One of the implicit assumptions made in research related to inventory control is to keep products indefinitely in inventory to meet future demand. However, such an assumption is not true for a large wide of products characterized by a limited lifetime. The economic impact of managing such products led to substantial work in perishable inventory control literature. Investigations developed so far underline the complexity of modeling perishable inventory. Moreover, the dependency of the lifetime to temperature conditions in which products are handled adds more complexity since the lifetime of products stemming from the same order may vary from product to another. In this context, the ability of Time Temperature Integrators to capture the effects of temperature variations on products' lifetime, offers an opportunity to reduce spoilage and therefore ensure product's freshness and safety. The general aim of this thesis is to model perishable inventory systems. Particularly, three different problem areas are considered. The first one concerns perishable inventory with fixed lifetime, often referred as Fixed Life Perishability Problem, where an approximate (r;Q) inventory policy is developed. This model relaxes some assumptions made in previous related works. The second problem considered is a (T; S) perishable inventory system with random lifetime. Results of this model contribute to the development of a theoretical background for perishable inventory systems which are based on Markov renewal process approach. The third area incorporates the impact of temperature variations on products' lifetime throughout inventory systems that use TTIs technology. More general settings regarding the demand and the lifetime distributions are considered throughout simulation analysis. The economic relevance stemming from the deployment of this technology is therefore quantified.

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.

Companies face competition that comes at them from different directions in the current environment of globalization, deregulation and the push for greater mass customization of products, which still can be differentiated from other products and services. A large number of companies have outsourced a large percentage of their non-core activities in order to concentrate on their core competencies with transportation of their goods being one of the aspects that they have outsourced. Companies are faced with shorter lead times, inaccurate forecasts, unexpected delays in production and need to seek out alternative transportation modes in order to get their goods to market on time. Transportation by air ends up being the best choice to handle requirements of time sensitivity and the transportation of high value goods. The purpose of this thesis was to investigate how the air freight supply chain and network that is in place in the Jönkoping region is constructed; in addition to seeking out information in regards to the type of air freight goods being transported into and out of the region; along with the buying behavior and promotion strategies utilized in the promotion of air freight within the region of Jonkoping. The conclusions from this thesis show that there are a number of key actors (integrators and freight forwarders) involved in the air freight network within the Jönköping region. A number of them indicated that the actors they mainly interacted with, in terms of activity links and resource ties, were limited to the airports that were outside of the Jönköping region. There were a few of the actors in terms of integrators that did interact with the Jönköping airport in a capacity that was greater than other actors. In terms of the type of air freight goods that were transported into and out of the region spare parts made up a major portion of the goods transported, followed by clothing and textiles, and other mechanical industry products. The promotion of air freight mostly performed by integrators to their customers is done in terms of emphasizing reliability, punctuality, regularity and security to their customers.

Most discrete time filters use Switched Capacitor structures, but Switched capacitor circuits have finite sampling rate and high power consumption. In this paper we use Switched Current structure to increase sampling rate and reduce power consumption. In this paper, we use a Class-AB structure to compose a double sampling third order low-pass filter. In this paper there are two integrator types. Modified backward Euler and modified forward Euler integrators were realized with double sampling technology from the backward Euler and forward Euler integrators. Compared with other circuits, the circuit has low power supply¡Blow power consumption ¡Bhigh sampling speed. We employ HSPICE and MATLAB to simulate and design the circuit. We use TSMC 0.35£gm process to implement this circuit. The power supply is 1.8V, the cut-off frequency is 3.6MHz, the sampling frequency is 72MHz, and the power consumption is 1.303mW.

Accurate numerical solution of time-dependent, high-dimensional partial differential equations (PDEs) usually requires efficient numerical techniques and massive-scale parallel computing. In this thesis, we implement and evaluate discretization schemes suited for PDEs of higher dimensionality, focusing on high order of accuracy and low computational cost. Spatial discretization is particularly challenging in higher dimensions. The memory requirements for uniform grids quickly grow out of reach even on large-scale parallel computers. We utilize high-order discretization schemes and implement adaptive mesh refinement on structured hyperrectangular domains in order to reduce the required number of grid points and computational work. We allow for anisotropic (non-uniform) refinement by recursive bisection and show how to construct, manage and load balance such grids efficiently. In our numerical examples, we use finite difference schemes to discretize the PDEs. In the adaptive case we show how a stable discretization can be constructed using SBP-SAT operators. However, our adaptive mesh framework is general and other methods of discretization are viable. For integration in time, we implement exponential integrators based on the Lanczos/Arnoldi iterative schemes for eigenvalue approximations. Using adaptive time stepping and a truncated Magnus expansion, we attain high levels of accuracy in the solution at low computational cost. We further investigate alternative implementations of the Lanczos algorithm with reduced communication costs. As an example application problem, we have considered the time-dependent Schrödinger equation (TDSE). We present solvers and results for the solution of the TDSE on equidistant as well as adaptively refined Cartesian grids. / eSSENCE

L’une des hypothèses implicites faites dans la recherche liée à la gestion des stocks est de maintenir les produits indéfiniment pour satisfaire la demande future. Toutefois, cette hypothèse n’est pas vraie pour les produits caractérisés par une durée de vie limitée. L’impact économique de la gestion de tels produits a conduit à d’importants travaux de recherche. Les investigations développées jusqu’ici ont souligné la complexité de modéliser les stocks de produits périssables. En plus, la dépendance de la durée de la vie à la température à laquelle les produits sont maintenus crée un challenge majeur en termes de modélisation puisque la durée de vie des produits provenant d’une même commande peut varier d’un produit à un autre. La capacité des nouvelles technologies de contrôle de fraîcheur telles que les intégrateurs temps - température de capturer les effets des variations de la température sur la durée de vie offre une opportunité de réduire les pertes et donc d’assurer la fraîcheur des produits vendus. L’objectif général de cette thèse est de modéliser des politiques de gestion de stock des produits périssables. En premier lieu, nous nous intéressons `a la politique (r;Q) o`u les produits ont une durée de vie constante. Le modèle que nous proposons relaxe certaines hypothèses formulées dans les précédents travaux. La deuxième politique considérée est la politique (T; S) où les produits ont une durée de vie aléatoire. Enfin, nous étudions l’impact des nouvelles technologies de contrôle de fraîcheur des produits périssables sur la gestion des stocks. Nous nous intéressons à la pertinence économique découlant du déploiement des intégrateurs temps températures dans la gestion des stocks. / One of the implicit assumptions made in research related to inventory control is to keep products indefinitely in inventory to meet future demand. However, such an assumption is not true for a large wide of products characterized by a limited lifetime. The economic impact of managing such products led to substantial work in perishable inventory control literature. Investigations developed so far underline the complexity of modeling perishable inventory. Moreover, the dependency of the lifetime to temperature conditions in which products are handled adds more complexity since the lifetime of products stemming from the same order may vary from product to another. In this context, the ability of Time Temperature Integrators to capture the effects of temperature variations on products’ lifetime, offers an opportunity to reduce spoilage and therefore ensure product’s freshness and safety. The general aim of this thesis is to model perishable inventory systems. Particularly, three different problem areas are considered. The first one concerns perishable inventory with fixed lifetime, often referred as Fixed Life Perishability Problem, where an approximate (r;Q) inventory policy is developed. This model relaxes some assumptions made in previous related works. The second problem considered is a (T; S) perishable inventory system with random lifetime. Results of this model contribute to the development of a theoretical background for perishable inventory systems which are based on Markov renewal process approach. The third area incorporates the impact of temperature variations on products’ lifetime throughout inventory systems that use TTIs technology. More general settings regarding the demand and the lifetime distributions are considered throughout simulation analysis. The economic relevance stemming from the deployment of this technology is therefore quantified.

This dissertation presents results of the study on symplectic and multisymplectic numerical methods for solving linear and nonlinear Hamiltonian wave equations. The emphasis is put on the second order space and time discretizations of the linear wave, the Klein-Gordon and the sine-Gordon equations. For those equations we develop two multisymplectic (MS) integrators and compare their performance to other popular symplectic and non-symplectic numerical methods. Tools used in the linear analysis are related to the Fourier transform and consist of the dispersion relationship and the power spectrum of the numerical solution. Nonlinear analysis, in turn, is closely connected to the temporal evolution of the total energy (Hamiltonian) and can be viewed from the topological perspective as preservation of the phase space structures. Using both linear and nonlinear diagnostics we find qualitative differences between MS and non-MS methods. The first difference can be noted in simulations of the linear wave equation solved for broad spectrum Gaussian initial data. Initial wave profiles of this type immediately split into an oscillatory wave-train with the high modes traveling faster (MS schemes), or slower (non-MS methods), than the analytic group velocity. This result is confirmed by an analysis of the dispersion relationship, which also indicates improved qualitative agreement of the dispersive curves for MS methods over non-MS ones. Moreover, observations of the convergence patterns in the wave profile obtained for the sine-Gordon equation for the initial data corresponding to the double-pole soliton and the temporal evolution of the Hamiltonian functional computed for solutions obtained from different discretizations suggest a change of the geometry of the phase space. Finally, we present some theoretical considerations concerning wave action. Lagrangian formulation of linear partial differential equations (PDEs) with slowly varying solutions is capable of linking the wave action conservation law with the dispersion relationship thus suggesting the possibility to extend this connection to multisymplectic PDEs.

The first and most imperative step when designing a biologically inspired robot is to identify the underlying mechanics of the system or animal of interest. It is most common, perhaps, that this process generates a set of coupled nonlinear ordinary or partial differential equations. For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and complex. This is particularly true if joint and link flexibility are included in the model. In addition to complexities that arise from morphology of the animal, some of the external forces that influence the dynamics of animal motion are very hard to model. A very well-established example of these forces is the unsteady aerodynamic forces applied to the wings and the body of insects, birds, and bats. These forces result from the interaction of the flapping motion of the wing and the surround- ing air. These forces generate lift and drag during flapping flight regime. As a result, they play a significant role in the description of the physics that underlies such systems. In this research we focus on dynamic and kinematic models that govern the motion of ground based robots that emulate flapping flight. The restriction to ground based biologically inspired robotic systems is predicated on two observations. First, it has become increasingly popular to design and fabricate bio-inspired robots for wind tunnel studies. Second, by restricting the robotic systems to be anchored in an inertial frame, the robotic equations of motion are well understood, and we can focus attention on flapping wing aerodynamics for such nonlinear systems. We study nonlinear modeling, identification, and control problems that feature the above complexities. This document summarizes research progress and plans that focuses on two key aspects of modeling, identification, and control of nonlinear dynamics associated with flapping flight. / Ph. D.

This dissertation develops a variety of structure-preserving algorithms for mechanical systems with external forcing and also extends those methods to systems that evolve on non-Euclidean manifolds. The dissertation is focused on numerical schemes derived from variational principles – schemes that are general enough to apply to a large class of engineering problems. A theoretical framework that encapsulates variational integration for mechanical systems with external forcing and time-dependence and which supports the extension of these methods to systems that evolve on non-Euclidean manifolds is developed. An adaptive time step, energy-preserving variational integrator is developed for mechanical systems with external forcing. It is shown that these methods track the change in energy more accurately than their fixed time step counterparts. This approach is also extended to rigid body systems evolving on Lie groups where the resulting algorithms preserve the geometry of the configuration space in addition to being symplectic as well as energy and momentum-preserving. The advantages of structure-preservation in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching. / Doctor of Philosophy / Accurate numerical simulation of dynamical systems over long time horizons is essential in applications ranging from particle physics to geophysical fluid flow to space hazard analysis. In many of these applications, the governing physical equations derive from a variational principle and their solutions exhibit physically meaningful invariants such as momentum, energy, or vorticity. Unfortunately, most traditional numerical methods do not account for the underlying geometric structure of the physical system, leading to simulation results that may suggest nonphysical behavior. In this dissertation, tools from geometric mechanics and computational methods are used to develop numerical integrators that respect the qualitative features of the physical system. The research presented here focuses on numerical schemes derived from variational principles– schemes that are general enough to apply to a large class of engineering problems. Energy-preserving algorithms are developed for mechanical systems by exploiting the underlying geometric properties. Numerical performance comparisons demonstrate that these algorithms provide almost exact energy preservation and lead to more accurate prediction. The advantages of these methods in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.

The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.