Matching Items (6)

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Network Based Models of Opinion Formation: Consensus and Beyond

Description

Understanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.

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2021

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On the rigidity of disordered networks

Description

The rigidity of a material is the property that enables it to preserve its structure when deformed. In a rigid body, no internal motion is possible since the degrees of freedom of the system are limited to translations and rotations

The rigidity of a material is the property that enables it to preserve its structure when deformed. In a rigid body, no internal motion is possible since the degrees of freedom of the system are limited to translations and rotations only. In the macroscopic scale, the rigidity and response of a material to external load can be studied using continuum elasticity theory. But when it comes to the microscopic scale, a simple yet powerful approach is to model the structure of the material and its interparticle interactions as a ball$-$and$-$spring network. This model allows a full description of rigidity in terms of the vibrational modes and the balance between degrees of freedom and constraints in the system.

In the present work, we aim to establish a microscopic description of rigidity in \emph{disordered} networks. The studied networks can be designed to have a specific number of degrees of freedom and/or elastic properties. We first look into the rigidity transition in three types of networks including randomly diluted triangular networks, stress diluted triangular networks and jammed networks. It appears that the rigidity and linear response of these three types of systems are significantly different. In particular, jammed networks display higher levels of self-organization and a non-zero bulk modulus near the transition point. This is a unique set of properties that have not been observed in any other types of disordered networks. We incorporate these properties into a new definition of jamming that requires a network to hold one extra constraint in excess of isostaticity and have a finite non-zero bulk modulus. We then follow this definition by using a tuning by pruning algorithm to build spring networks that have both these properties and show that they behave exactly like jammed networks. We finally step into designing new disordered materials with desired elastic properties and show how disordered auxetic materials with a fully convex geometry can be produced.

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2018

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Broken ergodicity and 1

Description

Fluctuations with a power spectral density depending on frequency as $1/f^\alpha$ ($0<\alpha<2$) are found in a wide class of systems. The number of systems exhibiting $1/f$ noise means it has far-reaching practical implications; it also suggests a possibly universal explanation,

Fluctuations with a power spectral density depending on frequency as $1/f^\alpha$ ($0<\alpha<2$) are found in a wide class of systems. The number of systems exhibiting $1/f$ noise means it has far-reaching practical implications; it also suggests a possibly universal explanation, or at least a set of shared properties. Given this diversity, there are numerous models of $1/f$ noise. In this dissertation, I summarize my research into models based on linking the characteristic times of fluctuations of a quantity to its multiplicity of states. With this condition satisfied, I show that a quantity will undergo $1/f$ fluctuations and exhibit associated properties, such as slow dynamics, divergence of time scales, and ergodicity breaking. I propose that multiplicity-dependent characteristic times come about when a system shares a constant, maximized amount of entropy with a finite bath. This may be the case when systems are imperfectly coupled to their thermal environment and the exchange of conserved quantities is mediated through their local environment. To demonstrate the effects of multiplicity-dependent characteristic times, I present numerical simulations of two models. The first consists of non-interacting spins in $0$-field coupled to an explicit finite bath. This model has the advantage of being degenerate, so that its multiplicity alone determines the dynamics. Fluctuations of the alignment of this model will be compared to voltage fluctuations across a mesoscopic metal-insulator-metal junction. The second model consists of classical, interacting Heisenberg spins with a dynamic constraint that slows fluctuations according to the multiplicity of the system's alignment. Fluctuations in one component of the alignment will be compared to the flux noise in superconducting quantum interference devices (SQUIDs). Finally, I will compare both of these models to each other and some of the most popular models of $1/f$ noise, including those based on a superposition of exponential relaxation processes and those based on power law renewal processes.

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2018

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On the origin of the living state

Description

The origin of Life on Earth is the greatest unsolved mystery in the history of science. In spite of progress in almost every scientific endeavor, we still have no clear theory, model, or framework to understand the processes that led

The origin of Life on Earth is the greatest unsolved mystery in the history of science. In spite of progress in almost every scientific endeavor, we still have no clear theory, model, or framework to understand the processes that led to the emergence of life on Earth. Understanding such a processes would provide key insights into astrobiology, planetary science, geochemistry, evolutionary biology, physics, and philosophy. To date, most research on the origin of life has focused on characterizing and synthesizing the molecular building blocks of living systems. This bottom-up approach assumes that living systems are characterized by their component parts, however many of the essential features of life are system level properties which only manifest in the collective behavior of many components. In order to make progress towards solving the origin of life new modeling techniques are needed. In this dissertation I review historical approaches to modeling the origin of life. I proceed to elaborate on new approaches to understanding biology that are derived from statistical physics and prioritize the collective properties of living systems rather than the component parts. In order to study these collective properties of living systems, I develop computational models of chemical systems. Using these computational models I characterize several system level processes which have important implications for understanding the origin of life on Earth. First, I investigate a model of molecular replicators and demonstrate the existence of a phase transition which occurs dynamically in replicating systems. I characterize the properties of the phase transition and argue that living systems can be understood as a non-equilibrium state of matter with unique dynamical properties. Then I develop a model of molecular assembly based on a ribonucleic acid (RNA) system, which has been characterized in laboratory experiments. Using this model I demonstrate how the energetic properties of hydrogen bonding dictate the population level dynamics of that RNA system. Finally I return to a model of replication in which replicators are strongly coupled to their environment. I demonstrate that this dynamic coupling results in qualitatively different evolutionary dynamics than those expected in static environments. A key difference is that when environmental coupling is included, evolutionary processes do not select a single replicating species but rather a dynamically stable community which consists of many species. Finally, I conclude with a discussion of how these computational models can inform future research on the origins of life.

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2018

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Wave-packet Phase-space Monte Carlo approach to the Modeling of Quantum Devices

Description

Advanced and mature computer simulation methods exist in fluid dynamics, elec-

tromagnetics, semiconductors, chemical transport, and even chemical and material

electronic structure. However, few general or accurate methods have been developed

for quantum photonic devices. Here, a novel approach utilizing phase-space quantum

mechanics is

Advanced and mature computer simulation methods exist in fluid dynamics, elec-

tromagnetics, semiconductors, chemical transport, and even chemical and material

electronic structure. However, few general or accurate methods have been developed

for quantum photonic devices. Here, a novel approach utilizing phase-space quantum

mechanics is developed to model photon transport in ring resonators, a form of en-

tangled pair source. The key features the model needs to illustrate are the emergence

of non-classicality and entanglement between photons due to nonlinear effects in the

ring. The quantum trajectory method is subsequently demonstrated on a sequence

of elementary models and multiple aspects of the ring resonator itself.

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Date Created
2020

Collaborating in Motion: Distributed and Stochastic Algorithms for Emergent Behavior in Programmable Matter

Description

The world is filled with systems of entities that collaborate in motion, both natural and engineered. These cooperative distributed systems are capable of sophisticated emergent behavior arising from the comparatively simple interactions of their members. A model system for emergent

The world is filled with systems of entities that collaborate in motion, both natural and engineered. These cooperative distributed systems are capable of sophisticated emergent behavior arising from the comparatively simple interactions of their members. A model system for emergent collective behavior is programmable matter, a physical substance capable of autonomously changing its properties in response to user input or environmental stimuli. This dissertation studies distributed and stochastic algorithms that control the local behaviors of individual modules of programmable matter to induce complex collective behavior at the macroscale. It consists of four parts. In the first, the canonical amoebot model of programmable matter is proposed. A key goal of this model is to bring algorithmic theory closer to the physical realities of programmable matter hardware, especially with respect to concurrency and energy distribution. Two protocols are presented that together extend sequential, energy-agnostic algorithms to the more realistic concurrent, energy-constrained setting without sacrificing correctness, assuming the original algorithms satisfy certain conventions. In the second part, stateful distributed algorithms using amoebot memory and communication are presented for leader election, object coating, convex hull formation, and hexagon formation. The first three algorithms are proven to have linear runtimes when assuming a simplified sequential setting. The final algorithm for hexagon formation is instead proven to be correct under unfair asynchronous adversarial activation, the most general of all adversarial activation models. In the third part, distributed algorithms are combined with ideas from statistical physics and Markov chain design to replace algorithm reliance on memory and communication with biased random decisions, gaining inherent self-stabilizing and fault-tolerant properties. Using this stochastic approach, algorithms for compression, shortcut bridging, and separation are designed and analyzed. Finally, a two-pronged approach to "programming" physical ensembles is presented. This approach leverages the physics of local interactions to pair theoretical abstractions of self-organizing particle systems with experimental robot systems of active granular matter that intentionally lack digital computation and communication. By physically embodying the salient features of an algorithm in robot design, the algorithm's theoretical analysis can predict the robot ensemble's behavior. This approach is applied to phototaxing, aggregation, dispersion, and object transport.

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Date Created
2021