Multi-directional polymer matrix composite materials are increasingly used in load-bearing structural applications ranging from primary aircraft structures and automotive parts to rehabilitation of bridges. Long-term durability, characterized by time-dependent degradation in strength (known as creep-rupture) and modulus (known as creep), is an important concern in these applications. Despite the experimental evidence on the influence of time-dependent damage on creep and creep rupture of multi-directional composites, current level of understanding of this is very limited. Hence, the focus of this thesis is to develop a clear understanding of the time dependent evolution of various damage modes and their influence on creep rupture of polymer matrix composite laminates.Three laminates [0/90/0], [±45/902]s, and [0/902]s were subjected to a wide range of constant stresses at various test temperatures and creep rupture time was recorded.The various damage modes that developed, with stress during tensile testing, and with time during constant stress creep rupture testing were transverse cracking, vertical cracking, delamination, vertical splitting and fiber fracture.The appearance of these damages were time dependent confirming that the FPF stress is time-dependent, while the conventional wisdom is to consider it to be time-independent in design. Beyond FPF, the damage continued to evolve for a certain period of time beyond which additional damage modes started to evolve influencing the evolution rate of one-another.The percentage of creep rupture time during which a single mode of damage was evolving decreased with increase in applied stress and test temperature.Based on these results it is concluded that creep rupture of multidirectional laminates is influenced by contributions from a complex interaction of various damage modes that evolve with time, suggesting that creep rupture predictions could be good approximations only.

Multi-directional polymer matrix composite materials are increasingly used in load-bearing structural applications ranging from primary aircraft structures and automotive parts to rehabilitation of bridges. Long-term durability, characterized by time-dependent degradation in strength (known as creep-rupture) and modulus (known as creep), is an important concern in these applications. Despite the experimental evidence on the influence of time-dependent damage on creep and creep rupture of multi-directional composites, current level of understanding of this is very limited. Hence, the focus of this thesis is to develop a clear understanding of the time dependent evolution of various damage modes and their influence on creep rupture of polymer matrix composite laminates.Three laminates [0/90/0], [±45/902]s, and [0/902]s were subjected to a wide range of constant stresses at various test temperatures and creep rupture time was recorded.The various damage modes that developed, with stress during tensile testing, and with time during constant stress creep rupture testing were transverse cracking, vertical cracking, delamination, vertical splitting and fiber fracture.The appearance of these damages were time dependent confirming that the FPF stress is time-dependent, while the conventional wisdom is to consider it to be time-independent in design. Beyond FPF, the damage continued to evolve for a certain period of time beyond which additional damage modes started to evolve influencing the evolution rate of one-another.The percentage of creep rupture time during which a single mode of damage was evolving decreased with increase in applied stress and test temperature.Based on these results it is concluded that creep rupture of multidirectional laminates is influenced by contributions from a complex interaction of various damage modes that evolve with time, suggesting that creep rupture predictions could be good approximations only.

Multi-directional polymer matrix composite materials are increasingly used in load-bearing structural applications ranging from primary aircraft structures and automotive parts to rehabilitation of bridges. Long-term durability, characterized by time-dependent degradation in strength (known as creep-rupture) and modulus (known as creep), is an important concern in these applications. Despite the experimental evidence on the influence of time-dependent damage on creep and creep rupture of multi-directional composites, current level of understanding of this is very limited. Hence, the focus of this thesis is to develop a clear understanding of the time dependent evolution of various damage modes and their influence on creep rupture of polymer matrix composite laminates.Three laminates [0/90/0], [±45/902]s, and [0/902]s were subjected to a wide range of constant stresses at various test temperatures and creep rupture time was recorded.The various damage modes that developed, with stress during tensile testing, and with time during constant stress creep rupture testing were transverse cracking, vertical cracking, delamination, vertical splitting and fiber fracture.The appearance of these damages were time dependent confirming that the FPF stress is time-dependent, while the conventional wisdom is to consider it to be time-independent in design. Beyond FPF, the damage continued to evolve for a certain period of time beyond which additional damage modes started to evolve influencing the evolution rate of one-another.The percentage of creep rupture time during which a single mode of damage was evolving decreased with increase in applied stress and test temperature.Based on these results it is concluded that creep rupture of multidirectional laminates is influenced by contributions from a complex interaction of various damage modes that evolve with time, suggesting that creep rupture predictions could be good approximations only. / May 2008

archives@tulane.edu / Abstract: A search in a research database for “large specific rotation” or anything similar produces few articles. Large specific rotation is not commonly used as an indicator for extraordinary chiroptical response. Alternatively, anisotropy factors obtained from circular dichroism spectra and calculated rotational strengths are more widely used to gauge chiroptical response. To another point, a search for “large chiroptical response” gives few articles that discuss pure organic compounds, and the result list is populated by organometallic clusters, nanostructures, and thin films. A search of the Reaxys database for organic compounds with [α]Ds larger than 1000 revealed that there are about 600, and there are only two that have [α]Ds larger than 10,000.30 We wondered if we could design a compound that would break the record in specific rotation and possess extraordinary chiroptical properties. Guided by time-dependent density functional theory (TD-DFT) calculations, various chiral, polycyclic aromatic compounds (PACs) were chosen as candidates to display extraordinary chiroptical properties, such as high optical rotation, strong circular dichroism, or a high degree of circularly polarized luminescence (CPL). PACs comprise a large class of organic compounds. In addition to synthetic PACs, numerous naturally occurring PACs exist in coal tar and as decomposition products of organic material. Since their pi electrons are delocalized, PACs have interesting and possibly useful electronic properties and a variety of applications. The PACs described in this dissertation, e.g., helical mesobenzanthrones, a cyclophane, are twisted pentacenes are chiral and have interesting optoelectronic properties. TD-DFT was primarily used to predict which compounds had the greatest potential to yield record-breaking specific rotations or other chiroptical properties, and ordinary DFT calculation were used to determine if these compounds had sufficiently high racemization barriers to be resolved at room temperature. With regard to specific rotation, the accuracy of TD-DFT calculations was examined by comparing experimental specific rotations to the calculated values. / 1 / Kelly Jane Dougherty

There are two sources of information available in empirical research in finance: one corresponding to historical data and the other to prices currently observed in the markets. When proposing a model, it is desirable to use information from both sources. However in modern finance, where stochastic differential equations have been one of the main modeling tools, the common models are typically different for historical data and for current market data. The former are usually assumed to be time homogeneous, while the latter are typically time in-homogeneous. This practice can be explained by the fact that a time-homogeneous model is stationary and easier to estimate, while time-inhomogeneous model are required in order to replicate market data sufficiently well without creating arbitrage opportunities. In this thesis, we study methods of statistical inference, both parametric and non-parametric, for stochastic differential equations with time-dependent parameters. In the first part, we propose a new class of stochastic differential equation with time-dependent drift and diffusion terms, where some of the parameters change according to a hidden Markov process. We show that under some technical conditions this innovative way of modeling switching times renders the resulting model stationary. We also explore different approaches to estimate parameters in our proposed model. Our simulation studies demonstrate that the parameters of the model can be efficiently estimated by using a version of the filtering method proposed in the literature. We illustrate our model and the proposed estimation method by applying them to interest rate data, and we detect significant time variations in early 1980s, when targets of the monetary policy in the United States were changed. One of the known drawbacks of parametric models is the risk of model misspecification. In the second part of the thesis, we allow the drift to be time-dependent and nonparametric, and our objective is to estimate it using a single trajectory of the process. The main idea underlying this method is to approximate the time-dependent function with a sequence of polynomials. Since we can estimate efficiently only a finite number of parameters for any finite length of data, in our method we propose to relate the number of parameters to the length of the observed trajectory. This idea is similar to the method of sieves proposed by Grenander (Abstract Inference, 1981). The asymptotic analysis that we present is based on the assumption that the length of available data $T$ increases to infinity. We investigate two cases, one is a Brownian motion with time-dependent drift and the other corresponds to a class of mean-reverting stochastic differential equations with time-dependent mean-reversion level. In both cases we prove asymptotic consistency and normality of a modified maximum likelihood estimator of the projected time-dependent component. The main challenge in proving our results in the second case stems from two features of the problem: one is due to the fact that coefficients of projections change with $T$ and the other is related to the confounding effect between the mean-reversion speed and the level function. By applying our method to the same interest rate data we use in the first part, we find another evidence of time-variation in the drift term.

In this thesis, we study time-dependent empirical processes, which extend the classical empirical processes to have a time parameter; for example the empirical process for a sequence of independent stochastic processes {Yi : i ∈ N}: (1) ν_n(t, y) = n^(−1/2 )Sigma[1_(Y i(t)¬<=y) – P(Yi(t) <= y)] from i=1 to n, t ∈ E, y ∈ R. In the case of independent identically distributed samples (that is {Yi(t) : i ∈ N} are iid), Kuelbs et al. (2013) proved a Central Limit Theorem for ν_n(t, y) for a large class of stochastic processes. In Chapter 3, we give a sufficient condition for the weak convergence of the weighted empirical process for iid samples from a uniform process: (2) α_n(t, y) := n^(−1/2 )Sigma[w(y)(1_(X (t)<=y) – y)] from i=1 to n, t ∈ E, y ∈ [0, 1] where {X (t), X1(t), X2(t), • • • } are independent and identically distributed uniform processes (for each t ∈ E, X (t) is uniform on (0, 1)) and w(x) is a “weight” function satisfying some regularity properties. Then we give an example when X (t) := Ft(Bt) : t ∈ E = [1, 2], where Bt is a Brownian motion and Ft is the distribution function of Bt. In Chapter 4, we investigate the weak convergence of the empirical processes for non-iid samples. We consider the weak convergence of the empirical process: (3) β_n(t, y) := n^(−1/2 )Sigma[(1_(Y (t)<=y) – Fi(t,y))] from i=1 to n, t ∈ E ⊂ R, y ∈ R where {Yi(t) : i ∈ N} are independent processes and Fi(t, y) is the distribution function of Yi(t). We also prove that the covariance function of the empirical process for non-iid samples indexed by a uniformly bounded class of functions necessarily uniformly converges to the covariance function of the limiting Gaussian process for a CLT.

No description available.

There are two sources of information available in empirical research in finance: one corresponding to historical data and the other to prices currently observed in the markets. When proposing a model, it is desirable to use information from both sources. However in modern finance, where stochastic differential equations have been one of the main modeling tools, the common models are typically different for historical data and for current market data. The former are usually assumed to be time homogeneous, while the latter are typically time in-homogeneous. This practice can be explained by the fact that a time-homogeneous model is stationary and easier to estimate, while time-inhomogeneous model are required in order to replicate market data sufficiently well without creating arbitrage opportunities. In this thesis, we study methods of statistical inference, both parametric and non-parametric, for stochastic differential equations with time-dependent parameters. In the first part, we propose a new class of stochastic differential equation with time-dependent drift and diffusion terms, where some of the parameters change according to a hidden Markov process. We show that under some technical conditions this innovative way of modeling switching times renders the resulting model stationary. We also explore different approaches to estimate parameters in our proposed model. Our simulation studies demonstrate that the parameters of the model can be efficiently estimated by using a version of the filtering method proposed in the literature. We illustrate our model and the proposed estimation method by applying them to interest rate data, and we detect significant time variations in early 1980s, when targets of the monetary policy in the United States were changed. One of the known drawbacks of parametric models is the risk of model misspecification. In the second part of the thesis, we allow the drift to be time-dependent and nonparametric, and our objective is to estimate it using a single trajectory of the process. The main idea underlying this method is to approximate the time-dependent function with a sequence of polynomials. Since we can estimate efficiently only a finite number of parameters for any finite length of data, in our method we propose to relate the number of parameters to the length of the observed trajectory. This idea is similar to the method of sieves proposed by Grenander (Abstract Inference, 1981). The asymptotic analysis that we present is based on the assumption that the length of available data $T$ increases to infinity. We investigate two cases, one is a Brownian motion with time-dependent drift and the other corresponds to a class of mean-reverting stochastic differential equations with time-dependent mean-reversion level. In both cases we prove asymptotic consistency and normality of a modified maximum likelihood estimator of the projected time-dependent component. The main challenge in proving our results in the second case stems from two features of the problem: one is due to the fact that coefficients of projections change with $T$ and the other is related to the confounding effect between the mean-reversion speed and the level function. By applying our method to the same interest rate data we use in the first part, we find another evidence of time-variation in the drift term.

This thesis presents analytic and computational advances in the prediction of perturbative nonlinear optical spectroscopies. The contributions of this thesis are packaged together in an open source, freely available piece of software called ultrafast spectroscopy suite (UFSS). It is designed to automatically simulate nonlinear optical spectroscopies for any phase-matching or phase-cycling condition, including finite pulse effects. UFSS includes an algorithm called the diagram generator (DG) that automates the process of writing out all of the Feynman diagrams that contribute to a desired phase-matching or phase-cycling condition, and includes all pulse overlap diagrams when relevant, paving the way toward automation of perturbative calculations. Further, many diagrams can be automatically combined into composite diagrams, giving an exponential decrease in computation time of high-order calculations. Composite diagrams even allow for the efficient study of Rabi oscillations as a function of pulse amplitude, by summing many orders of perturbation theory. The perturbative calculations are done using a novel algorithm presented in this thesis called Ultrafast Ultrafast spectroscopy (UF2). UF2 is an efficient method for determining diagrammatic contributions to spectra including arbitrary (whether analytical or experimentally measured) pulse shapes. It uses the speed of the fast Fourier transform to be as much as 500 times faster than direct propagation techniques for small model Hamiltonians (for Hamiltonian dimension of 100 or less). UF2 outperforms direct propagation techniques for a wide range of model systems, with the speed boost diminishing as the dimension of the model Hamiltonian increases. UF2 can predict spectra for any model system whose relevant Hilbert space that can be described using a finite basis and that can be diagonalized numerically, and users are free to specify their own model. UFSS includes a model generator that generates Hamiltonians and Liouvillians of vibronic systems, allowing users to easily simulate NLOSs for a wide range of model system parameters. UFSS is a fully functional piece of software for simulating any NLOS, to any desired order in perturbation theory.

<p> We look for time-dependent solutions to a general class of supergravity models in an arbitrary amount of dimensions. Previously, many static solutions of these models have been found and studied, of which a subclass of these solutions support membrane-like configurations. While many properties of these solutions are known, their dynamics - and therefore stability - are not. We follow this motivation, and investigate the possibility of time dependent solutions that will also support this membrane configuration. Under various conditions, it turns out this is the case, bringing a better understanding to the stability of these branes. In addition, the form of the time dependence found suggest possible applications of supergravity to cosmological models.</p> / Thesis / Master of Science (MSc)