Showing papers on "Inertia published in 2014"
TL;DR: In this article, the authors investigated the settling speeds and root mean square (r.m.s.) velocities of inertial particles in isotropic turbulence with gravity using experiments with water droplets in air turbulence from 32 loudspeaker jets and direct numerical simulations (DNS).
Abstract: We investigate the settling speeds and root mean square (r.m.s.) velocities of inertial particles in isotropic turbulence with gravity using experiments with water droplets in air turbulence from 32 loudspeaker jets and direct numerical simulations (DNS). The dependence on particle inertia, gravity and the scales of both the smallest and largest turbulent eddies is investigated. We isolate the mechanisms of turbulence settling modification and find that the reduced settling speeds of large particles in experiments are due to nonlinear drag effects. We demonstrate using DNS that reduced settling speeds with linear drag (e.g. see Nielsen, J. Sedim. Petrol., vol. 63, 1993, pp. 835–838) only arise in artificial flows that, by design, eliminate preferential sweeping by the eddies. Gravity and inertia both reduce the particle r.m.s. velocities and falling particles are more responsive to vertical than to horizontal fluctuations. The model by Wang & Stock (J. Atmos. Sci., vol. 50, 1993, pp. 1897–1913) captures these trends.
146 citations
TL;DR: In this paper, an online algorithm for estimating the time of disturbance and inertia after a disturbance is proposed, which is in contrast to previous inertia estimation methods that operated offline and could provide support for adaptive frequency control.
Abstract: Offnominal power system frequency regimes play a key role in the propagation of disturbed system conditions and blackouts. The evolution of power systems will make the availability of frequency-control services more uncertain, increasing the risk of large frequency deviations. Furthermore, the reduction in the inherent inertia of power systems and their increased variability will be a critical threat to the quality of frequency control. This paper proposes an online algorithm for estimating the time of disturbance and inertia after a disturbance. This is in contrast to previous inertia estimation methods that operated offline. The algorithm processes wide-area measurements of frequency and active power and could provide support for adaptive frequency control. Simulations, laboratory tests, and real transmission system measurements have been used to demonstrate the algorithm's ability to correctly detect a disturbance, accurately estimate the time of the disturbance and the inertia, and prevent false disturbance detections.
142 citations
TL;DR: In this paper, a mean-field analysis of a Kuramoto model with inertia was performed for fully coupled and diluted systems, and it was shown that the transition from incoherence to coherence is hysteretic.
Abstract: We report finite-size numerical investigations and mean-field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine, for a gaussian distribution of the frequencies, the transition from incoherence to coherence for increasingly large system size and inertia. For sufficiently large inertia the transition is hysteretic, and within the hysteretic region clusters of locked oscillators of various sizes and different levels of synchronization coexist. A modification of the mean-field theory developed by Tanaka, Lichtenberg, and Oishi [Physica D 100, 279 (1997)] allows us to derive the synchronization curve associated to each of these clusters. We have also investigated numerically the limits of existence of the coherent and of the incoherent solutions. The minimal coupling required to observe the coherent state is largely independent of the system size, and it saturates to a constant value already for moderately large inertia values. The incoherent state is observable up to a critical coupling whose value saturates for large inertia and for finite system sizes, while in the thermodinamic limit this critical value diverges proportionally to the mass. By increasing the inertia the transition becomes more complex, and the synchronization occurs via the emergence of clusters of whirling oscillators. The presence of these groups of coherently drifting oscillators induces oscillations in the order parameter. We have shown that the transition remains hysteretic even for randomly diluted networks up to a level of connectivity corresponding to a few links per oscillator. Finally, an application to the Italian high-voltage power grid is reported, which reveals the emergence of quasiperiodic oscillations in the order parameter due to the simultaneous presence of many competing whirling clusters.
124 citations
TL;DR: In this paper, the authors combine finite element, immersed-boundary and lattice Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers.
Abstract: The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing, and only a limited number of experimental and theoretical studies are available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that the Segre‐Silberberg effect is suppressed with respect to the particle deformability. Depending on the deformability and strength of inertial effects, inward or outward lateral migration of the particles takes place. In particular, for increasing Reynolds numbers and strongly deformable particles, a hitherto unreported distinct flow focusing effect emerges, which is accompanied by a non-monotonic behaviour of the apparent suspension viscosity and thickness of the particle-free layer close to the channel walls. This effect can be explained by the behaviour of a single particle and the change of the particle collision mechanism when both deformability and inertia effects are relevant.
103 citations
TL;DR: A microscopic ordinary differential equation (ODE)-based model for pedestrian dynamics: the gradient navigation model, which uses a superposition of gradients of distance functions to directly change the direction of the velocity vector and which introduces a method to calibrate parameters by theoretical arguments based on empirical assumptions rather than by numerical tests.
Abstract: We present a microscopic ordinary differential equation (ODE)-based model for pedestrian dynamics: the gradient navigation model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is then integrated to obtain the location. The approach differs fundamentally from force-based models needing only three equations to derive the ODE system, as opposed to four in, e.g., the social force model. Also, as a result, pedestrians are no longer subject to inertia. Several other advantages ensue: Model-induced oscillations are avoided completely since no actual forces are present. The derivatives in the equations of motion are smooth and therefore allow the use of fast and accurate high-order numerical integrators. At the same time, the existence and uniqueness of the solution to the ODE system follow almost directly from the smoothness properties. In addition, we introduce a method to calibrate parameters by theoretical arguments based on empirically validated assumptions rather than by numerical tests. These parameters, combined with the accurate integration, yield simulation results with no collisions of pedestrians. Several empirically observed system phenomena emerge without the need to recalibrate the parameter set for each scenario: obstacle avoidance, lane formation, stop-and-go waves, and congestion at bottlenecks. The density evolution in the latter is shown to be quantitatively close to controlled experiments. Likewise, we observe a dependence of the crowd velocity on the local density that compares well with benchmark fundamental diagrams.
78 citations
TL;DR: In this paper, a corotational beam element for nonlinear dynamic analysis of 3D flexible frames is presented, where cubic interpolations are adopted to formulate both inertia and internal local terms.
75 citations
TL;DR: In this article, the resonance of a rectangular plate due to multiple traveling masses is studied and the peak values of DAF are determined with respect to the variation of loads velocity and inertia as well as their spacing.
69 citations
TL;DR: Usabiaga et al. as mentioned in this paper developed an inertial coupling method for modeling the dynamics of point-like "blob" particles immersed in an incompressible fluid, generalizing previous work for compressible fluids.
65 citations
TL;DR: In this article, the motion of a solid spheroid particle in a simple shear flow was investigated using a lattice Boltzmann method, and individual effects of fluid inertia and particle rotary inertia were examined.
Abstract: In this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.
60 citations
TL;DR: Results show that while displacement patterns are affected by inertial forces mainly by invasion of throats with higher capillary resistance, phase entrapment is largely unaffected by inertia, limiting inertial effects on hydrological properties behind a front.
Abstract: The seemingly regular and continuous motion of fluid displacement fronts in porous media at the macroscopic scale is propelled by numerous (largely invisible) pore-scale abrupt interfacial jumps and pressure bursts. Fluid fronts in porous media are characterized by sharp phase discontinuities and by rapid pore-scale dynamics that underlie their motion; both attributes challenge standard continuum theories of these flow processes. Moreover, details of pore-scale dynamics affect front morphology and subsequent phase entrapment behind a front and thereby shape key macroscopic transport properties of the unsaturated zone. The study presents a pore-throat network model that focuses on quantifying interfacial dynamics and interactions along fluid displacement fronts. The porous medium is represented by a lattice of connected pore throats capable of detaining menisci and giving rise to fluid-fluid interfacial jumps (the study focuses on flow rate controlled drainage). For each meniscus along the displacement front we formulate a local inertial, capillary, viscous, and hydrostatic force balance that is then solved simultaneously for the entire front. The model enables systematic evaluation of the role of inertia and boundary conditions. Results show that while displacement patterns are affected by inertial forces mainly by invasion of throats with higher capillary resistance, phase entrapment (residual saturation) is largely unaffected by inertia, limiting inertial effects on hydrological properties behind a front. Interfacial jump velocities are often an order of magnitude larger than mean front velocity, are strongly dependent on geometrical throat dimensions, and become less predictable (more scattered) when inertia is considered. Model simulations of the distributions of capillary pressure fluctuations and waiting times between invasion events follow an exponential distribution and are in good agreement with experimental results. The modeling approach provides insights into the rich pore-scale dynamics of displacement fronts; these insights not only improve the basic understanding of these ubiquitous processes, but could shed light on solute dispersion and colloids mobilization at fronts and the mechanical consequences of passing fronts.
59 citations
TL;DR: This paper investigates a simple propulsion mechanism --an up-down asymmetric dumbbell rotating about its axis of symmetry-- unable to propel in the absence of inertia in a Newtonian fluid, and derives the optimal dumbbell geometry.
Abstract: The fluid mechanics of small-scale locomotion has recently attracted considerable attention, due to its importance in cell motility and the design of artificial micro-swimmers for biomedical applications. Most studies on the topic consider the ideal limit of zero Reynolds number. In this paper, we investigate a simple propulsion mechanism --an up-down asymmetric dumbbell rotating about its axis of symmetry-- unable to propel in the absence of inertia in a Newtonian fluid. Inertial forces lead to continuous propulsion for all finite values of the Reynolds number. We study computationally its propulsive characteristics as well as analytically in the small-Reynolds-number limit. We also derive the optimal dumbbell geometry. The direction of propulsion enabled by inertia is opposite to that induced by viscoelasticity.
TL;DR: It is demonstrated that the dynamics of a system of coupled oscillators of distributed natural frequencies undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values, and the escape time out of metastable states scales exponentially with the number of oscillators.
Abstract: We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.
TL;DR: In this paper, the authors used Lagrange's equations associated with the finite element method to predict the dynamic behavior of a rotating rotor in the presence of base excitations, and derived the second-order differential equations of vibratory motion of the rotating rotor relative to the moving rigid base.
Abstract: In the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to rotary inertia, gyroscopic inertia, and shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor's rigid base. The use of Lagrange's equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.
TL;DR: This paper proposes a method that estimates the parameters of a velocity-controlled servo using the steady-state response produced by steps and sine-wave signals and employs the estimate of the viscous friction coefficient obtained in the first step.
Abstract: This paper proposes a method that estimates the parameters of a velocity-controlled servo. A proportional-integral controller, which uses only position measurements, closes the loop. The proposed approach uses the steady-state response produced by steps and sine-wave signals; they do not produce high levels of vibration on the servo compared with random signals commonly used with the least squares algorithm; moreover, it relies on simple numerical calculations. The method, which is called in the sequel as the steady-state response method (SSRM), consists of two steps. The first step uses three constant reference inputs in order to identify a constant disturbance and the viscous and Coulomb friction coefficients of the servo. In the second step, the SSRM estimates the servo inertia using a sine wave plus a constant signal as a velocity reference input and employs the estimate of the viscous friction coefficient obtained in the first step. Experiments on a testbed employing a brushless servomotor allow comparing the results obtained using the SSRM and those produced by a standard recursive least squares method (RLSM).
Patent•
07 May 2014
TL;DR: In this article, a high-precision three-dimensional posture inertia measurement system and method based on MEMS (Micro Electro Mechanical Systems), which relate to a highprecision 3D position inertia measurement method, is presented.
Abstract: The invention discloses a high-precision three-dimensional posture inertia measurement system and method based on MEMS (Micro Electro Mechanical Systems), which relate to a high-precision three-dimensional posture inertia measurement method. The system and the method disclosed by the invention aim for solving the problems that the existing three-dimensional posture inertia measurement equipment is low in cost and low in precision due to adoption of a sensor. A three-axis gyroscope sensor is used for sending measured angular speed data to an ARM (Advanced RISC Machines) processor; a three-axis accelerometer sensor is used for sending measured acceleration data to the ARM processor; a three-axis magnetometer sensor is used for sending measured magnetic strength data to the ARM processor; a temperature sensor is used for measuring and sending obtained temperature excursion data of the three-axis gyroscope sensor to the ARM processor; the ARM processor is used for processing the received data by means of front low-pass digital filtration, front-end data processing and expansion Kalman filtration respectively so as to obtain Euler angle three-dimensional posture inertia data or quaternion three-dimensional posture inertia data. The system and the method disclosed by the invention can be applied to the field of navigation control.
TL;DR: In this article, the authors study the asymptotic complete entrainment of Kuramoto oscillators with inertia on symmetric and connected networks and provide several sufficient conditions for the convergence in terms of initial phase-frequency configurations, strengths of inertia and coupling, and natural frequency distributions.
TL;DR: In this paper, the authors numerically analyze fluid flow through porous media up to a limiting Reynolds number of O(103) and derive a novel filtration law which is consistent with Darcy's law at small Re, reproduces Forchheimer's law and exhibits higher-order leading terms in the weak inertia regime.
Abstract: We numerically analyze fluid flow through porous media up to a limiting Reynolds number of O(103). Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of Re. On the macroscopic scale, inertial transition implies nonlinearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia-based extensions to the linear Darcy equation have been discussed in the literature; most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity, and interfacial drag, is inherently of sigmoidal shape. Based on this observation, we derive a novel filtration law which is consistent with Darcy's law at small Re, reproduces Forchheimer's law at large Re, and exhibits higher-order leading terms in the weak inertia regime.
TL;DR: In this paper, the authors proposed a theoretical model and an experimental methodology for defining the friction torque in a modified thrust ball bearing, operating in mixed and full film lubrication conditions, using a spin-down method.
TL;DR: In this article, a new mathematical model has been developed for the peristaltic transport of Maxwell fluid with heat and mass transfer, while taking into account the effect of thermal diffusion (Soret), occurring in an asymmetric channel with creeping flow.
TL;DR: In this article, a model of a rigid satellite around a planet, which is considered a spheroid with the gravitational potential calculated up to coefficient J4, is studied, and two simulation examples are carried out by using the exact and approximate models of the gravitational force and torque.
Abstract: Gravitational orbit-rotation coupling of a rigid satellite around a planet, which is considered a spheroid with the gravitational potential calculated up to coefficient J4, is studied. By introducing the satellite’s inertia integrals, a model of its gravitational force and torque up to the fourth order is established in the form of explicit formulations. Some interesting conclusions about the model are reached. These conclusions are useful in truncating the planet’s gravitational field and the satellite’s inertia integrals with the demanded precision of the gravitational force and torque given. Then the equations of motion are presented. With a special rigid satellite consisted of 36 point masses, two simulation examples are carried out by using the exact and approximate models of the gravitational force and torque. By comparisons between the errors of different order approximate models, the effects of the planet’s harmonic coefficients and the satellite’s inertia integrals are investigated in det...
TL;DR: In this article, the free vibration of a mass grounded by linear and nonlinear springs in series is studied and a nonlinear ordinary differential equation with inertia and static type cubic nonlinearities represents the governing equation of the system.
TL;DR: In this paper, the axial-torsional vibrations of rotating pretwisted thin-walled composite box beams exhibiting primary and secondary warping are investigated and coupled nonlinear axial torsional equations of motion are derived using Hamilton's principle.
TL;DR: In this article, the stability of the vertical path of a gravity- or buoyancy-driven disk of arbitrary thickness falling or rising in a viscous fluid, recently studied through direct numerical simulation by Auguste et al., is investigated numerically in the framework of global linear stability.
Abstract: The stability of the vertical path of a gravity- or buoyancy-driven disk of arbitrary thickness falling or rising in a viscous fluid, recently studied through direct numerical simulation by Auguste et al. (2013), is investigated numerically in the framework of global linear stability. The disk is allowed to translate and rotate arbitrarily and the stability analysis is carried out on the fully coupled system obtained by linearizing the Navier-Stokes equations for the fluid and Newton’s equations for the body. Three disks with different diameter-to-thickness ratios are considered: one is assumed to be infinitely thin, the other two are selected as archetypes of thin and thick cylindrical bodies, respectively. The analysis spans the whole range of body-to-fluid inertia ratios and considers Reynolds numbers (based on the fall/rise velocity and body diameter) up to 350. It reveals that four unstable modes with an azimuthal wavenumber m = ±1 exist in each case. Three of these modes result from a Hopf bifurcation while the fourth is associated with a stationary bifurcation. Varying the body-to-fluid inertia ratio yields rich and complex stability diagrams with several branch crossings resulting in frequency jumps; destabilization/restabilization sequences are also found to take place in some subdomains. The spatial structure of the unstable modes is also examined. Analyzing differences between their real and imaginary parts (which virtually correspond to two different instants of time in the dynamics of a given mode) allows us to assess qualitatively the strength of the mutual coupling between the body and fluid. Qualitative and quantitative differences between present predictions and known results for wake instability past a fixed disk enlighten the fact that the first non-vertical regimes generally result from an intrinsic coupling between the body and fluid and not merely from the instability of the sole wake.
TL;DR: In this article, the authors proposed a new approach to solve the non-convex economic dispatch problem using particle swarm optimization with smart inertia factor (PSO-SIF) algorithm in which, inertia coefficients are controlled with respect to cost function in each population.
Abstract: SUMMARY
This paper proposes a new approach to solve the non-convex economic dispatch problem using particle swarm optimization with smart inertia factor (PSO-SIF) algorithm in which, inertia coefficients are controlled with respect to cost function in each population. Hence, each population has unique inertia coefficient and as a result unique velocity in convergent direction for the best group solution. The new algorithm has been implemented on four test systems in different dimensions (6, 15, 20 and 40 units) with convex and non-convex cost functions. The numerical results have been compared with the results of a few PSO variants and some recently published results. The results prove the robustness and effectiveness of the proposed method and show that it could be used as a reliable tool for solving optimization problems. Copyright © 2013 John Wiley & Sons, Ltd.
TL;DR: In this article, a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation is studied.
Abstract: We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes previously studied Sakaguchi-Kuramoto, Hamiltonian and Brownian mean-field, and Tanaka-Lichtenberg-Oishi and Acebron-Bonilla-Spigler models. We derive an exact solution of the self-consistent equations for the order parameter in the stationary state, valid for arbitrary parameters in the dynamics, and demonstrate nontrivial phase transitions to synchrony that include reentrant synchronous regimes.
TL;DR: In this article, a piezoelectric bending actuator was designed for a resonant-type inertia linear motor, and the actuator's movement in a periodical sawtooth-shaped waveform was generated by composing two sinusoidal resonant bending vibrations with a frequency ratio of 1:2.
Abstract: Traditional piezoelectric inertia motors are generally driven at the quasi-static frequency range, which results in a relatively slow moving speed. In this paper, a piezoelectric bending actuator was designed for a resonant-type inertia linear motor. The driving mechanism of the actuator was also studied. The actuator's movement in a periodical sawtooth-shaped waveform was generated by composing two sinusoidal resonant bending vibrations with a frequency ratio of 1:2. A prototype inertia motor was fabricated. Experimental results confirmed the effectiveness of the design. The no-load maximum speed was 28.2 mm/s with drive voltage of 300 Vp–p for a base frequency of 587 Hz. At a preload force of 9.6 N and a driving voltage of 400 Vp–p for the base frequency, the linear speed was 18.5 mm/s with 0.02 N drag load. The moving direction could be reversed by changing the driving voltage's phase.
TL;DR: In this article, a probabilistic approach to assess the collective inertial contributions from wind generation across a power system is proposed and is applied to the Great Britain power system and the impact of the aggregate inertial response on arresting frequency fall is examined for the case of a sudden generation loss of 1.8 GW at the time of minimum load on both a mid summer and a mid-winter day.
Abstract: With the increasing wind penetration level in power systems, transmission system operators have become concerned about frequency stability. The inertia of a variable speed wind turbine is decoupled by power electronic converters from the power network and therefore does not intrinsically contribute to power system inertia. Moreover, as wind plant progressively displaces conventional generation and their inertia, a substantial reduction in power system inertia may occur. Variable speed wind turbines can be controlled to provide synthetic inertial response to compensate for their lack of direct contribution to power system inertia. A probabilistic approach to assessing the collective inertial contributions from wind generation across a power system is proposed and is applied to the Great Britain power system. The impact of the aggregate inertial response on arresting frequency fall is examined for the case of a sudden generation loss of 1.8 GW at the time of minimum load on both a mid-summer and a mid-winter day. The results show that synthetic inertial response from wind can reduce the rate of fall of frequency and the minimum system frequency (nadir) following the loss of generation event.
TL;DR: In this paper, a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation is studied.
Abstract: We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes previously studied Sakaguchi-Kuramoto, Hamiltonian and Brownian mean-field, and Tanaka-Lichtenberg-Oishi and Acebron-Bonilla-Spigler models. We derive an exact solution of the self-consistent equations for the order parameter in the stationary state, valid for arbitrary parameters in the dynamics, and demonstrate nontrivial phase transitions to synchrony that include reentrant synchronous regimes.
TL;DR: In this paper, a new inextensible theory of beam and plate deformation has been developed for static loading and deformation of a beam, which produces results in excellent agreement with experiment.
Abstract: A new inextensible theory of beam and plate deformation has been developed. For validation of this inextensible beam and plate theory, computational codes for the static and dynamic nonlinear beam and plate modal equations have been developed. The computations and experiments for static loading and deformation of a beam show that the inextensible theory produces results in excellent agreement with experiment. Also a comparison of the inextensible theory for a plate with a static experiment is encouraging. Finally a numerical study of dynamic deflection for a inextensible beam and plate also has been made. The results show a hysteresis dynamic response that depends on whether the excitaion frequency is increasing or decreasing for the stiffness nonlinearity only or for the inertia nonlinearity only. The inertia nonlinear force has a significant effect on the dynamic response in the resonant frequency range.
TL;DR: In this article, a finite-dimensional variational inequality model is formulated to describe the cross-state equilibrium conditions among heterogeneous travelers with different inertial degrees and knowledge structures, which allows for traveler's partial understanding and inertial effect in perceiving varying network conditions and provides a different perspective to describe traffic flow variations across multiple network scenarios.
Abstract: As an alternative effort for quantifying recurrent traffic dynamics caused by network variations and analyzing the impact on the network performance from information provision, we describe in this paper a new equilibrium modeling scheme for stochastic networks with a finite number of states, which takes into account the behavioral inertia. A finite-dimensional variational inequality model is formulated to describe the cross-state equilibrium conditions among heterogeneous travelers with different inertial degrees and knowledge structures. Our model allows for traveler’s partial understanding and inertial effect in perceiving varying network conditions and provides a different perspective (from existing stochastic and Markovian network equilibrium approaches) to describe traffic flow variations across multiple network scenarios. A disaggregate simplicial decomposition algorithm is suggested to solve the variational inequality problem. Numerical results from a few stochastic network examples demonstrate the validity and effectiveness of our methodology in modeling the inertia phenomenon within route choice behavior and the efficacy of using traveler information systems to eliminate the inertia effect.