Probability theory is the study of random phenomena. Many dynamical systems with random influence, in nature or artificial complex systems, are better modeled by equations incorporating the intrinsic stochasticity involved. In probability theory, stochastic partial differential equations (SPDEs) generalize partial differential equations through random force terms and coefficients, while stochastic differential equations (SDEs) generalize ordinary differential equations. They are both abound in models involving Brownian motion throughout science, engineering and economics. However, Brownian motion is just one example of a random noisy input. The goal of this thesis is to make contributions in the study and applications of stochastic dynamical systems involving a wider variety of stochastic processes and noises. This is achieved by considering different models arising out of applications in thermal engineering, population dynamics and mathematical finance.<br><div><br></div><div>1. Power-type non-linearities in SDEs with rough noise: We consider a noisy differential equation driven by a rough noise that could be a fractional Brownian motion, a generalization of Brownian motion, while the equation's coefficient behaves like a power function. These coefficients are interesting because of their relation to classical population dynamics models, while their analysis is particularly challenging because of the intrinsic singularities. Two different methods are used to construct solutions: (i) In the one-dimensional case, a well-known transformation is used; (ii) For multidimensional situations, we find and quantify an improved regularity structure of the solution as it approaches the origin. Our research is the first successful analysis of the system described under a truly rough noise context. We find that the system is well-defined and yields non-unique solutions. In addition, the solutions possess the same roughness as that of the noise.<br></div><div><br></div><div>2. Parabolic Anderson model in rough environment: The parabolic Anderson model is one of the most interesting and challenging SPDEs used to model varied physical phenomena. Its original motivation involved bound states for electrons in crystals with impurities. It also provides a model for the growth of magnetic field in young stars and has an interpretation as a population growth model. The model can be expressed as a stochastic heat equation with additional multiplicative noise. This noise is traditionally a generalized derivative of Brownian motion. Here we consider a one dimensional parabolic Anderson model which is continuous in space and includes a more general rough noise. We first show that the equation admits a solution and that it is unique under some regularity assumptions on the initial condition. In addition, we show that it can be represented using the Feynman-Kac formula, thus providing a connection with the SPDE and a stochastic process, in this case a Brownian motion. The bulk of our study is devoted to explore the large time behavior of the solution, and we provide an explicit formula for the asymptotic behavior of the logarithm of the solution.<br></div><div><br></div><div>3. Heat conduction in semiconductors: Standard heat flow, at a macroscopic level, is modeled by the random erratic movements of Brownian motions starting at the source of heat. However, this diffusive nature of heat flow predicted by Brownian motion is not observed in certain materials (semiconductors, dielectric solids) over short length and time scales. The thermal transport in these materials is more akin to a super-diffusive heat flow, and necessitates the need for processes beyond Brownian motion to capture this heavy tailed behavior. In this context, we propose the use of a well-defined Lévy process, the so-called relativistic stable process to better model the observed phenomenon. This process captures the observed heat dynamics at short length-time scales and is also closely related to the relativistic Schrödinger operator. In addition, it serves as a good candidate for explaining the usual diffusive nature of heat flow under large length-time regimes. The goal is to verify our model against experimental data, retrieve the best parameters of the process and discuss their connections to material thermal properties.<br></div><div><br></div><div>4. Bond-pricing under partial information: We study an information asymmetry problem in a bond market. Especially we derive bond price dynamics of traders with different levels of information. We allow all information processes as well as the short rate to have jumps in their sample paths, thus representing more dramatic movements. In addition we allow the short rate to be modulated by all information processes in addition to having instantaneous feedbacks from the current levels of itself. A fully informed trader observes all information which affects the bond price while a partially informed trader observes only a part of it. We first obtain the bond price dynamic under the full information, and also derive the bond price of the partially informed trader using Bayesian filtering method. The key step is to perform a change of measure so that the dynamic under the new measure becomes computationally efficient.</div>

In modern wireless communication systems, a base station typically serves a few hundred users within its cell coverage. To combat the near-far problem – the situation where a nearby user’s strong cellular signal masks the cellular signal of a faraway user – base stations continually enforce power control. That is, nearby users must lower their transmit power. In CDMA technology, power control can be as large as 70-80dB. At low power outputs, this greatly impacts the performance of the RF power amplifier (PA) in the cellular device. For small RF drives, the magnitude of the output RF current approaches the magnitude of the DC current and thus the efficiency suffers. Operating the RF PA in class C operation improves the efficiency, but results in poor linearity. Several methods of so-called dynamic biasing have been proposed. These strategies entail lowering the bias of the PA as the RF drive increases. The proposed methods, however, fail to explain how to achieve linearity and low third-order intermodulation distortion. Additionally, the methods utilize open-loop implementations. This work presents a novel dynamic biasing topology that results in a much improved linear class C PA. The topology utilizes a closed loop that cleverly senses the operating conditions of the "power device." Particularly, the loop operates on the principle of keeping the conduction angle remarkably constant and thereby ensuring linearity. The work details a thorough design methodology that should provide assistance to a designer wanting to implement the topology in an RF integrated circuit. Agilent ADS simulations and laboratory results from a functional PCB prototype bring merit to the topology.

This Paper deals with a design of tribometer for pin-on-disc and disc-on-disc tests. The purpose of these tests is Investigation of friction coefficient during hot forming. The main emphases of this paper are tool heating and quick tool change. The conductive sample heating is analyzed with FEM software Ansys and the results of this snalysis are taken into design consideration. Existing pin mounting design is considered as satisfying. Various disc mounting concepts are compared. The best solution - specimen mounting by an inside clamping cone with integrated specimen ejector was manufactured (heating excluding) and successfully tested.

In this thesis an equation of heat conduction including phase and structural changes is derived, involving various boundary conditions. It seems to be the most suitable to calculate the equation by enthalpy method. In this equation not only enthalpy occurs, but also the temperature, and in consequence the relationship between these variables is quite complicated. In this paper I use the values measured or calculated using solidifcation models. The calculation is implemented in Matlab Simulink, which is a very popular blocks scheme in common practice of regulation. The calculation is based on steady state set up with help of experts and as a result, the program could be put into practice. The program calculates the intensity of cooling according to the initial casting speed, casting inlet temperature and the desired temperature curves. The rate of inuence of cooling can be changed according to the given criteria. The thesis compares the surface temperatures and cooling in the case of a predictive controller is or is not applied in the program.

It is very important to develop efficient but still accurate and stable numerical methods for solving heat and mass transfer processes in many industrial applications. The thesis deals with an inverse heat conduction problem which is used to compute boundary conditions (temperatures, heat flux or heat transfer coefficient). Nowadays, two approaches are often used for inverse task - sequential estimation and whole domain estimation. The main goal of this work is to develop a new approach, the so-called sub-domain method, which emphasizes advantages just as reduce disadvantages of both methods mentioned above. This approach is then tested on generated prototypic data and on data from real experiments. All methods are compared with respect to accuracy of results as well as to computational efficiency.

abstract: Granular material can be found in many industries and undergo process steps like drying, transportation, coating, chemical, and physical conversions. Understanding and optimizing such processes can save energy as well as material costs, leading to improved products. Silica beads are one such granular material encountered in many industries as a catalyst support material. The present research aims to obtain a fundamental understanding of the hydrodynamics and heat transfer mechanisms in silica beads. Studies are carried out using a hopper discharge bin and a rotary drum, which are some of the most common process equipment found in various industries. Two types of micro-glass beads with distinct size distributions are used to fill the hopper in two possible packing arrangements with varying mass ratios. For the well-mixed configuration, the fine particles clustered at the hopper bottom towards the end of the discharge. For the layered configuration, the coarse particles packed at the hopper bottom discharge first, opening a channel for the fine particles on the top. Also, parameters such as wall roughness (WR) and particle roughness (PR) are studied by etching the particles. The discharge rate is found to increase with WR, and found to be proportional to (Root mean square of PR)^(-0.58). Furthermore, the drum is used to study the conduction and convection heat transfer behavior of the particle bed with varying process conditions. A new non-invasive temperature measurement technique is developed using infrared thermography, which replaced the traditional thermocouples, to record the temperatures of the particles and the drum wall. This setup is used to understand the flow regimes of the particle bed inside the drum and the heat transfer mechanisms with varying process conditions. The conduction heat transfer rate is found to increase with decreasing particle size, decreasing fill level, and increasing rotation speed. The convection heat transfer rate increased with increasing fill level and decreasing particle size, and rotation speed had no significant effect. Due to the complexities in these systems, it is not always possible to conduct experiments, therefore, heat transfer models in Discrete Element Method codes (MFIX-DEM: open-source code, and EDEM: commercial code) are adopted, validated, and the effects of model parameters are studied using these codes. / Dissertation/Thesis / Doctoral Dissertation Chemical Engineering 2020

This project investigated the manufacturing of large diameter welded PTFE rings.This welding process is time consuming and can take over ten hours for one complete weld cycle. Additionally, the welds can have poor quality in the center of the material due to insufficient heating across the weld face. The goal of this research was to address these two issues by analyzing the current process to determine the root cause of weld failures while also determining the feasibility of reducing the weld cycle time. The scope of this thesis was to develop a model to better understand and simulate the current process which could then be used for design future improvements.<div><br></div><div>A MATLAB model of the current process was developed to simulate the transient heating cycle of the most common weld cycle for PTFE currently used by a manufacturer of PTFE seals. The data for the material properties was gathered from the manufacturer test data as well as from Lau et al. (1984). Temperature dependent material properties were used in the program because the PTFE is heated above its melting point during the weld cycle. Because of the complexity of this heat transfer problem, the heat flux in the model was tuned so that it accurately reflected the current process. This is because the goal of this study was not to determine the exact heat fluxas it was unknown, but to develop an accurate model. Thus, the heat flux was assumed and the model was then verified with process data. Results from the model were compared to validation results from a FLIR thermal camera. The model predicted the compared temperatures to within 3.1% error at both 15-minute and 90-minute intervals. Though there are many potential sources of error in the process and the thermal camera measurement, the model was deemed acceptable as a model of the current process. A semi-infinite heat analysis was calculated to simulate a hot plate welding method on the PTFE. This showed that the temperature of the weld face could be raised by 57.275°C. It is believed that a method similar to hot plate welding applied to PTFE could heat the material faster and more evenly than the current process, reducing the weld failures and cycle time.<br></div>

Interactions between neurons and glia occupy a central role in many aspects of development, maintenance, and function of the central nervous system (CNS). A fundamental event in CNS development is the elaboration of two distinct neuronal processes, axons and dendrites. The overall aim of this research was to characterize the interactions between central nervous system neurons and astroglial cells that regulate dendrite growth from cerebral cortical neurons. Embryonic (E18) mouse cerebral cortical neurons were cocultured with early postnatal (P4) rat astroglia derived from cerebral cortex, retina, olfactory bulb, mesencephalon, striatum and spinal cord. Axon and dendrite outgrowth from isolated neurons was quantified using morphological and double-labeling immunohistochemical techniques at 18 hours and 1, 3 and 5 days in vitro. Neurons initially extended the same number of neurites, regardless of the source of glial monolayer; however, astroglial cells differed in their ability to maintain primary dendrites. Homotypic cortical astroglia maintained the greatest number of primary dendrites. Astroglia derived from the olfactory bulb and retina maintained intermediate numbers of dendrites, whereas only a small number of primary dendrites were maintained by astroglia derived from striatum, spinal cord or mesencephalon. Initially longer axons were observed from neurons grown on astroglia that did not maintain dendrite number. After 5 days in vitro, axon growth was similar on the various monolayers, total primary dendrite outgrowth, however, was nearly threefold greater on astroglia derived from the cortex, retina and olfactory bulb than on astroglia derived from mesencephalon, striatum or spinal cord. This effect was principally on the number of primary dendrites rather than the elongation of individual dendrites and was independent of neuron survival. Similar morphological differences were observed after 5 days in vitro when cortical neurons were grown on polylysine in either a noncontact coculture system where astroglia continuously conditioned the culture medium or in astroglial conditioned medium. Preliminary biochemical analysis of the medium conditioned by cortical astroglia using heat and trypsin degradation, ultracentrifugation, dialysis, and heparin affinity chromatography suggested that a heparin binding protein with a molecular weight between 10 and 100kDa may be responsible for astroglial mediated dendrite growth. Neurons that were grown in medium conditioned by either mesencephalic or cortical astroglia for the first 24 hours followed by culture medium from astroglia of the alternate source for 4 days in vitro, confirmed that astroglia maintained, rather than initiated, the outgrowth of the primary dendritic arbor. In the next series of experiments, E18 mouse cortical neurons were cocultured with neonatal (P4) or mature (P12) rat astroglia derived from cortex and mesencephalon or astroglia derived from P4 and P12 lesioned cortex. After 5 days in vitro, the maturational age of astroglia did not appear to alter the extent of primary dendrite growth; instead dendrite growth reflected the region of the CNS from which the astroglia were derived. By contrast, a reduced ability to support axon growth from mouse cortical neurons in culture was observed on astroglia derived from mature rat cortex or mesencephalon. Reactive astroglia demonstrated similar neurite supporting characteristics to mature astroglia and were able to maintain dendrite growth, principally primary dendrite number. Axon elongation, however, was reduced on both neonatal and mature reactive astroglia. Neuron survival did not correlate with the ability of the various astroglia to support process outgrowth. Collectively these results indicate: 1) neuron-glial interactions are critical for the regulation of process outgrowth from embryonic cortical neurons in vitro, 2) axon and dendrite growth appear to be differently controlled by astroglia, 3) CNS astroglia demonstrate regional differences in maintaining, but not initiating growth of the primary dendritic arbor, 4) this effect may be due, in part, to release of a diffusible heparin binding protein factor, and 5) mature and reactive astroglia support primary dendrite, but limited axon growth. We propose therefore that the local astroglial environment maintains primary dendrite growth from neurons until synaptic contacts can be established. A mechanism that maintains the primary dendritic arbor and allows separate regulation of axon and dendrite growth, prior to the arrival of afferents, may be critical for establishing appropriate and specific synaptic connections. These findings have important implications in understanding development and function of the mammalian central nervous system and may lead to novel strategies for intervention in acute and chronic neurological disorders.

This work studied the hot wire method in measuring thermal conductivity at room temperature. The purpose is to find the optimized experimental conditions to minimize natural convection in liquid for this method, which will be taken as reference for high temperature thermal conductivity measurement of slag. Combining room temperature experiments and simulation with COMSOL Multiphysics 4.2a, the study on different experimental parameters which may influence the accuracy of the measured thermal conductivity was conducted. The parameters studied were the diameter of crucible, the position of wire in the liquid, including z direction and x-y plane position, diameter of the hot wire, and current used in the measurement. In COMSOL simulations, the maximum natural convection velocity value was used to evaluate the natural convection in the liquid. The experiment results showed after 4~5 seconds of the measuring process, the natural convection already happened. Also when current was fixed, the thinner the hot wire, the larger convection it would cause. This is because thinner wire generates more heat per unit surface area. Using higher current in measuring, more heat generation improved accuracy of result but also had earlier and larger effect on convection. Both simulation and experiments showed that with the height of the liquid fixed, the smaller diameter of the crucible (not small to the level which is comparable with hot wire diameter), the higher the position in z direction (still covered by liquid), the less natural convection effect existed. But the difference was not significant. The radius-direction position change didn’t influence the result much as long as the wire was not too close to the wall.

The scope of cardiac pathophysiology in sepsis has not been fully defined. Accordingly, we evaluated the effects of sepsis on heart rate (HR), HR variability, and conduction parameters in a murine model of sepsis. Electrocardiograms were recorded noninvasively from conscious mice before and after cecal ligation and puncture (CLP) or sham surgery. Responses of isolated atria to tyramine and isoproterenol were quantified to assess the functional state of sympathetic nerves and postjunctional sensitivity to adrenergic stimulation. Cecal ligation and puncture mice had lower HR compared with sham at 16 to 18 h postsurgery (sham, 741 ± 7 beats/min; CLP, 557 ± 31 beats/min; n = 6/group; P < 0.001), and there was significant prolongation of the PR, QRS, and QTc intervals. Slowing of HR and conduction developed within 4 to 6 h after CLP and were preceded by a decrease in HR variability. Treatment of CLP mice with isoproterenol (5 mg/kg, intraperitoneally) at 25 h after surgery failed to increase HR or decrease conduction intervals. The lack of in vivo response to isoproterenol cannot be attributed to hypothermia because robust chronotropic and inotropic responses to isoproterenol were evoked from isolated atria at 25°C and 30°C. These findings demonstrate that impaired regulation of HR (i.e., reduced HR variability) develops before the onset of overt cardiac rate and conduction changes in septic mice. Subsequent time-dependent decreases in HR and cardiac conduction can be attributed to hypothermia and would contribute to decreased cardiac output and organ perfusion. Because isolated atria from septic mice showed normal responsiveness to adrenergic stimulation, we conclude that impaired effectiveness of isoproterenol in vivo can be attributed to reversible effects of systemic factors on adrenergic receptors and/or postreceptor signaling.