This study aims to develop an oscillatory wave-energy acquisition system with adjustable system characteristics. The system is designed to efficiently acquire energy from the sea waves with a wide frequency band. Based on the past studies, the oscillatory wave-energy acquisition system, designed previously, can only acquire energy from the sea waves with a narrow frequency band. Such a limit causes the system to have a low efficiency in acquiring power if the wave has a large frequency band. The main goal of this novel design to allow the system adjusting its system characteristics, based on the dynamic characteristics of sea wave, to attain the optimal power acquisition. In the study, different types of oscillatory systems are first examined whether they are effective to transform their dynamic characteristics when the system parameters are varied. The effectiveness of such transformation is evaluated through an optimization procedure. This procedure is to evaluate whether the frequency response of system can acquire the highest power from a given property of sea wave. Through a detailed analysis, the system structure of a three degree-of-freedom oscillatory wave-energy system is chosen for current purpose. A careful study about the effectiveness of dynamic transformation, via the adjustment of different system parameters, is then studied. The study shows that the selected system with adjustable capability can effectively acquire energy from a sea wave with large frequency band. The acquired efficiency can increase up to 70% compared to the earlier system.

The main aim of this thesis is to design efficient and novel numerical algorithms for a class of deterministic and stochastic dynamical systems with multiple time scales. Classical numerical methods for such problems need temporal resolution to resolve the finest scale and become, therefore, inefficient when the much longer time intervals are of interest. In order to accelerate computations and improve the long time accuracy of numerical schemes, we take advantage of various multiscale structures established from a separation of time scales. This dissertation is organized into four chapters: an introduction followed by three chapters, each based on one of three different papers. The framework of the heterogeneous multiscale method (HMM) is considered as a general strategy both for the design and the analysis of multiscale methods. In Chapter 2, we consider a new class of multiscale methods that use a technique related to the construction of a Poincaré map. The main idea is to construct effective paths in the state space whose projection onto the slow subspace shows the correct dynamics. More precisely, we trace the evolution of the invariant manifold M(t), identified by the level sets of slow variables, by introducing a slowly evolving effective path which crosses M(t). The path is locally constructed through interpolation of neighboring points generated from our developed map. This map is qualitatively similar to a Poincaré map, but its construction is based on the procedure which solves two split equations successively backward and forward in time only over a short period. This algorithm does not require an explicit form of any slow variables. In Chapter 3, we present efficient techniques for numerical averaging over the invariant torus defined by ergodic dynamical systems which may not be mixing. These techniques are necessary, for example, in the numerical approximation of the effective slow behavior of highly oscillatory ordinary differential equations in weak near-resonance. In this case, the torus is embedded in a higher dimensional space and is given implicitly as the intersection of level sets of some slow variables, e.g. action variables. In particular, a parametrization of the torus may not be available. Our method constructs an appropriate coordinate system on lifted copies of the torus and uses an iterated convolution with respect to one-dimensional averaging kernels. Non-uniform invariant measures are approximated using a discretization of the Frobenius-Perron operator. These two numerical averaging strategies play a central role in designing multiscale algorithms for dynamical systems, whose fast dynamics is restricted not to a circle, but to the tori. The efficiency of these methods is illustrated by numerical examples. In Chapter 4, we generalize the classical two-scale averaging theory to multiple time scale problems. When more than two time scales are considered, the effective behavior may be described by the new type of slow variables which do not have formally bounded derivatives. Therefore, it is necessary to develop a theory to understand them. Such theory should be applied in the design of multiscale algorithms. In this context, we develop an iterated averaging theory for highly oscillatory dynamical systems involving three separated time scales. The relevant multiscale algorithm is constructed as a family of multilevel solvers which resolve the different time scales and efficiently computes the effective behavior of the slowest time scale. / text

Nanoemulsions with extremely small droplet sizes (<100 nm) have shown several advantages over conventional emulsions. However, almost all nanoemulsions in usage are liquids that restrict their use in many soft materials. The aim of this thesis is to understand the formation and long-term stability of viscoelastic nanogels developed from liquid nanoemulsions. At first, gelation in 40 wt% canola oil-in-water nanoemulsions were investigated as a function of emulsifier type (anionic sodium dodecyl sulfate (SDS) or nonionic Tween 20) and concentration. Three different regimes of colloidal interactions were observed as a function of SDS concentration. 1) At low SDS concentration (0.5 – 2 times CMC) the counterion shell layer increased the effective volume fraction of the dispersed phase (eff) close to the random jamming, resulting in repulsive gelation. 2) At SDS concentration between 5 – 15 times CMC, micelle induced depletion attractions led to extensive droplet aggregation and gelation. 3) At very high SDS concentration, however, oscillatory structural forces (OSF) due to layered-structuring of excess micelles in the interdroplet regions led to loss of gelation. In repulsive gelation, reduction in droplet size coupled with the electrical double layer resulted in a linear increase of Gʹ. On the contrary, attractive nanoemulsions showed rapid increase in gel strength below a critical droplet radius, and was explained by transformation of OSF into depletion attraction. No gelation was seen in Tween 20 nanoemulsions, due to lack of repulsive interactions and weak depletion attraction. Next the influence of the dispersed phase volume fraction () on repulsive nanoemulsion gelation was investigated and the Gʹ values were modeled using empirical scaling law developed by Mason et al. (1995). It was found that an initial liquid regime transformed into glassy phase at a eff = g ~ 0.58, where droplets are entrapped in a cage of neighbouring droplets due to crowding. It was followed by jamming transition at a critical volume fraction (j), where droplet deformation led to large increase in elasticity. The model predicted j = 0.7, which is close to the predictions for repulsive polydispersed emulsions found in the literature. In the final phase long-term stability of the nanogels was evaluated until 90 days, during which the nanogels remained stable to creaming and coalescence. However, repulsive nanogels showed a significant decrease in Gʹ and the gels converted into flowable liquids over time. For attractive nanogels decrease in Gʹ was much less, although given enough time they would also transformed into weak gels. It was hypothesized that surface active compounds generated due to lipid oxidation altered interfacial charge cloud leading to loss of gel strength for repulsive nanogels. For attractive nanogels slippery bonds in the aggregates permitted rotational and translational diffusion of nanodroplets on the surface of each other leading to network compactness and a decrease in gel strength with time. Overall, it was concluded that it is possible to form nanogels from canola oil nanoemulsions using ionic emulsifiers. The gel strength and stability of the nanogels depends on emulsifier concentration, droplet size,  and the chemical stability of the oil used. More investigation is needed in order to improve the long-term stability of the nanogels. The nanogels possess high potential for use in low-fat foods, pharmaceuticals, and cosmetic products.

We calculate the stress response, or rheology, of a micro-mechanical model suspension of rigid, Brownian spheroids in a Newtonian fluid in an oscillatory shear flow. The straining and rotation components of a linear flow affects the microstructure, or particle orientation in space and time, and thus, the suspension stress. A statistical description of the microstructure is given by an orientation probability distribution function, which quantifies the likelihood of a particle possessing a particular orientation at an instance in time. The evolution of the microstructure results from the memory of the material, advection from the flow, and rotational Brownian motion. The macroscopic stress response is calculated from ensemble averages of the stresslet weighted by the orientation distribution function. First, we calculate the linear stress response of a dilute suspension of rigid, spheroidal, self-propelled particles under a small-amplitude oscillatory shear deformation using regular perturbation theory. The particle activity leads to a direct contribution to the material stress, via self-propulsion, and an indirect contribution due to correlated tumbling events. The mechanism and strength of self-propulsion and correlation between tumbling events can be determined from the linear stress response of an active suspension. Next, we develop a framework for determining the relaxation moduli of a viscoelastic material through the combination of a memory integral expansion and a multimode-frequency oscillatory shear flow. We analytically determine the first nonlinear relaxation modulus of the model suspension through a comparison of the second normal stress difference from the microstructural stress response, calculated via regular perturbation theory, and a co-rotational memory integral expansion. The stress response of the system is reconstructed for the start-up and cessation of steady simple shear and uniaxial extension. Finally, we numerically calculate the nonlinear viscoelasticity of the model system subject to a large-amplitude oscillatory shear flow. In a sufficiently strong flow with oscillation frequency comparable to the material relaxation rate, secondary overshoots in the stress response occur. We attribute the origin of secondary overshoots to particles undergoing a Jeffery orbit during a (half) cycle of the oscillation, analogous to the case of non-Brownian spheroids in steady shear flow.

The microcantilever has become a ubiquitous tool for surface science, chemical sensing, biosensing, imaging, and energy harvesting, among many others. It is a device of relatively simple geometry with a static and dynamic response that is well understood. Further, because of it's small size, it is extremely sensitive to small external perturbations. These characteristics make the microcantilever an ideal candidate for a multitude of sensing applications. In this thesis dissertation we use the microcantilever to conduct numerous physical measurements and to study fundamental phenomena in the areas of fluid dynamics, turbulence, and biology. In each area we use the cantilever as a sensitive transducer in order to probe fluctuating forces. In micro and nanometer scale flows the characteristic length scale of the flow approaches and is even exceeded by the fluid mean free path. This limit is beyond the applicability of the Navier-Stokes equations, requiring a rigorous treatment using kinetic theory. In our first study, we conduct a series of experiments in which we use a microcantilever to measure gas dissipation in a nanoscopically confined system. Here, the distance between the gas molecules is of the same order as the separation between the cantilever and the walls of its container. As the cantilever is brought towards the wall, the flow becomes confined in the gap between the cantilever and the wall, affecting the resonant frequency and dissipation of the cantilever. By carefully tuning the separation distance, the gas pressure, and the cantilever oscillation frequency, we study the flow over a broad range of dimensionless parameters. Using these measurements, we provide an in-depth characterization of confinement effects in oscillating nanoflows. In addition, we propose a scaling function which describes the flow in the entire parameter space and which unifies previous theories based on the slip boundary condition and effective viscosity. In our next study, we seek to gain a better understanding of the transition to turbulence in a channel flow. We use a cantilever embedded in the channel wall to perform two sets of experiments: first, we study transition to turbulence triggered by the natural imperfections of the channel walls and second, we study transition under artificially added inlet noise. Our results point to two very different paths to turbulence. In the first case, wall effects lead to an extremely intermittent transitional flow and in the second case, broadband fluctuations originating at the inlet lead to less intermittent flow that is more reminiscent of homogeneous turbulence. The two experiments result in random flows in which high-order moments of near-wall fluctuations differ by orders of magnitude. Surprisingly however, the lowest order statistics in both cases appear qualitatively similar and can be described by a proposed noisy Landau equation. The noise, regardless of its origin, regularizes the Landau singularity of the relaxation time and makes transitions driven by different noise sources appear similar. Our results provide evidence of the existence of a finite turbulent relaxation time in transitional flows due to the persistent nature of noise in the system. In our last study, we turn to biologically-driven fluctuations from bacterial motion. Recent studies suggest that the motion of living bacteria could serve as a good indicator of bacteria species and resistance to antibiotics. To gain a better understanding of these fluctuations, we measure the nanomechanical motion of bacteria adhered to a chemically functionalized silicon microcantilever. A non-specific binding agent is used to attach E. coli to the surface of the device. The motion of the bacteria couples efficiently to the cantilever well below its resonance frequency, causing a measurable increase in its mechanical fluctuations. We vary the bacterial concentration over two orders of magnitude and are able to observe a corresponding change in the amplitude of fluctuations. Additionally, we administer antibiotics (Streptomycin) to kill the bacteria and observe a decrease in the fluctuations. A basic physical model is used to explain the observed spectral distribution of the mechanical fluctuations. These results lay the groundwork for understanding the motion of microorganisms adhered to surfaces and for developing micromechanical sensors for rapid bacterial identification and antibiotic resistance testing.

We obtain an upper bound for decay rate of p-adic oscillatory integrals of with analytic phase function and constructible amplitude map. / Thesis / Doctor of Philosophy (PhD)

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A lot of fluids are more complex than water: polymers, paints, gels, ketchup etc., because of big particles and their complicated microstructures, for instance, molecule entanglement. Due to this structure complexity, some material can display that it is still in yielded state when the imposed stress is released. This is referred to as thixotropy. This dissertation establishes mathematical analysis on a thixotropic yield stress fluid using a viscoelastic model under the limit that the ratio of retardation time versus relaxation time approaches zero. The differential equation model (the PEC model) describing the evolution of the conformation tensor is analyzed. We model the flow when simple shearing is imposed by prescribing a total stress. One part of this dissertation focuses on oscillatory shear stresses. In shear flow, different fluid states corresponding to yielded and unyielded phases occur. We use asymptotic analysis to study transition between these phases when slow oscillatory shearing is set up. Simulations will be used to illustrate and supplement the analysis. Another part of the dissertation focuses on planar Poiseuille flow. Since the flow is spatially inhomogeneous in this situation, shear bands are observed. The flow is driven by a homogeneous pressure gradient, leading to a variation of stress in the cross-stream direction. In this setting, the flow would yield in different time scales during the evolution. Formulas linking the yield locations, transition width, and yield time are obtained. When we introduce Korteweg stress in the transition, the yield location is shifted. An equal area rule is identified to fit the shifted locations. / Ph. D.