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Teses / dissertações sobre o tema "Bernoulli systems"
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1
Bishop, Michael Anthony. "Quantum Systems in Bernoulli Potentials". Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293431.
Texto completo da fonteResumo:
Quantum mechanics is a theory developed to explain both particle and wave-like properties of small matter such as light and electrons. The consequences of the theory can be counter-intuitive but lead to mathematical and physical theory rich in fascinating phenomena and challenging questions. This dissertation investigates the nature of quantum systems in Bernoulli distributed random potentials for systems on the one dimensional lattice {0, 1, ..., L, L+1} ⊂ Z in the large system limit L → ∞. For single particle systems, the behavior of the low energy states is shown to be approximated by systems where positive potential is replaced by infinite potential. The approximate shape of these states is described, the asymptotics of their eigenvalues are calculated in the large system limit L → ∞, and a Lifschitz tail estimate on the sparsity of low energy states is proven. For interacting multi-particle systems, a Lieb-Liniger model with Bernoulli distributed potential is studied in the Gross-Pitaevskii approximation. First, to investigate localization in these settings, a general inequality is proven to bound from below the support of the mean-field. The bound depends on the per particle energy, number of particles, and interaction strength. Then, the ground state for the one-dimensional lattice with Bernoulli potential is studied in the large system limit. Specifically, the case where the product of interaction strength and particle density is near zero is considered to investigate whether localization can be recovered.
2
Komori, Yasushi, Kohji Matsumoto e Hirofumi Tsumura. "Zeta and L-functions and Bernoulli polynomials of root systems". Japan Academy, 2008. http://hdl.handle.net/2237/13843.
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3
Tillich, Daniel, e Christoph Lehmann. "Estimation in discontinuous Bernoulli mixture models applicable in credit rating systems with dependent data". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-222582.
Texto completo da fonteResumo:
Objective:
We consider the following problem from credit risk modeling: Our sample (Xi; Yi), 1 < i < n, consists of pairs of variables. The first variable Xi measures the creditworthiness of individual i. The second variable Yi is the default indicator of individual i. It has two states: Yi = 1 indicates a default, Yi = 0 a non-default. A default occurs, if individual i cannot meet its contractual credit obligations, i. e. it cannot pay back its outstandings regularly. In afirst step, our objective is to estimate the threshold between good and bad creditworthiness in the sense of dividing the range of Xi into two rating classes: One class with good creditworthiness and a low probability of default and another class with bad creditworthiness and a high probability of default.
Methods:
Given observations of individual creditworthiness Xi and defaults Yi, the field of change point analysis provides a natural way to estimate the breakpoint between the rating classes. In order to account for dependency between the observations, the literature proposes a combination of three model classes: These are a breakpoint model, a linear one-factor model for the creditworthiness Xi, and a Bernoulli mixture model for the defaults Yi. We generalize the dependency structure further and use a generalized link between systematic factor and idiosyncratic factor of creditworthiness. So the systematic factor cannot only change the location, but also the form of the distribution of creditworthiness.
Results:
For the case of two rating classes, we propose several estimators for the breakpoint and for the default probabilities within the rating classes. We prove the strong consistency of these estimators in the given non-i.i.d. framework. The theoretical results are illustrated by a simulation study. Finally, we give an overview of research opportunities.
4
Tsumura, Hirofumi, Kohji Matsumoto e Yasushi Komori. "A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems". Research Institute for Mathematical Sciences , Kyoto University, 2011. http://hdl.handle.net/2237/20334.
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5
Liu, Yang. "MODELING AND ANALYSIS OF SPLIT AND MERGE PRODUCTION SYSTEMS". UKnowledge, 2008. http://uknowledge.uky.edu/gradschool_theses/523.
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Many production systems have split and merge operations to increase production capac- ity and variety, improve product quality, and implement product control and scheduling policies. This thesis presents analytical methods to model and analyze split and merge production systems with Bernoulli and exponential reliability machines under circulate, priority and percentage policies. The recursive procedures for performance analysis are de- rived, and the convergence of the procedures and uniqueness of the solutions, along with the structural properties, are proved analytically, and the accuracy of the estimation is justi¯ed numerically with high precision. In addition, comparisons among the e®ects of di®erent policies in system performance are carried out.
6
Tsumura, Hirofumi, Kohji Matsumoto e Yasushi Komori. "On Witten multiple zeta-functions associated with semisimple Lie algebras II". 日本数学会, 2010. http://hdl.handle.net/2237/20065.
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Evans, Katie Allison. "Reduced Order Controllers for Distributed Parameter Systems". Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11063.
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Distributed parameter systems (DPS) are systems defined on infinite dimensional spaces. This includes problems governed by partial differential equations (PDEs) and delay differential equations. In order to numerically implement a controller for a physical system we often first approximate the PDE and the PDE controller using some finite dimensional scheme. However, control design at this level will typically give rise to controllers that are inherently large-scale. This presents a challenge since we are interested in the design of robust, real-time controllers for physical systems. Therefore, a reduction in the size of the model and/or controller must take place at some point. Traditional methods to obtain lower order controllers involve reducing the model from that for the PDE, and then applying a standard control design technique. One such model reduction technique is balanced truncation. However, it has been argued that this type of method may have an inherent weakness since there is a loss of physical information from the high order, PDE approximating model prior to control design. In an attempt to capture characteristics of the PDE controller before the reduction step, alternative techniques have been introduced that can be thought of as controller reduction methods as opposed to model reduction methods. One such technique is LQG balanced truncation. Only recently has theory for LQG balanced truncation been developed in the infinite dimensional setting. In this work, we numerically investigate the viability of LQG balanced truncation as a suitable means for designing low order, robust controllers for distributed parameter systems. We accomplish this by applying both balanced reduction techniques, coupled with LQG, MinMax and central control designs for the low order controllers, to the cable mass, Klein-Gordon, and Euler-Bernoulli beam PDE systems. All numerical results include a comparison of controller performance and robustness properties of the closed loop systems.Ph. D.
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Baruah, Monita. "Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations". Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/14524.
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The purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs.
9
Khalaf, Rehab F. "On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys". Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6416.
Texto completo da fonteResumo:
This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study.
10
Tartibu, Kwanda. "A simplified analysis of the vibration of variable length blade as might be used in wind turbine systems". Thesis, Cape Peninsula University of Technology, 2008. http://hdl.handle.net/20.500.11838/1244.
Texto completo da fonteResumo:
Vibration is an inherent phenomenon in dynamic mechanical systems. The work undertaken in this thesis is to identify natural frequencies of a variable length blade. Therefore designers can ensure that natural frequencies will not be close to the frequency (or integer multiples) of the main excitation forces in order to avoid resonance. For a wind turbine blade, the frequency range between 0.5 Hz and 30 Hz is relevant. The turbine blade is approximated by a cantilever, therefore, it is fully constrained where attached to a turbine shaft/hub. Flap-wise, edge-wise and torsional natural frequencies are calculated.
The MATLAB program “BEAMANALYSIS.m” has been developed for the finite element analysis of a one dimensional model of the beam. Similarly, a three dimensional model of the beam has been developed in a finite element program Unigraphics NX5. The results found using the MATLAB program are compared with those found with NX5. Satisfactory agreement between the results is found for frequencies up to almost 500 Hz. Additionally, the frequencies one might expect in an experiment are identified.
Experimental modal analysis has been performed on a uniform and stepped beam made of mild steel to extract the first five flap-wise natural frequencies. The results found have been compared to numerical results and the exact solution of an Euler-Bernoulli beam. Concurrence is found for the frequency range of interest. Although, some discrepancies exist at higher frequencies (above 500 Hz), finite element analysis proves to be reliable for calculating natural frequencies.
Finally, the fixed portion and moveable portion of the variable length blade are approximated respectively by a hollow and a solid beam which can be slid in and out. Ten different configurations of the variable length blade, representing ten different positions of the moveable portion are investigated. A MATLAB program named VARIBLADEANALYSIS.m was developed to predict natural frequencies. Similarly three dimensional models of the variable length blade have been developed in the finite element program Unigraphics NX5.This work was supported by the Research office of CPUT.
11
Hidalgo, Francisco Luiz Campos. "Quantificação da incerteza do problema de flexão estocástica de uma viga de Euler-Bernoulli, apoiada em fundação de Pasternak, utilizando o método estocástico de Galerkin e o método dos elementos finitos estocásticos". Universidade Tecnológica Federal do Paraná, 2014. http://repositorio.utfpr.edu.br/jspui/handle/1/1069.
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Este trabalho apresenta uma metodologia, baseada no método de Galerkin, para quantificar a incerteza no problema de flexão estocástica da viga de Euler-Bernoulli repousando em fundação de Pasternak. A incerteza nos coeficientes de rigidez da viga e da fundação é representada por meio de processos estocásticos parametrizados. A limitação em probabilidade dos parâmetros randômicos e a escolha adequada do espaço de soluções aproximadas, necessárias à posterior demonstração de unicidade e existência do problema, são consideradas por meio de hipóteses teóricas. O espaço de soluções aproximadas de dimensão finita é construído pelo produto tensorial entre espaços (determinístico e randômico), obtendo-se um espaço denso no espaço das soluções teóricas. O esquema de Wiener-Askey dos polinômios do caos generalizados é utilizado na representação do processo estocástico de deslocamento da viga. O método dos elementos finitos estocásticos é apresentado e empregado na solução numérica de exemplos selecionados. Os resultados, em termos de momentos estatísticos, são comparados aos obtidos por meio de simulações de Monte Carlo.This study presents a methodology, based on the Galerkin method, to quantify the uncertainty in the stochastic bending problem of an Euler-Bernoulli beam resting on a Pasternak foundation. The uncertainty in the stiffness coefficients of the beam and foundation is represented by parametrized stochastic processes. The probability limitation on the random parameters and the choice of an appropriated approximate solution space, necessary for the subsequent demonstration of uniqueness and existence of the problem, are considered by means of theoretical hypothesis. The finite dimensional space of approximate solutions is built by tensor product between spaces (deterministic and randomic), obtaining a dense space in the theoretical solution space. The Wiener-Askey scheme of generalizes chaos polynomials is used to represent the stochastic process of the beam deflection. The stochastic finite element method is presented and employed in the numerical solution of selected examples. The results, in terms of statistical moments, are compared to results obtained through Monte Carlo simulations.
12
Schnellmann, Daniel. "Viana maps and limit distributions of sums of point measures". Phd thesis, KTH, Matematik (Inst.), 2009. http://tel.archives-ouvertes.fr/tel-00694201.
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This thesis consists of five articles mainly devoted to problems in dynamical systems and ergodic theory. We consider non-uniformly hyperbolic two dimensional systems and limit distributions of point measures which are absolutely continuous with respect to the Lebesgue measure. Let $f_{a_0}(x)=a_0-x^2$ be a quadratic map where the parameter $a_0\in(1,2)$ is chosen such that the critical point $0$ is pre-periodic (but not periodic). In Papers A and B we study skew-products $(\th,x)\mapsto F(\th,x)=(g(\th),f_{a_0}(x)+\al s(\th))$, $(\th,x)\in S^1\times\real$. The functions $g:S^1\to S^1$ and $s:S^1\to[-1,1]$ are the base dynamics and the coupling functions, respectively, and $\al$ is a small, positive constant. Such quadratic skew-products are also called Viana maps. In Papers A and B we show for several choices of the base dynamics and the coupling function that the map $F$ has two positive Lyapunov exponents and for some cases we further show that $F$ admits also an absolutely continuous invariant probability measure. In Paper C we consider certain Bernoulli convolutions. By showing that a specific transversality property is satisfied, we deduce absolute continuity of the to these Bernoulli convolutions associated distributions. In Papers D and E we consider sequences of real numbers in the unit interval and study how they are distributed. The sequences in Paper D are given by the forward iterations of a point $x\in[0,1]$ under a piecewise expanding map $T_a:[0,1]\to[0,1]$ depending on a parameter $a$ contained in an interval $I$. Under the assumption that each $T_a$ admits a unique absolutely continuous invariant probability measure $\mu_a$ and that some technical conditions are satisfied, we show that the distribution of the forward orbit $T_a^j(x)$, $j\ge1$, is described by the distribution $\mu_a$ for Lebesgue almost every parameter $a\in I$. In Paper E we apply the ideas in Paper D to certain sequences which are equidistributed in the unit interval and give a geometrical proof of an old result by Koksma.
13
Benzoni, Séverin. "Classification des filtrations dynamiques et étude des systèmes d'entropie positive". Electronic Thesis or Diss., Normandie, 2024. https://theses.hal.science/tel-04835404.
Texto completo da fonteResumo:
Dans cette thèse, nous explorons les structures possibles des systèmes dynamiques de la forme $\bfX :=(X, \A, \mu, T)$ et leurs tribus facteur $\B \subset \A$. Les deux premiers chapitres étudient les différentes façons dont une tribu facteur $\B$ peut s'inclure dans un système dynamique $\bfX :=(X, \A, \mu, T)$, c'est-à-dire que nous étudions certaines structures possibles de l'\emph{extension} $\A \arr \B$. Dans le premier chapitre, nous considérons les concepts de \emph{super-innovations} et de \emph{standardité} des extensions, inspirés de la théorie des filtrations. Un point important est l'introduction de la notion d'\emph{extensions confinées}, qui nous intéressent parce qu'elles n'ont pas de super-innovation. Nous donnons plusieurs exemples et étudions des propriétés supplémentaires de ces extensions, y compris des résultats de relèvement. Ensuite, nous montrons notre résultat principal : l'existence d'extensions non-standard. Enfin, ce résultat trouve une application dans l'étude des filtrations dynamiques, qui sont les filtrations de la forme $(\F_n)_{n \leq 0}$ telles que chaque $\F_n$ est une tribu facteur. Nous montrons qu'il existe des \emph{filtrations dynamiques I-confortables non standard}.Le deuxième chapitre approfondit l'étude des extensions confinées en trouvant un nouveau type de telles extensions, dans le cadre des suspensions de Poisson : nous prenons un système dynamique $(X, \mu, T)$ en mesure $\s$-finie infinie et une extension compacte $(X \times G, \mu \otimes m_G, T_\phi)$, puis nous considérons l'extension de Poisson correspondante $((X \times G)^*, (\mu \otimes m_G)^*, (T_\phi)_*) \to (X^*, \mu^*, T_*)$. Nous donnons des conditions sous lesquelles cette extension est confinée et construisons un exemple qui correspond à ces conditions.Enfin, le troisième chapitre se concentre sur une famille de filtrations dynamiques : les \emph{filtrations de Pinsker faible}. L'existence de ces filtrations sur tout système ergodique provient d'un résultat récent d'Austin \cite{austin}, et elles se présentent comme un outil potentiel pour décrire les systèmes à entropie positive. Nous explorons les liens entre la structure asymptotique des filtrations de Pinsker faible et les propriétés du système dynamique sous-jacent. Naturellement, nous demandons aussi si, sur un système donné, la structure des filtrations de Pinsker faible est unique à isomorphisme près. Nous donnons une réponse partielle, dans le cas où le système sous-jacent est un schéma de Bernoulli. Nous concluons notre travail en donnant deux exemples explicites de filtrations de Pinsker faibleIn this thesis, we explore the possible structures of measure preserving dynamical systems of the form $\bfX :=(X, \A, \mu, T)$ and their factor $\s$-algebras $\B \subset \A$. The first two chapters investigate various ways in which a factor $\s$-algebra $\B$ can sit in a dynamical system $\bfX :=(X, \A, \mu, T)$, i.e. we study some possible structures of the \emph{extension} $\A \arr \B$. In the first chapter, we consider the concepts of \emph{super-innovations} and \emph{standardness} of extensions, which are inspired from the theory of filtrations. An important focus of our work is the introduction of the notion of \emph{confined extensions}, which first interested us because they have no super-innovation. We give several examples and study additional properties of confined extensions, including several lifting results. Then, we show our main result: the existence of non-standard extensions. Finally, this result finds an application to the study of dynamical filtrations, i.e. filtrations of the form $(\F_n)_{n \leq 0}$ such that each $\F_n$ is a factor $\s$-algebra. We show that there exist \emph{non-standard I-cosy dynamical filtrations}.The second chapter furthers the study of confined extensions by finding a new kind of such extensions, in the setup of Poisson suspensions: we take an infinite $\s$-finite measure-preserving dynamical system $(X, \mu, T)$ and a compact extension $(X \times G, \mu \otimes m_G, T_\phi)$, then we consider the corresponding Poisson extension $((X \times G)^*, (\mu \otimes m_G)^*, (T_\phi)_*) \to (X^*, \mu^*, T_*)$. We give conditions under which that extension is confined and build an example which fits those conditions.Lastly, the third chapter focuses on a family of dynamical filtrations: \emph{weak Pinsker filtrations}. The existence of those filtrations on any ergodic system comes from a recent result by Austin \cite{austin}, and they present themselves as a potential tool to describe positive entropy systems. We explore the links between the asymptotic structure of weak Pinsker filtrations and the properties of the underlying dynamical system. Naturally, we also ask whether, on a given system, the structure of weak Pinsker filtrations is unique up to isomorphism. We give a partial answer, in the case where the underlying system is Bernoulli. We conclude our work by giving two explicit examples of weak Pinsker filtrations
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Gautam, S. Vijay. "Performance Analysis Of A Variation Of The Distributed Queueing Access Protocol". Thesis, Indian Institute of Science, 1995. https://etd.iisc.ac.in/handle/2005/149.
Texto completo da fonteResumo:
"A distributed queueing Medium Access Control (MAC) protocol is used in Distributed Queue Dual Bus (DQDB) networks. A modified version of the MAC protocol was proposed by R.R. Pillai and U. Mukherji in an attempt to overcome some of the shortcomings of the DQDB MAC protocol. They analyzed the performance of the system for Bernoulli arrivals and for large propagation delays between the nodes. We extend the performance analysis of the modified MAC protocol for a DQDB type of Network. The parameter of interest to us is the bus access delay. This has two components, viz., the request bus access delay and the data bu6 access delay. We use the model at the request point at node and present methods to evaluate the delay experienced in such a model. The model is an n-priority ./D/l queue with D vacations (non-preemptive priority) where n is the number of nodes sending requests on the request bus for transmission on the data bus. The methods presented help to evaluate the request bus access delay when the arrivals at each node are Markovian Arrival Processes (MAPs). The algorithms for evaluating the mean request bus access delay are based on matrix geometric techniques. Thus, one can use the algorithms developed in the literature to solve for the finite buffers case too. This model, for the request bus access delay, holds irrespective of the propagation delay between the nodes.
We also evaluate the inter-departure time of class 1 customers and virtual customers in a 2-priority M/G/l system with G vacations (non-preemptive priority). In the case of Poisson arrivals at all the nodes, we would have a 2-priority M/D/l system with D vacations (non-preemptive priority). We thus evaluate the inter-arrival time of the free slots on the data bus as seen by Node 2. Note that this is independent of the number of active nodes in the network
We then develop methods to evaluate the mean data bus access delay experienced by the customers at Node 2 in a three-node network with 2 nodes communicating with the third when the propagation delay between the nodes is large. We consider the case of finite Local Queue buffers at the two nodes. Using this assumption we arrive at process of arrivals to the Combined Queue and the process of free slots on the data bus to be Markov Modulated Bernoulli processes. The model at the combined queue at Node 2 then has a Quasi Birth-Death evolution. Thus, this system is solved by using the Ramaswami-Latouche algorithm. The stationary probabilities are then used to evaluate the mean data bus access delay experienced at Node 2. The finite buffer case of this system can be solved by G.Wi Stewart's algorithm. The method in modelling the system and the results are presented in detail for Poisson arrivals. The extension of this to more complex processes is also explained. We encounter in the analysis an explosion of the state-space of the system. We try to counter this by considering approximations to the process of free slots on the data bus. The approximations considered are on the basis of what are known as Idealized Aggregates. The performance of the approximation is also detailed. It works very well under low and moderate load but underestimates the mean delay under heavy load.
Thereafter, we discuss the performance of the system with reference to the mean of the access delay and the standard deviation of the access delay under varying traffic at the two nodes. For this part we use simulation results to discuss the performance. The comparison between the performance measures at both the nodes is also done.
Then we develop methods/techniques to understand the performance of the system when we have finite propagation delays between the nodes. We concentrate on the 3-node problem and calculate performance bounds based on linear programs. This is illustrated in detail for Bernoulli arrivals for the case of 1 slot propagation delay between the nodes as well as for the case of 2 slots propagation delay. The performance of the bounds obtained is also detailed. The presence of an idling system at the combined queue of Node 2 makes the bounds somewhat loose. Finally, we discuss the performance of the system with reference to the mean access delay and the standard deviation of the access delay under varying load on the system. Again, we rely on simulation studies.
Finally, we study the performance of the system as a multiplexer. For this, we restrict the traffic to Markov Modulated Processes (or those which would satisfy the Gartner-Ellis Theorem requirements). The traffic is characterized by what are known as Envelope Processes - Lower and Upper. The class of processes which satisfy the conditions of the
Gartner-Ellis theorem come under the category where both the Envelope Processes exist and the Minimum Envelope Rate and the Maximum Lower Envelope Rate are the same. We use the system evolution equations at the combined queue at any node to develop relations between the various input and output processes. First, this is done for a. system of this kind, in isolation. Then, we consider this system as a part of the modified protocol and present relations, among the various input and output processes, which are specific to the modified protocol. The possible use of all of the above to do Admission Control at the entry point to the Asynchronous Transfer Mode (ATM) network is also presented.
15
Gautam, S. Vijay. "Performance Analysis Of A Variation Of The Distributed Queueing Access Protocol". Thesis, Indian Institute of Science, 1995. http://hdl.handle.net/2005/149.
Texto completo da fonteResumo:
"A distributed queueing Medium Access Control (MAC) protocol is used in Distributed Queue Dual Bus (DQDB) networks. A modified version of the MAC protocol was proposed by R.R. Pillai and U. Mukherji in an attempt to overcome some of the shortcomings of the DQDB MAC protocol. They analyzed the performance of the system for Bernoulli arrivals and for large propagation delays between the nodes. We extend the performance analysis of the modified MAC protocol for a DQDB type of Network. The parameter of interest to us is the bus access delay. This has two components, viz., the request bus access delay and the data bu6 access delay. We use the model at the request point at node and present methods to evaluate the delay experienced in such a model. The model is an n-priority ./D/l queue with D vacations (non-preemptive priority) where n is the number of nodes sending requests on the request bus for transmission on the data bus. The methods presented help to evaluate the request bus access delay when the arrivals at each node are Markovian Arrival Processes (MAPs). The algorithms for evaluating the mean request bus access delay are based on matrix geometric techniques. Thus, one can use the algorithms developed in the literature to solve for the finite buffers case too. This model, for the request bus access delay, holds irrespective of the propagation delay between the nodes.
We also evaluate the inter-departure time of class 1 customers and virtual customers in a 2-priority M/G/l system with G vacations (non-preemptive priority). In the case of Poisson arrivals at all the nodes, we would have a 2-priority M/D/l system with D vacations (non-preemptive priority). We thus evaluate the inter-arrival time of the free slots on the data bus as seen by Node 2. Note that this is independent of the number of active nodes in the network
We then develop methods to evaluate the mean data bus access delay experienced by the customers at Node 2 in a three-node network with 2 nodes communicating with the third when the propagation delay between the nodes is large. We consider the case of finite Local Queue buffers at the two nodes. Using this assumption we arrive at process of arrivals to the Combined Queue and the process of free slots on the data bus to be Markov Modulated Bernoulli processes. The model at the combined queue at Node 2 then has a Quasi Birth-Death evolution. Thus, this system is solved by using the Ramaswami-Latouche algorithm. The stationary probabilities are then used to evaluate the mean data bus access delay experienced at Node 2. The finite buffer case of this system can be solved by G.Wi Stewart's algorithm. The method in modelling the system and the results are presented in detail for Poisson arrivals. The extension of this to more complex processes is also explained. We encounter in the analysis an explosion of the state-space of the system. We try to counter this by considering approximations to the process of free slots on the data bus. The approximations considered are on the basis of what are known as Idealized Aggregates. The performance of the approximation is also detailed. It works very well under low and moderate load but underestimates the mean delay under heavy load.
Thereafter, we discuss the performance of the system with reference to the mean of the access delay and the standard deviation of the access delay under varying traffic at the two nodes. For this part we use simulation results to discuss the performance. The comparison between the performance measures at both the nodes is also done.
Then we develop methods/techniques to understand the performance of the system when we have finite propagation delays between the nodes. We concentrate on the 3-node problem and calculate performance bounds based on linear programs. This is illustrated in detail for Bernoulli arrivals for the case of 1 slot propagation delay between the nodes as well as for the case of 2 slots propagation delay. The performance of the bounds obtained is also detailed. The presence of an idling system at the combined queue of Node 2 makes the bounds somewhat loose. Finally, we discuss the performance of the system with reference to the mean access delay and the standard deviation of the access delay under varying load on the system. Again, we rely on simulation studies.
Finally, we study the performance of the system as a multiplexer. For this, we restrict the traffic to Markov Modulated Processes (or those which would satisfy the Gartner-Ellis Theorem requirements). The traffic is characterized by what are known as Envelope Processes - Lower and Upper. The class of processes which satisfy the conditions of the
Gartner-Ellis theorem come under the category where both the Envelope Processes exist and the Minimum Envelope Rate and the Maximum Lower Envelope Rate are the same. We use the system evolution equations at the combined queue at any node to develop relations between the various input and output processes. First, this is done for a. system of this kind, in isolation. Then, we consider this system as a part of the modified protocol and present relations, among the various input and output processes, which are specific to the modified protocol. The possible use of all of the above to do Admission Control at the entry point to the Asynchronous Transfer Mode (ATM) network is also presented.
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Chidurala, Manohar. "Dynamic Characteristics of Biologically Inspired Hair Receptors for Unmanned Aerial Vehicles". ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2040.
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The highly optimized performance of nature’s creations and biological assemblies has inspired the development of their engineered counter parts that can potentially outperform conventional systems. In particular, bat wings are populated with air flow hair receptors which feedback the information about airflow over their surfaces for enhanced stability and maneuverability during their flight. The hairs in the bat wing membrane play a role in the maneuverability tasks, especially during low-speed flight. The developments of artificial hair sensors (AHS) are inspired by biological hair cells in aerodynamic feedback control designs. Current mathematical models for hair receptors are limited by strict simplifying assumptions of creeping flow hair Reynolds number on AHS fluid-structure interaction (FSI), which may be violated for hair structures integrated on small-scaled Unmanned Aerial Vehicles (UAVs). This study motivates by an outstanding need to understand the dynamic response of hair receptors in flow regimes relevant to bat-scaled UAVs. The dynamic response of the hair receptor within the creeping flow environment is investigated at distinct freestream velocities to extend the applicability of AHS to a wider range of low Reynolds number platforms. Therefore, a threedimensional FSI model coupled with a finite element model using the computational fluid dynamics (CFD) is developed for a hair-structure and multiple hair-structures in the airflow. The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. The grid independence of the FSI solution is studied from the simulations of the hairstructure mesh and flow mesh around the hair sensor. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the finite element model, are compared with the excitation frequencies in vacuum. This model is described with both the boundary layer effects and effects of inertial forces due to fluid-structure xiv interaction of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow.
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Barrachina, Sergio, Peter Benner e Enrique S. Quintana-Ortí. "Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign Function". Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601684.
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We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
18
Rollet, Marc. "Etude des applications du procede flash aux systemes d'ecoute passive et optimisation par deconvolution bernoulli-gaussienne". Cergy-Pontoise, 1997. http://www.theses.fr/1997CERG0032.
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Le sujet de cette these a concerne l'etude des applications d'un nouveau procede aux systemes d'ecoute passive et son optimisation par une technique de deconvolution standard. Ce travail a comporte deux phases. La premiere a traite de l'application d'un nouveau concept denomme flash a l'ecoute passive large bande de signaux radars dans le domaine hyperfrequence. Dans un premier temps, apres une definition du contexte d'emploi, une technique de goniometrie par balayage electronique a ete etudiee. Apres avoir analyse l'analogie avec le concept flash, des proprietes ont ete mises en evidence et plusieurs scenarii ont ete envisages. Dans un second temps, la meme demarche a ete menee pour l'etude d'un frequencemetre large bande. Les differents cas de figure rencontres ont enfin fait l'objet de simulations numeriques qui ont debouche sur des conclusions partielles. La deuxieme phase a alors consiste a etudier l'emploi d'une technique de deconvolution multi-impulsionnelle pour ameliorer les resultats et la robustesse des dispositifs sous des contraintes de rsb degrades. La demarche, incrementale dans l'integration des contraintes, a mene mutatis mutandis a l'adaptation et l'implementation d'un algorithme bayesien de deconvolution bernoulli-gaussienne. Les resultats obtenus ont revele un fort gain en termes de performances.
19
Ngo, Quoc hoan. "Double régularisation des polyzêtas en les multi-indices négatifs et extensions rationnelles". Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCD023/document.
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Dans ce travail, nous nous intéressons aux problèmes relatifs aux polylogarithmes et aux sommes harmoniques pris en les multiindices négatifs(au sens large, appelés dans la suite non-positifs) et en les indices mixtes. Notre étude donnera des résultats généraux sur ces objets en relation avec les algèbres de Hopf. Les techniques utilisées sont basées sur la combinatoire des séries formelles non commutatives, formes linéaires sur l’algèbre de Hopf de φ−Shuffle. Notre travail donnera aussi un processus global pour renormaliser les polyzetâs divergents. Enfin, nous appliquerons les structures mises en évidence aux systèmes dynamiques non linéaires avec entrées singulièresIn this memoir are studied the polylogarithms and the harmonic sums at non-positive (i.e. weakly negative) multi-indices. General results about these objects in relation with Hopf algebras are provided. The technics exploited here are based on the combinatorics of non commmutative generating series relative to the Hopf φ−Shuffle algebra. Our work will also propose a global process to renormalize divergent polyzetas. Finally, we will apply these ideas to non-linear dynamical systems with singular inputs
20
Fustini, Lorenzo. "Mechatronic solutions in agritech: design of post-harvesting robotic system for strawberries and prototyping of mobile soil-testing platform". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.
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Il settore agro-alimentare sta diventando un notevole business per le industrie a causa del crescente interesse per il concetto di sicurezza alimentare e della necessità di nutrire il mondo globale. In particolare, il Regno Unito ha investito considerevoli risorse nella ricerca e nello sviluppo per ottimizzare la produttività: questo lavoro di tesi si inserisce in quest’ambito. In particolare le soluzioni meccatroniche analizzate, vertono su due diversi casi di studio:
• la progettazione di un’innovativa linea di confezionamento per le fragole;
• sviluppo di una piattaforma mobile per il test del suolo.
Il primo progetto, in collaborazione con Berry Gardens, azienda leader nel Regno Unito nel commercio della frutta rossa, consiste nel ri-progettare una linea di confezionamento fragole. Partendo da un attuatore di Bernoulli, lo studio preliminare si è concentrato sulla progettazione di una nuova generazione di manipolatori in grado di minimizzare i danni sul prodotto, con annessi relativi test per valutare le sue potenzialità. Inoltre, è stata sviluppata una stazione di trattamento UV in grado di trattare fragole su entrambe le superfici per massimizzare l’effetto di decontaminazione. Infine è stata presentata la soluzione finale della linea di confezionamento.
Il secondo progetto, in collaborazione con l'università norvegese University of Life Sciences, ha come obiettivo quello di assemblare una piattaforma composta dal robot mobile Thorvald II sviluppato dall'Università norvegese, e un robot cartesiano, prodotto dalla società SMC, al fine di costituire una piattaforma mobile autonoma per l’analisi del suolo.
Entrambi i progetti sono stati sviluppati presso l'Università di Lincoln, Regno Unito, con la collaborazione di School of Engineering, School of Computer Science, Lincoln Institute for Agri-Food Technology (LIAT) e di partner industriali dell'Università.
21
Bergtold, Jason Scott. "Advances in Applied Econometrics: Binary Discrete Choice Models, Artificial Neural Networks, and Asymmetries in the FAST Multistage Demand System". Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/27266.
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The dissertation examines advancements in the methods and techniques used in the field of econometrics. These advancements include: (i) a re-examination of the underlying statistical foundations of statistical models with binary dependent variables. (ii) using feed-forward backpropagation artificial neural networks for modeling dichotomous choice processes, and (iii) the estimation of unconditional demand elasticities using the flexible multistage demand system with asymmetric partitions and fixed effects across time.
The first paper re-examines the underlying statistical foundations of statistical models with binary dependent variables using the probabilistic reduction approach. This re-examination leads to the development of the Bernoulli Regression Model, a family of statistical models arising from conditional Bernoulli distributions. The paper provides guidelines for specifying and estimating a Bernoulli Regression Model, as well as, methods for generating and simulating conditional binary choice processes. Finally, the Multinomial Regression Model is presented as a direct extension.
The second paper empirically compares the out-of-sample predictive capabilities of artificial neural networks to binary logit and probit models. To facilitate this comparison, the statistical foundations of dichotomous choice models and feed-forward backpropagation artificial neural networks (FFBANNs) are re-evaluated. Using contingent valuation survey data, the paper shows that FFBANNs provide an alternative to the binary logit and probit models with linear index functions. Direct comparisons between the models showed that the FFBANNs performed marginally better than the logit and probit models for a number of within-sample and out-of-sample performance measures, but in the majority of cases these differences were not statistically significant. In addition, guidelines for modeling contingent valuation survey data and techniques for estimating median WTP measures using FFBANNs are examined.
The third paper estimates a set of unconditional price and expenditure elasticities for 49 different processed food categories using scanner data and the flexible and symmetric translog (FAST) multistage demand system. Due to the use of panel data and the presence of heterogeneity across time, temporal fixed effects were incorporated into the model. Overall, estimated price elasticities are larger, in absolute terms, than previous estimates. The use of disaggregated product groupings, scanner data, and the estimation of unconditional elasticities likely accounts for these differences.Ph. D.
22
Pace, Michele. "Stochastic models and methods for multi-object tracking". Phd thesis, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651396.
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La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.
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Favuzzi, Pedro Antonio. "Ab-initio design methods for selective and efficient optomechanical control of nanophotonic structures". 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/185207.
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24
Ammari, Kaïs. "Stabilisation d'une classe d'équations d'évolution du deuxième ordre en temps". Palaiseau, Ecole polytechnique, 2000. http://www.theses.fr/2000EPXX0001.
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Les methodes utilisees pour la stabilisation des systemes d'equations aux derivees partielles sont variees et necessitent des techniques fines d'analyse mathematiques. Dans le cas de systemes de dimension finie avec capteurs et actionneurs co-localises, il est connu que la stabilisabilite est equivalente a la controlabilite exacte du systeme. Ce resultat a ete generalise par a. Haraux pour les systemes de dimension infinie, avec l'hypothese que l'operateur de controle est borne. Le principal resultat de ma these est de generaliser ce resultat a une classe d'operateurs de controle non bornes. Ce type de resultat a des nombreux applications. En effet, au lieu de traiter directement la stabilisabilite, on peut etudier la controlabilite exacte qui en general un probleme plus aise.
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NDRECA, SOKOL. "Queueing models for air traffic". Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/1113.
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In this thesis we study
some queueing models that are worthwhile to
understand the air-traffic congestion.
From the point of view of classical queueing theory the air traffic
system is difficult to study, mainly because it is hard even to define
the basic quantities of the theory.
The system becomes complex, since there are a many factor, that
influence the air-traffic like weather conditions, technical problems,
air turbulences caused by the different types of aircrafts.
Thus is necessary to investigate the
impact of the arrivals of aircraft on air traffic.
A common hypothesis in literature is to assume that the arrivals of
aircrafts are very well modeled by a Poisson process. This assumption
is suitable for mathematical modelling,
due to the memoryless property of Poisson process that simplifies
the study of congestion in such systems.
Our first goal is to study the
property of a model of the arrival process to a system
and to compare its features to the Poisson process.
We will show in this work why
the Poissonian hypothesis for air-traffic is doomed to failure
even if the Poisson process is very similar to our process
if it is observed on a time scale sufficiently short.
We found interesting connections of this model with the statistical
mechanics of Fermi particles.
Once one understands the properties of arrival process to the system,
to study its evolution we use the theory of Markov chain.
Our second goal is
the study of the stochastic properties of other queueing systems,
relevant in the applications,
where the arrivals are described according general independent
stochastic process and the service is delivered according to various
disciplines. This
corresponds to the study of the stationary measure of a Markov chain.
In order to find the stationary distribution of such Markov chain we use
the generating function technique.
Part of this thesis is a discussion of the criteria usually presented
in literature to evaluate the goodness of various approximation
schemes. It will turn out, actually, that the generating function is
not always possible to compute explicitly, and some numerical
procedures are necessary in order to compute the relevant quantities
of the system.In questa tesi studiamo dei modelli di coda che sono utili per capire la congestione del traffico aereo. Dal punto di vista della teoria delle code classica e' difficile studiare il sistema del traffico aereo, soprattutto perche' e' complesso definire le quantita' di base della teoria. Il sistema diventa complesso, poiche' ci sono molti fattori che influiscano sul traffico aereo, ad esempio le condizioni meteo, problemi tecnici, le turbolenze dell'aria causate da diversi tipi di aeromobili. Quindi per capire il traffico aereo diventa necessario studiare la distribuzione degli arrivi degli aeroplani. In letteratura l'ipotesi comune e' di assumere che gli arrivi degli aeroplani sono descritti molto bene dal processo di Poisson. Questa assunzione e' adatto per i modelli matematici, per la proprieta' di assenza di memoria del processo di Poisson che semplifica lo studio della congestione in tale sistema. Il primo obiettivo di questa tesi e' di studiare le proprieta' di un processo degli arrivi degli aeromobili al sistema e di confrontare tale processo con il processo di Poisson. In questo lavoro mostriamo come l'ipotesi Poissoniana per il traffico aereo e' destinato a fallire anche se il processo Poissoniano e' molto simile al nostro modello degli arrivi se viene osservato su una scala di tempo opportunamente corta. Troviamo poi, nella trattazione del nostro processo, una connessione interessante del nostro modello con la meccanica statistica di Fermioni. Una volta comprese le proprieta' del processo degli arrivi al sistema, per studiare la sua evoluzione usiamo la teoria Markoviana. Il secondo obiettivo di questa tesi e' lo studio delle proprieta' stocastiche di altri sistemi di coda, sempre rilevanti nelle applicazioni, in cui gli arrivi sono generali ma indipendenti, e discipline di servizio particolari rendono non banale lo studio della distribuzione stazionaria della catena. Questo corrisponde a studiare la misura stazionaria di certe catene di Markov. Per trovare la distribuzione stazionaria usiamo il metodo della funzione generatrice. Una parte di questa tesi e' la discussione dei criteri, di solito presentati in letteratura, per valutare l'ottimalita' dei vari schemi di approssimazione.
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De, la Rue Thierry. "Quelques résultats sur les systèmes dynamiques gaussiens réels". Rouen, 1994. https://tel.archives-ouvertes.fr/tel-01546012.
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Le premier chapitre de cette thèse établit que l'entropie d'un système dynamique gaussien est soit nulle, soit infinie, suivant respectivement que sa mesure spectrale est singulière ou non par rapport à la mesure de Lebesgue. Ce résultat est étendu au cas d'une action multidimensionnelle. Dans le second chapitre, on développe un nouveau modèle pour les systèmes gaussiens, qui sont vus comme une transformation de la trajectoire brownienne plane. Cette transformation peut être insérée dans un flot, pour lequel on calcule un mouvement moyen. Ce modèle est utilisé dans le troisième chapitre pour construire deux systèmes gaussiens d'entropie nulle non équivalents au sens de Kakutani: l'un n'est pas lâchement Bernoulli, alors que l'autre, qui est un gaussien-Kronecker, est lâchement Bernoulli. Pour cela, on a aussi besoin de montrer une propriété du mouvement brownien plan: certains angles formes par les accroissements du brownien suffisent pour reconstituer toute la trajectoire
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Shih, Chien-Cheng, e 施建成. "Performance Analysis of Variable Speed Pump Systems by Applying Bernoulli Equation". Thesis, 2014. http://ndltd.ncl.edu.tw/handle/tn778e.
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碩士國立臺北科技大學
能源與冷凍空調工程系碩士班
102
The energy consumed by air conditioning system for general commercial building is about 40~50% of the total energy consumption, therefore, there is still a lot of room for energy saving on air conditioning system. Popular energy saving method includes using variable air volume for fan system and using variable water volume for pump system. The system speed will adjust air and water volume according to the loading to optimize energy consumption. Fan and pump of air conditioning system are both in the field of fluid mechanics where fan affinity laws and pump affinity laws are applicable. There is a cubic relationship between the shaft horsepower in theoretical affinity law and the shaft horsepower in variable air volume and variable water volume. However, in reality, the difference between real shaft horsepower and theoretical shaft horsepower is significant. This study will simulate and calculate the energy consumption at one operating point in an air conditioning variable speed pump piping system and come up with the energy consumption in all operating points in the system by using Bernoulli''s equation. The result will be compared with the theoretical energy consumption calculated by using pump affinity laws and derive a formula for the energy consumption of air conditioning variable speed pump piping system.
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Gong, Xiang. "CONSENSUS ANALYSIS ON NETWORKED MULTI-AGENT SYSTEMS WITH STOCHASTIC COMMUNICATION LINK FAILURE". Thesis, 2013. http://hdl.handle.net/10222/21379.
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This thesis is to develop a novel consensus algorithm or protocol for multi-agent systems in the event of communication link failure over the network. The structure or topology of the system is modeled by an algebraic graph theory, and defined as a discrete time-invariant system with a second-order dynamics. The communication link failure is governed by a Bernoulli process. Lyapunov-based methodologies and Linear Matrix Inequality (LMI) techniques are then applied to find an appropriate controller gain by satisfying the sufficient conditions of the error dynamics. Therefore, the controller with the calculated gain is guaranteed to drive the system to reach a consensus. Finally, simulation and experiment studies are carried out by using two Mobile Robot Pioneer 3-DXs and one Pioneer 3-AT as a team to verify the proposed work.
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Κωστοπούλου, Καλλιρρόη. "Αριθμός ροών επιτυχιών και αξιοπιστία συνεχόμενων συστημάτων αποτυχίας". Thesis, 2007. http://nemertes.lis.upatras.gr/jspui/handle/10889/721.
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Θεωρούμε μια ακολουθία από n δυαδικά πειράματα. Ροή επιτυχιών μήκους k είναι μια ακολουθία από k συνεχόμενες επιτυχίες οι οποίες έπονται και ακολουθούνται από αποτυχίες ή τίποτα. Στην εργασία αυτή αρχικά μελετάται η τυχαία μεταβλητή Ν(n,k) η οποία παριστάνει τον αριθμό των ροών επιτυχιών μήκους k σε n δυαδικά πειράματα. Προσδιορίζεται η ακριβής κατανομή μέσω συνδιαστικών μεθόδων, αναδρομικών σχέσεων και μέσω της μεθόδου εμβάπτισης τυχαίας μεταβλητής σε Μαρκοβιανή αλυσίδα. Η μελέτη γίνεται για ανεξάρτητες και ισόνομες και για ανεξάρτητες όχι κατ’ ανάγκην ισόνομες δυαδικές ακολουθίες. Μελετάται επίσης η τυχαία μεταβλητή M(n,k)η οποία παριστάνει τον αριθμό των ροών επιτυχιών τουλάχιστον k σε n δυαδικά πειράματα.
Ένα συνεχόμενο-k -από-τα-n:F σύστημα αποτυχίας είναι ένα σύστημα n συνιστωσών το οποίο αποτυγχάνει αν και μόνο αν αποτύχουν τουλάχιστον k συνεχόμενες συνιστώσες του. Τα συνεχόμενα-k-από-τα-n:F συστήματα αποτυχίας έχουν προταθεί ως κατάλληλα πρότυπα για συστήματα μεταφοράς πετρελαίου, τηλεπικοινωνιακά συστήματα κ.α. Ένα m-συνεχόμενο-k-από-τα-n:F σύστημα αποτυχίας είναι ένα σύστημα n συνιστωσών το οποίο αποτυγχάνει αν και μόνο αν υπάρχουν τουλάχιστον m ροές από k συνεχόμενες αποτυχημένες συνιστώσες του. Μελετάται η σχέση της αξιοπιστίας των ανωτέρω συστημάτων με τη συνάρτηση πιθανότητας και τη συνάρτηση κατανομής της τυχαίας μεταβλητής N(n,k). Αναπτύσσονται οι μέθοδοι που έχουν δοθεί για τον προσδιορισμό της αξιοπιστίας τους και δίνονται ακριβείς εκφράσεις της μέσω πολυωνυμικών συντελεστών, διωνυμικών συντελεστών, αναδρομικών σχέσεων και της μεθόδου εμβάπτισης σε Μαρκοβιανή αλυσίδα. Η μελέτη γίνεται για συστήματα με ανεξάρτητες συνιστώσες, γαι συστήματα με ομογενή Μαρκοβιανή εξάρτηση ενός βήματος και για συστήματα με Μαρκοβιανά εξαρτημένες συνιστώσες (k-1) βημάτων. Τέλος παρουσιάζονται αριθμητικά παραδείγματα για περαιτέρω διευκρίνηση και σύγκριση των μεθόδων υπολογισμού της κατανομής της N(n,k) και της αξιοπιστίας των ανωτέρω συστημάτων αποτυχιών.Consider a sequence of n two state (success-failure) trials. A success run of length k is a sequence of k consecutive successes proceeded and succeeded by failures or nothing. In this thesis the random variable N(n,k) denoting the number of success runs of length k in n binary trials is studied. The exact distribution of N(n,k) is given, via combinatorial analysis, recursive relations and using the Markov chain imbedding technique. The study is carried out for independent but not identically distributed binary sequences. Further, the random variable M(n,k)denoting the number of success runs of length at least k in n binary trials is also studied. A consecutive-k-out-of-n : F system is a system which consists of n components ordered on a line, which fails if and only if at least k consecutive components fail. Such systems have been used to model telecommunication, oil pipeline systems e.t.c. An m-consecutive-k -out-of-n : F system consists of n components ordered on a line, which fails if and only if there are at least m non-overlapping runs of k consecutive failed components. The reliability of the above mentioned systems is related to the cumulative distribution function of the random variable N(n,k) . Exact formulae for the reliability is given by means of binomial and multinomial coefficients, via recursive relations and using the Markov chain imbedding technique. The study is accomplished for systems with independent and Markov dependent components. Finally, numerical examples are given for comparison of the various used methods and to illustrate the theoretical results.
30
Kvěš, Martin. "Rekurentní vlastnosti součinů a skosných součinů konečně stavových náhodných procesů". Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-331711.
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In this work, we study return and hitting times in measure-preserving dy- namical systems. We consider a special type of skew-products of two Bernoulli schemes, called a random walk in random scenery. For these systems, the limit distribution of normalized hitting times for cylinders of increasing length is proved to be exponential under the assumption of finite variance of the first order dis- tribution of the Bernoulli scheme representing the walk, and provided the drift is non-zero or the scenery alphabet is finite. Mixing properties of the skew-products are discussed in order to relate our work with some known results on rescaled hitting times for strongly-mixing systems. 1
31
Mahaffey, Patrick Brian. "Bending, Vibration and Buckling Response of Conventional and Modified Euler-Bernoulli and Timoshenko Beam Theories Accounting for the von Karman Geometric Nonlinearity". Thesis, 2013. http://hdl.handle.net/1969.1/151319.
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Beams are among the most commonly used structural members that are encountered in virtually all systems of structural design at various scales. Mathematical models used to determine the response of beams under external loads are deduced from the three-dimensional elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. The kinematic assumptions exploit the fact that such structures do not experience significant trans- verse normal and shear strains and stresses. For example, the solution of the three- dimensional elasticity problem associated with a straight beam is reformulated as a one-dimensional problem in terms of displacements whose form is presumed on the basis of an educated guess concerning the nature of the deformation.
In many cases beam structures are subjected to compressive in-plane loads that may cause out-of-plane buckling of the beam. Typically, before buckling and during compression, the beam develops internal axial force that makes the beam stiffer. In the linear buckling analysis of beams, this internal force is not considered. As a result the buckling loads predicted by the linear analysis are not accurate. The present study is motivated by lack of suitable theory and analysis that considers the nonlinear effects on the buckling response of beams.
This thesis contains three new developments: (1) the conventional beam theories are generalized by accounting for nonlinear terms arising from εzz and εxz that are of the same magnitude as the von K´arm´an nonlinear strains appearing in εxx. The equations of motion associated with the generalized Euler–Bernoulli and Timoshenko beam theories with the von K´arm´an type geometric nonlinear strains are derived using Hamilton’s principle. These equations form the basis of investigations to determine certain microstructural length scales on the bending, vibration and buckling response of beams used in micro- and nano-devices. (2) Analytical solutions of the conventional Timoshenko beam theory with the von K´arm´an nonlinearity are de- veloped for the case where the inplane inertia is negligible when compared to other terms in the equations of motion. Numerical results are presented to bring out the effect of transverse shear deformation on the buckling response. (3) The development of a nonlinear finite element model for post-buckling behavior of beams.
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Lahey, Timothy John. "Modelling the Dynamics of Mass Capture". Thesis, 2013. http://hdl.handle.net/10012/7505.
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This thesis presents an approach to modelling dynamic mass capture which is applied to a number of system models. The models range from a simple 2D Euler-Bernoulli beam with point masses for the end-effector and target to a 3D Timoshenko beam model (including torsion) with rigid bodies for the end-effector and target. In addition, new models for torsion, as well as software to derive the finite element equations from first principles were developed to support the modelling. Results of the models are compared to a simple experiment as done by Ben Rhody. Investigations of offset capture are done by simulation to show why one would consider using a 3D model that includes torsion.
These problems have relevance to both terrestrial robots and to space based robotic systems such as the manipulators on the International Space Station capturing payloads such as the SpaceX Dragon capsule. One could increase production in an industrial environment if industrial robots could pick up items without having to establish a zero relative velocity between the end effector and the item. To have a robot acquire its payload in this way would introduce system dynamics that could lead to the necessity of modelling a previously ‘rigid’ robot as flexible.