Academic literature on the topic 'Discrete step walk'
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Journal articles on the topic "Discrete step walk"
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Chisaki, Kota, Norio Konno, Etsuo Segawa, and Yutaka Shikano. "Crossovers induced by discrete-time quantum walks." Quantum Information and Computation 11, no. 9&10 (September 2011): 741–60. http://dx.doi.org/10.26421/qic11.9-10-2.
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We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in some limits. At first we generalize our previous study [Phys. Rev. A \textbf{81}, 062129 (2010)] on the DTQW with position measurements. We show that the position measurements per each step with probability $p \sim 1/n^\beta$ can be evaluated, where $n$ is the final time and $0<\beta<1$. We also give a corresponding continuous-time case. As a consequence, crossovers from the diffusive spreading (random walk) to the ballistic spreading (quantum walk) can be seen as the parameter $\beta$ shifts from 0 to 1 in both discrete- and continuous-time cases of the weak convergence theorems. Secondly, we introduce a new class of the DTQW, in which the absolute value of the diagonal parts of the quantum coin is proportional to a power of the inverse of the final time $n$. This is called a final-time-dependent DTQW (FTD-DTQW). The CTQW is obtained in a limit of the FTD-DTQW. We also obtain the weak convergence theorem for the FTD-DTQW which shows a variety of spreading properties. Finally, we consider the FTD-DTQW with periodic position measurements. This weak convergence theorem gives a phase diagram which maps sufficiently long-time behaviors of the discrete- and continuous-time quantum and random walks.
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Eon, Nathanaël, Giuseppe Di Molfetta, Giuseppe Magnifico, and Pablo Arrighi. "A relativistic discrete spacetime formulation of 3+1 QED." Quantum 7 (November 8, 2023): 1179. http://dx.doi.org/10.22331/q-2023-11-08-1179.
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This work provides a relativistic, digital quantum simulation scheme for both 2+1 and 3+1 dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step Δt=Δx. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.
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Lal, Ram, and U. Narayan Bhat. "Correlated random walks with stay." Journal of Applied Mathematics and Simulation 1, no. 3 (January 1, 1988): 197–222. http://dx.doi.org/10.1155/s1048953388000152.
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A random walk describes the movement of a particle in discrete time, with the direction and the distance traversed in one step being governed by a probability distribution. In a correlated random walk (CRW) the movement follows a Markov chain and induces correlation in the state of the walk at various epochs. Then, the walk can be modelled as a bivariate Markov chain with the location of the particle and the direction of movement as the two variables. In such random walks, normally, the particle is not allowed to stay at one location from one step to the next. In this paper we derive explicit results for the following characteristics of the CRW when it is allowed to stay at the same location, directly from its transition probability matrix: (i) equilibrium solution and the fast passage probabilities for the CRW restricted on one side, and (ii) equilibrium solution and first passage characteristics for the CRW restricted on bath sides (i.e., with finite state space).
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Katzenbeisser, W., and W. Panny. "Simple random walk statistics. Part I: Discrete time results." Journal of Applied Probability 33, no. 2 (September 1996): 311–30. http://dx.doi.org/10.2307/3215056.
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In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.
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Katzenbeisser, W., and W. Panny. "Simple random walk statistics. Part I: Discrete time results." Journal of Applied Probability 33, no. 02 (June 1996): 311–30. http://dx.doi.org/10.1017/s0021900200099745.
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In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.
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Michelitsch, Thomas M., Federico Polito, and Alejandro P. Riascos. "Semi-Markovian Discrete-Time Telegraph Process with Generalized Sibuya Waiting Times." Mathematics 11, no. 2 (January 16, 2023): 471. http://dx.doi.org/10.3390/math11020471.
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In a recent work we introduced a semi-Markovian discrete-time generalization of the telegraph process. We referred to this random walk as the ‘squirrel random walk’ (SRW). The SRW is a discrete-time random walk on the one-dimensional infinite lattice where the step direction is reversed at arrival times of a discrete-time renewal process and remains unchanged at uneventful time instants. We first recall general notions of the SRW. The main subject of the paper is the study of the SRW where the step direction switches at the arrival times of a generalization of the Sibuya discrete-time renewal process (GSP) which only recently appeared in the literature. The waiting time density of the GSP, the ‘generalized Sibuya distribution’ (GSD), is such that the moments are finite up to a certain order r≤m−1 (m≥1) and diverging for orders r≥m capturing all behaviors from broad to narrow and containing the standard Sibuya distribution as a special case (m=1). We also derive some new representations for the generating functions related to the GSD. We show that the generalized Sibuya SRW exhibits several regimes of anomalous diffusion depending on the lowest order m of diverging GSD moment. The generalized Sibuya SRW opens various new directions in anomalous physics.
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Fayard, Patrick, and Timothy R. Field. "Discrete Models for Scattering Populations." Journal of Applied Probability 48, no. 1 (March 2011): 285–92. http://dx.doi.org/10.1239/jap/1300198150.
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Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.
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Fayard, Patrick, and Timothy R. Field. "Discrete Models for Scattering Populations." Journal of Applied Probability 48, no. 01 (March 2011): 285–92. http://dx.doi.org/10.1017/s0021900200007774.
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Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.
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ORENSHTEIN, TAL, and IGOR SHINKAR. "Greedy Random Walk." Combinatorics, Probability and Computing 23, no. 2 (November 20, 2013): 269–89. http://dx.doi.org/10.1017/s0963548313000552.
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We study a discrete time self-interacting random process on graphs, which we call greedy random walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not yet been crossed by the walker. At each step, the walker, being at some vertex, picks an adjacent edge among the edges that have not traversed thus far according to some (deterministic or randomized) rule. If all the adjacent edges have already been traversed, then an adjacent edge is chosen uniformly at random. After picking an edge the walker jumps along it to the neighbouring vertex. We show that the expected edge cover time of the greedy random walk is linear in the number of edges for certain natural families of graphs. Examples of such graphs include the complete graph, even degree expanders of logarithmic girth, and the hypercube graph. We also show that GRW is transient in$\mathbb{Z}^d$for alld≥ 3.
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Hajri, Hatem. "On the csáki-vincze transformation." Studia Scientiarum Mathematicarum Hungarica 50, no. 2 (June 1, 2013): 266–79. http://dx.doi.org/10.1556/sscmath.50.2013.2.1240.
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Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T. We prove that T is exact: ∩k≧1σ(Tk(S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scaling limit, all iterations of T “converge” to the corresponding iterations of the continuous Lévy transform of Brownian motion.
Dissertations / Theses on the topic "Discrete step walk"
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El, Sokhen Rabih. "Two-dimensional topological properties of photonic mesh lattices subject to discrete step walks." Electronic Thesis or Diss., Université de Lille (2022-....), 2024. http://www.theses.fr/2024ULILR067.
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Cette thèse explore expérimentalement et numériquement les invariants de volume et de bord dans un réseau photonique synthétique 2D soumis à des marches discrètes. Le réseau est réalisé par multiplexage temporal d'impulsions lumineuses dans deux anneaux de fibres optiques de longueurs inégales, couplés à un coupleur variable (VBS). Dans cette configuration, une dimension présente une dynamique dans l'espace réel, tandis que l'autre est gouvernée par un modulateur de phase externe (PM). En utilisant la détection hétérodyne, nous accédons aux informations spectrales et mesurons les valeurs propres et les vecteurs propres, ce qui permet d'extraire les invariants de volume tels que la courbure de Berry et le nombre de Chern associés aux bandes photoniques. De plus, nous dérivons une expression pour le nombre d'enroulement et démontrons que l'émergence des états de bord est liée à des frontières géométriques spécifiques. Enfin, nous soulignons l'impact de la topologie des bords sur la topologie globale du système, qui peut soit supprimer soit induire la présence d'états de bordThis thesis presents experimental and numerical investigations into bulk and edge invariants within a 2D synthetic photonic lattice subjected to discrete step walks. The lattice is engineered by time-multiplexing light pulses in two unequal-length optical fiber rings coupled with a variable beam splitter (VBS). In this configuration, one dimension exhibits real-space dynamics, while the other is governed by an external phase modulator (PM). Employing heterodyne detection, we access spectral information and measure eigenvalues and eigenvectors, enabling the extraction of bulk invariants such as Berry curvature and Chern number associated with the photonic bands. Furthermore, we derive an expression for the winding number and demonstrate that the emergence of edge states is tied to specific geometric boundaries. Finally, we highlight the impact of edge topology on the overall system topology, which can either suppress or induce the presence of edge states
Books on the topic "Discrete step walk"
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Sokolov, I. M., and J. Klafter. First Steps in Random Walks: From Tools to Applications. Oxford University Press, 2011.
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Klafter, J. First Steps in Random Walks: From Tools to Applications. Oxford University Press, 2016.
Find full textBook chapters on the topic "Discrete step walk"
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Atkins, Peter, Julio de Paula, and Ronald Friedman. "Probability theory." In Physical Chemistry: Quanta, Matter, and Change. Oxford University Press, 2013. http://dx.doi.org/10.1093/hesc/9780199609819.003.0072.
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Probability theory deals with quantities and events that are distributed randomly and shows how to calculate average values of various kinds. We shall consider variables that take discrete values (as in a one-dimensional random walk with a fixed step length) and continuous values (as...
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Dewey, T. Gregory. "Encoded Walks and Correlations in Sequence Data." In Fractals In Molecular Biophysics, 187–206. Oxford University PressNew York, NY, 1998. http://dx.doi.org/10.1093/oso/9780195084474.003.0008.
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Abstract The statistical analysis of sequence data has generated ongoing interest. The statistical properties of nucleic acid and protein sequences (see Doolittle, 1990; Volkenstein, 1994) provides important information on both the evolution and thermodynamic stability of biomacromolecules. In addition to conventional statistical approaches (for reviews, see, Karlin et al. (1991) and White (1994), fractal analyses of DNA and protein sequences have: given new insight into sequence correlations (Peng et al., 1992; Voss, 1992; Buldyrev et al., 1993; Dewey, 1993; Pande et al., 1994; Balafas and Dewey, 1995). In this chapter, we consider such analyses. They represent a problem in discrete dynamics very different from those discussed in the previous chapter. Lattice walks can be constructed from sequence information in a variety of ways. These encoded walks result from assigning a specific numerical value and spatial direction to the members in the sequence. For instance, in DNA problems it is common to give purines a+ 1 step on a one-dimensional lattice and pyrimidines a—1 step (Peng et al., 1992; Voss, 1992; Buldyrev et al., 1993). Similar walks have been studied in protein sequences and have been based on a specific chemical or physical property of the monomeric unit (Pande et al., 1994). The resulting trajectories of these encoded walks can be analyzed as diffusion problems. Deviation of the encoded walk from random behavior provides evidence for long-range correlations.
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Zinn-Justin, Jean. "The random walk: Universality and continuum limit." In From Random Walks to Random Matrices, 1–12. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0001.
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The first chapter discusses the asymptotic properties at large time and space of the familiar example of the random walk. The universality of a large scale behaviour and, correspondingly, the existence of a macroscopic continuum limit emerge as collective properties of systems involving a large number of random variables whose individual distribution is sufficiently localized. These properties, as well as the appearance of an asymptotic Gaussian distribution when the random variables are statistically independent, are illustrated with the simple example of the random walk with discrete time steps. The emphasis here is on locality, universality, continuum limit, path integral, Brownian motion, Gaussian distribution and scaling. These properties are first derived from an exact solution and then recovered by renormalization group (RG) methods. This makes it possible to introduce all the RG terminology.
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Zinn-Justin, Jean. "The Higgs boson: A major discovery and a problem." In From Random Walks to Random Matrices, 195–208. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0012.
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Chapter 12 describes the main steps in the construction of the electroweak component of the Standard Model of particle physics. The classical Abelian Landau–Ginzburg–Higgs mechanism is recalled, first introduced in the macroscopic description of a superconductor in a magnetic field. It is based on a combination of spontaneous symmetry breaking and gauge invariance. It can be generalized to non–Abelian gauge theories, quantized and renormalized. The recent discovery of the predicted Higgs boson has been the last confirmation of the validity of the model. Some aspects of the Higgs model and its renormalization group (RG) properties are illustrated by simplified models, a self–interacting Higgs model with the triviality issue, and the Gross–Neveu–Yukawa model with discrete chiral symmetry, which illustrates spontaneous fermion mass generation and possible RG flows.
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Douglas, Raymond S., and Robert A. Goldberg. "Evaluation and Spectrum of Orbital Diseases." In Surgery of the Eyelid, Lacrimal System, and Orbit. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780195340211.003.0024.
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Although orbital disorders are not frequently encountered in the comprehensive ophthalmologist’s practice, it is essential to be able to diagnose patients with orbital disease and manage them accordingly. Various disease processes can affect the orbit. This chapter endeavors to provide a thoughtful, stepwise, and logical approach to the evaluation of orbital disease. The discussion begins with differential diagnosis, adds an intelligent history-taking and physical examination, and then focuses on efficient use of diagnostic tests to finally arrive at the correct diagnosis. The staging and management of two common orbital disorders, orbital inflammation and thyroid-associated ophthalmopathy, will also be discussed. The differential diagnosis of orbital disease is extensive, and most listings of orbital disease divide the causes between histopathologic and mechanistic categories. This type of grouping is intellectually sound and scientifically useful but does not provide a framework that the clinical practitioner can easily grasp and directly use in sorting through the differential diagnosis of any given patient. In broad terms, orbital disease can be considered in terms of location, extent, and biologic activity. The classification used in this chapter is broken down along clinical lines and takes advantage of the fact that the orbit has a somewhat limited repertoire of ways that it can respond to pathologic conditions. Orbital disease can be categorized into five basic clinical patterns: inflammatory, mass effect, structural, vascular, and functional. Although many cases cross over into several categories, the vast majority of clinical presentations fit predominantly into one of these patterns. As the clinician walks through each step of the evaluation process—history, physical examination, laboratory testing, orbital imaging—a conscious effort should be made to categorize the presentation within this framework. If the practitioner approaches orbital disease with this framework of discrete patterns of clinical presentation, then at every step of the diagnostic pathway (history, physical examination, orbital imaging studies, and special tests), he or she can draw from a defined set of differential diagnoses that characterize each pattern of orbital disease and use that information to efficiently and confidently orchestrate diagnosis and management.
Conference papers on the topic "Discrete step walk"
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Bhounsule, Pranav A., Ezra Ameperosa, Scott Miller, Kyle Seay, and Rico Ulep. "Dead-Beat Control of Walking for a Torso-Actuated Rimless Wheel Using an Event-Based, Discrete, Linear Controller." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59563.
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In this paper, we present dead-beat control of a torso-actuated rimless wheel model. We compute the steady state walking gait using a Poincaré map. When disturbed, this walking gait takes a few steps to cancel the effect of the disturbance but our goal is to develop a faster response. To do this, we develop an event-based, linear, discrete controller designed to cancel the effect of the disturbance in a single step — a one-step dead-beat controller. The controller uses the measured deviation of the stance leg velocity at mid-stance to set the torso angle to get the wheel back to the limit cycle at the following step. We show that this linear controller can correct for a height disturbance up to 3% leg length. The same controller can be used to transition from one walking speed to another in a single step. We make the model-based controller insensitive to modeling errors by adding a small integral term allowing the robot to walk blindly on a 7° uphill incline and tolerate a 30% added mass. Finally, we report preliminary progress on a hardware prototype based on the model.
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Shulman, Ami, and Jorge Soto-Andrade. "A random walk in stochastic dance." In LINK 2021. Tuwhera Open Access, 2021. http://dx.doi.org/10.24135/link2021.v2i1.71.
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Stochastic music, developed last century by Xenakis, has older avatars, like Mozart, who showed how to compose minuets by tossing dice, in a similar way that contemporary choreographer Cunningham took apart the structural elements of what was considered to be a cohesive choreographic work (including movement, sound, light, set and costume) and reconstructed them in random ways. We intend to explore an enactive and experiential analogue of stochastic music, in the realm of dance, where the poetry of a choreographic spatial/floor pattern is elicited by a mathematical stochastic process, to wit a random walk – a stochastic dance of sorts. Among many possible random walks, we consider two simple examples, embodied in the following scenarios, proposed to the students/dancers: - a frog, jumping randomly on a row of stones, choosing right and left as if tossing a coin, - a person walking randomly on a square grid, starting a given node, and choosing each time randomly, equally likely N, S, E or W, and walking non-stop along the corresponding edge, up to the next node, and so on.When the dancers encounter these situations, quite natural questions arise for the choreographer, like: Where will the walker/dancer be after a while? Several ideas for a choreography emerge, which are more complex than just having one or more dancers perform the random walk, and which surprisingly turn our random process into a deterministic one!For instance, for the first random walk, 16 dancers start at the same node of a discrete line on the stage, and execute, each one, a different path of the 16 possible 4 – jump paths the frog can follow. They would need to agree first on how to carry this out. Interestingly, they may proceed without a Magister Ludi handing out scripts to every dancer. After arriving to their end node/position, they could try to retrace their steps, to come back all to the starting node.Analogously for the grid random walk, where we may have now 16 dancers enacting the 16 possible 2-edge paths of the walker. The dancers could also enter the stage (the grid or some other geometric pattern to walk around), one by one, sequentially, describing different random paths, or deterministic intertwined paths, in the spirit of Beckett’s Quadrat. Also, the dancers could choose their direction ad libitum, after some spinning, each time, on a grid-free stage, but keeping the same step length, as in statistician Pearson’s model for a mosquito random flight.We are interested in various possible spin-offs of these choreographies, which intertwine dance and mathematical cognition: For instance, when the dancers choose each one a different path, they will notice that their final distribution on the nodes is uneven (interesting shapes emerge). In this way, just by moving, choreographer and dancers can find a quantitative answer to the impossible question: where will the walker/dancer be after a while? Indeed, the percentage of dancers ending up at each node gives the probability of the random walker landing there.
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Vadgama, Nikul, Marios Kapsis, Peter Forsyth, Matthew McGilvray, and David R. H. Gillespie. "Development and Validation of a Continuous Random Walk Model for Particle Tracking in Accelerating Flows." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-16026.
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Abstract Stochastic particle tracking models coupled to RANS fluid simulations are frequently used to simulate particulate transport and hence predict component damage in gas turbines. In simple flows the Continuous Random Walk (CRW) model has been shown to model particulate motion in the diffusion-impaction regime significantly more accurately than Discrete Random Walk implementations. To date, the CRW model has used turbulent flow statistics determined from DNS in channels and experiments in pipes. Robust extension of the CRW model to accelerating flows modelled using RANS is important to enable its use in design studies of rotating engine-realistic geometries of complex curvature. This paper builds on previous work by the authors to use turbulent statistics in the CRW model directly from Reynolds Stress Models (RSM) in RANS simulations. Further improvements are made to this technique to account for strong gradients in Reynolds Stresses in all directions; improve the robustness of the model to the chosen time-step; and to eliminate the need for DNS/experimentally derived statistical flow properties. The effect of these changes were studied using a commercial CFD solver for a simple pipe flow, for which integral deposition prediction accuracy equal to that using the original CRW was achieved. These changes enable the CRW to be applied to more complex flow cases. To demonstrate why this development is important, in a more complex flow case with acceleration, deposition in a turbulent 90° bend was investigated. Critical differences in the predicted deposition are apparent when the results are compared to the alternative tracking models suitable for RANS solutions. The modified CRW model was the only model which captured the more complex deposition distribution, as predicted by published LES studies. Particle tracking models need to be accurate in the spatial distribution of deposition they predict in order to enable more sophisticated engineering design studies.
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Forsyth, Peter, David R. H. Gillespie, Matthew McGilvray, and Vincent Galoul. "Validation and Assessment of the Continuous Random Walk Model for Particle Deposition in Gas Turbine Engines." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57332.
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Threats to engine integrity and life from deposition of environmental particulates that can reach the turbine cooling systems (i.e. <10 micron) have become increasing important within the aero-engine industry, with an increase of flight paths crossing sandy, tropical storm-infested, or polluted airspaces. This has led to studies in the turbomachinery community investigating environmental particulate deposition, largely applying the Discrete Random Walk (DRW) model in CFD simulations of air paths. However, this model was conceived to model droplet dispersion in bulk flow regimes, and therefore has fundamental limitations for deposition studies. One significant limitation is an insensitivity to particle size in the turbulent deposition size regime, where deposition is strongly linked to particle size. This is highlighted within this study through comparisons to published experimental data. Progress made within the wider particulate deposition community has recently led to the development and application of the Continuous Random Walk (CRW) model. This new model provides significantly improved predictions of particle deposition seen experimentally in comparison to the DRW for low temperature pipe flow experiments. However, the CRW model is not without its difficulties. This paper highlights the sensitivities within the CRW model and actions taken to alleviate them where possible. For validation of the model at gas turbine conditions, it should be assessed at engine-representative conditions. These include high-temperature and swirling flows, with thermophoretic and wall-roughness effects. Thermophoresis is a particle force experienced in the negative direction of the temperature gradient, and can strongly effect deposition efficiency from certain flows. Previous validation of the model has centred on low temperatures and pipe flow conditions. Presented here is the validation process which is currently being undertaken to assess the model at gas turbine-relevant conditions. Discussion centres on the underlying principles of the model, how to apply this model appropriately to gas turbine flows and initial assessment for flows seen in secondary air systems. Verification of model assumptions is undertaken, including demonstrating that the effect of boundary layer modelling of anisotropic turbulence is shown to be Reynolds-independent. The integration time step for numerical solution of the non-dimensional Langevin equation is redefined, showing improvement against existing definitions for the available low temperature pipe flow data. The grid dependence of particle deposition in numerical simulations is presented and shown to be more significant for particle conditions in the diffusional deposition regime. Finally, the model is applied to an engine-representative geometry to demonstrate the improvement in sensitivity to particle size that the CRW offers over the DRW for wall-bounded flows.
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Klobas, Nina, George B. Mertzios, Hendrik Molter, Rolf Niedermeier, and Philipp Zschoche. "Interference-free Walks in Time: Temporally Disjoint Paths." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/563.
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We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically increasing time steps. Two paths (or walks) are temporally disjoint if they never use the same vertex at the same time; otherwise, they interfere. This reflects applications in robotics, traffic routing, or finding safe pathways in dynamically changing networks. On the one extreme, we show that on general graphs the problem is computationally hard. The "walk version" is W[1]-hard when parameterized by the number of routes. However, it is polynomial-time solvable for any constant number of walks. The "path version" remains NP-hard even if we want to find only two temporally disjoint paths. On the other extreme, restricting the input temporal graph to have a path as underlying graph, quite counterintuitively, we find NP-hardness in general but also identify natural tractable cases.
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Lee, Dongjun, and Ke Huang. "On Passive Non-Iterative Variable-Step Numerical Integration of Mechanical Systems for Haptic Rendering." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2257.
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This paper consists of three parts. First, with a slightly-different, yet, more physically-plausible, discrete supply-rate (i.e. power), we propose a non-iterative (i.e. fast) and variable-step numerical integration algorithm for (scalar) discrete-passive mechanical systems, consisting of constant mass and damper, and a certain class of nonlinear spring. In the second part, we propose a fast passive collision handling algorithm with a spring-damper type virtual wall, which, to detect exact time of contacts, requires at most three intermediate non-iterative computations within each integration-step. We then propose a way of how to passively connect this discrete-passive, non-iterative, and variable-step mechanical integrators (with passive collision handling) to a continuous haptic device.
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Kunz, Pascal, Hendrik Molter, and Meirav Zehavi. "In Which Graph Structures Can We Efficiently Find Temporally Disjoint Paths and Walks?" In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/21.
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A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do not visit any vertex at the same time. The study of the computational complexity of finding temporally disjoint paths or walks in temporal graphs has recently been initiated by Klobas et al.. This problem is motivated by applications in multi-agent path finding (MAPF), which include robotics, warehouse management, aircraft management, and traffic routing. We extend Klobas et al.’s research by providing parameterized hardness results for very restricted cases, with a focus on structural parameters of the so-called underlying graph. On the positive side, we identify sufficiently simple cases where we can solve the problem efficiently. Our results reveal some surprising differences between the “path version” and the “walk version” (where vertices may be visited multiple times) of the problem, and answer several open questions posed by Klobas et al.
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Taylor, Robert P., J. Keith Taylor, M. H. Hosni, and Hugh W. Coleman. "Heat Transfer in the Turbulent Boundary Layer With a Step Change in Surface Roughness." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-266.
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Measurements of Stanton numbers, velocity profiles, temperature profiles, and turbulence intensity profiles are reported for turbulent flat plate boundary layer flows with a step change in surface roughness. The first 0.9 m length of the test surface is roughened with 1.27 mm diameter hemispheres spaced 2 base diameters apart in a staggered array. The remaining 1.5 m length is smooth. The experiments show that the step change from a rough to a smooth surface has a dramatic effect on the convective heat transfer. In many cases, the Stanton number drops below the smooth-wall correlation immediately downstream of the change in roughness. The Stanton number measurements are compared with predictions using the discrete element method with excellent results.
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Andreoli, Valeria, David G. Cuadrado, and Guillermo Paniagua. "Prediction of the Turbine Tip Convective Heat Flux Using Discrete Green Functions." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64080.
Full textAbstract:
The complex heat and mass transfer across the turbine tip gap requires a detailed analysis which cannot be expressed using the classical Newton heat convection approach. In this portion of the turbine, characterized by tight moving clearances, pressure gradients are counterbalanced by viscous effects. Hence, non-dimensional analysis, based on the boundary layer, is inadequate and therefore the use of an adiabatic wall temperature is questionable. In this paper, we propose an alternative approach to predict the convective heat transfer problem across the turbine rotor tip using Discrete Green Functions. The linearity of the energy equation can be applied with a superposition technique to measure the data extracted from flow simulations to determine the Green’s function distribution. The Discrete Green Function is a matrix of coefficients that relate the increment of temperature observed in a surface with the heat flux integrated on the same surface. These coefficients are independent on the inlet temperature of the flow and are associated to the geometry. The controlled surface is discretized into cells and each cell is associated to a vector of coefficients. The Discrete Green Function coefficients are calculated using the temperature response of the cell to a heat flux pulse imposed at different locations. The methodology was previously applied to a backward facing step to prove its validity. Several simulations were performed applying a representative pulse of heat flux in different locations in the bottom wall of the backward facing step. From these simulations, the increment of temperature in each node of the geometry was retrieved and the Discrete Green Function coefficients associated to the bottom wall were calculated. A numerical validation was performed imposing a random pattern of heat flux and predicting the increment of temperature on the bottom wall under different inlet flow conditions. The final aim of this paper is to demonstrate the method in the rotor turbine tip. A turbine stage at engine-like conditions was assessed using a CFD software. The heat flux pulses were applied at different locations in the rotor tip geometry, and the increment of temperature in this zone was evaluated for different clearances, with a consequent variation of the Discrete Green Function coefficients. A validation of the rotor tip heat flux was accomplished by imposing different heat flux distributions in the studied region. Ultimately, a detailed uncertainty analysis of the methodology was included based in the magnitude of the heat flux pulses used in the Discrete Green Function coefficients calculation and the uncertainty in the experimental measurements of the wall temperature.
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Marshall, J. S. "Particulate Aggregate Formation and Wall Adhesion in Microchannel Flows." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98117.
Full textAbstract:
A multiple-time step discrete-element approach is presented for efficient computational modeling of the transport, collision and adhesion of small particles in microchannel flows. Adhesive particulates have been identified as a leading cause of failure in many different microfluidic devices, including those currently being developed by different research groups for rapid biological and chemical contaminant sensing, fluid drag reduction, etc. As these microfluidic devices enter into the marketplace and become more extensively used in field conditions, the importance of particle adhesion and clogging will increasingly limit the reliability of such systems. At a larger scale, clogging of vehicle radiators by small adhesive particles is currently a major problem for construction vehicles operating in certain environmental conditions and certain soil types. Cooling system fouling leads to the need for frequent maintenance and machine down time. Dust fouling of equipment is also of concern for potential human occupation on dusty planets, such as Mars. The discrete-element method presented in this paper is developed to enable efficient prediction of aggregate structure and breakup, for prediction of the effect of aggregate formation on the bulk fluid flow, and for prediction of the effects of small-scale flow features (e.g., due to surface roughness or lithographic patterning) on the aggregate formation and particle deposition. We present an overview of the computational structure and modeling assumptions, including models for various forces and torques present during particle-particle collisions. We then utilize the computational method to examine the physical processes involved in aggregate formation and capture of particulate aggregates by walls in microchannel flows.