Jump Process Research Articles

ABSTRACT Power, and recently force-velocity (F-V) profiling, are well-researched and oft cited critical components for sports performance but both are still debated; some would say misused. A neat, applied formulation of power and linear F-V in the literature is practically useful but there is a dearth of fundamental explanations of how power and F-V interact with human and environmental constraints. To systematically explore the interactions of a linear F-V profile, peak power, gravity, mass, range of motion (ROM), and initial activation conditions, a forward dynamics point mass model of vertical jumping was parameterised from an athlete. With no constraints and for a given peak power, F-V favouring higher velocity performed better, but were impacted more under real-world conditions of gravity and finite ROM meaning the better F-V was dependent on constraints. Increasing peak power invariably increased jump height but improvement was dependent on the initial F-V and if it was altered by changing maximal force or velocity. When mass was changed along with power and F-V there was a non-linear interaction and jump improvement could be almost as large for a F-V change as an increase in power. An ideal F-V profile cannot be identified without knowledge of mass and ROM.

Jumping robots possess the capability to surmount formidable obstacles and are well-suited for navigating through complex terrain environments. However, most of the existing jumping robots face challenges in achieving stable jumping and they also have low energy utilization efficiency, which limits their practical applications. In this work, a two-module jumping robot based on tensegrity structure is put forward. Firstly, the structural design and jumping mechanism of the robot are elaborated in the article. Then, dynamic models, including the two modules’ simultaneous jumping and step-up jumping process of the robot, are established utilizing the Lagrange dynamic modeling method. On this basis, the effects of parameters, including the stiffness of elastic cables and the initial tilt angle of the robot, on the jumping performance of the robot can be obtained. Finally, simulations are carried out and a prototype is developed to verify the rationality of the tensegrity-based jumping robot proposed in this work. The experiment results show that our jumping robot can achieve a stable jumping process and the step-up jumping of each module of the prototype can have higher energy efficiency than that of simultaneous jumping of each module, which enables the robot a better jumping performance. This research serves as a valuable reference for the design and analysis of jumping robots.

Rare events in the first-passage distributions of jump processes are capable of triggering anomalous reactions or series of events. Estimating their probability is particularly important when the jump probabilities have broad-tailed distributions, and rare events are therefore not so rare. We formulate a general approach for estimating the contribution of fast rare events to the exit probabilities in the presence of fat-tailed distributions. Using this approach, we study three jump processes that are used to model a wide class of phenomena ranging from biology to transport in disordered systems, ecology, and finance: discrete time random walks, Lévy walks, and the Lévy-Lorentz gas. We determine the exact form of the scaling function for the probability distribution of fast rare events, in which the jump process exits from an interval in a very short time at a large distance opposite to the starting point. In particular, we show that events occurring on timescales orders of magnitude smaller than the typical timescale of the process can make a significant contribution to the exit probability. Our results are confirmed by extensive numerical simulations.

We study a continuous-review stock management of a retailer for a single item in a limited storage (buffer) in a random environment. The stock level fluctuates according to two independent compound Poisson processes with discrete amounts of items (batches) that enter and leave the storage facility. The storage facility is controlled by a three-parameter base-stock replenishment policy. All items exceeding the storage capacity are transferred to an unlimited foreign facility. In addition, a restricted backlogging possibility is permitted; additional demands for items are lost sales. We further assume a random shelf life, the possibility of total inventory collapse, and a random lead time. Applying Markov theory, we derive the optimal control parameters minimizing the long-run expected total cost. A sensitivity analysis is conducted focusing on the comparison between the pure lost-sales policy and a partial backordering policy. Accordingly, we identify cases where one policy is cost effective compared to the other, particularly with respect to the batch patterns (sign, rate, average, and variability), and the associated costs.

Water molecules are essential to determine the structure of nucleic acids and mediate their interactions with other biomolecules. Here, we characterize the hydration dynamics of analogous DNA and RNA double helices with unprecedented resolution and elucidate the molecular origin of their differences: first, the localization of the slowest hydration water molecules─in the minor groove in DNA, next to phosphates in RNA─and second, the markedly distinct hydration dynamics of the two phosphate oxygen atoms OR and OS in RNA. Using our Extended Jump Model for water reorientation, we assess the relative importance of previously proposed factors, including the local topography, water bridges, and the presence of ions. We show that the slow hydration dynamics at RNA OR sites is not due to bridging water molecules but is caused by both the larger excluded volume and the stronger initial H-bond next to OR, due to the different phosphate orientations in A-form double helical RNA.

In this present paper, the event-triggered sliding mode control (SMC) issue for a type of singular networked Markov jump systems with partly unknown transition probabilities (TPs) is mainly investigated, and it is modeled by discrete-time Takagi–Sugeno fuzzy systems. To save network resources, a mode-dependent event-triggered scheme (ETS) is applied to improve transmission efficiency. Subsequently, a common sliding surface is designed, which can effectively reduce the impact of the jumping process. Therein, the stochastic admissibility criterion for the system with [Formula: see text] performance [Formula: see text] is derived in the sense of partly unknown TPs. Moreover, a novel SMC law that guarantees the reachability of the quasi-sliding mode is given in view of the reaching condition. Finally, the validity of the presented theorems is demonstrated by a numerical example.

Homotopic ADP based [formula omitted] integral sliding mode secure control for Markov jumping cyber-physical systems

To study the impact of upwarp deformation in the ballastless track on the jumping behavior of the high-speed vehicle, utilizing UM and ANSYS joint simulation, a vertical vibration model of high-speed vehicle on CRTS II slab ballastless track was developed based on the non-Hertz wheel–rail contact model of virtual penetration theory. By using the single-wave cosine curve simulating the characteristics of upwarp deformation in the track slab, we calculated the whole process of wheel jumping. This allowed us to analyze how the amplitude and wavelength of the track slab upward deformation influence the vibration response of the vehicle–track system. Our findings indicate that when a wheel passes through the arch section of the track slab, the entire wheel jumping process consists of distinct stages: “wheel–rail bonding, wheel–rail separation, wheel–rail impact (one or more times), and wheel–rail bonding.” As the amplitude of upwarp deformation increases and the wavelength decreases, significant changes occur in several parameters, including the vertical force between the wheel and rail, wheel unloading rate, wheel jump height, frequency, duration, and vertical displacement of the rail. Additionally, when the wavelength is between 2 and 6[Formula: see text]m and the amplitude is 8[Formula: see text]mm, the vertical force between the wheel and rail becomes zero, the wheel load reduction rate is one, and the wheel jumps. When the wavelength is less than 3[Formula: see text]m, the wheel jump height exceeds the flange height, increasing the risk of derailment. Meanwhile, during the first wheel–rail impact, the wheel–rail vertical force and the rail vertical displacement reach their maximum, potentially impacting rail service performance negatively. Finally, compared to the amplitude of the track slab camber deformation, its wavelength has a greater impact on the entire process of wheel jumping. It is recommended that attention be paid to the change in the wavelength of the track slab camber during the maintenance and repair of the ballastless track.

This paper is devoted to symmetric mixture stable-like processes on metric measure space.Assume that the process enjoys upper bounds of heat kernel,characterization of near diagonal lower bounds of heat kernel is given.different from previous work which is usually based on regularity of elliptic harmonic functions,here we make full use of smooth properties of functions space associated with the generator of the process.

(1) Background: Previous studies have compared research into ski jumping in different motor processes, but there is a lack of comparative analysis of the biomechanical research methods used to investigate different ski jumping sports. (2) Content: Our study compared the advantages and disadvantages of six research methods and proposes future research directions. Motion video collection and analysis show that controlling angular momentum and achieving stable flight attitude in the take-off process are the most critical factors in ski jumping performance. Most research on force platforms focuses on dynamic performance at the time of take-off, but there are few training sites with an embedded force platform, and so, more empirical research is required. Wearable inertial measurement units, including gyroscopes and accelerometers, can be used to determine a series of forces, calculate the joint angle, and speculate the position of the centroid during motion. Surface EMG studies are primarily used to compare the activity characteristics of the lower limb muscles in the actual field of the jump, the exercise simulation, and the lack of complete training process data. Wind tunnel measurement can satisfy fluid mechanics simulation experiments and provide theoretical support for optimizing special ski jumping technology. Based on the theory of computational fluid dynamics, the optimal drag reduction posture data of ski jumpers can be derived using computer simulations. (3) Conclusions: Due to the wide range of ski jumping sports, the present research focused on the kinematics and dynamics of different movement stages, lacking the study of the complete exercise training process. The range of wearable inertial measurement and sensor equipment can cover the whole process of ski jumping, including kinematics and dynamics data, and is a feasible and reliable test method for monitoring ski jump training in natural environments. The simultaneous testing of surface electromyography, kinematics, and dynamics requires further exploration. (4) Future direction of development: Under computational fluid dynamics, wearable inertial measurement units and global navigation satellite systems (GNSSs), intelligent wind tunnel experimental training areas will become essential tools for ski jumping research.

Highly diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase of many-variable model ecosystems with disordered species interactions, when species are supported by migration from outside the system at a small rate. We show that these and other phenomena can be understood through the existence of a scaling regime in the limit of small migration, in which large fluctuations and long timescales emerge. We construct an exact analytical theory for this asymptotic regime that provides scaling predictions on timescales and abundance distributions that are verified exactly in simulations. In this regime, a clear separation emerges between rare and abundant species at any given time, despite species moving back and forth between the rare and abundant subsets. The number of abundant species is found to lie strictly below a well-known stability bound, maintaining the system away from marginality. At the same time, other measures of diversity, which also include some of the rare species, go above this bound. In the asymptotic limit where the migration rate goes to zero, trajectories of individual species abundances are described by non-Markovian jump-diffusion processes, which proceeds as follows: A rare species remains so for some time, then experiences a jump in population sizes after which it becomes abundant (a species turnover event) and later sees its population size gradually decreasing again until rare, due to the competition with other species. The asymmetry of abundance trajectories under time reversal is maintained at a small but finite migration rate. These features may serve as fingerprints of endogenous fluctuations in highly diverse ecosystems. Published by the American Physical Society 2024

The coalescence-induced droplet jumping is a self-propelled water removal phenomenon on superhydrophobic surfaces, which has attracted considerable attention due to its potential in a wide range of applications such as self-cleaning and anti-icing/frosting. Improving the energy conversion efficiency, from the excessive surface energy to the kinetic energy, is pivotal to facilitate droplet jumping. In this study, we numerically investigated the dynamics of droplet coalescence on superhydrophobic surfaces with macro-stepped structures, with particular interest in understanding the role of the stepped structure on the droplet jumping process. Three-dimensional simulations were performed by using the lattice Boltzmann method, with the pseudopotential multiphase model and the multiple-relaxation-time collision operator being adopted to achieve high liquid–gas density/viscosity ratios. A wide range of nondimensional height difference of the stepped structure (0–1.5) and droplet radius ratio (0.5–2) was covered. Results show that adding macro-stepped structures can significantly enhance the droplet-wall interaction, thus yielding increased droplet velocity. The enhancement of droplet jumping is more remarkable for droplets of similar sizes, and the dimensionless height difference of the stepped structure is required to exceed a threshold of approximately 0.5. Among the present simulations, the maximum dimensionless droplet jumping velocity reaches 0.66, corresponding to an energy conversion efficiency of 35%. The present findings are helpful for the development of novel superhydrophobic surfaces that pursue efficient droplet removal.

This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. Based on Gillespie’s stochastic simulation algorithm, a corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including random jump times. We uncover a time-shifted synchronization in the sense that—after some initial waiting time—one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behavior occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems.

The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial mathematical burden which is usually circumvented by using well-known generic distributional approximations or simulations. This article provides a novel approximation method that tailors the dynamics of a time-homogeneous Markov jump process to meet those of its time-inhomogeneous counterpart on an increasingly fine Poisson grid. Strong convergence of the processes in terms of the Skorokhod J1 metric is established, and convergence rates are provided. Under traditional regularity assumptions, distributional convergence is established for unconditional proxies, to the same limit. Special attention is devoted to the case where the target process has one absorbing state and the remaining ones transient, for which the absorption times also converge. Some applications are outlined, such as univariate hazard-rate density estimation, ruin probabilities, and multivariate phase-type density evaluation. Funding: M. Bladt and O. Peralta would like to acknowledge financial support from the Swiss National Science Foundation Project 200021_191984. O. Peralta acknowledges financial support from NSF Award #1653354 and AXA Research Fund Award on “Mitigating risk in the wake of the pandemic”.

Abstract In this work we study the design of filters for phase‐type (PH) semi‐Markov jump linear systems, considering partial information on the system's operating mode and possible parameter uncertainties. With respect to the mode of operation, it is assumed that the state space of the semi‐Markov chain can be written as the union of disjoint sets, called clusters, and the only information available to the filter is which cluster the state of the semi‐Markov chain belongs to. A new linear matrix inequality (LMI) parameterization employing the slack variable technique is introduced for the design of switching full‐order filters according to the cluster observations so that suitable bounds on the norm of the estimation error are guaranteed for the uncertain system. If the system is restricted to be a Markov jump linear system and the Markov chain is assumed to be perfectly measured, the design conditions are shown to be also necessary leading to the optimal full‐order filter. Furthermore, the general filter can be particularized into an observer form for the case in which the system matrices are the same within each cluster and there are no parameter uncertainties except for possible uncertainties affecting the transition rates of the jumping process. The paper concludes with an illustrative example in the context of networked control systems.

Unveiling the principles of stochastic resonance and complex potential functions for bearing fault diagnosis

Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the static response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.

In denim washing industry pumice stone is a very popular material in enzyme or jumping process. Pumice stone is less costly and that's the only reason behind it's higher application. But pumice stone creates more sludge in ETP & requires more water in process which is not sustainable. Also for usage of pumice stone there is a higher possibility of damage issue in case of very light wash. In this study Eco Stone were used instead of Pumice stone to observe it's all kinds of outcome against Pumice stone with its sustainability. Because Eco stone require less water and create less sludge as its corrosion is lesser than Pumice stone. And for its smooth surface the possibility of physical damage of garments is lower.

The existence of density function of the running maximum of a stochastic differential equation (SDE) driven by a Brownian motion and a nontruncated pure-jump process is verified. This is proved by the existence of density function of the running maximum of the Wiener–Poisson functionals resulting from Bismut’s approach to the Malliavin calculus for jump processes.

Design and Control of Continuous Jumping Gaits for Humanoid Robots Based on Motion Function and Reinforcement Learning