# Browsing by Subject "Statistical physics"

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Item Open Access An Information-Theoretic Analysis of X-Ray Architectures for Anomaly Detection(2018) Coccarelli, David ScottX-ray scanning equipment currently establishes a first line of defense in the aviation security space. The efficacy of these scanners is crucial to preventing the harmful use of threatening objects and materials. In this dissertation, I introduce a principled approach to the analyses of these systems by exploring performance limits of system architectures and modalities. Moreover, I validate the use of simulation as a design tool with experimental data as well as extend the use of simulation to create high-fidelity realizations of a real-world system measurements.

Conventional performance analysis of detection systems confounds the effects of the system architecture (sources, detectors, system geometry, etc.) with the effects of the detection algorithm. We disentangle the performance of the system hardware and detection algorithm so as to focus on analyzing the performance of just the system hardware. To accomplish this, we introduce an information-theoretic approach to this problem. This approach is based on a metric derived from Cauchy-Schwarz mutual information and is analogous to the channel capacity concept from communications engineering. We develop and utilize a framework that can produce thousands of system simulations representative of a notional baggage ensembles. These simulations and the prior knowledge of the virtual baggage allow us to analyze the system as it relays information pertinent to a detection task.

In this dissertation, I discuss the application of this information-theoretic approach to study variations of X-ray transmission architectures as well as novel screening systems based on X-ray scatter and phase. The results show how effective use of this metric can impact design decisions for X-ray systems. Moreover, I introduce a database of experimentally acquired X-ray data both as a means to validate the simulation approach and to produce a database ripe for further reconstruction and classification investigations. Next, I show the implementation of improvements to the ensemble representation in the information-theoretic material model. Finally I extend the simulation tool toward high-fidelity representation of real-world deployed systems.

Item Open Access Caging and Transport in Simple Disordered Systems(2021) Hu, YiRecent advances on the glass problem motivate reexamining classical models of caging and transport. In particular, seemingly incompatible percolation and mean-field caging descriptions on the localization transition call for better understanding both. In light of this fundamental inconsistency, we study the caging and transport of a series of simple disordered systems.

We first consider the dynamics of site percolation on hypercubic lattices. Using theory and simulations, we obtain that both caging and subdiffusion scale logarithmically for dimension d ≥ d_u, the upper critical dimension of percolation. The theoretical derivation on Bethe lattice and a random graph confirm that logarithmic scalings should persist in the limit d→∞. The computational validation evaluates directly the dynamical critical exponents below d_u as well as their logarithmic scaling above d_u. Our numerical results improve various earlier estimates and are fully consistent with our theoretical predictions.

Recent implementation of efficient simulation algorithms for high-dimensional systems also facilitates the study of dense packing lattices beyond the conventional hypercubic ones. Here, we consider the percolation problem on checkerboard D_d lattices and on E_8 relatives for d=6 to 9. Precise estimates for both site and bond percolation thresholds obtained from invasion percolation simulations are compared with dimensional series expansion based on lattice animal enumeration for D_d lattices. As expected, the bond percolation threshold rapidly approaches the Bethe lattice limit as d increases for these high-connectivity lattices. Corrections, however, exhibit clear yet unexplained trends.

The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. Here, we first extend analytical expectations for asymptotic high-d bounds on the void percolation threshold, and then computationally evaluate both the threshold and its criticality in various d. A simple modification of the RLG is found to bring the mean-field-like caging down to d=3.

The RLG also provides a toy model of particle caging, which is known to be relevant for describing the discontinuous dynamical transition of glasses. Following the percolation studies, we consider its exact mean-field solution in the d→∞ limit and perform simulation in d=2...20. We find that for sufficiently high d the mean-field caging transition precedes and prevents the percolation transition, which only happens on timescales diverging with d. This perturbative correction is associated with the cage heterogeneity. We further show that activated processes related to rare cage escapes destroy the glass transition in finite dimensions, leading to a rich interplay between glassiness and percolation physics. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of particle hopping in structural glasses.

While the cages in the RLG are formed by non-interacting obstacles, cage structure is important for the hopping process in three-dimensional glasses. As a final note and also a future direction, a study on the three-dimensional polydisperse hard spheres with modification, named as the Mari-Kurchan-Krzakala (MKK) model was proposed. This consideration provides a controllable way to interpolate between the mean-field and the real space glasses. These insights help chart a path toward a complete description of finite-dimensional glasses.

Item Open Access Characterization and Mechanism of Rigidity in Columns of Star-shaped Granular Particles(2020) Zhao, YuchenAn important challenge in the science of granular materials is to understand the connection between the shapes of individual grains and the macroscopic response of the aggregate. Granular packings of concave or elongated particles can form free-standing structures like walls or arches, in sharp contrast to the behaviors of spherical grains. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of rigidity for non-interlocking particles remains unclear. In addition to their intrinsic interest, these packings are relevant to lightweight and reconfigurable structures in civil, geotechnical and material engineering applications.

In this thesis, we report on experiments and numerical simulations of packings of star-shaped particles consisting of three mutually orthogonal sphero-cylinders whose centers coincide. The first set of experiments studies the chance of obtaining a free-standing column when the confining tube of the column is removed, which we will call it as ``intrinsic stability''. We prepare monodisperse packings of star-shaped particles with different length-to-arm diameter aspect ratio α, interparticle friction and particle-base friction. We also vary packing density by vibrating the packings when they are in the tube. We find that the intrinsic stability depends on packing dimension: columns of greater diameter or shorter height are more stable. Both arm length and interparticle friction can greatly increase the intrinsic stability, while the packing density and basal friction have limited effects on the intrinsic stability.

The second set of experiments involves stability of free-standing columns (prepared from the first set of experiments) under three different external perturbations: (1) base tilting; (2) static axial loading; and (3) vertical vibration. For the base tilting test, we gradually tilt the base of the column and observe column collapse as a function of tilt angle. We find that columns of low friction particles are more fragile than those of high friction particles. For the axial loading test, we gradually increase the loading on a column until it collapses. We find that tall columns are more fragile. For the vibration test, we apply vertical sinusoidal vibration from the base to destabilize the column. Both interparticle and basal friction improve packing stability in terms of increasing relaxation time under vibration. We also find that tall columns are more sensitive to the vibration in the sense that they collapse faster than short ones under the same vibration.

In the third set of experiments, we vary α and subject the packings to quasistatic direct shear. For small α, we observe a finite yield stress. For large α, however, the packings become rigid when sheared, supporting stresses that increase sharply with increasing strain. Analysis of x-ray micro-computed tomography data collected during the shear reveals that the stiffening is associated with a tilted, oblate cluster of particles near the nominal shear plane in which particle deformation and average contact number both increase.

Molecular dynamics simulations that closely match the third experiments are used to investigate the finite yield stress and the stiffening. In simulation, interparticle contact forces are known to us. For yield packings (small α), simulations suggest no apparent cohesion. For stiffening packings (large α), simulation results show that the particles are collectively under tension along one direction even though they do not interlock pairwise. These tensions come from contact forces with large associated torques, and they are perpendicular to the compressive stresses in the packing. They counteract the tendency to dilate, thus stabilizing the particle cluster.

Item Open Access Numerical Transfer Matrix Method of Next-nearest-neighbor Ising Models(2021) Hu, YiIn statistical physics, the exact partition function of simple (quasi)-one-dimensional models can be obtained from the numerical transfer matrix (TM) method. This method involves solving for the leading eigenvalues of a matrix representing all possible interactions between the states that a unit of the system can take. Because the size of this matrix grows exponentially with the number of those units, the TM method is ideally suited for models that have a finite state space and short-range interactions. Its success nevertheless relies on the use of efficient iterative eigensolvers and on leveraging system symmetry, whenever possible.

By careful finite-size extrapolation of sufficiently large systems, the TM method can also be used to examine two-dimensional models. A particularly interesting series of such systems are Ising models modified with next-nearest-neighbor frustration, which recapitulate the formation of equilibrium modulated phases in systems as varied as magnetic alloys, lipid surfactants, and cell morphogenesis. In these models, frustration results in large mixing times for Markov chain Monte Carlo simulations, but the TM approach sidesteps this slowdown and thus provides a putatively well-controlled computational scheme. The effectiveness of TM approach for these models, however, had previously been obfuscated by the limited range of system sizes computationally available for the numerical analysis. In this thesis, I build on the sparse matrix decomposition and take advantage of the structure and symmetry of the TM to develop optimized algorithms for the method, and thereby overcome the computational challenge. The resulting algorithm is implemented in various canonical frustrated next-nearest-neighbor Ising models, aiming to solve long-standing physical problems in these models. The approach provides benchmark results for related statistical physics models. It could also inspire the development of adapted eigensolver for similarly structured matrices.

Item Open Access Poisson Percolation on the Square Lattice(2019-04-01) Cristali, IrinaIn this paper, we examine two versions of inhomogeneous percolation on the 2D lattice, which we will refer to as non-oriented and oriented percolation, and describe the limiting shape of the component containing the origin in both cases. To define the nonoriented percolation process that we study, we consider the square lattice where raindrops fall on an edge with midpoint $x$ at rate $\|x\|_\infty^{-\alpha}$. The edge becomes open when the first drop falls on it. We call this process "nonoriented Poisson percolation". Let $\rho(x,t)$ be the probability that the edge with midpoint $x=(x_1,x_2)$ is open at time $t$ and let $n(p,t)$ be the distance at which edges are open with probability $p$ at time $t$. We show that with probability tending to 1 as $t \to \infty$: (i) the cluster containing the origin $\CC_0(t)$ is contained in the square of radius $n(p_c-\ep,t)$, and (ii) the cluster fills the square of radius $n(p_c+\ep,t)$ with the density of points near $x$ being close to $ \theta(\rho(x,t))$ where $\theta(p)$ is the percolation probability when bonds are open with probability $p$ on $\ZZ^2$. Results of Nolin suggest that if $N=n(p_c,t)$ then the boundary fluctuations of $\CC_0(t)$ are of size $N^{4/7}$. In the second part of the paper, we prove similar, yet not-studied-before, results for the asymptotic shape of the cluster containing the origin in the oriented case of Poisson percolation. We show that the density of occupied sites at height $y$ in the open cluster is close to the percolation probability in the corresponding homogeneous percolation process, and we study the fluctuations of the boundary.Item Open Access Stochastic and Agent-based Modeling of Gene Expression and Cell Fate Decisions(2021) Mines, Robert CarlAs new experimental techniques expand our capacity to understand the internal states of single cells and to track the behavior of individual enzymes, classical modeling techniques for deterministic chemical kinetics break down. Thus, more flexible stochastic and agent-based modeling techniques need to be employed. Two paradigmatic are considered. First, a stochastic agent-based model of transcription with nucleosome-induced pausing that maps onto the ddTASEP was constructed to demonstrate a potential mechanism of transcriptional bursting. In lieu of using a mean-field approach, Markov chain techniques were used to calculate the moments of the first passage time from the nucleosome dynamic rate constants. A mean first passage rate was calculated and utilized to construct a new axis to the TASEP phase diagram that contained a jamming transition between initiation- and dynamic defect-limited regions. Second, an integrated Notch/Delta and Wnt/β-catenin gene circuit with crosstalk through the expression of Hes1 was constructed on a lattice model of the intestinal crypt. The distributed control of Hes1 expression, the mechanisms of Wnt secretion, and the redundant role of Paneth cells as a Wnt source were investigated. Tunable mosaic pattern formation at the crypt base was observed, and the addition of the secondary Wnt feedback loop offered a slight increase in model robustness to parameter changes and intrinsic stochasticity.

Item Open Access Understanding the Structure and Formation of Protein Crystals Using Computer Simulation and Theory(2019) Altan, IremThe complexity of protein-protein interactions enables proteins to self-assemble into a rich array of structures, such as virus capsids, amyloid fibers, amorphous aggregates, and protein crystals. While some of these assemblies form under biological conditions, protein crystals, which are crucial for obtaining protein structures from diffraction methods, do not typically form readily. Crystallizing proteins thus requires significant trial and error, limiting the number of structures that can be obtained and studied. Understanding how proteins interact with one another and with their environment would allow us to elucidate the physicochemical processes that lead to crystal formation and provide insight into other self-assembly phenomena. This thesis explores this problem from a soft matter theory and simulation perspective.

We first attempt to reconstruct the water structure inside a protein crystal using all-atom molecular dynamics simulations with the dual goal of benchmarking empirical water models and increasing the information extracted from X-ray diffraction data. We find that although water models recapitulate the radial distribution of water around protein atoms, they fall short of reproducing its orientational distribution. Nevertheless, high-intensity peaks in water density are sufficiently well captured to detect the protonation states of certain solvent-exposed residues.

We next study a human gamma D-crystallin mutant, the crystals of which have inverted solubility. We parameterize a patchy particle and show that the temperature-dependence of the patch that contains the solubility inverting mutation reproduces the experimental phase diagram. We also consider the hypothesis that the solubility is inverted because of increased surface hydrophobicity, and show that even though this scenario is thermodynamically plausible, microscopic evidence for it is lacking, partly because our understanding of water as a biomolecular solvent is limited.

Finally, we develop computational methods to understand the self-assembly of a two-dimensional protein crystal and show that specialized Monte Carlo moves are necessary for proper sampling.