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Stochastic pump effect and geometric phases in dissipative and stochastic systems

Description: The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Date: January 1, 2008
Creator: Sinitsyn, Nikolai
Partner: UNT Libraries Government Documents Department

Regional Stochastic Generation of Streamflows using an Arima (1, 0, 1) Process and Disaggregation

Description: From abstract: An ARIMA (1, 0, 1) model is used to generate annual flow sequence at three sites in the Juniata River basin, Pennsylvania. The study was designed to analyze low-flow frequency characteristics of a basin. The model preserves the mean, variance, and cross-correlations of the observed station data.
Date: May 1979
Creator: Armbuster, Jeffrey T.
Partner: UNT Libraries Government Documents Department

Emergence of Complexity from Synchronization and Cooperation

Description: The dynamical origin of complexity is an object of intense debate and, up to moment of writing this manuscript, no unified approach exists as to how it should be properly addressed. This research work adopts the perspective of complexity as characterized by the emergence of non-Poisson renewal processes. In particular I introduce two new complex system models, namely the two-state stochastic clocks and the integrate-and-fire stochastic neurons, and investigate its coupled dynamics in different network topologies. Based on the foundations of renewal theory, I show how complexity, as manifested by the occurrence of non-exponential distribution of events, emerges from the interaction of the units of the system. Conclusion is made on the work's applicability to explaining the dynamics of blinking nanocrystals, neuron interaction in the human brain, and synchronization processes in complex networks.
Date: May 2008
Creator: Geneston, Elvis L.
Partner: UNT Libraries

COMPLEXITY&APPROXIMABILITY OF QUANTIFIED&STOCHASTIC CONSTRAINT SATISFACTION PROBLEMS

Description: Let D be an arbitrary (not necessarily finite) nonempty set, let C be a finite set of constant symbols denoting arbitrary elements of D, and let S and T be an arbitrary finite set of finite-arity relations on D. We denote the problem of determining the satisfiability of finite conjunctions of relations in S applied to variables (to variables and symbols in C) by SAT(S) (by SATc(S).) Here, we study simultaneously the complexity of decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. We present simple yet general techniques to characterize simultaneously, the complexity or efficient approximability of a number of versions/variants of the problems SAT(S), Q-SAT(S), S-SAT(S),MAX-Q-SAT(S) etc., for many different such D,C ,S, T. These versions/variants include decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. Our unified approach is based on the following two basic concepts: (i) strongly-local replacements/reductions and (ii) relational/algebraic represent ability. Some of the results extend the earlier results in [Pa85,LMP99,CF+93,CF+94O]u r techniques and results reported here also provide significant steps towards obtaining dichotomy theorems, for a number of the problems above, including the problems MAX-&-SAT( S), and MAX-S-SAT(S). The discovery of such dichotomy theorems, for unquantified formulas, has received significant recent attention in the literature [CF+93,CF+94,Cr95,KSW97]
Date: January 1, 2001
Creator: Hunt, H. B. (Harry B.); Marathe, M. V. (Madhav V.) & Stearns, R. E. (Richard E.)
Partner: UNT Libraries Government Documents Department

Two-Fold Role of Randomness: A Source of Both Long-Range Correlations and Ordinary Statistical Mechanics

Description: The role of randomness as a generator of long range correlations and ordinary statistical mechanics is investigated in this Dissertation. The difficulties about the derivation of thermodynamics from mechanics are pointed out and the connection between the ordinary fluctuation-dissipation process and possible anomalous properties of statistical systems is highlighted.
Date: December 1998
Creator: Rocco, A. (Andrea)
Partner: UNT Libraries

Accelerating DSMC data extraction.

Description: In many direct simulation Monte Carlo (DSMC) simulations, the majority of computation time is consumed after the flowfield reaches a steady state. This situation occurs when the desired output quantities are small compared to the background fluctuations. For example, gas flows in many microelectromechanical systems (MEMS) have mean speeds more than two orders of magnitude smaller than the thermal speeds of the molecules themselves. The current solution to this problem is to collect sufficient samples to achieve the desired resolution. This can be an arduous process because the error is inversely proportional to the square root of the number of samples so we must, for example, quadruple the samples to cut the error in half. This work is intended to improve this situation by employing more advanced techniques, from fields other than solely statistics, for determining the output quantities. Our strategy centers on exploiting information neglected by current techniques, which collect moments in each cell without regard to one another, values in neighboring cells, nor their evolution in time. Unlike many previous acceleration techniques that modify the method itself, the techniques examined in this work strictly post-process so they may be applied to any DSMC code without affecting its fidelity or generality. Many potential methods are drawn from successful applications in a diverse range of areas, from ultrasound imaging to financial market analysis. The most promising methods exploit relationships between variables in space, which always exist in DSMC due to the absence of shocks. Disparate techniques were shown to produce similar error reductions, suggesting that the results shown in this report may be typical of what is possible using these methods. Sample count reduction factors of approximately three to five were found to be typical, although factors exceeding ten were shown on some variables under some techniques.
Date: October 1, 2006
Creator: Gallis, Michail A. & Piekos, Edward Stanley
Partner: UNT Libraries Government Documents Department

Some Results on the Analysis of Stochastic Processes with Uncertain Transition Probabilities and Robust Optimal Control

Description: This paper investigates stochastic processes that are modeled by a finite number of states but whose transition probabilities are uncertain and possibly time-varying. The treatment of uncertain transition probabilities is important because there appears to be a disconnection between the practice and theory of stochastic processes due to the difficulty of assigning exact probabilities to real-world events. Also, when the finite-state process comes as a reduced model of one that is more complicated in nature (possibly in a continuous state space), existing results do not facilitate rigorous analysis. Two approaches are introduced here. The first focuses on processes with one terminal state and the properties that affect their convergence rates. When a process is on a complicated graph, the bound of the convergence rate is not trivially related to that of the probabilities of individual transitions. Discovering the connection between the two led us to define two concepts which we call 'progressivity' and 'sortedness', and to a new comparison theorem for stochastic processes. An optimality criterion for robust optimal control also derives from this comparison theorem. In addition, this result is applied to the case of mission-oriented autonomous robot control to produce performance estimate within a control framework that we propose. The second approach is in the MDP frame work. We will introduce our preliminary work on optimistic robust optimization, which aims at finding solutions that guarantee the upper bounds of the accumulative discounted cost with prescribed probabilities. The motivation here is to address the issue that the standard robust optimal solution tends to be overly conservative.
Date: September 1, 2007
Creator: Li, Keyong; Kang, Seong-Cheol & Paschalidis, I. Ch.
Partner: UNT Libraries Government Documents Department

Operational Impacts of Wind Energy Resources in the Bonneville Power Administration Control Area - Phase I Report

Description: This report presents a methodology developed to study the future impact of wind on BPA power system load following and regulation requirements. The methodology uses historical data and stochastic processes to simulate the load balancing processes in the BPA power system, by mimicking the actual power system operations. Therefore, the results are close to reality, yet the study based on this methodology is convenient to conduct. Compared with the proposed methodology, existing methodologies for doing similar analysis include dispatch model simulation and standard deviation evaluation on load and wind data. Dispatch model simulation is constrained by the design of the dispatch program, and standard deviation evaluation is artificial in separating the load following and regulation requirements, both of which usually do not reflect actual operational practice. The methodology used in this study provides not only capacity requirement information, it also analyzes the ramp rate requirements for system load following and regulation processes. The ramp rate data can be used to evaluate generator response/maneuverability requirements, which is another necessary capability of the generation fleet for the smooth integration of wind energy. The study results are presented in an innovative way such that the increased generation capacity or ramp requirements are compared for two different years, across 24 hours a day. Therefore, the impact of different levels of wind energy on generation requirements at different times can be easily visualized.
Date: July 15, 2008
Creator: Makarov, Yuri V. & Lu, Shuai
Partner: UNT Libraries Government Documents Department

Anomalous diffusion and scaling in coupled stochastic processes

Description: Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. The diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.
Date: January 1, 2009
Creator: Bel, Golan & Nemenman, Ilya
Partner: UNT Libraries Government Documents Department

Practical Issues in Component Aging Analysis

Description: This paper examines practical issues in the statistical analysis of component aging data. These issues center on the stochastic process chosen to model component failures. The two stochastic processes examined are repair same as new, leading to a renewal process, and repair same as old, leading to a nonhomogeneous Poisson process. Under the first assumption, times between failures can treated as statistically independent observations from a stationary process. The common distribution of the times between failures is called the renewal distribution. Under the second process, the times between failures will not be independently and identically distributed, and one cannot simply fit a renewal distribution to the cumulative failure times or the times between failures. The paper illustrates how the assumption made regarding the repair process is crucial to the analysis. Besides the choice of stochastic process, other issues that are discussed include qualitative graphical analysis and simple nonparametric hypothesis tests to help judge which process appears more appropriate. Numerical examples are presented to illustrate the issues discussed in the paper.
Date: September 1, 2008
Creator: Kelly, Dana L.; Rodionov, Andrei & Uwe-Klugel, Jens
Partner: UNT Libraries Government Documents Department

Review of Upscaling Methods for Describing Unsaturated Flow

Description: Representing samll-scale features can be a challenge when one wants to model unsaturated flow in large domains. In this report, the various upscaling techniques are reviewed. The following upscaling methods have been identified from the literature: stochastic methods, renormalization methods, volume averaging and homogenization methods. In addition, a final technique, full resolution numerical modeling, is also discussed.
Date: September 26, 2000
Creator: Wood, Brian D.
Partner: UNT Libraries Government Documents Department

Method of sampling certain probability densities without inversion of their distribution functions

Description: A Monte Carlo device is described which bypasses the inversion x = p/sup -1/(r) involved in directly sampling the distribution P(x) of a stochastic variable x with given density p(x). The method is practical for all linear and a broad class of quadratic densities. (auth)
Date: September 1, 1973
Creator: Everett, C.J.; Cashwell, E.D. & Turner, G.D.
Partner: UNT Libraries Government Documents Department

Limit theorem for the maximum term in an EARMA(1,1) sequence when the parameter rho is one

Description: The EARMA(1,1) process was defined by Jacobs and Lewis (Advances in Applied Probability, 1977). Chernick (Ph.D. dissertation, Stanford University, 1978) showed that the limit for the maximum term is the same as for a sequence of independent, identically distributed exponential random variables when the parameter rho is less than one. When rho equals one, a different limit theorem is obtained. The resulting limit distribution is not an extreme value type. It is, however, of the general form given by Galambos (The Asymptotic Theory of Extreme Order Statistics, Wiley, 1978). The sequence is exchangeable.
Date: January 1, 1979
Creator: Chernick, M R
Partner: UNT Libraries Government Documents Department

Controlling chaos in a high dimensional system with periodic parametric perturbations

Description: The effect of applying a periodic perturbation to an accessible parameter of a high-dimensional (coupled-Lorenz) chaotic system is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic system can result in limit cycles or significantly reduced dimension for relatively small perturbations.
Date: October 1, 1998
Creator: Mirus, K. A. & Sprott, J. C.
Partner: UNT Libraries Government Documents Department

Study of the effects of background and motion camera on the efficacy of Kalman and particle filter algorithms.

Description: This study compares independent use of two known algorithms (Kalmar filter with background subtraction and Particle Filter) that are commonly deployed in object tracking applications. Object tracking in general is very challenging; it presents numerous problems that need to be addressed by the application in order to facilitate its successful deployment. Such problems range from abrupt object motion, during tracking, to a change in appearance of the scene and the object, as well as object to scene occlusions, and camera motion among others. It is important to take into consideration some issues, such as, accounting for noise associated with the image in question, ability to predict to an acceptable statistical accuracy, the position of the object at a particular time given its current position. This study tackles some of the issues raised above prior to addressing how the use of either of the aforementioned algorithm, minimize or in some cases eliminate the negative effects
Date: August 2009
Creator: Morita, Yasuhiro
Partner: UNT Libraries

Stochastic Mechanical Systems

Description: To understand the phenomena associated with such stochastic processes and to predict, at least qualitatively, the behavior of mechanical systems within environments which are completely random in time, new mechanical tools are necessary. Fortunately, the derivation of these tools does not necessitate a complete departure from existing theories. In fact, they may be considered as an extension of the well-defined theory of the integral transform, in particular, the exponential Fourier integral transform.
Date: August 1960
Creator: Bost, Robert Berton
Partner: UNT Libraries

Dynamics of density fluctuations in a non-Markovian Boltzmann- Langevin model

Description: In the course of the past few years, the nuclear Boltzmann-Langevin (BL)model has emerged as a promising microscopic model for nuclear dynamics at intermediate energies. The BL model goes beyond the much employed Boltzmann-Uehling-Uhlenbeck (BUU) model, and hence it provides a basis for describing dynamics of density fluctuations and addressing processes exhibiting spontaneous symmetry breaking and catastrophic transformations in nuclear collisions, such as induced fission and multifragmentation. In these standard models, the collision term is treated in a Markovian approximation by assuming that two-body collisions are local in both space and time, in accordance with Boltzmann`s original treatment. This simplification is usually justified by the fact that the duration of a two-body collision is short on the time scale characteristic of the macroscopic evolution of the system. As a result, transport properties of the collective motion has then a classical character. However, when the system possesses fast collective modes with characteristic energies that are not small in comparision with the temperature, then the quantum-statistical effects are important and the standard Markovian treatment is inadequate. In this case, it is necessary to improve the one-body transport model by including the memory effect due to the finite duration of two-body collisions. First we briefly describe the non-Markovian extension of the BL model by including the finite memory time associated with two-body collisions. Then, using this non-Markovian model in a linear response framework, we investigate the effect of the memory time on the agitation of unstable modes in nuclear matter in the spinodal zone, and calculate the collisional relaxation rates of nuclear collective vibrations.
Date: March 1, 1996
Creator: Ayik, S.
Partner: UNT Libraries Government Documents Department

Polarization of atomic radiation in stochastic plasma fields

Description: When a laser pulse of certain polarization or an electron beam excites atoms in a plasma, the atomic spectrum of the radiation emitted by the atoms exhibits differently polarized line core and line wings. This unusual effect, which is predicted to occur under a variety of conditions, can be accompanied by the appearance of the forbidden component in the spectrum, with polarization opposite to that of the exciting laser pulse.
Date: May 12, 1997
Creator: Savchenko, V.I. & Fisch, N.J.
Partner: UNT Libraries Government Documents Department

Algorithms for fusion of multiple sensors having unknown error distributions

Description: The authors presented recent results on a general sensor fusion problem, where the underlying sensor error distributions are not known, but a sample is available. They presented a general method for obtaining a fusion rule based on scale-sensitive dimension of the function class. Two computationally viable methods are reviewed based on the Nadaraya-Watson estimator, and the finite dimensional vector spaces. Several computational issues of the fusion rule estimation are open problems. It would be interesting to obtain necessary and sufficient conditions under which polynomial-time algorithms can be used to solve the fusion rule estimation problem under the criterion. Also, conditions under which the composite system is significantly better than best sensor would be extremely useful. Finally, lower bound estimates for various sample sizes will be very important in judging the optimality of sample size estimates.
Date: June 1, 1997
Creator: Rao, N. S. V.
Partner: UNT Libraries Government Documents Department

Structural model uncertainty in stochastic simulation

Description: Prediction uncertainty in stochastic simulation models can be described by a hierarchy of components: stochastic variability at the lowest level, input and parameter uncertainty at a higher level, and structural model uncertainty at the top. It is argued that a usual paradigm for analysis of input uncertainty is not suitable for application to structural model uncertainty. An approach more likely to produce an acceptable methodology for analyzing structural model uncertainty is one that uses characteristics specific to the particular family of models.
Date: September 1, 1997
Creator: McKay, M.D. & Morrison, J.D.
Partner: UNT Libraries Government Documents Department

Linear kinetic theory and particle transport in stochastic mixtures. Third year and final report, June 15, 1993--December 14, 1996

Description: The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results.
Date: May 1, 1997
Creator: Pomraning, G.C.
Partner: UNT Libraries Government Documents Department