Asymmetric composite laminates can have a bistable response to loading. The potentially large structural deformations which can be achieved during snap-through from one stable state to another with small and removable energy input make them of interest for a wide range of engineering applications. After 30 years of research effort the shapes and response to applied loads of laminates of general layup can be quantitatively predicted. With attention switching to the incorporation of bistable laminates for practical applications, tools for the design and optimisation of actuated bistable devices are desirable. This thesis describes the analytical and experimental studies undertaken to develop novel modelling and optimisation techniques for the design of actuated asymmetric bistable laminates. These structures are investigated for practical application to morphing structures and the developing technology of piezoelectric energy harvesting. Existing analytical models are limited by the need for a numerical solver to determine stable laminate shapes. As the problem has multiple equilibria, convergence to the desired solution cannot be guaranteed and multiple initial guesses are required to identify all possible solutions. The approach developed in this work allows the efficient and reliable prediction of the stable shapes of laminates with off-axis ply orient at ions in a closed form manner. This model is validated against experimental data and finite element predictions, with an extensive sensitivity study presented to demonstrate the effect of uncertainty and imperfections in the laminate composition. This closed-form solution enables detailed optimisation studies to tailor the design of bistable devices for a range of applications. The first study considers tailoring of the directional stiffness properties of bistable laminates to provide resistance to externally applied loads while allowing low energy actuation. The optimisation formulation is constrained to guarantee bistability and to ensure a useful level of deformation. It is demonstrated that 'cross-symmetric' layups can provide stiffness in an arbitrary loading direction which is five times greater than in a chosen actuation direction.

Thesis (Ph. D.)--Drexel University, 2004. / Includes abstract and vita. Includes bibliographical references (leaves 116-118).

Two-photon optical bistability in commercial thin-film interference filters with ZnS and ZnSe spacers is observed with switching times ≳ 200 μs. The accompanying drifting of the bistability loop in time and laser-induced "damage" indicate a thermal mechanism. The problem of water vapor absorption in such filters must be addressed before the inherent potential and advantages of these devices in two-dimensional image processing applications can be realized. Trans- verse effects in GaAs superlattice etalons are observed which cannot be explained on the basis of a plane-wave analysis. The optical nonlinearity in GaAs and diffraction combine to produce drastic effects on the measured beam profiles and bistable loops, due to an intensity-dependent virtual focus. Lastly, the first observation of optical bistability due to a biexcitonic nonlinearity in CuCl etalons is reported with detector-limited switching times of 600 ps. In addition, lasing action along the pump axis in a cavity defined by the end mirrors is observed in a very thin (2.0 μm) CuCl etalon. The lasing transition is unique in that it involves the creation of a virtual excitation of biexcitons which decay to the longitudinal exciton state.

The quorum-sensing response of Vibrio fischeri involves a complex network of genes (encoding regulatory proteins as well as sRNAs), that govern host-association and production of bioluminescence. A key regulator of this system is LuxR, which is the transcriptional activator of the lux operon as well as several other genes in. LuxR also autoregulates its own transcription, which we have shown causes bistability and hysteresis in the quorum-sensing response. This behavior allows the system to maintain a stable and robust response in the face of environmental fluctuation or decreases in external autoinducer concentration caused by other sources. There are many factors that are known to regulate luxR expression, including the ArcA redox-responsive regulator, the cAMP-CRP secondary metabolism regulator, and components of the quorum-sensing pathway like LitR. Because of this, LuxR levels are critical in both the timing of quorum-sensing induction, as well as the maintenance of the response over time. This makes it a potential target for multiple levels of regulation in response to factors such as environmental and metabolic conditions, as well as other components of the quorum-sensing network. Another important global regulatory protein in V. fischeri (and most other species of Gram-negative proteobacteria) is the post-transcriptional regulator CsrA. CsrA controls processes involved in carbon storage and utilization, as well as the transition from exponential to stationary phase growth. We have demonstrated that CsrA is regulated by two sRNAs (CsrB1 and CsrB2) in V. fischeri. Because CsrA regulates changes in cell behavior and is an important metabolic regulator, there is a good possibility that it has some interactions with the quorum-sensing regulon, whose endproduct, bioluminescence, creates a large metabolic demand from the cell. In an effort to determine at which point in the quorum-sensing regulatory network CsrA regulation is important, epistasis experiments were designed using factorial design, which is a subset of statistical analysis of variance (ANOVA). This method was used to generate a high degree of confidence in the data, so that even minor interactions in the regulatory networks could be established. By altering the levels of CsrA expression in various mutant strains of V. fischeri, we have demonstrated that CsrA acts by an unknown mechanism to increase the transcription of luxR when the quorum-sensing regulator LitR is absent. Our results also demonstrated that CsrA mediates this effect through repression of ArcA activity, which is known to act directly on the luxR and luxI intergenic region as a repressor. This indicates that CsrA may bypass the upstream parts of the quorum-sensing regulatory cascade that lead to litR activation, so that LitR and LuxR may be regulated differently in response to certain conditions. This work has shown that the interactions between global regulons can coordinately control the amount of quorum-sensing induction by affecting the level of LuxR in the cell. The balance of these regulatory networks allows the cell to tightly regulate the quorum-sensing response. Thus, LuxR serves as a critical regulatory hub in the cell, at which multiple signals can be integrated in order to generate the appropriate cellular response. / Ph. D.

In 1993, Novak and Tyson published a comprehensive mathematical model of the regulation of M-phase promoting factor (MPF) activity in Xenopus laevis eggs and egg extracts. Although this model was in agreement with existing and subsequent experimental data, fundamental predictions that the cell cycle is driven by a hysteresis loop have never been validated experimentally. The model's predictions of bifurcations that create and destroy MPF activity, indicative of hysteresis, were tested in this study. <u>Prediction 1: The threshold concentration of cyclin B required to activate MPF is measurably higher than the threshold concentration required to inactivate MPF.</u> The difference in thresholds implies that the MPF control system is hysteretic and bistable. To measure these thresholds, extracts in interphase or M-phase were supplemented with varying concentrations of non-degradable human cyclin B1 protein. MPF activity was determined by the morphology of sperm nuclei and by assays of histone H1 kinase activity. Consistent with the model, the activation threshold was determined to be 40 nM, which is two-fold higher than the inactivation threshold, 20 nM. <u>Prediction 2: For cyclin levels marginally above the activation threshold concentration of cyclin B, there is a dramatic "slowing-down" in the rate of MPF activation.</u> Supra-threshold concentrations of nondegradable cyclin B1 were added to cycloheximide-treated CSF-released extracts, and samples taken at various time-points were analyzed for MPF activity. At 40 nM cyclin B1, just above the activation threshold, the lag time for MPF activation was 45 - 60 minutes; at 50 nM cyclin B1, the lag time was between 30 - 45 minutes; and at 60 nM or higher concentrations of cyclin B1, the lag time was 20 - 30 minutes, thus confirming the prediction of the Novak-Tyson model. <u>Prediction 3: DNA replication checkpoint increases the activation threshold concentration of cyclin B by increasing the hysteresis loop.</u> Cycloheximide-treated, CSF-released extracts containing 1200 sperm nuclei/&#956;l were treated with aphidicolin, then supplemented with varying concentrations of nondegradable cyclin B1. The activation threshold was 100 nM, 2.5 fold higher than in extracts lacking aphidicolin. <u>Conclusions:</u> These studies confirm three predictions of the Novak-Tyson model and indicate that hysteresis underlies cell cycle control in Xenopus egg extracts. These experiments validate use of mathematical models to study complex biological control systems such as the eukayotic cell cycle. / Master of Science

Since the discovery of optical bistability a considerable amount of research activity has been aimed toward the realization of general-purpose all-optical computers. The basic premise for most of this work is the widely held notion that a reliable optical switch can be fabricated from a piece of optically bistable material. To date only a very small number of published articles have addressed the subject of the engineering issues (that is, the optimization and tolerancing) of these optical switches. This dissertation is a systematic treatment of these issues. From the starting point of Maxwell's equations a simple model of optically bistable Fabry-Perot etalons is outlined, in which the material is assumed to be a pure Kerr medium having linear absorption. This model allows for a relatively straightforward optical switch optimization procedure. The procedure is applicable for optimizing any number of switch parameters. The emphasis in this dissertation is on the optimization of the contrast of the switch's output signals, with the other parameters (switching energy, tolerance sensitivity) assuming a secondary yet critical role. Following the optimization of the optical switch is a tolerance analysis which addresses the manufacturability and noise immunity of the optimized switch. In the first part of this analysis equations describing the propagation of errors through a large scale system of like devices are derived from the truth tables of the switches themselves. From these equations worst case tolerances are established on the optical switch's transfer function parameters. In the second part of the tolerance analysis the bistability model is used to arrive at tolerances on the physical parameters of the switch. These tolerances are what determine the manufacturability of the optical switches. The major conclusion of the dissertation is that, within the range of validity of the model and the other simplifying assumptions, optically bistable Fabry-Perot etalons cannot be used reliably as logic gates in large-scale computing systems.

The synchronization of coupled semiconductor lasers with delay is investigated by numerical simulations of the nonlinear dynamic models complemented by a stability analysis of the linearized system. The equations used in the dissertation are based on the well known "Lang-Kobayashi" model modified to include unidirectional and bidirectional coupling. Stability diagrams are calculated and supplemented by numerically integrated time series. Synchronization is determined and quantified by computing the cross-correlation function. It is found that synchronized states are achievable for a wide range of coupling constants and delay times. These findings have implications for experiment and technological applications, notably in cryptography. / by Michael S. London. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center. We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents' parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-Bӧtzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described.

Cancer is an ongoing problem all over the world. To find a cure to this disease, both clinicians and scientists are looking for a reasonable treatment method. According to Hanahan and Weinberg, one of the hallmarks of cancer is evasion of programmed cell death, referred to as apoptosis. Apoptosis is an important cellular process, and is regulated by many different pathways. Proteins in these pathways contribute to either cell death or cell survival depending on the cell stresses. Much research in systems biology has been devoted to understanding these pathways at the molecular level. In this study a mathematical model is built to describe apoptosis, and the pathways involving the related proteins p53 and Akt. The primary purpose of the construction of the kinetic model is to verify that this network can exhibit bistability between cell survival and cell death. Sensitivity and bifurcation analysis are conducted to determine which parameters have the greatest effect on the system behavior.

<p>Bistable switches are commonly observed in the regulation of critical processes such as cell cycles and differentiation. The switches possess two fundamental properties: memory and bimodality. Once switched ON, the switches can remember their ON state despite a drastic drop in stimulus levels. Furthermore, at intermediate stimulus levels with cellular noise, the switches can cause a population to exhibit bimodal distribution of cell states. Till date, experimental studies have focused primarily on cellular mechanisms that generate bistable switches and their impact on cellular dynamics. </p><p>Here, I study emergent bistability due to bacterial interactions with either synthetic gene circuits or antibiotics. A synthetic gene circuit is often engineered by considering the host cell as an invariable "chassis". Circuit activation, however, may modulate host physiology, which in turn can drastically impact circuit behavior. I illustrate this point by a simple circuit consisting of mutant T7 RNA polymerase (T7 RNAP*) that activates its own expression in bacterium Escherichia coli. Although activation by the T7 RNAP* is noncooperative, the circuit caused bistable gene expression. This counterintuitive observation can be explained by growth retardation caused by circuit activation, which resulted in nonlinear dilution of T7 RNAP* in individual bacteria. Predictions made by models accounting for such effects were verified by further experimental measurements. The results reveal a novel mechanism of generating bistability and underscore the need to account for host physiology modulation when engineering gene circuits.</p><p>In the context of antibiotic treatment, I investigate bistability as the underlying mechanism of inoculum effect. The inoculum effect refers to the decreasing efficacy of an antibiotic with increasing bacterial density. Despite its implication for the design of antibiotic treatment strategies, its mechanism remains poorly understood. Here I show that, for antibiotics that target the core replication machinery, the inoculum effect can be explained by bistable bacterial growth. My results suggest that a critical requirement for this bistability is sufficiently fast turnover of the core machinery induced by the antibiotic via the heat shock response. I further show that antibiotics that exhibit the inoculum effect can cause a "band-pass" response of bacterial growth on the frequency of antibiotic treatment, whereby the treatment efficacy drastically diminishes at intermediate frequencies. The results have implications on optimal design of antibiotic treatment.</p> / Dissertation