quasicrystals with a first order phase transition to a solid phase without any crystalline order.Show more Item Statistical mechanics of 2-D fluids(1994) Padhye, Nikhil Subhash, 1970-; Morrison, Philip J.Show more Item The statistical mechanics of non-equilibrium phenomena(1955-07) Uhlenbeck, George E.Show more Item Statistics of turbulence in a rapidly rotating system(2005) Jung, Sunghwan; Swinney, H. L., 1939-; Morrison, Philip J.Show more Turbulence raises many issues such as fundamental questions in mathematics, continuum mechanics in physics and various industrial problems. Turbulence is characterized as a state of fluid flow that is influenced strongly by nonlinear processes compared to dissipation. Turbulence of fluids with strong rotation is of interest in turbo-machinery and geophysical flows that occur in the earth’s atmosphere and oceans. Strong rotation can bring a turbulent system into a quasi two-dimensional (2D) turbulence. Rotation causes anisotropic turbulent motions on large scales. However, on small scales the turbulence is believed to be homogeneous and isotropic and that fluid motions are independent of rotation and large-scale topography. Despite this general belief, in our experiments we find that the energy spectrum in a rotating turbulent flow strongly depends on large-scale topography and a rotation. A 2D fluid system with forcing and dissipation neglected has a Hamiltonian structure with conserved quantities. These conserved quantities constrain the dynamics of 2D fluid. For a long time, it has been quite mysterious why only quadratic conserved quantities (energy and the square of vorticity) should be important in a statistical mechanical description of turbulence, especially, in 2D turbulence, where there are an infinite number of conserved quantities (the so-called Casimir invariants). Previous models of statistical mechanics of 2D turbulence have not explicitly taken into account statistical independence of macroscopic subparts, and consequently all or most of the conserved quantities have been used. However, experimental results support the use of only quadratic conserved quantities. Because of statistical independence, we show that only quadratic conserved quantities are crucial in statistical mechanics. In addition, we propose a statistical mechanical theory based on new coordinates that define statistically independent subsystems, and we compare the theory with experiments. Hamiltonian and action principles elucidate the physics in various fields, from quantum to plasma physics. Such a formulation has been used in plasma physics for the Vlasov-Poisson system to obtain fluctuation spectra. For a fluid, a similar process is possible. In this thesis, we use Hamiltonian principles to formulate the analogous fluctuation spectrum in the fluid case and compare it with experiments.Show more Item Theoretical and numerical study on adhesive interactions between graphene and substrate(2018-06-14) Wang, Peng, Ph. D.; Huang, Rui, Ph. D. in civil and environmental engineering.; Liechti, Kenneth M; Landis, Chad M; Ravi-Chandar, Krishnaswa; Ren, PengyuShow more This dissertation presents a set of theoretical and numerical studies on adhesive interactions between monolayer graphene membranes and their substrates. Both continuum mechanics models and molecular dynamics simulations are developed to investigate deformation of graphene membranes depending on the adhesive interactions with the substrates. First, a numerical study on snap transitions of gas-filled graphene blisters is presented, based on a continuum model combining a nonlinear plate theory with a nonlinear traction–separation relation. The numerical results may be used in conjunction with experiments for quantitative characterization of the interfacial properties of graphene and other two-dimensional (2D) membrane materials. Next, a statistical mechanics analysis on thermal rippling of monolayer graphene supported on a rigid substrate is presented and compared with molecular dynamics simulations to reveal the entropic effects of thermal rippling on van der Waals interactions between graphene and the substrate. While the amplitude of thermal rippling is reduced by the adhesive interactions, the entropic contribution of thermal rippling leads to an effective repulsion, thus reducing the effective adhesion. Moreover, the effect of a biaxial pre-strain in graphene is considered, and a buckling instability is predicted at a critical compressive strain that depends on both the temperature and the adhesive interactions. This motivates a systematic study on morphological transitions of monolayer graphene on a substrate under uniaxial compressive strain, from rippling to wrinkling/buckling and to folding. The presence of water at the interface has significant influence on the adhesive interactions between graphene and its substrate. Molecular dynamics simulations are performed to study the interactions between graphene and a wet substrate that is covered by a thin layer of water. Four stages of the traction-separation relations are identified and they are analyzed approximately by simple continuum models. When the thickness of water layer is below 1 nm, the water molecules form discrete monolayer or bilayer structures, leading to different traction-separation behaviors. Finally, with a finite number of water molecules trapped between a monolayer graphene and its substrate, water-filled graphene blisters form spontaneously. Based on molecular dynamics simulations and a simple theoretical model, the work of adhesion for the graphene/substrate interface may be estimated by measuring the aspect ratios of the graphene blisters. Unlike gas-filled graphene blisters in previous studies, the shape and size of the water-filled graphene blister depend on the wetting properties of graphene and the substrate. The results on wet adhesion and water-filled blisters can be readily extended to other 2D materials.Show more