Understanding Disordered Systems Through Numerical Simulation and Algorithm Development

Disordered systems arise in many physical contexts. Not all matter is uni- form, and impurities or heterogeneities can be modeled by fixed random disor- der. Numerous complex networks also possess fixed disorder, leading to appli- cations in transportation systems [1], telecommunications [2], social networks [3, 4], and epidemic modeling [5], to name a few. Due to their random nature and power law critical behavior, disordered systems are difficult to study analytically. Numerical simulation can help overcome this hurdle by allowing for the rapid computation of system states. In order to get precise statistics and extrapolate to the thermodynamic limit, large systems must be studied over many realizations. Thus, innovative al- gorithm development is essential in order reduce memory or running time requirements of simulations. This thesis presents a review of disordered systems, as well as a thorough study of two particular systems through numerical simulation, algorithm de- velopment and optimization, and careful statistical analysis of scaling proper- ties. Chapter 1 provides a thorough overview of disordered systems, the his- tory of their study in the physics community, and the development of tech- niques used to study them. Topics of quenched disorder, phase transitions, the renormalization group, criticality, and scale invariance are discussed. Several prominent models of disordered systems are also explained. Lastly, analysis techniques used in studying disordered systems are covered. In Chapter 2, minimal spanning trees on critical percolation clusters are studied, motivated in part by an analytic perturbation expansion by Jackson and Read [6] that I check against numerical calculations. This system has a direct mapping to the ground state of the strongly disordered spin glass [7]. We compute the path length fractal dimension of these trees in dimensions d = {2, 3, 4, 5} and find our results to be compatible with the analytic results suggested by Jackson and Read. In Chapter 3, the random bond Ising ferromagnet is studied, which is es- pecially useful since it serves as a prototype for more complicated disordered systems such as the random field Ising model and spin glasses. We investigate the effect that changing boundary spins has on the locations of domain walls in the interior of the random ferromagnet system. We provide an analytic proof that ground state domain walls in the two dimensional system are de- composable, and we map these domain walls to a shortest paths problem. By implementing a multiple-source shortest paths algorithm developed by Philip Klein [8], we are able to efficiently probe domain wall locations for all possible configurations of boundary spins. We consider lattices with uncorrelated dis- order, as well as disorder that is spatially correlated according to a power law. We present numerical results for the scaling exponent governing the probabil- ity that a domain wall can be induced that passes through a particular location in the system’s interior, and we compare these results to previous results on the directed polymer problem

Econometrics of network models

View of road and industry from Cumbala Hill.GrayscaleSorensen Safety Negatives, Binder: Asia

Decision Making in Networked Systems

Living in a networked world, human agents are increasingly connected as advances in technology facilitates the flow of information between and the availability of services to them. Through this research, we look at interacting agents in networked environments, and explore how their decisions are influenced by other people\u27s decisions. In this context, an individual\u27s decision may be regarding a concrete action, e.g., adoption of a product or service that is offered, or simply shape her opinion about a subject. Accordingly, we investigate two classes of such problems. The first problem is the dynamics of service adoption in networked environments, where one user\u27s adoption decision, influences the adoption decision of other users by affecting (positively or negatively) the benefits that they derive from the service. We consider this problem in the context of User-Provided Connectivity , or UPC. The service offers an alternative to traditional infrastructure-based communication services by allowing users to share their home base connectivity with other users, thereby increasing their access to connectivity. We investigate when such services are viable, and propose a number of pricing policies of different complexities. The pricing policies exhibit differences in their ability to maximize the total welfare created by the service, and distributing the welfare between different stakeholders. The second problem is the spread of opinions in a networked environment, where one agent\u27s opinion about an issue, influences and is influenced by that of other agents to whom she is connected. We are particularly interested in the role that people\u27s adherence to specific groups or parties may play in how final opinions are formed. We approach this problem using a model of interactions inspired by the Ising spin-glass model from classical Physics. We consider two related but distinct settings, and show that when party memberships directly influence user interactions, even slightest statistical partisan biases result in partisan final outcomes: where everyone in a party shares the same opinion, opposite to that of the other party. On the other hand, if party membership plays an indirect role in biasing agent interactions, then there is room for intra-party heterogeneity of opinions

FORETELL: Aggregating Distributed, Heterogeneous Information from Diverse Sources Using Market-based Techniques

Predicting the outcome of uncertain events that will happen in the future is a frequently indulged task by humans while making critical decisions. The process underlying this prediction and decision making is called information aggregation, which deals with collating the opinions of different people, over time, about the future event’s possible outcome. The information aggregation problem is non-trivial as the information related to future events is distributed spatially and temporally, the information gets changed dynamically as related events happen, and, finally, people’s opinions about events’ outcomes depends on the information they have access to and the mechanism they use to form opinions from that information. This thesis addresses the problem of distributed information aggregation by building computational models and algorithms for different aspects of information aggregation so that the most likely outcome of future events can be predicted with utmost accuracy. We have employed a commonly used market-based framework called a prediction market to formally analyze the process of information aggregation. The behavior of humans performing information aggregation within a prediction market is implemented using software agents which employ sophisticated algorithms to perform complex calculations on behalf of the humans, to aggregate information efficiently. We have considered five different yet crucial problems related to information aggregation, which include: (i) the effect of variations in the parameters of the information being aggregated, such as its reliability, availability, accessibility, etc., on the predicted outcome of the event, (ii) improving the prediction accuracy by having each human (software-agent) build a more accurate model of other humans’ behavior in the prediction market, (iii) identifying how various market parameters effect its dynamics and accuracy, (iv) applying information aggregation to the domain of distributed sensor information fusion, and, (v) aggregating information on an event while considering dissimilar, but closely-related events in different prediction markets. We have verified all of our proposed techniques through analytical results and experiments while using commercially available data from real prediction markets within a simulated, multi-agent based prediction market. Our results show that our proposed techniques for information aggregation perform more efficiently or comparably with existing techniques for information aggregation using prediction markets

Structural vibration damping using lightweight, low-wave-speed media

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 157-162).Incorporation of a low-density, low-wave-speed medium (LWSM) into a structure yields significant damping if the speed of wave propagation in the medium is low enough for standing waves to arise in it. In this thesis, we characterize wave propagation in low-density granular media and foams for use as structural damping treatments and develop analytical and numerical techniques for prediction of the damping attained in structures that incorporate LWSM. Structural damping by incorporation of LWSM is attractive for hollow thin-walled structures. We develop analytical approximations for the loss-factor in the structural modes of cylindrical shells and Timoshenko beams and attain predictions in good agreement with measurements. For more complicated geometries, it is often necessary to employ a finite element model to predict the dynamics of structures. But inclusion of LWSM into a finite element model significantly increases the size of the model, introduces frequency-dependent material properties, and introduces a large number of modes that are dominated by deformation of the LWSM. Hence, the eigenvalue problem becomes significantly more difficult by addition of the LWSM.(cont.) We develop an iterative approach based on the eigensolution of a structure without LWSM and the forced response of the LWSM to obtain approximations for the complex eigensolution. Damping by inclusion of LWSM is an attractive option for reduction of the sound radiated from vehicle driveshafts, which are typically thin-walled hollow cylinders with yokes welded at each end. The bending and ovaling modes of the driveshaft between 500 and 3000 Hz are efficient radiators of sound and are excited by gear transmission error in the rear differential. Filling the driveshaft with a. lossy, low-density foam adds significant damping to these modes and thus reduces the radiated sound.by Justin Matthew Verdirame.Ph.D