VTechWorks Repository :: Browsing by Author "Tauber, Uwe C."

Browsing by Author "Tauber, Uwe C."

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Application of Network Reliability to Analyze Diffusive Processes on Graph Dynamical Systems
Nath, Madhurima (Virginia Tech, 2019-01-22)
Moore and Shannon's reliability polynomial can be used as a global statistic to explore the behavior of diffusive processes on a graph dynamical system representing a finite sized interacting system. It depends on both the network topology and the dynamics of the process and gives the probability that the system has a particular desired property. Due to the complexity involved in evaluating the exact network reliability, the problem has been classified as a NP-hard problem. The estimation of the reliability polynomials for large graphs is feasible using Monte Carlo simulations. However, the number of samples required for an accurate estimate increases with system size. Instead, an adaptive method using Bernstein polynomials as kernel density estimators proves useful. Network reliability has a wide range of applications ranging from epidemiology to statistical physics, depending on the description of the functionality. For example, it serves as a measure to study the sensitivity of the outbreak of an infectious disease on a network to the structure of the network. It can also be used to identify important dynamics-induced contagion clusters in international food trade networks. Further, it is analogous to the partition function of the Ising model which provides insights to the interpolation between the low and high temperature limits.
Applications of Field Theory to Reaction Diffusion Models and Driven Diffusive Systems
Mukherjee, Sayak (Virginia Tech, 2009-08-25)
In this thesis, we focus on the steady state properties of two systems which are genuinely out of equilibrium. The first project is an application of dynamic field theory to a specific non equilibrium critical phenomenon, while the second project involves both simulations and analytical calculations. The methods of field theory are used on both these projects. In the first part of this thesis, we investigate a generalization of the well-known field theory for directed percolation (DP). The DP theory is known to describe an evolving population, near extinction. We have coupled this evolving population to an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (model A) dynamics. We find two marginal couplings with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point. Some open questions and future work remain. In the second project, we focus on a simple particle transport model far from equilibrium, namely, the totally asymmetric simple exclusion process (TASEP). While its stationary properties are well studied, many of its dynamic features remain unexplored. Here, we focus on the power spectrum of the total particle occupancy in the system. This quantity exhibits unexpected oscillations in the low density phase. Using standard Monte Carlo simulations and analytic calculations, we probe the dependence of these oscillations on boundary effects, the system size, and the overall particle density. Our simulations are fitted to the predictions of a linearized theory for the fluctuation of the particle density. Two of the fit parameters, namely the diffusion constant and the noise strength, deviate from their naive bare values [6]. In particular, the former increases significantly with the system size. Since this behavior can only be caused by nonlinear effects, we calculate the lowest order corrections in perturbation theory. Several open questions and future work are discussed.
Applications of gauged linear sigma models
Chen, Zhuo (Virginia Tech, 2019-05-17)
This thesis is devoted to a study of applications of gauged linear sigma models. First, by constructing (0,2) analogues of Hori-Vafa mirrors, we have given and checked proposals for (0,2) mirrors to projective spaces, toric del Pezzo and Hirzebruch surfaces with tangent bundle deformations, checking not only correlation functions but also e.g. that mirrors to del Pezzos are related by blowdowns in the fashion one would expect. Also, we applied the recent proposal for mirrors of non-Abelian (2,2) supersymmetric two-dimensional gauge theories to examples of two-dimensional A-twisted gauge theories with exceptional gauge groups G_2 and E_8. We explicitly computed the proposed mirror Landau-Ginzburg orbifold and derived the Coulomb ring relations (the analogue of quantum cohomology ring relations). We also studied pure gauge theories, and provided evidence (at the level of these topologicalﬁeld-theory-type computations) that each pure gauge theory (with simply-connected gauge group) ﬂows in the IR to a free theory of as many twisted chiral multiplets as the rank of the gauge group. Last, we have constructed hybrid Landau-Ginzburg models that RG ﬂow to a new family of non-compact Calabi-Yau threefolds, constructed as ﬁber products of genus g curves and noncompact Kahler threefolds. We only considered curves given as branched double covers of P^1. Our construction utilizes nonperturbative constructions of the genus g curves, and so provides a new set of exotic UV theories that should RG ﬂow to sigma models on Calabi-Yau manifolds, in which the Calabi-Yau is not realized simply as the critical locus of a superpotential.
Aspects of population dynamics
Swailem, Mohamed (Virginia Tech, 2024-05-24)
Natural ecologies are prone to stochastic effects and changing environments that shape their dynamical behavior. Ecological systems can be modeled through relatively simple population dynamics models. There is a plethora of models describing deterministic models of ecological systems evolving in a constant environment. However, stochasticity can lead to extinction or fixation events, noise-stabilized patterns, and nontrivial correlations. Likewise, changing environments can greatly affect the behavior and ultimate fate of ecological systems. In fact, the dynamics of evolution are mostly driven by randomness and changing environments. Therefore, it is of utmost importance to develop population dynamics models that are able to capture the effects of noise and environmental drive. In this thesis, we use both theoretical tools and simulations to investigate population dynamics in the following contexts: We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for the prey exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The stationary regime of our periodically varying LV system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast- and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the stationary state. The mean-field analysis of the Lotka-Volterra predator-prey model with seasonally varying carrying capacity is extended to the resonant regime. This is done by introducing a homotopy mapping from this model to another model that allows for the application of Floquet theory. The stability of the coexistence fixed point is studied and the period doubling is related to a bifurcation point in the homotopy mapping. However, we find that the predator-prey ecology's coexistence is stable for most of its parameter region. We apply a perturbative Doi–Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-Paper-Scissors (RPS) and May–Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka–Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models. Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale, long-time kinetics in such systems are effective, scale-dependent renormalized parameters that need to be either measured experimentally or computed by means of a microscopic model. In a Monte Carlo simulation of stochastic reactiondiffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. To match the results of any computer simulation to observations or experiments carried out on the macroscale, a mapping is required between the microscopic probabilities that define the Monte Carlo algorithm and the macroscopic reaction rates that are experimentally measured. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities (subject to specific rules of interaction) is a very difficult problem, and there is currently no systematic, accurate analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using lattice Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka–Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka–Volterra model as well as its May–Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a more thorough and deeper understanding of coarse-graining in spatially extended stochastic reactiondiffusion systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters, with a focus on ecological systems. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.
Casimir Force in Non-Planar Geometric Configurations
Cho, Sung Nae (Virginia Tech, 2004-03-22)
The Casimir force for charge-neutral, perfect conductors of non-planar geometric configurations have been investigated. The configurations were: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical shell. The resulting Casimir forces for these physical arrangements have been found to be attractive. The repulsive Casimir force found by Boyer for a spherical shell is a special case requiring stringent material property of the sphere, as well as the specific boundary conditions for the wave modes inside and outside of the sphere. The necessary criteria in detecting Boyer's repulsive Casimir force for a sphere are discussed at the end of this thesis.
Computational Studies of Polyetherimides: Beyond All-Atom Molecular Dynamics Simulations
Wen, Chengyuan (Virginia Tech, 2020-01-24)
Polyetherimides are an important class of engineering thermoplastics used in a broad range of industries and applications because of their high heat resistance and stability, high strength and moduli, excellent electrical properties over a wide range of temperatures and frequencies, good processability, good adhesive properties, and chemical stability. All-atom molecular dynamics (MD) simulation is a useful tool to study polymers, but the accessible length and time scales are limited. In this thesis, we explore several computational methods that go beyond all-atom MD simulations to investigate polyetherimides. First, we have developed a transferable coarse-grained MD model of polyetherimides that captures their mechanical and thermal expansion properties. Our results show that in order to make the model transferable, it is critical to include an entropic correction term in the coarse-grained force field and require the coarse-grained model to capture the thermal expansion property of polyetherimides. Secondly, we have constructed a predictive model of the glass transition temperature (Tg) for polyimides by using machine-learning algorithms to analyze existing data on Tg reported in the literature. The predictive model is validated by comparing its predictions to experimental data not used in the training process of the model. We further demonstrate that the diffusion coefficients of small gas molecules can be quickly computed with all-atom MD simulations and used to determine Tg. Finally, we have developed a Monte Carlo (MC) program to model the polymerization process of branched polyetherimides and to compute their molecular weight distribution for a wide range of systems, including fully reacted, partially reacted, stoichiometric, and nonstoichiometric ones. The MC results are compared to the predictions of the Flory-Stockmayer theory of branched polymers and an excellent agreement is found below the gel point of the system under consideration. Above the gel point, the Flory- Stockmayer theory starts to fail but the MC method can still be used to quickly determine the molecular weight distribution of branched polyetherimides under very general conditions.
Controlling non-equilibrium dynamics in lattice gas models
Mukhamadiarov, Ruslan Ilyich (Virginia Tech, 2021-03-05)
In recent years a new interesting research avenue has emerged in non-equilibrium statistical physics, namely studies of collective responses in spatially inhomogeneous systems. Whereas substantial progress has been made in understanding the origins and the often universal nature of cooperative behavior in systems far from equilibrium, it is still unclear whether it is possible to control their global collective stochastic dynamics through local manipulations. Therefore, a comprehensive characterization of spatially inhomogeneous non-equilibrium systems is required. In the first system, we explore a variant of the Katz–Lebowitz–Spohn (KLS) driven lattice gas in two dimensions, where the lattice is split into two regions that are coupled to heat baths with distinct temperatures T > T_c and T_c respectively, where T_c indicates the critical temperature for phase ordering. The geometry was arranged such that the temperature boundaries are oriented perpendicular or parallel to the external particle drive and resulting net current. For perpendicular orientation of the temperature boundaries, in the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. This blockage is induced by extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high- and low-temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power-law density decay near the interfaces into the cooler region. For parallel orientation of the temperature boundaries, we have explored the changes in the dynamical behavior of the hybrid KLS model that are induced by our choice of the hopping rates across the temperature boundaries. If these hopping rates at the interfaces satisfy particle-hole symmetry, the current difference across them generates a vector flow diagram akin to an infinite flat vortex sheet. We have studied the finite-size scaling of the particle density fluctuations in both temperature regions, and observed that it is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature, while the hotter subsystem's temperature is set much higher, the interface current greatly suppresses particle exchange between the two regions. As a result of the ensuing effective subsystem decoupling, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale according to the totally asymmetric exclusion process. We have also measured the entropy production rate in both subsystems; it displays intriguing algebraic decay in the critical region, while it saturates quickly at a small but non-zero level in the hotter region. The second system is a lattice gas that simulates the spread of COVID-19 epidemics using the paradigmatic stochastic Susceptible-Infectious-Recovered (SIR) model. In our effort to control the spread of the infection of a lattice, we robustly find that the intensity and spatial spread on the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak).
Controlling Quantum Systems for Computation and Communication
Li, Bikun (Virginia Tech, 2023-02-02)
Quantum information processing has the potential of implementing faster algorithms for numerous problems, communicating with more secure channels, and performing higher precision sensing compared to classical methods. Recent experimental technology advancement has brought us a promising future of harnessing such quantum advantage. Yet, quantum engineering entails wise control and strategy under the current noisy intermediate-scale quantum era. Developing robust and efficient approaches to manipulating quantum systems based on constrained and limited resources is imperative. This dissertation focuses on two major topics theoretically. In the first part, this work present how to conceive robust quantum control on matter-based qubits with a geometric approach. We have proposed the method of designing noise robust control pulses suitable for practical devices by combining spatial curves, filter functions, and machine learning. In the second part, this work stresses the topic of photonic multipartite entangled graph states. An improved protocol of generating arbitrary graph states is introduced. We show that one can efficiently find the deterministic photon emission circuit with minimal overhead on the number of quantum emitters.
DNA Electronics
Zwolak, Michael Philip (Virginia Tech, 2003-05-07)
DNA is a potential component in molecular electronics. To explore this end, there has been an incredible amount of research on how well DNA conducts and by what mechanism. There has also been a tremendous amount of research to find new uses for it in nanoscale electronics. DNA's self-assembly and recognition properties have found a unique place in this area. We predict, using a tight-binding model, that spin-dependent transport can be observed in short DNA molecules sandwiched between ferromagnetic contacts. In particular, we show that a DNA spin-valve can be realized with magnetoresistance values of as much as 26% for Ni and 16% for Fe contacts. Spin-dependent transport can broaden the possible applications of DNA as a component in molecular electronics and shed new light into the transport properties of this important biological molecule.
Driven Magnetic Flux Lines in Type-II Superconductors: Nonequilibrium Steady States and Relaxation Properties
Klongcheongsan, Thananart (Virginia Tech, 2009-03-31)
We investigate the nonequilibrium steady state of driven magnetic flux lines in type-II superconductors subject to strong point or columnar pinning centers and the aging dynamics of nonequilibrium relaxation process in the presence of weak point pinning centers. We employ a three-dimensional elastic line model and Metropolis Monte Carlo simulations. For the first part, we characterize the system by means of the force-velocity / current-voltage curve, static structure factor, mean vortex radius of gyration, number of double-kink and half-loop excitations, and velocity / voltage noise features. We compare the results for the above quantities for randomly distributed point and columnar defects. Most of both numerical works have been done in two-dimensional systems such as thin film in which the structure of flux lines is treated as a point-like particle. Our main point of investigation in this paper is to demonstrate that the vortex structure and its other transport properties may exhibit a remarkable variety of complex phenomena in three-dimensional or bulk superconductors. The second part devotes to the study of aging phenomena in the absence of a driving force in disordered superconductors with much weaker point disorder. By investigating the density autocorrelation function, we observe all three crucial properties of the aging phenomena; slow power-law relaxation, breaking of time-translation invariance, and the presence of the dynamical scaling. We measure the dynamical exponents b and lambda_c/z and compare to other work. We find exponent values increase for increasing pinning strength, smaller interaction range, lower temperature, and denser defect density while the exponents measured in other approach tend to decrease.
Dynamics of Competition using a Bit String Model with Age Structure and Mutations
Astalos, Robert Joseph (Virginia Tech, 2001-04-17)
Using Monte Carlo simulations and analytic methods, we examine the dynamics of inter-species competition using the Penna bit-string model. We begin with a study of the steady state with a single species, then proceed to the dynamics of competition between two species. When the species are not evenly matched in fitness, a simple differential equation provides a satisfactory model of the behavior of the system. However, when the species are equally fit, we show that a model, originally proposed to describe population genetics [Fisher,Wright], is required. When mutations are allowed between the competing species, the dynamics becomes more interesting. The mutation rate becomes a parameter that dictates the steady state behavior. If the two species are not equally fit, the value of the mutation rate determines whether the longer-lived or faster reproducing species is favored. With two species that are equally fit, the steady state varies with mutation rate from a single peaked to a double peaked distribution. This behavior is shown to be well described by an extension to the Fisher-Wright model mentioned above. Finally, we describe the preliminary results of a few new lines of investigation, and suggest ideas for further study of the dynamics of this model.
Dynamics of Driven Vortices in Disordered Type-II Superconductors
Chaturvedi, Harshwardhan Nandlal (Virginia Tech, 2019-01-22)
We numerically investigate the dynamical properties of driven magnetic flux vortices in disordered type-II superconductors for a variety of temperatures, types of disorder and sample thicknesses. We do so with the aid of Langevin molecular dynamics simulations of a coarsegrained elastic line model of flux vortices in the extreme London limit. Some original findings of this doctoral work include the discovery that flux vortices driven through random point disorder show simple aging following drive quenches from the moving lattice state to both the pinned glassy state (non-universal aging) and near the critical depinning region (universal aging); estimations of experimentally consistent critical scaling exponents for the continuous depinning phase transition of vortices in three dimensions; and an estimation of the boundary curve separating regions of linear and non-linear electrical transport for flux lines driven through planar defects via novel direct measurements of vortex excitations.
Electroproduction of Phi(1020) Mesons at High Q² with CLAS
Santoro, Joseph Peter (Virginia Tech, 2004-08-05)
This analysis studies the reaction ep → e′p′ϕ in the kinematical range 1.6 ≤ Q² ≤ 3.8 GeV² and 2.0 ≤ W ≤ 3:0 GeV at CLAS. After successful signal identification, total and differential cross sections are measured and compared to the world data set. Comparisons are made to the predictions of the Jean-Marc Laget(JML) model based on Pomeron plus 2-gluon exchange. The overall scaling of the total cross section was determined to be 1/Q^4.6±1.7 which is compatible within errors to the Vector Meson Dominance prediction of 1/Q⁴ as well as to the expected behavior of a quark and gluon exchange-dominated model described by Generalized Parton Distributions of 1/Q⁶. The differential cross section dσ/dφ was used to determine that the s-channel helicity conservation (SCHC) assumption is valid within the precision of the current data. SCHC leads to a simple expression for the decay angular distribution from which R, the ratio of the longitudinal to the transverse cross section, can be extracted. Under the assumption of SCHC, we determine R = 1.33 ± 0.18 at an average Q² of 2.21 GeV² which leads to a determination of the longitudinal cross section σ_L = 5.3 ± 1.3 nb for exclusive ϕ production.
Examining the Dynamics of Biologically Inspired Systems Far From Equilibrium
Carroll, Jacob Alexander (Virginia Tech, 2019-04-23)
Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of "patterns" learned from previous images as basis elements. The network attempts to do so "sparsely," so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size.
Extending the Geometric Tools of Heterotic String Compactification and Dualities
Karkheiran, Mohsen (Virginia Tech, 2020-06-15)
In this work, we extend the well-known spectral cover construction first developed by Friedman, Morgan, and Witten to describe more general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form but can rather contain fibral divisors or multiple sections (i.e., a higher rank Mordell-Weil group). In these cases, general vector bundles defined over such Calabi-Yau manifolds cannot be described by ordinary spectral data. To accomplish this, we employ well-established tools from the mathematics literature of Fourier-Mukai functors. We also generalize existing tools for explicitly computing Fourier-Mukai transforms of stable bundles on elliptic Calabi-Yau manifolds. As an example of these new tools, we produce novel examples of chirality changing small instanton transitions. Next, we provide a geometric formalism that can substantially increase the understood regimes of heterotic/F-theory duality. We consider heterotic target space dual (0,2) GLSMs on elliptically fibered Calabi-Yau manifolds. In this context, each half of the ``dual" heterotic theories must, in turn, have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple $K3$-fibrations of the same elliptically fibered Calabi-Yau manifold. We investigate this conjecture in the context of both 6-dimensional and 4-dimensional effective theories and demonstrate that in general, (0,2) target space duality cannot be explained by such a simple phenomenon alone. In all cases, we provide evidence that non-geometric data in F-theory must play at least some role in the induced F-theory correspondence while leaving the full determination of the putative new F-theory duality to the future work. Finally, we consider F-theory over elliptically fibered manifolds, with a general conic base. Such manifolds are quite standard in F-theory sense, but our goal is to explore the extent of the heterotic/F-theory duality over such manifolds. We consider heterotic target space dual (0,2) GLSMs on elliptically fibered Calabi-Yau manifolds. In this context, each half of the ``dual" heterotic theories must, in turn, have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple $K3$-fibrations of the same elliptically fibered Calabi-Yau manifold. We investigate this conjecture in the context of both 6-dimensional and 4-dimensional effective theories and demonstrate that in general, (0,2) target space duality cannot be explained by such a simple phenomenon alone. In all cases, we provide evidence that non-geometric data in F-theory must play at least some role in the induced F-theory correspondence while leaving the full determination of the putative new F-theory duality to the future work. Finally, we consider F-theory over elliptically fibered manifolds, with a general conic base. Such manifolds are quite standard in F-theory sense, but our goal is to explore the extent of the heterotic/F-theory duality over such manifolds.
Fluctuation Relations for Stochastic Systems far from Equilibrium
Dorosz, Sven (Virginia Tech, 2010-03-26)
Fluctuations are of great importance in systems of small length and energy scales. Measuring the pulling of single molecules or the stationary fiow of mesospheres dragged through a viscous media enables the direct analysis of work and entropy distributions. These probability distributions are the result of a large number of repetitions of the same experiment. Due to the small scale of these experiments, the outcome can vary significantly from one realization to the next. Strong theoretical predictions exist, collectively called Fluctuation Theorems, that restrict the shape of these distributions due to an underlying time reversal symmetry of the microscopic dynamics. Fluctuation Theorems are the strongest existing statements on the entropy production of systems that are out of equilibrium. Being the most important ingredient for the Fluctuation Theorems, the probability distribution of the entropy change is itself of great interest. Using numerically exact methods we characterize entropy distributions for various stochastic reaction-diffusion systems that present different properties in their underlying dynamics. We investigate these systems in their steady states and in cases where time dependent forces act on them. This study allows us to clarify the connection between the microscopic rules and the resulting entropy production. The present work also adds to the discussion of the steady state properties of stationary probabilities and discusses a non-equilibrium current amplitude that allows us to quantify the distance from equilibrium. The presented results are part of a greater endeavor to find common rules that will eventually lead to a general understanding of non-equilibrium systems.
A General Study of the Complex Ginzburg-Landau Equation
Liu, Weigang (Virginia Tech, 2019-07-02)
In this dissertation, I study a nonlinear partial differential equation, the complex Ginzburg-Landau (CGL) equation. I first employed the perturbative field-theoretic renormalization group method to investigate the critical dynamics near the continuous non-equilibrium transition limit in this equation with additive noise. Due to the fact that time translation invariance is broken following a critical quench from a random initial configuration, an independent ``initial-slip'' exponent emerges to describe the crossover temporal window between microscopic time scales and the asymptotic long-time regime. My analytic work shows that to first order in a dimensional expansion with respect to the upper critical dimension, the extracted initial-slip exponent in the complex Ginzburg-Landau equation is identical to that of the equilibrium model A. Subsequently, I studied transient behavior in the CGL through numerical calculations. I developed my own code to numerically solve this partial differential equation on a two-dimensional square lattice with periodic boundary conditions, subject to random initial configurations. Aging phenomena are demonstrated in systems with either focusing and defocusing spiral waves, and the related aging exponents, as well as the auto-correlation exponents, are numerically determined. I also investigated nucleation processes when the system is transiting from a turbulent state to the ``frozen'' state. An extracted finite dimensionless barrier in the deep-quenched case and the exponentially decaying distribution of the nucleation times in the near-transition limit are both suggestive that the dynamical transition observed here is discontinuous. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-SC0002308
Harnessing Systems Bioengineering Approaches to Study Microbe-Microbe and Host-Microbe Interactions in Health and Disease
Datla, Udaya Sree (Virginia Tech, 2024-03-22)
The core of the dissertation lies in developing two novel systems bioengineering approaches, a synthetic Escherichia coli killer-prey microecology, and a combined infection-inflammation NET-array system, to investigate the role of the mechanochemical complexity of the microenvironment in driving the microbe-microbe and host-microbe interactions, respectively. Herein, the first part of the dissertation includes designing and engineering a synthetic E. coli killer-prey microecological system where we quantified the quorum-sensing mediated interactions between the engineered killer and prey E. coli bacterial strains plated on nutrient-rich media. In this work, we developed the plate assay followed by plasmid sequencing and computational modeling that emphasizes the concept of the constant evolution of species or acquired resistance in the prey E. coli, in the vicinity of the killer strain. We designed the microecological system such that the killer cells (dotted at the center of the plate) constitutively produce and secrete AHL quorum-sensing molecules into the microenvironment. AHL then diffuses into the prey cells (spread throughout the plate) and upregulates the expression of a protein that lyses the prey. Through time-lapse imaging on petri plates automated using a scanner, we recorded the "kill wave" that originates outside the killer colony and travels outward as the prey dies. We found that the prey population density surrounding the killer decreased in comparison to other locations on the plate far from the killer. However, some of the prey colonies evolve to be resistant to the effects of AHL secreted by the killer. These prey colonies resistant to the killer were then selected and confirmed by plasmid sequencing. Using this empirical data, we developed the first ecological model emphasizing the concept of the constant evolution of species, where the survival of the prey species is dependent on the location (distance from the killer) or the evolution of resistance. The importance of this work lies in the context of the evolution of antibiotic-resistant bacterial strains and in understanding the communication between the microbial consortia, such as in the gut microbiome. Further, the second part of the dissertation includes quantifying the interactions between immune cells (primary healthy human neutrophils) and motile Pseudomonas aeruginosa bacteria in an inflammation-rich microenvironment. Neutrophils, being the first responding immune cells to infection, defend by deploying various defense mechanisms either by phagocytosing and killing the pathogen intracellularly or through a suicidal mechanism of releasing their DNA to the extracellular space in the form of Neutrophil Extracellular Traps (NETs) to trap the invading pathogens. Although the release of NETs is originally considered a protective mechanism, it is shown to increase the inflammation levels in the host if unchecked, ultimately resulting in end-organ damage (especially lung and kidney damage), as with the severe cases of sepsis and COVID-19. In our work, we developed a combined infection-inflammation NET-array system integrated with a live imaging assay to quantify the spatiotemporal dynamics of NET release in response to P. aeruginosa infection in an inflammatory milieu at a single-cell resolution. Importantly, we found increased NET release to P. aeruginosa PAO1 when challenged with inflammatory mediators tumor necrosis factor-α (TNF-α) and interleukin-6 (IL-6), but not leukotriene B4 (LTB4), compared to the infection alone. Our device platform is unique in that the nanoliter well-assisted individual neutrophil trapping enables us to quantify NET release with single-cell precision. Besides, incorporating confined side loops in the device helped us study the role of mechanical confinement on NET release, showing reduced NET release from neutrophils confined in the side loops compared to the relatively wider chambers of our microsystem. In summary, our work emphasizes the importance of studying the heterogeneity of NET release in host defense and inflammation. In the future, our system can be used for screening novel neutrophil-based immunotherapies and serve as a valuable research tool in precision medicine.
Inhomogeneous Totally Asymmetric Simple Exclusion Processes: Simulations, Theory and Application to Protein Synthesis
Dong, Jiajia (Virginia Tech, 2008-03-26)
In the process of translation, ribosomes, a type of macromolecules, read the genetic code on a messenger RNA template (mRNA) and assemble amino acids into a polypeptide chain which folds into a functioning protein product. The ribosomes perform discrete directed motion that is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. We incorporate the essential components of the translation process: Ribosomes, cognate tRNA concentrations, and mRNA templates correspond to particles (covering ell > 1 sites), hopping rates, and the underlying lattice, respectively. As the hopping rates in an mRNA are given by its sequence (in the unit of codons), we are especially interested in the effects of a finite number of slow codons to the overall stationary current. To study this matter systematically, we first explore the effects of local inhomogeneities, i.e., one or two slow sites of hopping rate q<1 in TASEP for particles of size ell > 1(in the unit of lattice site) using Monte Carlo simulation. We compare the results of ell =1 and ell >1 and notice that the existence of local defects has qualitatively similar effects to the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both ell =1 and ell >1 cases. In particular, we notice a novel "edge" effect, i.e., the interaction of a single slow codon with the system boundary. When two slow sites are introduced, more intriguing phenomena such as dramatic decreases in the current when the two are close together emerge. We analyze the simulation results using several different levels of mean-field theory. A finite-segment mean-field approximation is especially successful in understanding the "edge effect." If we consider the systems with finite defects as "contrived mRNA's", the real mRNA's are of more biological significance. Inspired by the previous results, we study several mRNA sequences from Escherichia coli. We argue that an effective translation rate including the context of each codon needs to be taken into consideration when seeking an efficient strategy to optimize the protein production.
Interface Effects and Deposition Process of Ionically Self-Assembled Monolayer Films: In Situ and Ex Situ Second Hamonic Generation Measurements
Brands, Charles (Virginia Tech, 2003-08-24)
In this thesis, detailed studies are presented into self-assembled, noncentrosymmetric, optically active films. Second harmonic generation (SHG) is used to measure the second order nonlinear optical susceptibility (?(2)) of ionically self-assembled monolayer (ISAM) thin films. Conventional ISAM films are fabricated by alternately immersing a substrate into oppositely-charged polyelectrolyte solutions. The polyelectrolytes bind electrostatically to the oppositely-charged substrate, and thus reverse the charge of the substrate. The charge reversal limits the amount of adsorbed material and primes the substrate for the next layer. During the deposition of the nonlinear optical (NLO) active layer, the chromophores are attracted to the oppositely-charged surface, which results in net orientation of the chromophores. Some of the net orientation is lost during the deposition of the next NLO-inactive layer as this layer orients some of the chromophores away from the substrate. A disadvantage of the polymer ISAM deposition method is that although there is a net orientation toward the substrate, a large number of chromophores are randomly or oppositely oriented. This reduces the nonlinear optical response. To overcome this problem, two alternative methods with a better net orientation are discussed: hybrid covalent / ionic deposition and multivalent monomer deposition. In both deposition methods, the NLO-active material is a monomer instead of a polymer. In hybrid covalent / ionic deposition, the NLO-inactive polymer is deposited using electrostatic attraction while the NLO-active monomer is deposited covalently. This forces alignment of the chromophores. The multivalent method uses chromophores with multiple charges on one side of the molecule and one charge (same sign) on the other. The difference in electrostatic attraction causes a preferential orientation of the chromophores during deposition. Attempts have been made to further improve the net orientation by complexation of the monomers with cyclodextrins (cone shaped organic molecules), so far with only limited success. The SHG response of NLO-active layers near the glass and air interfaces is much stronger than the SHG response of layers in the bulk of the film for all deposition methods and NLO-active materials investigated in this thesis. For larger number of bilayers (the bulk regime), the square root of the SHG signal increases linearly with the number of bilayers as expected for a uniform chromophore orientation. We isolated the interface effects through use of buffer layers of NLO-inactive polymers. The glass interface effect extends roughly one bilayer deep for all investigated materials. The air interface effect is different for polymers and monomers. For monomers, this effect extends only one bilayer deep, while it extends multiple layers deep for polymers. Using glass cells to contain the polyelectrolyte solutions, we were able to measure the SHG signal in situ, which proved to be a powerful tool to monitor the deposition rate as a function of chosen parameters. All depositions were rapid, on the order of one minute or less. Provided that a minimum concentration is met, the deposition rate and final SHG values are independent of concentration. Bulk layers deposit at the same rate as layers near the interface. For polymer NLO-active layers a secondary, slower growth of SHG is observed that is presumably due to reorganization of the adsorbed polymer layer. This secondary growth is not observed in the deposition of NLO-active monomers.

Browsing by Author "Tauber, Uwe C."

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