Non-zero Speed Research Articles

Phase transition in a kinetic mean-field game model of inertial self-propelled agents

The framework of mean-field games (MFGs) is used for modeling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. By analyzing the associated coupled forward–backward in a time system of nonlinear Fokker–Planck and Hamilton–Jacobi–Bellman equations, we obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed. Using a combination of analysis and numerical simulations, we show that when energetic cost of control is reduced below a critical value, this equilibrium loses stability, and the system transitions to a traveling wave solution. Our work provides a game-theoretic perspective to the problem of collective motion in non-equilibrium biological and bio-inspired systems.

Naturalistic Observations of Human Driving Perceptions and Vehicle Kinematics at Stop Sign-Controlled Intersections

Understanding the human factors of how drivers perceive hazards and behave at stop sign-controlled intersections is essential for developing effective roadway features. This study aimed to evaluate the naturalistic behaviors of drivers at stop sign-controlled intersections and to assess the speeds at which drivers maneuvered through stop signs when no cross-traffic was present. To this end, 62 vehicles were analyzed in two, two-lane, four-way roadway intersections in Michigan. Results of this study indicate that most drivers slow to non-zero minimum speeds before traveling through an intersection and measurably encroach beyond stop lines. Assessment of lines of sight and visual obstructions at the subject intersections indicate that drivers’ perceptions of risk, evaluation of potential hazards, and cost of compliance ultimately impact behavior, as seen through vehicle kinematics.

Angular traveling waves of the high‐dimensional Boussinesq equation

AbstractThis paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high‐dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the unique stationary solution, they lack positivity, radial symmetry, and exponential decay. By employing variational and geometric approaches, along with perturbation theory, we establish the orbital (in)stability and strong instability of these traveling waves.

Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation

Two-dimensional reductions of the Kadomtsev–Petviashvili(KP)–Whitham system, namely the overdetermined Whitham modulation system for five dependent variables that describe the periodic solutions of the KP equation, are studied and characterized. Three different reductions are considered corresponding to modulations that are independent of x, independent of y, and of t (i.e. stationary), respectively. Each of these reductions still describes dynamic, two-dimensional spatial configurations since the modulated cnoidal wave, generically, has a nonzero speed and a nonzero slope in the xy plane. In all three of these reductions, the integrability of the resulting systems of equations is proven, and various other properties are elucidated. Compatibility with conservation of waves yields a reduction in the number of dependent variables to two, three and four, respectively. As a byproduct of the stationary case, the Whitham modulation system for the classical Boussinesq equation is explicitly obtained.

A phase-time-path-difference approach for online wave direction and wave number estimation from measured ship motions in zero and forward speed using a single inertial measurement unit

This study investigates the potential capability of a relatively new and unexplored signal-based approach for shipboard wave estimation. The approach uses the phase-time-path-differences (PTPDs) from an array of shipboard sensors to uniquely resolve the wave propagation direction and wave number. We derive a kinematic PTPD model accounting for forward vessel speed and assess its theoretical foundation to model the sensor delays on a rigid body. The forward-speed PTPD model is structurally equivalent to the zero-speed model considered in previous works, thus retaining the same observability results provided by a noncollinear array of a minimum of three sensors. Moreover, based on the outlined theory and PTPD model, we propose a methodology to estimate the main wave propagation direction and wave number online by employing a fast Fourier transform (FFT), an unscented Kalman filter (UKF), and a rigid-body measurement transformation based on a single inertial measurement unit (IMU). Provided that the vessel in question can be considered a rigid body, a single IMU is sufficient to obtain the desired wave quantities instead of three IMUs, as initially proposed in our previous work. Additionally, our methodology incorporates a novel frequency threshold to avoid distorted wave components caused by the effect of vessel filtering. The performance of our PTPD method is evaluated on data collected from a wave tank and full-scale experiments involving a vessel with zero and non-zero forward speed. The results show very good agreement with the reference wave values reported from a commercial wave radar and wave buoys operating in proximity to the vessel, indicating that our proposed method is competitive with existing wave measurement technology in terms of accuracy and online performance while being cheap, easy to install, flexible, and robust against environmental influences.

Utilizing Dynamic Analysis in the Complex Design of an Unconventional Three-Wheeled Vehicle with Enhancing Cornering Safety

Current trends in the transportation industry prioritize competitive rivalry, compelling manufacturers to prioritize concepts such as quality and reliability. These concepts are closely associated with public expectations of safety, vehicle lifespan, and trouble-free operation. However, the public must recognize that a vehicle weighing several hundred kilograms, moving at a non-zero speed, only contacts the road surface through a few points (depending on the number of wheels), each no larger than a human palm. Therefore, it is imperative to operate the vehicle in a manner that optimizes the behavior of these contact points. There are situations where drivers find themselves requiring dynamic vehicle handling, often unpredictable with a high degree of uncertainty. Rapid changes in direction become necessary in these cases. Such maneuvers can pose a significant risk of rollover for three-wheeled vehicles. Hence, the vehicle itself should contribute to increased ride safety. This paper presents key findings from the development of an unconventional three-wheeled vehicle utilizing the delta arrangement. Rollover safety for three-wheeled vehicles is currently well-managed, thanks to the utilization of electronic or mechatronic systems in delta-type vehicles to enhance stability. However, these systems require additional components. In contrast, the proposed control system operates solely on a mechanical principle, eliminating operational costs, energy consumption, maintenance expenses, and similar factors. The study also explores the absence of equivalent suspension and steering systems for front-wheel steering. Such designs are lacking in both practical applications and theoretical realms. Analytical and simulation calculations are compared in this study, highlighting the effectiveness of the newly proposed control system in enhancing stability and safety compared to conventional front-wheel suspension systems. Simulation programs provide more realistic results than analytical calculations due to their ability to account for dynamic effects on vehicle components and passengers, which is practically unfeasible in analytical approaches. Furthermore, this study focuses on investigating the fatigue life of material frames subjected to dynamic loading, which is a crucial aspect of ensuring safety. It is essential to have various testing devices to examine the fatigue life of materials under both uniaxial and multiaxial loading conditions. However, obtaining experimental results for fatigue life measurements of specific materials, which can be directly applied to one’s research, poses significant challenges. Hence, the proposed testing device plays a vital role in measuring material fatigue life and advancing the development of unconventional transportation methods. The information about the original testing device aligns perfectly with the article’s emphasis on dynamic analysis. The ultimate objective of all these efforts is to put the vehicle into practical operation for commercial utilization.

Research on the Improvement of Safety Navigation Based on the Shipmaster’s Control of Ship Navigational Parameters When Sailing in Different Sea State Conditions

Shipmasters must make several quick decisions with respect to the ship’s speed and heading when new sea conditions approach. The implications for ship stability and risky situations are known but there are no guides on how they should be addressed in this limited period of time. In the present paper, and from three points of view, the ship’s rolling motion in the long-term domain is analysed. Firstly, the ship’s behaviour after the influence of a single and external force was studied. Secondly, the influence of successive regular beam seas, with resistance and at zero-speed conditions, was analysed. Finally, the influence of wave direction on a ship sailing at non-zero speed was investigated. Results showed that once five minutes elapse, the rolling angle tends to be null regardless of the ship’s loading condition and that after a certain period of time, a coupling of the ship’s rolling frequency with the waves’ period and angle amplitude occurs. This circumstance was noted after three minutes for all of the ship loading conditions. Finally, novel guides for shipmasters in the form of 3D maps and polar diagrams were proposed to improve the ship’s behaviour-altering navigational parameters (heading and ship’s speed) when sailing in changing weather conditions. Therefore, for the three approaches, the relevant results and novel mathematical relations of linear factors were obtained which can be considered useful and applicable by the ship operators of most fishing and merchant fleets (regardless of their sizes) when they are operating under normal loading conditions.

Aerodynamic Window Sealing of a Large-Aperture Channel for High-Power Laser Transmission

In this study, the sealing of a large-aperture channel for high-power laser transmission is achieved using an aerodynamic window. Further, a numerical model of the gas and dust particle motion in the channel is established under three different blowing schemes, and the sealing performance of the large-aperture channel is analyzed and compared under different blowing schemes. The results indicate that the larger the proportion of purge gas volume flows in the axial direction, the better the sealing effect of the channel. More importantly, the axial blowing scheme can ensure that the large-aperture channel maintains the relative positive pressure to the external environment, effectively blocking the ambient gas and dust particles blowing in. The axial blowing scheme can achieve the sealing requirements of the large-aperture channel in an environment where the ambient wind speed is less than 20 m/s, and the dust particle mass concentration is less than 8×10−3 kg/m3. In this case, the minimum non-zero z-directional wind speed is stable and positive at a position 100 mm away from the port in the channel, and the particle mass concentration is zero.

Generalized geodesic deviation in de Sitter spacetime

The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally treated as the same order in smallness as the separation itself. This assumption is discussed in various papers but is not articulated in any standard textbooks on general relativity. Relaxing this assumption leads to the generalized geodesic deviation equation (GGDE). We elucidate the distinction between the GDE and the GGDE by explicitly computing the relative acceleration between timelike geodesics in two-dimensional de Sitter spacetime. We do this by considering a fiducial geodesic and a secondary geodesic (both timelike) that cross with nonzero speed. These geodesics are spanned by a spacelike geodesic, whose tangent evaluated at the fiducial geodesic defines the separation. The second derivative of the separation describes the relative acceleration between the fiducial and secondary geodesics. Near the crossing point, where the separation between the timelike geodesics is small but their rates of separation can be large, we show that the GGDE holds but the GDE fails to apply.

A control scheme for 360°thrust vectoring of cycloidal propellers with forward speed

This paper introduces a control scheme to vector thrust in marine cycloidal propellers with non-zero forward speed, despite the presence of measurement noise and current-like disturbances. Cycloidal propellers utilize 360° thrust-vectoring to provide agile maneuvering to surface vessels like tugboats and double ended ferries, but have yet to be utilized in present-day unmanned and autonomous marine vehicles. This work strategizes a low-level cycloidal propeller controller to track a reference thrust magnitude and direction for use in high-level control of underwater vehicles. Unlike previous work that assumes zero inflow-speed, the propeller-shaft speed and propeller-blade phase are hydrodynamically coupled in cases with non-zero inflow. The incorporation of this coupling enables thrust-tracking over varying advance-speeds necessary for propulsion and maneuvering of unmanned and autonomous underwater vehicles. A torque controller for screw propellers is extended for thrust-tracking in cycloidal propellers. A propeller-phase control loop is added and the resultant controller is verified through simulations for 360° thrust vectoring of cycloidal propellers in currents and varying cruise speeds. This low-level controller will enable use of cycloidal propellers for high maneuverability and thrust-augmentation in applications like station-keeping, seakeeping, maneuvering, and teaming of unmanned and autonomous marine vehicles in complex marine environments like surf zones and restricted waters.

Force impact suppression of contact transition state in robot grinding and polishing of industrial blades

When using robots to carry out grinding and polishing processing of industrial blades, due to factors such as non-zero approach speed and discontinuous dynamic characteristics, the robot grinding and polishing processing has contact force impact and oscillation problems during the contact transition process, which seriously affects the quality of the blade surface processing, contour accuracy, and control system stability. In order to solve the problem of large impact of contact force in robot grinding and polishing, this paper proposes an optimization method for impact suppression in the transition state of robot grinding and polishing. Taking the robot abrasive belt grinding and polishing as the research object, the adaptive weighted particle swarm algorithm is used to optimize the input shaper and realize the parameter self-tuning of the input shaping technology. The experimental results show that the stabilization time is shortened by about 86.5%, and the maximum overshoot of contact force is reduced by about 88.5% during contact transition. The method proposed in this paper can realize the smooth transition of the blade grinding and polishing process, does not need system modeling, effectively shorten the system stabilization time, reduce the maximum overshoot, and accelerate the system response speed, and it has strong stability and flexibility.

Backstepping Control of a Hyperbolic PDE System with Zero Characteristic Speed

In this paper, we study the single-input boundary feedback stabilization of 3 × 3 linear hyperbolic partial differential equations (PDEs) with two counterconvecting PDEs and the third one with zero characteristic speed. We design a full-state backstepping controller which exponentially stabilizes the origin in the L2 sense. The zero transport velocity makes the previous backstepping designs inapplicable (their application would result in a controller with infinite gains). To employ backstepping in the presence of zero speed, we use an invertible Volterra transformation only for the PDEs with nonzero speeds, leaving the state of the zero-speed PDE unaltered in the target system, but making the target zero-speed PDE input-to-state stable with respect to the decoupled and stable counterconvecting nonzero-speed PDEs. In addition to achieving stabilization, we produce an explicit bound on the rate of convergence of the target system by a method of successive approximations and the use of Laplace transform. Simulation results are presented to illustrate the effectiveness of the proposed control design.

Biased random walk on supercritical percolation: anomalous fluctuations in the ballistic regime

We study biased random walk on the infinite connected component of supercritical percolation on the integer lattice Zd for d≥2. For this model, Fribergh and Hammond showed the existence of an exponent γ such that: for γ<1, the random walk is sub-ballistic (i.e. has zero velocity asymptotically), with polynomial escape rate described by γ; whereas for γ>1, the random walk is ballistic, with non-zero speed in the direction of the bias. They moreover established, under the usual diffusive scaling about the mean distance travelled by the random walk in the direction of the bias, a central limit theorem when γ>2. In this article, we explain how Fribergh and Hammond’s percolation estimates further allow it to be established that for γ∈(1,2) the fluctuations about the mean are of an anomalous polynomial order, with exponent given by γ−1.

Asymptotic behaviors of forced waves for the lattice Lotka–Volterra competition system with shifting habitats

This paper is concerned with the lattice Lotka–Volterra competition system under shifting habitats. By some delicate analyses, we establish the exactly exponential asymptotic decay of the forced wave with nonzero forced speed, the existence of which has been obtained by Wang et al. (2020). This gives a detailed description on the tail behaviors of the forced waves in a shifting environment.

Vibration Mode Analysis of ANSYS WORKBENCH-Based Garden Blower Impeller

This paper mainly takes the wind impeller, the main structural component of the blower and suction machine, as the research object, uses Solidworks software to model the blower and suction machine wind impeller, and then uses the finite element software, ANSYS WORKBENCH, to conduct a modal analysis, and obtain the natural frequencies and corresponding vibration modes of the impeller of the blower and suction machine at different speeds. Among them, for a non-zero speed, the corresponding centrifugal force will inevitably be generated when it rotates. Therefore, for the case of non-zero speed, first analyze the corresponding prestress, and then analyze the first five natural frequencies of the impeller at the corresponding speed under the influence of the prestress. Through the analysis, the excitation frequency and speed of the impeller resonance are obtained.

Experimental evidence for super-Alfvénic acceleration of the field-reversed configuration due to a magnetic pressure gradient

The super-Alfvénic acceleration of an extremely high beta plasmoid due to a magnetic pressure gradient is evidenced in translation experiments involving the field-reversed configuration (FRC) in the FRC amplification via the translation-collisional merging (FAT-CM) device. Inside the FRC, there is a population of unmagnetized particles that forms a volume with extremely high beta. Formed using the field-reversed theta pinch method, the FRC is accelerated and injected into a quasi-static confinement magnetic field that is weaker than the formation and acceleration fields. Because the FRC is injected with nonzero axial translation speed and cannot slow down, its speed exceeds the Alfvénic and sonic speed upon entering the confinement field. This phenomenon is predicted from two-dimensional resistive magnetohydrodynamic simulations, and experimental results that are consistent with the magnetohydrodynamic approximation show that the FRC acceleration process is due mainly to magnetic pressure on the thin magnetized layer.

Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes

This survey presents results on the stability of elevation solitary waves in axisymmetric elastic membrane tubes filled with a fluid. The elastic tube material is characterized by an elastic potential (elastic energy) that depends non-linearly on the principal deformations and describes the compliant elastic media. Our survey uses a simple model of an inviscid incompressible fluid, which nevertheless makes it possible to trace the main regularities of the dynamics of solitary waves. One of these regularities is the spectral stability (linear stability in form) of these waves. The basic equations of the ‘axisymmetric tube – ideal fluid’ system are formulated, and the equations for the fluid are averaged over the cross-section of the tube, that is, a quasi-one-dimensional flow with waves whose length significantly exceeds the radius of the tube is considered. The spectral stability with respect to axisymmetric perturbations is studied by constructing the Evans function for the system of basic equations linearized around a solitary wave type solution. The Evans function depends only on the spectral parameter , is analytic in the right-hand complex half-plane , and its zeros in coincide with unstable eigenvalues. The problems treated include stability of steady solitary waves in the absence of a fluid inside the tube (the case of constant internal pressure), together with the case of local inhomogeneity (thinning) of the tube wall, the presence of a steady fluid filling the tube (the case of zero mean flow) or a moving fluid (the case of non-zero mean flow), and also the problem of stability of travelling solitary waves propagating along the tube with non-zero speed. Bibliography: 83 titles.

Forced waves and gap formations for a Lotka–Volterra competition model with nonlocal dispersal and shifting habitats

This paper is mainly concerned with the forced waves and gap formations for a Lotka–Volterra competition model with nonlocal dispersal and shifting habitats. We first show that there exist two positive numbers c1∗ and c2∗ such that the system admits a forced wave provided that the forcing speed c∈(−c2∗,c1∗) by the iterative techniques combining with some known results for the forced moving KPP equations. Meanwhile, we use some delicate analysis to obtain the asymptotic behaviors at infinity of the forced waves with nonzero forcing speed c∈(−c2∗,0)∪(0,c1∗). Then, based on the comparison argument, we prove that the gap formations exist for c>c1∗ and c<−c2∗. Finally, some numeric simulation results are presented to confirm our theoretical results, which also contains the critical cases of c=c1∗ and c=−c2∗.

Implicit-explicit-compact methods for advection diffusion reaction equations

We provide a comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity, the error in the phase speed and scaled numerical diffusion coefficient of four spatiotemporal discretization schemes utilized for solving a linear, one-dimensional (1D) as well as a linear/nonlinear, two-dimensional (2D) advection diffusion reaction (ADR) equation: (a) Explicit (RK2) temporal integration combined with the Optimal Upwind Compact Scheme (or OUCS3, J. Comp. Phys., 192, pg. 677–694 (2003)) and the central difference scheme (CD2), (b) Fully implicit mid-point rule for time integration coupled with the OUCS3 and the Lele’s compact scheme (J. Comp. Phys., 103, pg. 16–42 (1992)), (c) Implicit (mid-point rule)-explicit (RK2) or IMEX time integration blended with OUCS3 and Lele’s compact scheme (where the IMEX time integration follows the same ideology as introduced by Ascher et al., SIAM J. Numer. Anal., 32(3), pg. 797–823 (1995)), and (d) IMEX (mid-point/RK2) time integration melded with the New Combined Compact Difference scheme (or NCCD scheme, J. Comp. Phys., 228, pg. 6150–6168 (2009)). Analysis reveals the superior resolution features of the IMEX-OUCS3-Lele scheme and the IMEX-NCCD scheme including an enhanced region of asymptotic stability (a region with numerical amplification factor less than unity), a diminished region of spurious propagation characteristics (or a region of negative scaled group velocity) and a smaller region of nonzero phase speed error. In particular, the IMEX-NCCD scheme captures the correct propagation feature (or positive scaled group velocity) in the largest possible region in the wavenumber-Courant-Friedrichs-Lewy (CFL) number, parameter space, in comparison with the other three numerical methods. The in silico experiments investigating the role of q−waves in the numerical solution of the linear, 1D ADR equation divulge excellent Dispersion Relation Preservation (DRP) properties of the IMEX-NCCD scheme including minimal dissipation via implicit filtering and negligible unphysical oscillations (or Gibbs’ phenomenon) on coarser grids. The numerical solution of the 2D viscous Burgers’ Equation underline the supremacy of the IMEX method with regard to handling the ‘stiff’ derivative terms in contrast with a fully explicit time integration method and lower computational time versus with a fully implicit scheme. The DRP resolution of the IMEX-NCCD scheme is further benchmarked by solving the classical two-dimensional (2D), Patlak-Keller-Segel (PKS) nonlinear parabolic model. Numerical results reveal that the spiky structure of the solution is oscillation free and, when compared with the Explicit-OUCS3-CD2 method, the solution is better resolved by the IMEX-NCCD method.

Random Walk on the Simple Symmetric Exclusion Process

We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole, so that its asymptotic behavior is expected to depend on the density rho in [0, 1] of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities rho except for at most two values rho _-, rho _+ in [0, 1]. The asymptotic speed we obtain in our LLN is a monotone function of rho . Also, rho _- and rho _+ are characterized as the two points at which the speed may jump to (or from) zero. Furthermore, for all the values of densities where the random walk experiences a non-zero speed, we can prove that it satisfies a functional central limit theorem (CLT). For the special case in which the density is 1/2 and the jump distribution on an empty site and on an occupied site are symmetric to each other, we prove a LLN with zero limiting speed. We also prove similar LLN and CLT results for a different environment, given by a family of independent simple symmetric random walks in equilibrium.