Doctor of Philosophy

dissertationTraditional associative plasticity theories have previously been shown to be incompatible with experimental data. For this reason, a nonassociative plasticity theory is commonly adopted. Nonassociative plasticity theories are prone to several forms of instability that result in the governing equations becoming ill-posed. Two of these instabilities are discussed: the localization instability and the Sandler-Rubin instability, which is a nonphysical instability that may occur with any degree of nonassociativity. The primary purpose of this dissertation is to describe how traditional nonassociative plasticity theory can be reformulated to eliminate the Sandler-Rubin instability while maintaining agreement with experimental data. Numerical and analytical techniques are used to investigate the effects of three nontraditional plasticity models on the existence of the Sandler-Rubin instability: viscoplasticity, incrementally non-linear plasticity, and nonlocal plasticity. Of these, it is shown that only incremental nonlinearity eliminates the instability while maintaining agreement with existing experimental data. Standard laboratory tests cannot detect nonlinearity in a material's incremental response. For this reason a new experimental method and a new data analysis technique are presented and used to validate incrementally nonlinear plasticity theory. The new technique uses a cyclic load path and an interpolation scheme to infer the material response to several loading directions at the same material state. This new technique was used to study the incremental response of aluminum 6061-T0. The new technique suggests that there is significant nonlinearity in the incremental response of this material. Though it will be demonstrated that the Sandler-Rubin instability is not eliminated with nonlocal theory, this theory is nevertheless well established at regularizing otherwise ill-posed localization problems. Few efficient numerical schemes exist for solving the equations of nonlocal plasticity. Schemes have previously been developed for solving these equations as part of a finite-element or element-free Galerkin method, but no general convergence criterion had been developed for these methods. A new numerical scheme for solving these equations using the material point method (MPM) is presented. The new scheme uses the MPM background grid for particle-to-particle communication, and results in a simple, matrix-free algorithm. A convergence crite- rion derived for the new method is furthermore shown to be applicable to some of the methods developed by other researchers

RNA secondary structure design

We consider the inverse-folding problem for RNA secondary structures: for a given (pseudo-knot-free) secondary structure find a sequence that has that structure as its ground state. If such a sequence exists, the structure is called designable. We implemented a branch-and-bound algorithm that is able to do an exhaustive search within the sequence space, i.e., gives an exact answer whether such a sequence exists. The bound required by the branch-and-bound algorithm are calculated by a dynamic programming algorithm. We consider different alphabet sizes and an ensemble of random structures, which we want to design. We find that for two letters almost none of these structures are designable. The designability improves for the three-letter case, but still a significant fraction of structures is undesignable. This changes when we look at the natural four-letter case with two pairs of complementary bases: undesignable structures are the exception, although they still exist. Finally, we also study the relation between designability and the algorithmic complexity of the branch-and-bound algorithm. Within the ensemble of structures, a high average degree of undesignability is correlated to a long time to prove that a given structure is (un-)designable. In the four-letter case, where the designability is high everywhere, the algorithmic complexity is highest in the region of naturally occurring RNA.Comment: 11 pages, 10 figure

THE PHYSICS OF IDEAS: INFERRING THE MECHANICS OF OPINION FORMATION FROM MACROSCOPIC STATISTICAL PATTERNS

In a microscopic setting, humans behave in rich and unexpected ways. In a macroscopic setting, however, distinctive patterns of group behavior emerge, leading statistical physicists to search for an underlying mechanism. The aim of this dissertation is to analyze the macroscopic patterns of competing ideas in order to discern the mechanics of how group opinions form at the microscopic level. First, we explore the competition of answers in online Q&A (question and answer) boards. We find that a simple individual-level model can capture important features of user behavior, especially as the number of answers to a question grows. Our model further suggests that the wisdom of crowds may be constrained by information overload, in which users are unable to thoroughly evaluate each answer and therefore tend to use heuristics to pick what they believe is the best answer. Next, we explore models of opinion spread among voters to explain observed universal statistical patterns such as rescaled vote distributions and logarithmic vote correlations. We introduce a simple model that can explain both properties, as well as why it takes so long for large groups to reach consensus. An important feature of the model that facilitates agreement with data is that individuals become more stubborn (unwilling to change their opinion) over time. Finally, we explore potential underlying mechanisms for opinion formation in juries, by comparing data to various types of models. We find that different null hypotheses in which jurors do not interact when reaching a decision are in strong disagreement with data compared to a simple interaction model. These findings provide conceptual and mechanistic support for previous work that has found mutual influence can play a large role in group decisions. In addition, by matching our models to data, we are able to infer the time scales over which individuals change their opinions for different jury contexts. We find that these values increase as a function of the trial time, suggesting that jurors and judicial panels exhibit a kind of stubbornness similar to what we include in our model of voting behavior

Single Molecule Fluorescence Image Patterns Linked to Dipole Orientation and Axial Position: Application to Myosin Cross-Bridges in Muscle Fibers

Photoactivatable fluorescent probes developed specifically for single molecule detection extend advantages of single molecule imaging to high probe density regions of cells and tissues. They perform in the native biomolecule environment and have been used to detect both probe position and orientation.Fluorescence emission from a single photoactivated probe captured in an oil immersion, high numerical aperture objective, produces a spatial pattern on the detector that is a linear combination of 6 independent and distinct spatial basis patterns with weighting coefficients specifying emission dipole orientation. Basis patterns are tabulated for single photoactivated probes labeling myosin cross-bridges in a permeabilized muscle fiber undergoing total internal reflection illumination. Emitter proximity to the glass/aqueous interface at the coverslip implies the dipole near-field and dipole power normalization are significant affecters of the basis patterns. Other characteristics of the basis patterns are contributed by field polarization rotation with transmission through the microscope optics and refraction by the filter set. Pattern recognition utilized the generalized linear model, maximum likelihood fitting, for Poisson distributed uncertainties. This fitting method is more appropriate for treating low signal level photon counting data than χ(2) minimization.Results indicate that emission dipole orientation is measurable from the intensity image except for the ambiguity under dipole inversion. The advantage over an alternative method comparing two measured polarized emission intensities using an analyzing polarizer is that information in the intensity spatial distribution provides more constraints on fitted parameters and a single image provides all the information needed. Axial distance dependence in the emission pattern is also exploited to measure relative probe position near focus. Single molecule images from axial scanning fitted simultaneously boost orientation and axial resolution in simulation

Automated Quality Assessment of Space-Continuous Models for Pedestrian Dynamics

In this work we propose a methodology for assessment of pedestrian models continuous in space. With respect to the Kolmogorov-Smirnov distance between two data clouds, representing for instance simulated and the corresponding empirical data, we calculate an evaluation factor between zero and one. Based on the value of the herein developed factor, we make a statement about the goodness of the model under evaluation. Moreover this process can be repeated in an automatic way in order to maximize the above mentioned factor and hence determine the optimal set of model parameters.Comment: 8 pages, 3 figures, accepted at the Proceedings of Traffic and Granular Flow '1