Autonomous navigation with high speed in rough terrain is one of the most challenging tasks for wheeled robots. To achieve mobility over this terrain, a high agility wheeled robot should adapt and react fast to optimally traverse this challenging environment. Therefore, this dissertation is geared towards the design and development of a novel reconfigurable wheeled robot paradigm for rough terrain applications. This research focuses on the design, modeling, analysis and control of the reconfigurable wheeled robot, TIGER, with an elastic actuated mechanism for improving the robot's dynamic stability on rough terrain by controlling the robot's ground clearance, body roll and pitch angles. The elastic actuated mechanism mainly consists of a linear actuator connected in series with a shock absorber. Four sets of the elastic actuated mechanism are used to create different robot configurations to adapt to the terrain. Three main aspects were considered in this research in order to extend the ability of the robot to effectively navigate in rough terrain. The first aspect focuses on designing an agile reconfigurable wheeled robot by including an elastic actuated mechanism for improving maneuverability, longitudinal/lateral stability, and rollover prevention. Robot agility, stability, and high speed have been considered during the design process. The new design provides different configuration modes. These configurations allow for controlling the robot's Center Of Mass (COM) height and optimally distribute the vertical force on each tire for enhancing the tractive efficiency, mobility and dynamic stability. The second aspect presents the robot kinematic and dynamic modeling and analysis. The robot dynamics model is represented with fourteen degrees of freedom (DOF), where the dynamic behaviors of the robot body, suspension system, forces and moments on the tires are included. The dynamic behavior is controlled using the linear actuators' position and speed as inputs to determine the resulting ground clearance, body roll, and pitch angles. Sensors are integrated onboard the robot to calculate the robot's states in real time for use in feedback control. The third aspect focuses on introducing a technique for estimating the robot state-space dynamic model and control the Elastic Actuated Mechanism (EAM) using only a noisy Inertial Measurement Unit (IMU) with COM position uncertainty. The simulation results show that the observer estimates the actual behavior of the robot with 95% accuracy and up to 20% COM uncertainty. The Root Mean Square (RMS) has been reduced by 21% for bounce, 51% for pitch and 50% for roll acceleration. / Ph. D. / Wheeled mobile robots are being used for rough terrain applications in the field of robotics as a practical solution to accomplish various tasks. Unfortunately, most of the wheeled robots are not able to perform high dynamically tasks with high speed in rough terrain due to complex suspension design, high power-to-weight ratio, high cost and complexity of controlling highly nonlinear model in real-time. Therefore, this dissertation is geared towards the design and development of a novel reconfigurable wheeled robot paradigm for rough terrain applications. This research focuses on the design, modeling, analysis and control of the reconfigurable wheeled robot, TIGER, with an elastic actuated mechanism for improving the robot’s dynamic stability on rough terrain by controlling the robot’s ground clearance, body roll and pitch angles. The elastic actuated mechanism mainly consists of a linear actuator connected in series with a shock absorber. Four sets of the elastic actuated mechanism are used to create different robot configurations to adapt to the terrain. Three main aspects were considered in this research in order to extend the ability of the robot to effectively navigate in rough terrain. The first aspect focuses on designing an agile reconfigurable wheeled robot by including an elastic actuated mechanism for improving maneuverability, longitudinal/lateral stability, and rollover prevention. Robot agility, stability, and high speed have been considered during the design process. The new design provides different configuration modes. These configurations allow for controlling the robot’s COM height and optimally distribute the vertical force on each tire for enhancing the tractive efficiency, mobility and dynamic stability. The second aspect presents the robot kinematic and dynamic modeling and analysis. The robot dynamics model is represented with fourteen degrees of freedom (DOF), where the dynamic behaviors of the robot body, suspension system, forces and moments on the tires are included. The dynamic behavior is controlled using the linear actuators’ position and speeds as inputs to determine the resulting ground clearance, body roll, and pitch angles. Sensors are integrated onboard the robot to calculate the robot’s states in real time for use in feedback control. The third aspect focuses on introducing a technique for estimating the robot state-space dynamic model and control the EAM using only a noisy IMU with COM position uncertainty. The simulation results show that the observer estimates the actual behavior of the robot with 95% accuracy and up to 20% COM uncertainty. The RMS has been reduced by 21% for bounce, 51% for pitch and 50% for roll acceleration.

We introduce a financial model for limit order book with two main features: First, the limit orders and market orders for the given asset both appear and interact with each other. Second, the high frequency trading (HFT, for short) activities are allowed and described by the scaling limit of nearly-unstable multi-dimensional Hawkes processes with power law decay. The model eventually becomes a stochastic partial differential equation (SPDE, for short) with the diffusion coefficient determined by a Volterra integral equation governed by a Hawkes process, whose Hurst exponent is less than 1/2, which makes the volatility path of the stochastic PDE rougher than that driven by a Brownian motion. We have further established the well-posedness of such a system so that a foundation is laid down for further studies in this direction.

Gray leaf spot, caused by Cercospora zeae-maydis, can be a yield-limiting factor in maize where continuous minimum tillage practices are followed. Commercial corn hybrids were evaluated for response to gray leaf spot for seven years at two Virginia locations (Shenandoah and Wythe Counties) and one year at a third location in Virginia (Montgomery County). Yield losses, when comparing resistant to susceptible classes, were approximately 2,000 kg ha⁻¹ at Wythe County in 1982, 750 kg ha⁻¹ at Shenandoah County in 1984, and 2,150 kg ha⁻¹ at Montgomery County in 1988. The inheritance of reaction to gray leaf spot was studied using a 14 inbred diallel in Montgomery and Wythe Counties, Virginia in 1987 and 1988 planted in randomized complete block designs. Resistance was found to be highly heritable and controlled by additive gene action. Inbreds producing high yielding, resistant, and agronomically superior hybrids were identified (B68, NC250, Pa875, Va14, Va17, and Va85); and several hybrids between these lines had high levels of resistance, high yield, and good general agronomic characters (B68 x KB1250, KB1250 x Pa875, and NC250 x Pa875). Currently available inbreds could be used to produce hybrids with higher levels of resistance than hybrids currently available to growers, and these could serve as a basis for gray leaf spot breeding programs. Lesion size measurements were not correlated with disease scores. Late-season photosynthesis rates were associated positively with resistance. The hybrids of some inbreds were found to produce high levels of pigment (believed to be anthocyanins) around the gray leaf spot lesions. These did not limit the size of the individual lesion later in the season. Some pigment(s)-producing genotypes were found to be resistant when the pigment character was expressed. This type of resistance must prevent or inhibit infection of the leaf but not later colonization, once established. Maize dwarf mosaic virus (MDMV) also limits maize production in some areas where johnsongrass (Sorghum halepense L.) is a problem. Resistance to MDMV was found to be mainly additive and highly heritable. However, a strong specific combining ability component was found, indicating that the background of the material receiving resistance genes may have a strong effect on the expression of resistance. Inbreds capable of producing high-yielding, resistant, and agronomically acceptable hybrids are available (B68, NC250, A632, Pa875, Va17, and Va85); and several hybrids between these lines have high levels of resistance, high yield, and good general agronomic characters (B68 x KB1250, KB1250 x Pa875, and NC250 x Pa875). / Ph. D.

The velocity fields of high Reynolds number, turbulent, wall boundary layers in non-equilibrium pressure gradients are experimentally investigated. Experiments in two wall configurations were performed; one with a hydrodynamically smooth test wall composed of flat aluminum panels, and the other with a rough surface consisting of 2 mm tall, staggered, circular cylindrical elements. A representative set of pressure gradient distributions were generated on the research wall by a systematically rotated NACA 0012 airfoil placed in a wind tunnel section to determine the functional dependence of the boundary layer formation on pressure gradient. Particle image velocimetry (PIV) was the primary measurement technique used to determine time-resolved features of the velocity flow field. newline{}newline{} It is shown that regardless of wall condition and Reynolds number, the non-equilibrium turbulent boundary layers exhibit increasingly non-local behavior with streamwise development. This is apparent as a lag to the pressure gradient distribution observed in the streamwise developing integrated boundary layer parameters. These ``history effects" are also prevalent in mean velocity profiles which are exhibited as a cross-over of the favorable and adverse pressure gradient profiles in the logarithmic layer. Similar cross-over points are observed in the Reynolds shear and normal stresses, particularly at the streamwise station downstream of the pressure gradient switch. The primary effect of the rough wall is to increase the magnitude of flow scales, and, while they exhibit the same qualitative history effects as the smooth wall, the rough wall flows show an earlier relaxation to equilibrium. Despite inherent uncertainties of indirect skin friction methods for the rough wall, the effective sandgrain roughness parameter k_s does not show a functional dependency to pressure gradient history. An evaluation of the wall-similarity hypothesis solely based on boundary layer thickness to roughness parameter ratios delta/k_s is insufficient and additional parameters such as pressure gradient histories, local roughness Reynolds numbers, and bias uncertainties due to instrument spatial resolution must be considered. / Doctor of Philosophy / In the interface between a surface and a moving fluid is the boundary layer where high shear and viscous stresses cause the bulk velocity to decrease to zero. When turbulent, this region of fluid is characterized by random, chaotic, and fluctuating motions of varying sizes. Parameters such as pressure gradients and geometric irregularities of the surface, referred to as roughness, can increase fluctuating pressures and velocities within the boundary layer and cause unwanted noise, vibration, and increased drag. Although many studies have evaluated boundary layers with either roughness or pressure gradient independently, most surfaces in practical application are susceptible to the compounding influences of both of these parameters. Thus, it is necessary to expand the current knowledge database to include complex flow fields necessary to improve data driven modeling and vehicle design.newline{}newline{} This study focuses on experimental observations of the turbulent velocity field developing in both a rough and smooth wall boundary layer that is induced to a family of bi-directional pressure gradients generated by the pressure field of a rotating airfoil inside in a wind tunnel. Through statistical observations of the velocity field it was found that the varying pressure gradients caused the flow to develop non-local dependencies such that the response of the downstream boundary layer was dependent on the upstream flow history. The principal effect of roughness was to increase the magnitude of turbulent scales, but to show the same qualitative response to the pressure gradient history as seen in a smooth wall flow. However, direct comparison of rough and smooth wall turbulence statistics by means of the ``wall-similarity hypothesis" requires careful consideration of multiple parameters including these flow histories, scales prescribed by roughness parameters, and bias errors from experiment under-resolution of the velocity field.

Up to 70 percent of rough mill manufacturing expenses stem from raw material (lumber) cost. Rough mill costs can be reduced by optimizing the lumber grade or grades that are purchased. This solution is known as the least-cost lumber grade-mix solution. The least-cost lumber grade-mix solutions has been a topic of great interest to both the secondary hardwood industry and to academia since even small changes in raw material cost can contribute to substantial reduction in rough mill expenses. A statistical model was developed for finding the least-cost lumber grade-mix which uses the rough mill simulator, ROMI-RIP 2.0, and the statistical package, SAS 8.2. The SAS 8.2-based least-cost lumber grade-mix model was validated by comparing SAS 8.2-based least-cost grade-mix solutions to OPTIGRAMI 2.0, a least-cost lumber grade-mix solver that relies on linear modeling. The SAS 8.2-based least-cost lumber grade-mix solver found lower cost solutions in 9 of 10 cutting bills that were tested. The SAS 8.2-based least-cost lumber grade-mix solver was packaged with ROMI 3.0, an updated version of ROMI-RIP, and provided to industry free of charge by the USDA Forest Service. The USDA Forest Service also purchased a SAS server license to allow least-cost lumber grade-mix solver users free access to SAS 8.2. However, industry users were reluctant to use the USDA Forest Service SAS server since it requires the user to enter individual cost and yield data to a government computer. This solution also required the user to have internet access and limited access to one user at any time. Thus, the goal of this research was to incorporate the least-cost lumber grade-mix solver into ROMI using the free, open source statistical package R 2.7.2. An R 2.7.2-based least-cost lumber grade-mix solver was developed and validated by comparing the R 2.7.2-based least-cost lumber grade-mix solutions to the updated SAS 9.2-based least-cost lumber grade-mix solutions. No differences were found in the least-cost lumber grade-mix solutions from either solver. Thus, a new least-cost lumber grade-mix solver using the R 2.7.2 open source statistical package was created. R 2.7.2 is installed on each personal computer on which the USDA Forest Service's ROMI rough mill simulation software is installed and, thus, no external computing resources are needed when solving the least-cost lumber grade-mix problem. / Master of Science

No / This paper presents an integration procedure for the Reynolds-averaged Navier-Stokes equations for the determination of the distribution of the streamwise velocity using the vertical component. This procedure is dedicated to the outer region and central part of channels. The proposed model is applicable to both rough and smooth flow regimes, provided the velocity at the inner-outer boundary has been properly defined. To generate a simplified expansion, a number of hypotheses are proposed, focusing in particular on the analytical modeling of the vertical component by adopting a negligible viscosity. The proposed hypotheses are validated by the experimental data existing in the literature. The proposed simplified expansion is studied through a sensitivity analysis and proved consistent in regards to model experimental data. The proposed model seems capable of demonstrating different kinds of flows, including dip phenomenon flow patterns.

Yes / The Prandtl second kind of secondary current occurs in any narrow channel flow causing velocity dip in the flow velocity distribution by introducing the anisotropic turbulence into the flow. Here, a study was conducted to explain the occurrence of the secondary current in the outer region of flow velocity distribution using a universal expression. Started from the basic Navier-Stokes equation, the velocity profile derivation was accomplished in a universal way for both smooth and rough open channel flows. However, the outcome of the derived theoretical equation shows that the smooth and rough bed flows give different boundary conditions due to the different formation of log law for smooth and rough bed cases in the inner region of velocity distribution. Detailed comparison with a wide range of different measurement results from literatures (from smooth, rough and field measured data) evidences the capability of the proposed law to represent flow under all bed roughness conditions.

The main motivation behind writing this thesis was to construct numerical methods to approximate solutions to differential equations driven by rough paths, where the solution is considered in the rough path-sense. Rough paths of inhomogeneous degree of smoothness as driving noise are considered. We also aimed to find applications of these numerical methods to stochastic differential equations. After sketching the core ideas of the Rough Paths Theory in Chapter 1, the versions of the core theorems corresponding to the inhomogeneous degree of smoothness case are stated and proved in Chapter 2 along with some auxiliary claims on the continuity of the solution in a certain sense, including an RDE-version of Gronwall's lemma. In Chapter 3, numerical schemes for approximating solutions to differential equations driven by rough paths of inhomogeneous degree of smoothness are constructed. We start with setting up some principles of approximations. Then a general class of local approximations is introduced. This class is used to construct global approximations by pasting together the local ones. A general sufficient condition on the local approximations implying global convergence is given and proved. The next step is to construct particular local approximations in finite dimensions based on solutions to ordinary differential equations derived locally and satisfying the sufficient condition for global convergence. These local approximations require strong conditions on the one-form defining the rough differential equation. Finally, we show that when the local ODE-based schemes are applied in combination with rough polynomial approximations, the conditions on the one-form can be weakened. In Chapter 4, the results of Gyurko & Lyons (2010) on path-wise approximation of solutions to stochastic differential equations are recalled and extended to the truncated signature level of the solution. Furthermore, some practical considerations related to the implementation of high order schemes are described. The effectiveness of the derived schemes is demonstrated on numerical examples. In Chapter 5, the background theory of the Kusuoka-Lyons-Victoir (KLV) family of weak approximations is recalled and linked to the results of Chapter 4. We highlight how the different versions of the KLV family are related. Finally, a numerical evaluation of the autonomous ODE-based versions of the family is carried out, focusing on SDEs in dimensions up to 4, using cubature formulas of different degrees and several high order numerical ODE solvers. We demonstrate the effectiveness and the occasional non-effectiveness of the numerical approximations in cases when the KLV family is used in its original version and also when used in combination with partial sampling methods (Monte-Carlo, TBBA) and Romberg extrapolation.

In this thesis, we present a lattice theoretical approach to the field of approximations. Given a pair consisting of a kernel system and a closure system on an underlying lattice, one receives a lattice of approximations. We describe the theory of these lattices of approximations. Furthermore, we put a special focus on the case of concept lattices. As it turns out, approximation of formal concepts can be interpreted as traces, which are preconcepts in a subcontext. / In der vorliegenden Arbeit beschreiben wir einen verbandstheoretischen Zugang zum Thema Approximieren. Ausgehend von einem Kern- und einem Hüllensystem auf einem vollständigen Verband erhält man einen Approximationsverband. Wir beschreiben die Theorie dieser Approximationsverbände. Des Weiteren liegt dabei ein Hauptaugenmerk auf dem Fall zugrundeliegender Begriffsverbände. Wie sich nämlich herausstellt, lassen sich Approximationen formaler Begriffe als Spuren auffassen, welche diese in einem vorgegebenen Teilkontext hinterlassen.

In this thesis, we present a lattice theoretical approach to the field of approximations. Given a pair consisting of a kernel system and a closure system on an underlying lattice, one receives a lattice of approximations. We describe the theory of these lattices of approximations. Furthermore, we put a special focus on the case of concept lattices. As it turns out, approximation of formal concepts can be interpreted as traces, which are preconcepts in a subcontext.:Preface 1. Preliminaries 2. Approximations in Complete Lattices 3. Concept Approximations 4. Rough Sets List of Symbols Index Bibliography / In der vorliegenden Arbeit beschreiben wir einen verbandstheoretischen Zugang zum Thema Approximieren. Ausgehend von einem Kern- und einem Hüllensystem auf einem vollständigen Verband erhält man einen Approximationsverband. Wir beschreiben die Theorie dieser Approximationsverbände. Des Weiteren liegt dabei ein Hauptaugenmerk auf dem Fall zugrundeliegender Begriffsverbände. Wie sich nämlich herausstellt, lassen sich Approximationen formaler Begriffe als Spuren auffassen, welche diese in einem vorgegebenen Teilkontext hinterlassen.:Preface 1. Preliminaries 2. Approximations in Complete Lattices 3. Concept Approximations 4. Rough Sets List of Symbols Index Bibliography