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A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the ``magnetic catalysis" in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel. / text

In this thesis, we report a novel symmetry breaking system in single-beam optical trap. The breaking of symmetry is observed in Brownian dynamics of a linked pair of beads with substantially differing radii (500nm and 100nm). Such composite beads were originally conceived as a manipulation means to study of Brownian interactions between mesoscopic biological agents of the order of 100 – 200 nm (viruses or bacteria) with cell surfaces. During the initial testing of the composite bead system, we discovered that the system displayed thermally activated transitions and energetics of symmetry breaking. This thesis, while making a brief overview of the biological relevance of the composite bead system, focuses primarily on the analysis and experimentation that reveals the complex dynamics observed in the system. First, we theoretically analyze the origin of the observed symmetry breaking using electromagnetic theory under both Gaussian beam approximation and full Debye-type integral representation. The theory predicts that attachment of a small particle to a trapped microsphere results in creation of a bistable rotational potential with thermally activated transitions. The theoretical results are then verified using optical trapping experiments. We first quantify the top-down symmetry breaking based on measurement of the kinetic transition rates. The rotational potential is then explored using an experiment employing a novel algorithm to track rotational state of the composite bead. The results of the theory and experiments are compared with results of a Brownian dynamics simulation based on Smart Monte Carlo algorithm.

Thesis (Ph.D.)--Boston University / In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ~ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S > 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S > 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

A labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(D_n) is found where D_n is the dihedral group with 2n elements. From there, the generalized Petersen graphs, GP(n,k), are defined and the automorphism groups and distinguishing numbers of such graphs are given. / Master of Science

There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

No description available.

<p>Establishing an axis of cell polarity is central to cell motility, tissue morphogenesis, and cell proliferation. A highly conserved group of polarity regulators is responsible for organizing a wide variety of polarized morphologies. One of the most widely expressed polarity regulators is the Rho-type GTPase Cdc42. In response to cell cycle cues the budding yeast <italic>Saccharomyces cerevisiae</italic> polarizes Cdc42p to a discrete site on the cell periphery. GTP-Cdc42p recruits a number of effectors that aid in the organization of a polarized actin cytoskeleton. The polarized actin cytoskeleton acts as tracks to facilitate the delivery of the secretory vesicles that will grow the bud, an essential process for an organism that proliferates by budding. We have employed treatment with the actin depolymerizing drugs Latrunculin A and B as well as high-speed timelapse microscopy of fluorescently labeled polarity proteins to characterize the assembly of the incipient bud site. </p><p>Often, ensuring that only a single axis of polarity is established is as important as generating asymmetry in the cell. Even in the absence of positional cues dictating the direction of polarization, many cells are still able to self-organize and establish one, and only one, polarity axis through a process termed symmetry breaking. Symmetry breaking is thought to employ positive feedback to amplify stochastic fluctuations in protein concentration into a larger asymmetry. To test whether singularity could be guaranteed by the amplification mechanism we re-wired yeast to employ a synthetic positive feedback mechanism. The re-wired cells could establish polarity, however they occasionally made two buds simultaneously, suggesting that singularity is guaranteed by the amplification mechanism.</p> / Dissertation

Ant colonies are often considered to be a superorganism, exhibiting complex collective behaviors, reproducing at the colony level, and dividing functional roles among groups of workers. For this reason, it is often appropriate to study ant behavior at the colony, rather than the individual, level. In this study, I investigated decision-making and foraging behavior in colonies of several species belonging to the ant community of Sonoran Desert scrub habitat. First, I used laboratory experiments to examine how the spatial structure of Crematogaster torosa colonies changes in response to the availability of temporally stable food sources. I found that in this polydomous species the formation of nests is associated with foraging, but that colonies will build broodless structures called “oustations” regardless of food presence. Next, I examined colony spatial structure of a related polydomous species, Crematogaster opuntiae, in the field. I found that colonies used large foraging territories up to three hectares in size, containing up to twenty nest entrances interconnected by a network of trails. Nest location appeared to be related to foraging, with nests located close to extrafloral nectar-secreting cacti (Ferocactus wislizeni) and a negative relationship between cactus density and territory size. Within colonies, forager behavior on neighboring cacti was not independent at short distances, suggesting that separate plants in this system cannot be treated as independent replicates. In the third chapter, I used an individual-based simulation model to investigate the effects of individual worker behavior on the ability of pheromone-recruiting ant colonies to maintain trails to multiple food sources simultaneously. Interestingly, small changes in the behavior rules used by individuals led to large-scale changes in emergent behaviors at the colony level. Lastly, I used field experiments to relate the ability of colonies of three ant species to maintain multiple trails to their ranking in the community competitive dominance hierarchy. I found that the most dominant species tended to forage asymmetrically, whereas the least dominant species exhibited more symmetrical patterns of foraging. The ability of ant colonies to collectively maintain multiple trails may therefore be an adaptive trait linked to the foraging ecology of species.

The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.