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1
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.
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MACHIDA, TAKUYA. "A QUANTUM WALK WITH A DELOCALIZED INITIAL STATE: CONTRIBUTION FROM A COIN-FLIP OPERATOR." International Journal of Quantum Information 11, no. 05 (August 2013): 1350053. http://dx.doi.org/10.1142/s0219749913500536.
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A unit evolution step of discrete-time quantum walks (QWs) is determined by both a coin-flip operator and a position-shift operator. The behavior of quantum walkers after many steps delicately depends on the coin-flip operator and an initial condition of the walk. To get the behavior, a lot of long-time limit distributions for the QWs starting with a localized initial state have been derived. In this paper, we compute limit distributions of a 2-state QW with a delocalized initial state, not a localized initial state, and discuss how the walker depends on the coin-flip operator. The initial state induced from the Fourier series expansion, which is called the (α, β) delocalized initial state in this paper, provides different limit density functions from the ones of the quantum walk with a localized initial state.
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Agama, Theophilus. "On a function modeling an l-step self avoiding walk." AKCE International Journal of Graphs and Combinatorics 18, no. 3 (September 2, 2021): 158–65. http://dx.doi.org/10.1080/09728600.2021.1988831.
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Fang, Xiao, Han L. Gan, Susan Holmes, Haiyan Huang, Erol Peköz, Adrian Röllin, and Wenpin Tang. "Arcsine laws for random walks generated from random permutations with applications to genomics." Journal of Applied Probability 58, no. 4 (November 22, 2021): 851–67. http://dx.doi.org/10.1017/jpr.2021.14.
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AbstractA classical result for the simple symmetric random walk with 2n steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge when scaled to the arcsine law. Motivated by applications in genomics, we study the distributions of these statistics for the non-Markovian random walk generated from the ascents and descents of a uniform random permutation and a Mallows(q) permutation and show that they have the same asymptotic distributions as for the simple random walk. We also give an unexpected conjecture, along with numerical evidence and a partial proof in special cases, for the result that the number of steps above the origin by step 2n for the uniform permutation generated walk has exactly the same discrete arcsine distribution as for the simple random walk, even though the other statistics for these walks have very different laws. We also give explicit error bounds to the limit theorems using Stein’s method for the arcsine distribution, as well as functional central limit theorems and a strong embedding of the Mallows(q) permutation which is of independent interest.
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Aguech, Rafik, and Mohamed El Machkouri. "Corrigendum: Gaussian fluctuations of the elephant random walk with gradually increasing memory (2024 J. Phys. A: Math. Theor. 57 065203)." Journal of Physics A: Mathematical and Theoretical 57, no. 34 (August 12, 2024): 349501. http://dx.doi.org/10.1088/1751-8121/ad6655.
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Abstract The standard elephant random walk (ERW) is a discrete-time random walk introduced by Schütz and Trimper (2004 Phys. Rev. E 70 045101) with the particularity that the next step of the walker depends on its whole past through a parameter p ∈ [ 0 , 1 ] . In this note, we give a correction for the central limit theorem in the superdiffusive regime of the ERW with gradually increasing memory established by Aguech and El Machkouri (2024 J. Phys. A: Math. Theor. 57 065203, theorem 2). The mistake was pointed out by Roy et al (2024 arXiv:2403.02881, remark 1.1).
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Lamprou, Ioannis, Russell Martin, and Paul Spirakis. "Cover Time in Edge-Uniform Stochastically-Evolving Graphs." Algorithms 11, no. 10 (October 2, 2018): 149. http://dx.doi.org/10.3390/a11100149.
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We define a general model of stochastically-evolving graphs, namely the edge-uniform stochastically-evolving graphs. In this model, each possible edge of an underlying general static graph evolves independently being either alive or dead at each discrete time step of evolution following a (Markovian) stochastic rule. The stochastic rule is identical for each possible edge and may depend on the past k ≥ 0 observations of the edge’s state. We examine two kinds of random walks for a single agent taking place in such a dynamic graph: (i) The Random Walk with a Delay (RWD), where at each step, the agent chooses (uniformly at random) an incident possible edge, i.e., an incident edge in the underlying static graph, and then, it waits till the edge becomes alive to traverse it. (ii) The more natural Random Walk on what is Available (RWA), where the agent only looks at alive incident edges at each time step and traverses one of them uniformly at random. Our study is on bounding the cover time, i.e., the expected time until each node is visited at least once by the agent. For RWD, we provide a first upper bound for the cases k = 0 , 1 by correlating RWD with a simple random walk on a static graph. Moreover, we present a modified electrical network theory capturing the k = 0 case. For RWA, we derive some first bounds for the case k = 0 , by reducing RWA to an RWD-equivalent walk with a modified delay. Further, we also provide a framework that is shown to compute the exact value of the cover time for a general family of stochastically-evolving graphs in exponential time. Finally, we conduct experiments on the cover time of RWA in edge-uniform graphs and compare the experimental findings with our theoretical bounds.
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Chen, Qiming, Hong Cheng, Chunfeng Yue, Rui Huang, and Hongliang Guo. "Dynamic Balance Gait for Walking Assistance Exoskeleton." Applied Bionics and Biomechanics 2018 (July 2, 2018): 1–10. http://dx.doi.org/10.1155/2018/7847014.
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Purpose. Powered lower-limb exoskeleton has gained considerable interests, since it can help patients with spinal cord injury(SCI) to stand and walk again. Providing walking assistance with SCI patients, most exoskeletons are designed to follow predefined gait trajectories, which makes the patient walk unnaturally and feels uncomfortable. Furthermore, exoskeletons with predefined gait trajectories cannot always maintain balance walking especially when encountering disturbances. Design/Methodology/Approach. This paper proposed a novel gait planning approach, which aims to provide reliable and balance gait during walking assistance. In this approach, we model the exoskeleton and patient together as a linear inverted pendulum (LIP) and obtain the patients intention through orbital energy diagram. To achieve dynamic gait planning of exoskeleton, the dynamic movement primitive (DMP) is utilized to model the gait trajectory. Meanwhile, the parameters of DMP are updated dynamically during one step, which aims to improve the ability of counteracting external disturbance. Findings. The proposed approach is validated in a human-exoskeleton simulation platform, and the experimental results show the effectiveness and advantages of the proposed approach. Originality/Value. We decomposed the issue of obtain dynamic balance gait into three parts: (1) based on the sensory information of exoskeleton, the intention estimator is designed to estimate the intention of taking a step; (2) at the beginning of each step, the discrete gait planner utilized the obtained gait parameters such as step length S and step duration T and generate the trajectory of swing foot based on S,T; (3) during walking process, continuous gait regulator is utilized to adjust the gait generated by discrete gait planner to counteract disturbance.
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Cartwright, Donald I., and P. M. Soardi. "Random walks on free products, quotients and amalgams." Nagoya Mathematical Journal 102 (June 1986): 163–80. http://dx.doi.org/10.1017/s0027763000000507.
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Suppose that G is a discrete group and p is a probability measure on G. Consider the associated random walk {Xn} on G. That is, let Xn = Y1Y2 … Yn, where the Yj’s are independent and identically distributed G-valued variables with density p. An important problem in the study of this random walk is the evaluation of the resolvent (or Green’s function) R(z, x) of p. For example, the resolvent provides, in principle, the values of the n step transition probabilities of the process, and in several cases knowledge of R(z, x) permits a description of the asymptotic behaviour of these probabilities.
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Hayashi, Masafumi, So Oshiro, and Masato Takei. "Rate of moment convergence in the central limit theorem for the elephant random walk." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 2 (February 1, 2023): 023202. http://dx.doi.org/10.1088/1742-5468/acb265.
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Abstract The one-dimensional elephant random walk is a typical model of discrete-time random walk with step-reinforcement, and is introduced by Schütz and Trimper (2004 Phys. Rev. E 70 045101). It has a parameter α ∈ ( − 1 , 1 ) : the case α = 0 corresponds to the simple symmetric random walk, and when α > 0 (resp. α < 0), the mean displacement of the walker at time n grows (resp. vanishes) like n α . The walk admits a phase transition at α = 1 / 2 from the diffusive behavior to the superdiffusive behavior. In this paper, we study the rate of the moment convergence in the central limit theorem for the position of the walker when − 1 < α ⩽ 1 / 2 . We find a crossover phenomenon in the rate of convergence of the 2mth moments with m = 2 , 3 , … inside the diffusive regime − 1 < α < 1 / 2 .
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LIU, CHAOBIN, and NELSON PETULANTE. "On the von Neumann entropy of certain quantum walks subject to decoherence." Mathematical Structures in Computer Science 20, no. 6 (November 8, 2010): 1099–115. http://dx.doi.org/10.1017/s096012951000040x.
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In this paper, we consider a discrete-time quantum walk on the N-cycle governed by the condition that at every time step of the walk, the option persists, with probability p, of exercising a projective measurement on the coin degree of freedom. For a bipartite quantum system of this kind, we prove that the von Neumann entropy of the total density operator converges to its maximum value. Thus, when influenced by decoherence, the mutual information between the two subsystems corresponding to the space of the coin and the space of the walker must eventually diminish to zero. Put plainly, any level of decoherence greater than zero forces the system to become completely ‘disentangled’ eventually.
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Gupta, Deepak, and Bart Cleuren. "Optimizing cost through dynamic stochastic resetting." Journal of Statistical Mechanics: Theory and Experiment 2025, no. 1 (January 1, 2025): 013206. https://doi.org/10.1088/1742-5468/ada49d.
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Abstract The cost of stochastic resetting is considered within the context of a discrete random walk (RW) model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after each step, we introduce a novel resetting protocol which we dubbed dynamic resetting. This protocol entails an additional dynamic constraint related to the direction of successive steps of the RW. We study this novel protocol for a one-dimensional RW on an infinite lattice. We analyze the impact of the constraint on the walker’s mean-first passage time and the cost (fluctuations) of the resets as a function of distance of target from the resetting location. Further, cost optimized search strategies are discussed.
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Elliott, Terry. "The Mean Time to Express Synaptic Plasticity in Integrate-and-Express, Stochastic Models of Synaptic Plasticity Induction." Neural Computation 23, no. 1 (January 2011): 124–59. http://dx.doi.org/10.1162/neco_a_00061.
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Stochastic models of synaptic plasticity propose that single synapses perform a directed random walk of fixed step sizes in synaptic strength, thereby embracing the view that the mechanisms of synaptic plasticity constitute a stochastic dynamical system. However, fluctuations in synaptic strength present a formidable challenge to such an approach. We have previously proposed that single synapses must interpose an integration and filtering mechanism between the induction of synaptic plasticity and the expression of synaptic plasticity in order to control fluctuations. We analyze a class of three such mechanisms in the presence of possibly non-Markovian plasticity induction processes, deriving expressions for the mean expression time in these models. One of these filtering mechanisms constitutes a discrete low-pass filter that could be implemented on a small collection of molecules at single synapses, such as CaMKII, and we analyze this discrete filter in some detail. After considering Markov induction processes, we examine our own stochastic model of spike-timing-dependent plasticity, for which the probability density functions of the induction of plasticity steps have previously been derived. We determine the dependence of the mean time to express a plasticity step on pre- and postsynaptic firing rates in this model, and we also consider, numerically, the long-term stability against fluctuations of patterns of neuronal connectivity that typically emerge during neuronal development.
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Cooke, Ryan, Louise Welsh, Michele Fumagalli, and Max Pettini. "A limit on Planck-scale froth with ESPRESSO." Monthly Notices of the Royal Astronomical Society 494, no. 4 (May 6, 2020): 4884–90. http://dx.doi.org/10.1093/mnras/staa440.
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ABSTRACT Some models of quantum gravity predict that the very structure of space–time is ‘frothy’ due to quantum fluctuations. Although the effect is expected to be tiny, if these space–time fluctuations grow over a large distance, the initial state of a photon, such as its energy, is gradually washed out as the photon propagates. Thus, in these models, even the most monochromatic light source would gradually disperse in energy due to space–time fluctuations over large distances. In this paper, we use science verification observations obtained with ESPRESSO at the Very Large Telescope to place a novel bound on the growth of space–time fluctuations. To achieve this, we directly measure the width of a narrow Fe ii absorption line produced by a quiescent gas cloud at redshift $z$ ≃ 2.34, corresponding to a comoving distance of ≃5.8 Gpc. Using a heuristic model where the energy fluctuations grow as σE/E = (E/EP)α, where EP ≃ 1.22 × 1028 eV is the Planck energy, we rule out models with α ≤ 0.634, including models where the quantum fluctuations grow as a random walk process (α = 0.5). Finally, we present a new formalism where the uncertainty accrued at discrete space–time steps is drawn from a continuous distribution. We conclude, if photons take discrete steps through space–time and accumulate Planck-scale uncertainties at each step, then our ESPRESSO observations require that the step size must be at least ≳ 1013.2lP, where lP is the Planck length.
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Zadorozhnuyk, Anna O. "Monotonicity of random walks’ states on finite grids." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (April 1, 2022): 38–45. http://dx.doi.org/10.33581/2520-6508-2022-1-38-45.
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In this paper two ways to order the nodes of a graph with respect to an arbitrary node are considered, both connected to random walks on the graph. The first one is the order according to probabilities of states of a random walk of fixed length started in that arbitrary node. The walks considered here are lazy walks – instead of making a step they are allowed to stay in the same node. A class of graphs, where such order the corresponds to the weak order by geodesic distances, was found. Square and toric n-dimensional grids are shown to be instances of this class. The second way of ordering is resistance distance to a fixed node. For another class of graphs, a pair of vertices with maximal resistance distance between them is established. Grids are again shown to be an example of graphs belonging to this class.
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Lamb, Tania, and Jaynie F. Yang. "Could Different Directions of Infant Stepping Be Controlled by the Same Locomotor Central Pattern Generator?" Journal of Neurophysiology 83, no. 5 (May 1, 2000): 2814–24. http://dx.doi.org/10.1152/jn.2000.83.5.2814.
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This study examined the idea of whether the same central pattern generator (CPG) for locomotion can control different directions of walking in humans. Fifty-two infants, aged 2–11 mo, were tested. Infants were supported to walk on a treadmill at a variety of speeds. If forward stepping was elicited, stepping in the other directions (primarily sideways and backward) was attempted. The orientation of the infant on the treadmill belt determined the direction of stepping. In some infants, we also attempted to obtain a smooth transition from one direction to another by gradually changing the orientation of the infant during a stepping sequence. Limb segment motion and surface electromyography from the muscles of the lower limb were recorded. Most infants who showed sustained forward walking also could walk in all other directions. Thirty-three of 34 infants tested could step sideways. The success of eliciting backward stepping was 69%. Most of the infants who did not meet our backward stepping criteria did, however, make stepping movements. The different directions of stepping had similar responses to changes in treadmill speed. The relationship between stance and swing phase durations and cycle duration were the same regardless of the direction of stepping across a range of speeds. Some differences were noted in the muscle activation patterns during different directions of walking. For example, the hamstrings were much more active during the swing phase of backward walking compared with forward walking. The quadriceps was more active in the trailing leg during sideways walking. In some infants, we were able to elicit stepping along a continuum of directions. We found no discrete differences in either the electromyographic patterns or the temporal parameters of stepping as the direction of stepping was gradually changed. The results support the idea that the same locomotor CPG controls different directions of stepping in human infants. The fact that most infants were able to step in all directions, the similarity in the response to speed changes, and the absence of any discrete changes as the direction of stepping was changed gradually are all consistent with this hypothesis.
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Liu, Chengju, Jing Yang, Kang An, Ming Liu, and Qijun Chen. "Robust Control of Semi-passive Biped Dynamic Locomotion based on a Discrete Control Lyapunov Function." Robotica 38, no. 8 (November 26, 2019): 1345–58. http://dx.doi.org/10.1017/s0263574719001504.
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SUMMARYThis paper focuses on robust control of a simplest passive model, which is established on a DCLF (discrete control Lyapunov function) -based control system, and presents gait transition method based on the study of purely passive walker. Firstly, the DCLF is introduced to stabilize walking process between steps exponentially by modulating the length of next step. Next, the swing leg trajectory from mid-stance position to foot-strike can be planned. Then the control law is calculated to resist external disturbance. Besides, an impulse is added just before foot-strike to realize a periodic walking pattern on flat or uphill ground. With walking terrain varying, the robot can transit to an adaptive walking gait in a few steps. With different push or pull disturbances acting on hip joint and the robot gait transiting on a continuously slope-changing downhill, the effectiveness of the presented DCLF-based method is verified using simulation experiments. The ability to walk on a changing environment is also presented by simulation results. The insights of this paper can help to develop a robust control method and adaptive walking of dynamic passive locomotion robots.
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Huang, Feng, and Hanshuang Chen. "Non-equilibrium random walks on multiplex networks." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 10 (October 1, 2022): 103404. http://dx.doi.org/10.1088/1742-5468/ac9617.
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Abstract We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to one of its replicas in another layer. We derive the so-called supra-Markov matrix that governs the evolution of the occupation probability of the walker. The occupation probability at stationarity is different from the weighted average over the counterparts on each layer, unless the transition probabilities between layers vanish. However, they are approximately equal when the transition probabilities between layers are very small, which is given by the first-order degenerate perturbation theory. Moreover, we compute the mean first passage time (MFPT) and the graph MFPT (GrMFPT) that is the average of the MFPT over all pairs of distinct nodes. Interestingly, we find that the GrMFPT can be smaller than that of any layer taken in isolation. The result embodies the advantage of global search on multiplex networks.
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Navarro, Humberto J. "Automated detection of gait events using inertial sensor signals and a discrete wavelet transform approach." Periodicals of Engineering and Natural Sciences (PEN) 12, no. 3 (December 25, 2024): 577–94. https://doi.org/10.21533/pen.v12.i3.57.
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Detection of gait cycle events is a crucial step toward an effective evaluation and rehabilitation of pathologies or injuries in human locomotion. Recently, methods based on the Discrete Wavelet Transform (DWT) have been useful for this detection due to their robustness and the wide variety of options for analyzing and decomposing signals in time/frequency domains, as well as their ability to extract relevant features embedded in the signals. In this study, a detection method of main gait cycle events, using the Wavelet Symlets and Daubechies families, was developed. These events are the heel-strike (HS) and the toe–off (TO). Inertial signals were acquired by three different devices: a G–WALK (reference equipment), an Apple Watch (AW), and a noncommercial device based on Inertial Measurement Units (IMUs). The dataset was obtained from six–minute walking tests performed by 22 healthy subjects. First, the dataset was processed, and then the signals were synchronized regarding the reference system. Subsequently, the signals were decomposed into 6 levels using sym4 and db5 Wavelets to obtain multiple perspectives of the signals. Then, using automatic threshold techniques and symmetric windows, it was possible to detect HS and TO events. Finally, the IMUs–based system obtained a 94.398 % of recall, 100 % of precision, and 97.117 % of F_1–score, with absolute values delays in the detection between 10–20 ms. In contrast, the AW system performance was 90.168 %, 100 %, and 94.828 % for recall, precision, and F_1–score, respectively, with absolute values delays in the detection of 10–28 ms.
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Majumdar, Satya N., Philippe Mounaix, Sanjib Sabhapandit, and Grégory Schehr. "Record statistics for random walks and Lévy flights with resetting." Journal of Physics A: Mathematical and Theoretical 55, no. 3 (December 28, 2021): 034002. http://dx.doi.org/10.1088/1751-8121/ac3fc1.
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Abstract We compute exactly the mean number of records ⟨R N ⟩ for a time-series of size N whose entries represent the positions of a discrete time random walker on the line with resetting. At each time step, the walker jumps by a length η drawn independently from a symmetric and continuous distribution f(η) with probability 1 − r (with 0 ⩽ r < 1) and with the complementary probability r it resets to its starting point x = 0. This is an exactly solvable example of a weakly correlated time-series that interpolates between a strongly correlated random walk series (for r = 0) and an uncorrelated time-series (for (1 − r) ≪ 1). Remarkably, we found that for every fixed r ∈ 0 , 1 and any N, the mean number of records ⟨R N ⟩ is completely universal, i.e. independent of the jump distribution f(η). In particular, for large N, we show that ⟨R N ⟩ grows very slowly with increasing N as ⟨ R N ⟩ ≈ ( 1 / r ) ln N for 0 < r < 1. We also computed the exact universal crossover scaling functions for ⟨R N ⟩ in the two limits r → 0 and r → 1. Our analytical predictions are in excellent agreement with numerical simulations.
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Maeda, Rodrigo S., Shawn M. O'Connor, J. Maxwell Donelan, and Daniel S. Marigold. "Foot placement relies on state estimation during visually guided walking." Journal of Neurophysiology 117, no. 2 (February 1, 2017): 480–91. http://dx.doi.org/10.1152/jn.00015.2016.
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As we walk, we must accurately place our feet to stabilize our motion and to navigate our environment. We must also achieve this accuracy despite imperfect sensory feedback and unexpected disturbances. In this study we tested whether the nervous system uses state estimation to beneficially combine sensory feedback with forward model predictions to compensate for these challenges. Specifically, subjects wore prism lenses during a visually guided walking task, and we used trial-by-trial variation in prism lenses to add uncertainty to visual feedback and induce a reweighting of this input. To expose altered weighting, we added a consistent prism shift that required subjects to adapt their estimate of the visuomotor mapping relationship between a perceived target location and the motor command necessary to step to that position. With added prism noise, subjects responded to the consistent prism shift with smaller initial foot placement error but took longer to adapt, compatible with our mathematical model of the walking task that leverages state estimation to compensate for noise. Much like when we perform voluntary and discrete movements with our arms, it appears our nervous systems uses state estimation during walking to accurately reach our foot to the ground. NEW & NOTEWORTHY Accurate foot placement is essential for safe walking. We used computational models and human walking experiments to test how our nervous system achieves this accuracy. We find that our control of foot placement beneficially combines sensory feedback with internal forward model predictions to accurately estimate the body's state. Our results match recent computational neuroscience findings for reaching movements, suggesting that state estimation is a general mechanism of human motor control.
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Neves, Leonardo, and Graciana Puentes. "Photonic Discrete-time Quantum Walks and Applications." Entropy 20, no. 10 (September 24, 2018): 731. http://dx.doi.org/10.3390/e20100731.
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We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement.
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Mooney, Ciaran J., Roya Hakimjavadi, Emma Fitzpatrick, Eimear Kennedy, Dermot Walls, David Morrow, Eileen M. Redmond, and Paul A. Cahill. "Hedgehog and Resident Vascular Stem Cell Fate." Stem Cells International 2015 (2015): 1–16. http://dx.doi.org/10.1155/2015/468428.
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The Hedgehog pathway is a pivotal morphogenic driver during embryonic development and a key regulator of adult stem cell self-renewal. The discovery of resident multipotent vascular stem cells and adventitial progenitors within the vessel wall has transformed our understanding of the origin of medial and neointimal vascular smooth muscle cells (SMCs) during vessel repair in response to injury, lesion formation, and overall disease progression. This review highlights the importance of components of the Hh and Notch signalling pathways within the medial and adventitial regions of adult vessels, their recapitulation following vascular injury and disease progression, and their putative role in the maintenance and differentiation of resident vascular stem cells to vascular lineages from discrete niches within the vessel wall.
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Taylor, R. P., J. K. Taylor, H. H. Hosni, and H. W. Coleman. "Heat Transfer in the Turbulent Boundary Layer With a Step Change in Surface Roughness." Journal of Turbomachinery 114, no. 4 (October 1, 1992): 788–94. http://dx.doi.org/10.1115/1.2928032.
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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-dia 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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Monthus, Cécile. "Large deviations at level 2.5 and for trajectories observables of diffusion processes: the missing parts with respect to their random-walks counterparts." Journal of Physics A: Mathematical and Theoretical 57, no. 9 (February 16, 2024): 095002. http://dx.doi.org/10.1088/1751-8121/ad26ae.
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Abstract Behind the nice unification provided by the notion of the level 2.5 in the field of large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between the meaning of the level 2.5 for diffusion processes on one hand, and the meaning of the level 2.5 for Markov chains either in discrete-time or in continuous-time on the other hand. In order to analyze these differences in detail, it is thus useful to consider two types of random walks converging towards a given diffusion process in dimension d involving arbitrary space-dependent forces and diffusion coefficients, namely (i) continuous-time random walks on the regular lattice of spacing b; (ii) discrete-time random walks in continuous space with a small time-step τ. One can then analyze how the large deviations at level 2.5 for these two types of random walks behave in the limits b → 0 and τ → 0 respectively, in order to describe how the fluctuations of some empirical observables of the random walks are suppressed in the limit of diffusion processes. One can then also study the limits b → 0 and τ → 0 for any trajectory observable of the random walks that can be decomposed on its empirical density and its empirical flows in order to see how it is projected on the appropriate trajectory observable of the diffusion process involving its empirical density and its empirical current.
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Chen, Ming, Giuseppe M. Ferro, and Didier Sornette. "On the use of discrete-time quantum walks in decision theory." PLOS ONE 17, no. 8 (August 30, 2022): e0273551. http://dx.doi.org/10.1371/journal.pone.0273551.
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We present a short review of discrete-time quantum walks (DTQW) as a potentially useful and rich formalism to model human decision-making. We present a pedagogical introduction of the underlying formalism and main structural properties. We suggest that DTQW are particularly suitable for combining the two strands of literature on evidence accumulator models and on the quantum formalism of cognition. Due to the additional spin degree of freedom, models based on DTQW allow for a natural modeling of model choice and confidence rating in separate bases. Levels of introspection and self-assessment during choice deliberations can be modeled by the introduction of a probability for measurement of either position and/or spin of the DTQW, where each measurement act leads to a partial decoherence (corresponding to a step towards rationalization) of the deliberation process. We show how quantum walks predict observed probabilistic misperception like S-shaped subjective probability and conjunction fallacy. Our framework emphasizes the close relationship between response times and type of preferences and of responses. In particular, decision theories based on DTQW do not need to invoke two systems (“fast” and “slow”) as in dual process theories. Within our DTQW framework, the two fast and slow systems are replaced by a single system, but with two types of self-assessment or introspection. The “thinking fast” regime is obtained with no or little self-assessment, while the “thinking slow” regime corresponds to a strong rate of self-assessment. We predict a trade-off between speed and accuracy, as empirically reported.
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Baraldi, Daniele, Giosuè Boscato, Antonella Cecchi, and Claudia Brito de Carvalho Bello. "An Updated Discrete Element Model for the In-Plane Behaviour of NFRCM Strengthened Masonry Walls." Key Engineering Materials 916 (April 7, 2022): 249–55. http://dx.doi.org/10.4028/p-1853qe.
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Abstract. Masonry strengthened with natural fabric-reinforced cementitious matrix (NFRCM-strengthened masonry) is investigated by updating an existing discrete element model. Masonry walls are modelled by rigid blocks and elastoplastic interfaces that are able to account for mortar joints and block cracking. The reinforcement is modelled in a simplified manner considering perfect adhesion between wall and reinforcement and by adopting further spring elements connecting block centres. The model is validated by comparing it with an existing FEM based on a multi-step homogenization, where reinforced masonry is considered as a whole. Both approaches are used for performing nonlinear pushover tests with an increasing shear action applied to unreinforced and reinforced panels. The updated discrete model turns out to be able to represent the strength increment given by the reinforcement, but it is less able to represent the corresponding ductility increment.
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Zhou, Chuang, Nanjia Yu, Shuwen Wang, Shutao Han, Haojie Gong, Guobiao Cai, and Jue Wang. "The Influence of Thrust Chamber Structure Parameters on Regenerative Cooling Effect with Hydrogen Peroxide as Coolant in Liquid Rocket Engines." Aerospace 10, no. 1 (January 9, 2023): 65. http://dx.doi.org/10.3390/aerospace10010065.
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Liquid rocket engines with hydrogen peroxide and kerosene have the advantages of high density specific impulse, high reliability, and no ignition system. At present, the cooling problem of hydrogen peroxide engines, especially with regenerative cooling, has been little explored. In this study, a realizable k-epsilon turbulence model, discrete phase model, eddy dissipation concept model, and 10-step 10-component reaction mechanism of kerosene with oxygen are used. The increased rib height of the regenerative cooling channel causes the inner wall temperature of the engine increases, the average temperature of the coolant outlet decreases slightly, and the coolant pressure decreases. The overall wall temperature decreases as the rib width of the regenerative cooling channel increases. However, in the nozzle throat area, the wall temperature increases, the average coolant outlet temperature decreases, and the coolant pressure drop increases. A decrease in the inner wall thickness of the regenerative cooling channel results in a significant decrease in the wall temperature and a small increase in the average coolant outlet temperature. These findings contribute to the further development of the engine with hydrogen peroxide and can guide the design of its regenerative cooling process.
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Vaezipoor, Pashootan, Gil Lederman, Yuhuai Wu, Chris Maddison, Roger B. Grosse, Sanjit A. Seshia, and Fahiem Bacchus. "Learning Branching Heuristics for Propositional Model Counting." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 14 (May 18, 2021): 12427–35. http://dx.doi.org/10.1609/aaai.v35i14.17474.
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Propositional model counting, or #SAT, is the problem of computing the number of satisfying assignments of a Boolean formula. Many problems from different application areas, including many discrete probabilistic inference problems, can be translated into model counting problems to be solved by #SAT solvers. Exact #SAT solvers, however, are often not scalable to industrial size instances. In this paper, we present Neuro#, an approach for learning branching heuristics to improve the performance of exact #SAT solvers on instances from a given family of problems. We experimentally show that our method reduces the step count on similarly distributed held-out instances and generalizes to much larger instances from the same problem family. It is able to achieve these results on a number of different problem families having very different structures. In addition to step count improvements, Neuro# can also achieve orders of magnitude wall-clock speedups over the vanilla solver on larger instances in some problem families, despite the runtime overhead of querying the model.
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Okada, Hiroki, Shinsuke Ohnuki, Cesar Roncero, James B. Konopka, and Yoshikazu Ohya. "Distinct roles of cell wall biogenesis in yeast morphogenesis as revealed by multivariate analysis of high-dimensional morphometric data." Molecular Biology of the Cell 25, no. 2 (January 15, 2014): 222–33. http://dx.doi.org/10.1091/mbc.e13-07-0396.
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The cell wall of budding yeast is a rigid structure composed of multiple components. To thoroughly understand its involvement in morphogenesis, we used the image analysis software CalMorph to quantitatively analyze cell morphology after treatment with drugs that inhibit different processes during cell wall synthesis. Cells treated with cell wall–affecting drugs exhibited broader necks and increased morphological variation. Tunicamycin, which inhibits the initial step of N-glycosylation of cell wall mannoproteins, induced morphologies similar to those of strains defective in α-mannosylation. The chitin synthase inhibitor nikkomycin Z induced morphological changes similar to those of mutants defective in chitin transglycosylase, possibly due to the critical role of chitin in anchoring the β-glucan network. To define the mode of action of echinocandin B, a 1,3-β-glucan synthase inhibitor, we compared the morphology it induced with mutants of Fks1 that contains the catalytic domain for 1,3-β-glucan synthesis. Echinocandin B exerted morphological effects similar to those observed in some fks1 mutants, with defects in cell polarity and reduced glucan synthesis activity, suggesting that echinocandin B affects not only 1,3-β-glucan synthesis, but also another functional domain. Thus our multivariate analyses reveal discrete functions of cell wall components and increase our understanding of the pharmacology of antifungal drugs.
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Vadakkan, Unnikrishnan, Suresh V. Garimella, and Jayathi Y. Murthy. "Transport in Flat Heat Pipes at High Heat Fluxes From Multiple Discrete Sources." Journal of Heat Transfer 126, no. 3 (June 1, 2004): 347–54. http://dx.doi.org/10.1115/1.1737773.
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A three-dimensional model has been developed to analyze the transient and steady-state performance of flat heat pipes subjected to heating with multiple discrete heat sources. Three-dimensional flow and energy equations are solved in the vapor and liquid regions, along with conduction in the wall. Saturated flow models are used for heat transfer and fluid flow through the wick. In the wick region, the analysis uses an equilibrium model for heat transfer and a Brinkman-Forchheimer extended Darcy model for fluid flow. Averaged properties weighted with the porosity are used for the wick analysis. The state equation is used in the vapor core to relate density change to the operating pressure. The density change due to pressurization of the vapor core is accounted for in the continuity equation. Vapor flow, temperature and hydrodynamic pressure fields are computed at each time step from coupled continuity/momentum and energy equations in the wick and vapor regions. The mass flow rate at the interface is obtained from the application of kinetic theory. Predictions are made for the magnitude of heat flux at which dryout would occur in a flat heat pipe. The input heat flux and the spacing between the discrete heat sources are studied as parameters. The location in the heat pipe at which dryout is initiated is found to be different from that of the maximum temperature. The location where the maximum capillary pressure head is realized also changes during the transient. Axial conduction through the wall and wick are seen to play a significant role in determining the axial temperature variation.
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Ghasemi Monfared, Zahra, J. Gunnar I. Hellström, and Kentaro Umeki. "The Impact of Discrete Element Method Parameters on Realistic Representation of Spherical Particles in a Packed Bed." Processes 12, no. 1 (January 13, 2024): 183. http://dx.doi.org/10.3390/pr12010183.
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Packed bed reactors play a crucial role in various industrial applications. This paper utilizes the Discrete Element Method (DEM), an efficient numerical technique for simulating the behavior of packed beds of particles as discrete phases. The focus is on generating densely packed particle beds. To ensure the model accuracy, specific DEM parameters were studied, including sub-step and rolling resistance. The analysis of the packed bed model extended to a detailed exploration of void fraction distribution along radial and vertical directions, considering the impact of wall interactions. Three different samples, spanning particle sizes from 0.3 mm to 6 mm, were used. Results indicated that the number of sub-steps significantly influences void fraction precision, a key criterion for comparing simulations with experimental results. Additionally, the study found that both loosely and densely packed beds of particles could be accurately represented by incorporating appropriate values for rolling friction. This value serves as an indicator of both inter-particle friction and friction between particles and the walls. An optimal rolling friction coefficient has been thereby suggested for the precise representation for the densely packed bed of spherical char particles.
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Khan, J. A., and D. E. Beasley. "Two-Dimensional Effects on the Response of Packed Bed Regenerators." Journal of Heat Transfer 111, no. 2 (May 1, 1989): 328–36. http://dx.doi.org/10.1115/1.3250681.
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Packed beds have a wide range of applications as heat transfer and energy storage devices. Employed as a regenerator, a packed bed is subject to the flow of a heat transfer fluid, which alternately stores and recovers energy from a packing of discrete particles. The flow direction reverses during the addition and removal of energy. The nature of a packing of discrete particles in a container is such that variations in the resistance to flow and in the void fraction occur across the cross section of the packing. Particularly, the region of the bed near the boundary of the container has a markedly reduced resistance to flow. In addition, the wall effect on the packing geometry changes the void fraction in the near-wall region. The purpose of the present study is to quantify the two-dimensional effects of nonuniform void fraction, velocity, and temperature distributions in a packed bed regenerator on the dynamic and steady periodic behavior. A two-dimensional numerical model of the transient response of a packed bed subject to the flow of a heat transfer fluid has been developed and verified through comparison with measured responses. The model includes the effects of nonuniform velocity and porosity in the bed, and the effects of axial and radial thermal dispersion. The results of the present computations are compared with one-dimensional transient periodic results to demonstrate the two-dimensional effects on the transient response of a packed bed regenerator to a step change in fluid temperature. The classical dimensionless parameters, such as reduced length and reduced time, are not sufficient to characterize the two-dimensional transient nature of a packed bed regenerator. This study identifies the range of bed-to-particle-diameter ratios over which the transient response is significantly influenced by the wall effect on void fraction and flow.
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Guo, Wenqiang, and Guoxiang Hou. "Novel Schemes of No-Slip Boundary Conditions for the Discrete Unified Gas Kinetic Scheme Based on the Moment Constraints." Entropy 25, no. 5 (May 10, 2023): 780. http://dx.doi.org/10.3390/e25050780.
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The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole–wall collision, and Rayleigh–Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole–wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh–Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS.
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Nakano, Masami, Eisuke Outa, and Kiyohiro Tajima. "Noise and Vibration Related to the Patterns of Supersonic Annular Flow in a Pressure Reducing Gas Valve." Journal of Fluids Engineering 110, no. 1 (March 1, 1988): 55–61. http://dx.doi.org/10.1115/1.3243511.
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Cause of intense aerodynamic noise and vibration from a contoured type valve is revealed in close relation to the supersonic flow patterns. Simple conical plugs are used in the experiments, and the valve pressure ratio is up to twenty. Four typical patterns of the flow are observed by schlieren photography. In one of these patterns, the jet flow along the plug separates from the wall to form an annular jet impinging on the inner wall of the valve chest. Such flow oscillates significantly in resonance with the acoustic modes of the chest cavity. The radiated noise and the dynamic force acting on the valve stem reach intense levels, dominated by some discrete components of the corresponding frequencies. The mechanisms to generate or to suppress the flow oscillation, leading to the intense noise and vibration, are discussed.
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Staroszczyk, Ryszard. "Incompressible SPH Model for Simulating Violent Free-Surface Fluid Flows." Archives of Hydro-Engineering and Environmental Mechanics 61, no. 1-2 (June 1, 2014): 61–83. http://dx.doi.org/10.1515/heem-2015-0004.
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Abstract In this paper the problem of transient gravitational wave propagation in a viscous incompressible fluid is considered, with a focus on flows with fast-moving free surfaces. The governing equations of the problem are solved by the smoothed particle hydrodynamics method (SPH). In order to impose the incompressibility constraint on the fluid motion, the so-called projection method is applied in which the discrete SPH equations are integrated in time by using a fractional-step technique. Numerical performance of the proposed model has been assessed by comparing its results with experimental data and with results obtained by a standard (weakly compressible) version of the SPH approach. For this purpose, a plane dam-break flow problem is simulated, in order to investigate the formation and propagation of a wave generated by a sudden collapse of a water column initially contained in a rectangular tank, as well as the impact of such a wave on a rigid vertical wall. The results of simulations show the evolution of the free surface of water, the variation of velocity and pressure fields in the fluid, and the time history of pressures exerted by an impacting wave on a wall.
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Hudson, Thomas, Patrick van Meurs, and Mark Peletier. "Atomistic origins of continuum dislocation dynamics." Mathematical Models and Methods in Applied Sciences 30, no. 13 (December 15, 2020): 2557–618. http://dx.doi.org/10.1142/s0218202520500505.
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This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.
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Wibowo, Ari, Indradi Wijatmiko, and Christin R. Nainggolan. "Cyclic Behaviour of Expanded Polystyrene (EPS) Sandwich Reinforced Concrete Walls." Advances in Materials Science and Engineering 2018 (December 26, 2018): 1–9. http://dx.doi.org/10.1155/2018/7214236.
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Precast concrete walls become increasingly utilized due to the rapid needs of inexpensive fabricated house especially as traditional construction cost continues to climb, and also, particularly at damaged area due to natural disasters when the requirement of a lot of fast-constructed and cost-efficient houses are paramount. However, the performance of precast walls under lateral load such as earthquake or strong wind is still not comprehensively understood due to various types of reinforcements and connections. Additionally, the massive and solid wall elements also enlarge the building total weight and hence increase the impact of earthquake significantly. Therefore, the precast polystyrene-reinforced concrete walls which offer light weight and easy installment became the focus of this investigation. The laboratory test on two reinforced concrete wall specimens using EPS (expanded polystyrene) panel and wire mesh reinforcement has been conducted. Quasi-static load in the form of displacement controlled cyclic tests were undertaken until reaching peak load. At each discrete loading step, lateral load-deflection behaviour, crack propagation, and collapse mechanism were measured which then were compared with theoretical analysis. The findings showed that precast polystyrene-reinforced concrete walls gave considerable seismic performance for the low-to-moderate seismic region reaching up to 1% drift at 20% drop of peak load. However, it might not be sufficient for high seismic regions, at which double-panel wall type can be more suitable.
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Ghoshdastidar, P. S., and Indrajit Chakraborty. "A Coupled Map Lattice Model of Flow Boiling in a Horizontal Tube." Journal of Heat Transfer 129, no. 12 (March 27, 2007): 1737–41. http://dx.doi.org/10.1115/1.2768102.
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In this work laminar, stratified flow boiling of water is simulated qualitatively by the coupled map lattice (CML) method. The liquid is entering a constant wall temperature horizontal tube (Tw>Tsat at pentrance) in a subcooled condition. A CML is a dynamical system with discrete-time, discrete-space, and continuous states. The procedure basically consists of the following steps: (i) Choose a set of macroscopic variables on a lattice; (ii) decompose the problem into independent components, such as convection, diffusion, phase change, and so on; (iii) replace each component by a simple parallel dynamics on a lattice; and (iv) carry out each unit dynamics successively in each time step until some termination criterion is satisfied. In the present problem, the termination criterion is the laminar-turbulent transition, and hence, the results do not correspond to the steady state. The present modeling by CML is based on the assumption that the flow boiling is governed by (i) nucleation from cavities on the heated surface and migration of vapor into the core, (ii) forced convection, and (iii) phase change in the fluid bulk and mixing. The stirring action of the bubbles is modeled by increasing the fluid momentum and thermal diffusivities by an enhancement factor. The results show that the CML has been able to model flow boiling in a realistic manner.
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Pflugfelder, G. O., H. Schwarz, H. Roth, B. Poeck, A. Sigl, S. Kerscher, B. Jonschker, W. L. Pak, and M. Heisenberg. "Genetic and molecular characterization of the optomotor-blind gene locus in Drosophila melanogaster." Genetics 126, no. 1 (September 1, 1990): 91–104. http://dx.doi.org/10.1093/genetics/126.1.91.
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Abstract The Drosophila gene optomotor-blind (omb) is involved in the development of a set of giant neurons in the optic lobes and possibly other structures in the imaginal brain. Adult flies have discrete defects in optomotor behavior. The gene has previously been mapped in chromomeres 4C5-6, together with three other genes, bifid, Quadroon and lacqueredgls. We have localized the gene in a genomic walk of 340 kb of DNA. By mapping seven chromosome breakpoints with omb phenotype we determined its minimum size to about 80 kb. From this region more than 20 RNAs of different size and temporal expression pattern are transcribed. Three of them (T3, T7 and T7') stem from primary transcripts of 40-80 kb in length. In its distal part the omb gene overlaps in at least 19 kb with four other complementation units, bifid, l(1)bifid, Quadroon and lacqueredgls. The three nonlethals affect the external appearance of the fly and seem to be unrelated to brain development.
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Gazourian, Lee, Anna Maria F. Coronata, Angela J. Rogers, Gerald L. Weinhouse, Robert J. Soiffer, Joseph H. Antin, Jerome Ritz, Vincent T. Ho, Rebecca M. Baron, and George R. Washko. "Airway Dilation in Bronchiolitis Obliterans After Allogeneic Hematopoietic Stem Cell Transplantation." Blood 120, no. 21 (November 16, 2012): 3058. http://dx.doi.org/10.1182/blood.v120.21.3058.3058.
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Abstract Abstract 3058 Rationale: Bronchiolitis obliterans syndrome (BOS) is a late, non-infectious pulmonary complication following hematopoietic stem cell transplantation (HSCT). The prevalence is estimated to be between 5–10% after allogeneic HSCT with a significant increase in morbidity and mortality. We were interested in assessing quantitative radiologic characterization of airway remodeling in these subjects. Objectives: To examine quantitative measurements of airway morphology and their correlation with lung function in a cohort of patients who underwent HSCT and developed BOS. Methods: All patients who underwent an allogeneic HSCT at the Dana-Farber Cancer Institute/Brigham and Women's Hospital (n=1854) between January 1st 2000 and June 30th2010 were screened for the development of BOS using modified NIH diagnostic criteria. Clinically acquired high resolution CT (HRCT) scans of the chest were collected. Discrete measures of airway wall area were performed in a total of 16 manually selected airways in the right and left upper and lower lobes using Airway Inspector (www.airwayinspector.org). From these measures, the square root of wall area of a 10-mm luminal perimeter (Pi10) was calculated. Spearman correlation was used to assess the relationship between square root of wall area at Pi10 and pulmonary function measures. Paired t-test was used for within group comparisons. Analyses were performed with SAS v. 9.2. Measurements and Main Results: Within our cohort 89 cases of BOS were identified of which 37 patients had HRCT scans available for analysis. 33 patients had pulmonary function tests within 30 days of the HRCT (Table 1). Ten of the 37 BOS patients had a HRCT scan at or prior to transplantation and a HRCT scan available after the diagnosis of BOS. Square root of wall area at Pi10 correlated significantly with FEV1(r = 0.636, p<0.0001), RV/TLC (r = −0.736, p< 0.0001) (Fig. 1), and when adjusted for age, sex and total lung capacity, the correlations remained significant (p<0.0001). There was a significant decline in square root of wall area at Pi10 in BOS cases compared to pre-transplant CT scans (p<0.001) (Fig 2). Conclusions: On HRCT scan BOS is characterized by central airway dilation, the degree of which is correlated to decrements in lung function. Future studies will examine whether chest CT assessment of central airway dilation can be used as a sensitive and specific tool for diagnosis and staging of BOS. Disclosures: No relevant conflicts of interest to declare.
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Wu, Guorong, Yanggui Li, and Muhammad Israr. "Improvement of Relative DEM Time Step Range in Fast Fluidization Simulation of Type-A FCC Particles." Processes 11, no. 4 (April 10, 2023): 1155. http://dx.doi.org/10.3390/pr11041155.
Full textAbstract:
In many process engineering fields, gas-particle fluidized beds are widely used. In fluidized bed research, the discrete element method, or DEM, has been a powerful tool for design and operation purposes. However, with the use of Type-A powders, fluid catalytic cracking or FCC particles being classical cases, they have hardly been reported in DEM simulations of fast fluidization. This study paid close attention to the suitable selection of a stiffness constant and a DEM time step. To reflect their respective effects and complicated interactions, a so-called relative DEM time step was defined. The drag coefficient was correlated using the energy-minimization multi-scale (EMMS) approach to reasonably calculate the gas–solid interaction. Six representative cases with different relative time step values were chosen to simulate a micro-fluidized bed of Type-A FCC powders. The results showed that DEM employing EMMS-based drag force was able to greatly enlarge the suitable range of relative time steps in a fast fluidization simulation of Type-A powders. In addition, the typical macro flow structures of fast fluidization was successfully captured: axially dilute in the top and dense in the bottom, and radially dilute in the core and dense near the wall. Moreover, the distinct gas–solid backmixing, which is considered one of the most important pieces of evidence for the determination of fast fluidization regimes, was modeled. It was indicated that the EMMS-based drag model attenuated the overestimated drag force so that the soft-sphere contact model would be able to more appropriately deal with particle collision, and thus improve the suitable relative DEM time step range.