Inertial Dynamics Research Articles

Theroy of magnetic inertial dynamics in two-sublattice ferromagnets

The magnetic inertial dynamics have previously been investigated for one sublattice ferromagnets. Here, we develop the magnetization dynamics in two-sublattice ferromagnets including the intra- and inter-sublattice inertial dynamics. First, we derive the magnetic susceptibility of such a ferromagnet. Next, by finding the poles of the susceptibility, we calculate the precession and nutation resonance frequencies. Our results suggest that while the resonance frequencies show decreasing behavior with the increasing intra-sublattice relaxation time, the effect of inter-sublattice inertial dynamics has an opposite effect.

Inertial magnetization dynamics of ferromagnetic nanoparticles including thermal agitation

The appropriate magnetic Langevin equation, namely the inertial Landau-Lifshitz-Gilbert equation augmented by thermal noise, is written starting from an analogy with the dynamics of the magnetic dipole moment of a circular current-carrying loop (wire) viewed as a symmetric top. Hence the corresponding Fokker-Planck equation for the evolution of the probability density function in the phase space of angular velocities and orientations and its stationary solution are derived. Moreover, the inertial stochastic magnetization dynamics of ferromagnetic nanoparticles is also seen to be analogous to the stochastic dynamics of the electric dipole moment of a polar molecule visualized as a dipole lying along the axis of symmetry of a symmetric top ignoring friction about that axis--a conclusion reached by replacing electrical parameters with their magnetic analogs in the respective Langevin equations. Therefore, existing results from gyroscopic theory, as applied to dielectric relaxation of polar molecules, may with appropriate modifications be used to study inertial magnetization effects in ferromagnetic nanoparticles.

Intermittency of Velocity Circulation in Quantum Turbulence

The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation is quantized, taking discrete values that are directly related to the number and the orientation of thin vortex filaments enclosed by the path. By varying the size of such closed loop, the circulation provides a measure of the dependence of the flow structure on the considered scale. Here we consider the scale dependence of circulation statistics in quantum turbulence, using high resolution direct numerical simulations of a generalized Gross-Pitaevskii model. Results are compared to the circulation statistics obtained from simulations of the incompressible Navier-Stokes equations. When the integration path is smaller than the mean inter-vortex distance, the statistics of circulation in quantum turbulence displays extreme intermittent behavior due to the quantization of circulation, in stark contrast with the viscous scales of classical flows. In contrast, at larger scales, circulation moments display striking similarities with the statistics probed in the inertial range of classical turbulence. This includes the emergence of the power law scalings predicted from Kolmogorov's 1941 theory, as well as intermittency deviations that closely follow the recently proposed bifractal model for circulation moments in classical flows. To date, this is the most convincing evidence of intermittency in the large scales of quantum turbulence. Moreover, our results strongly reinforce the resemblance between classical and quantum turbulence, highlighting the universality of inertial range dynamics, including intermittency, across these two a priori very different systems.

Frequency Domain Analysis of Partial-Tensor Rotating Accelerometer Gravity Gradiometer.

The output model of a rotating accelerometer gravity gradiometer (RAGG) established by the inertial dynamics method cannot reflect the change of signal frequency, and calibration sensitivity and self-gradient compensation effect for the RAGG is a very important stage in the development process that cannot be omitted. In this study, a model based on the outputs of accelerometers on the disc of RGAA is established to calculate the gravity gradient corresponding to the distance, through the study of the RAGG output influenced by a surrounding mass in the frequency domain. Taking particle, sphere, and cuboid as examples, the input-output models of gravity gradiometer are established based on the center gradient and four accelerometers, respectively. Simulation results show that, if the scale factors of the four accelerometers on the disk are the same, the output signal of the RAGG only contains ( is the spin frequency of disc for RAGG) harmonic components, and its amplitude is related to the orientation of the surrounding mass. Based on the results of numerical simulation of the three models, if the surrounding mass is close to the RAGG, the input-output models of gravity gradiometer are more accurate based on the four accelerometers. Finally, some advantages and disadvantages of cuboid and sphere are compared and some suggestions related to calibration and self-gradient compensation are given.

Glow in the Dark: Smartphone Inertial Odometry for Vehicle Tracking in GPS Blocked Environments

Although vehicle location-based services are prevalent outdoors, we are back into darkness in many GPS blocked environments, such as tunnels, indoor parking garages, and multilevel flyovers. Existing smartphone-based solutions usually adopt inertial dead reckoning to infer the trajectory, but low-quality inertial sensors in phones are plagued by heavy noises, causing unbounded localization errors through double integrations for movements. In this article, we propose VeTorch, a smartphone inertial odometry that devises an inertial sequence learning framework to track vehicles in real time when GPS signal is not available. Specifically, we transform the inertial dynamics from the phone to the vehicle regardless of the arbitrary phone's placement in the car and explore a temporal convolutional network to learn the vehicle's moving dependencies directly from the inertial data. To tackle the heterogeneous smartphone properties and driving habits, we propose a federated learning-based active model training mechanism to produce customized models for individual smartphones, without incurring user privacy issues. We implement a highly efficient prototype and conduct extensive experiments on two large-scale real-world traffic data sets collected by a modern ride-hailing platform. Our results outperform the state-of-the-art vehicular inertial dead-reckoning solutions on both accuracy and efficiency.

Nutation in antiferromagnetic resonance

The effect of inertial spin dynamics is compared between ferromagnetic, antiferromagnetic and ferrimagnetic systems. The linear response to an oscillating external magnetic field is calculated within the framework of the inertial Landau--Lifshitz--Gilbert equation using analytical theory and computer simulations. Precession and nutation resonance peaks are identified, and it is demonstrated that the precession frequencies are reduced by the spin inertia, while the lifetime of the excitations is enhanced. The interplay between precession and nutation is found to be the most prominent in antiferromagnets, where the timescale of the exchange-driven sublattice dynamics is comparable to inertial relaxation times. Consequently, antiferromagnetic resonance techniques should be better suited for the search for intrinsical inertial spin dynamics on ultrafast timescales than ferromagnetic resonance.

Collective orientation of an immobile fish school and effect on rheotaxis.

We study the orientational order of an immobile fish school. Starting from the second Newton law, we show that the inertial dynamics of orientations is ruled by an Ornstein-Uhlenbeck process. This process describes the dynamics of alignment between neighboring fish in a shoal-a dynamics already used in the literature for mobile fish schools. First, in a fluid at rest, we calculate the global polarization (i.e., the mean orientation of the fish), which decreases rapidly as a function of noise. We show that the faster a fish is able to reorient itself the more the school can afford to reorder itself for important noise values. Second, in the presence of a stream, each fish tends to orient itself and swims against the flow: so-called rheotaxis. So, even in the presence of a flow, it results in an immobile fish school. By adding an individual rheotaxis effect to alignment interaction between fish, we show that in a noisy environment individual rheotaxis is enhanced by alignment interactions between fish.

Analytical model of the deformation-induced inertial dynamics of a magnetic vortex

We present an analytical model to account for the deformation-induced inertial dynamics of a magnetic vortex. The model is based on a deformation of the vortex core profile based on the Döring kinetic field, whereby the deformation amplitudes are promoted to dynamical variables in a collective-coordinate approach that provides a natural extension to the Thiele model. This extended model describes complex transients due to inertial effects and the variation of the effective mass with velocity. The model also provides a quantitative description of the inertial dynamics leading up to vortex core reversal, which is analogous to the Walker transition in domain wall dynamics. Our work paves the way for a standard prescription for describing the inertial effects of topological magnetic solitons.

A Sensory Instrumented Particle for Environmental Monitoring Applications: Development and Calibration

A plethora of environmental sensing applications, including geomorphic, ecohydraulic and turbulent flow processes, involve the monitoring of the stability of bed surface particles. This work presents a miniaturized sensory instrumented particle that aims to provide a direct, non-intrusive and low-cost method for environmental monitoring of the processes taking place at the interface between the water and sediment surface. Specifically a miniaturized particle (3cm) is designed and developed to simulate the behavior of coarse bed surface particles in aquatic environments, such as rivers and estuaries. This particle has the capability of precisely and at a high frequency (1000Hz) quantifying its inertial dynamics during motion, using embedded microelectromechanical (MEMS) sensors, consisting of a triaxial accelerometer (up to 16g), a triaxial gyroscope (up to 2000°/s) and a magnetometer. The sensors are calibrated using simple physical motions to estimate the uncertainties in the inertial sensor’s logged readings. The performance of the instrumented particle and data uncertainties after using inertial sensor fusion, are assessed with two physical experiments: a random rotating motion and a controlled motor transverse table. The results of the sensor fusion of the logged readings (corrected acceleration, corrected angular velocity and orientation) are deemed reliable with an infinitesimal error range. The instrumented particle is tested at a laboratory setting under well-controlled flow conditions. The results demonstrate that the instrumented particle can be used to sense particle’s motion, which is useful for a range of environmental monitoring applications.

Reproducing pyroclastic density current deposits of the 79 CE eruption of the Somma–Vesuvius volcano using the box-model approach

Abstract. We use PyBox, a new numerical implementation of the box-model approach, to reproduce pyroclastic density current (PDC) deposits from the Somma–Vesuvius volcano (Italy). Our simplified model assumes inertial flow front dynamics and mass deposition equations and axisymmetric conditions inside circular sectors. Tephra volume and density and total grain size distribution of EU3pf and EU4b/c, two well-studied PDC units from different phases of the 79 CE Pompeii eruption, are used as input parameters. Such units correspond to the deposits from variably dilute, turbulent PDCs. We perform a quantitative comparison and uncertainty quantification of numerical model outputs with respect to the observed data of unit thickness, inundation areas and grain size distribution as a function of the radial distance to the source. The simulations consider (i) polydisperse conditions, given by the total grain size distribution of the deposit, or monodisperse conditions, given by the mean Sauter diameter of the deposit; (ii) axisymmetric collapses either covering the whole 360∘ (round angle) or divided into two circular sectors. We obtain a range of plausible initial volume concentrations of solid particles from 2.5 % to 6 %, depending on the unit and the circular sector. Optimal modelling results of flow extent and deposit thickness are reached on the EU4b/c unit in a polydisperse and sectorialized situation, indicating that using total grain size distribution and particle densities as close as possible to the real conditions significantly improves the performance of the PyBox code. The study findings suggest that the simplified box-model approach has promise for applications in constraining the plausible range of the input parameters of more computationally expensive models. This could be done due to the relatively fast computational time of the PyBox code, which allows the exploration of the physical space of the input parameters.

Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling

<p style='text-indent:20px;'>In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely on the asymptotic behavior of an inertial system combining geometric damping with temporal scaling. The convex function to minimize enters the dynamic via its gradient. The dynamic includes three coefficients varying with time, one is a viscous damping coefficient, the second is attached to the Hessian-driven damping, the third is a time scaling coefficient. We study the convergence rate of the values under general conditions involving the damping and the time scale coefficients. The obtained results are based on a new Lyapunov analysis and they encompass known results on the subject. We pay particular attention to the case of an asymptotically vanishing viscous damping, which is directly related to the accelerated gradient method of Nesterov. The Hessian-driven damping significantly reduces the oscillatory aspects. We obtain an exponential rate of convergence of values without assuming the strong convexity of the objective function. The temporal discretization of these dynamics opens the gate to a large class of inertial optimization algorithms.</p>

Inertial forces in the Maxey–Riley equation in nonuniform flows

Here, inertial forces on particles in nonuniform ambient flows, previously missing from the Maxey---Riley formulation of inertial particle dynamics, are identified. These forces involve both local and convective fluid inertia and depend on the curvature of the ambient flow. These new terms provide quantitative corrections and qualitative additions to the Maxey---Riley equation and are relevant when the particle size is appreciable relative to the characteristic length scale of the ambient flow.

ИСПОЛЬЗОВАНИЕ ПОТЕНЦИАЛА РОСТА РОССИЙСКОЙ ЭКОНОМИКИ ДЛЯ ДОСТИЖЕНИЯ ЦЕЛЕЙ РАЗВИТИЯ ОБЩЕСТВА

The article considers the main directions of using the potential of economic growth in Russia to increase the pace and quality of growth, as well as improve the quality of life. It is noted that the inertial economic dynamics does not ensure the goals of the development of the Russian economy and maintaining its competitiveness in the world. It is stated that the greatest growth potential remains in the part of the population's demand, whose contribution to economic dynamics is limited due to income gaps and inefficient consumption structure. It is assumed that the greatest results can be achieved by combining social policy measures and stimulating private investment.

Second-Order Dynamics with Hessian-Driven Damping for Linearly Constrained Convex Minimization

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 5 March 2020Accepted: 14 June 2021Published online: 18 October 2021Keywordsdissipative inertial dynamics, Hessian-driven damping, Lyapunov analysis, asymptotic properties, Bregman distance, convex minimizationAMS Subject Headings37N40, 46N10, 49M30, 65K05, 90C25Publication DataISSN (print): 0363-0129ISSN (online): 1095-7138Publisher: Society for Industrial and Applied MathematicsCODEN: sjcodc

Inertial drag and lift forces for coarse grains on rough alluvial beds measured using in-grain accelerometers

Abstract. Quantifying the force regime that controls the movement of a single grain during fluvial transport has historically proven to be difficult. Inertial micro-electromechanical system (MEMS) sensors (sensor assemblies that mainly comprise micro-accelerometers and gyroscopes) can used to address this problem using a “smart pebble”: a mobile inertial measurement unit (IMU) enclosed in a stone-like assembly that can measure directly the forces on a particle during sediment transport. Previous research has demonstrated that measurements using MEMS sensors can be used to calculate the dynamics of single grains over short time periods, despite limitations in the accuracy of the MEMS sensors that have been used to date. This paper develops a theoretical framework for calculating drag and lift forces on grains based on IMU measurements. IMUs were embedded a spherical and an ellipsoidal grain and used in flume experiments in which flow was increased until the grain moved. Acceleration measurements along three orthogonal directions were then processed to calculate the threshold force for entrainment, resulting in a statistical approximation of inertial impulse thresholds for both the lift and drag components of grain inertial dynamics. The ellipsoid IMU was also deployed in a series of experiments in a steep stream (Erlenbach, Switzerland). The inertial dynamics from both sets of experiments provide direct measurement of the resultant forces on sediment particles during transport, which quantifies (a) the effect of grain shape and (b) the effect of varied-intensity hydraulic forcing on the motion of coarse sediment grains during bedload transport. Lift impulses exert a significant control on the motion of the ellipsoid across hydraulic regimes, despite the occurrence of higher-magnitude and longer-duration drag impulses. The first-order statistical generalisation of the results suggests that the kinetics of the ellipsoid are characterised by low- or no-mobility states and that the majority of mobility states are controlled by lift impulses.

Surfing and crawling macroscopic active particles under strong confinement: Inertial dynamics

This work studies the dynamics of inertial active particles under strong confinement and observe that he probability density of position peaks at a finite distance away from the confining wall, and that individual particles exhibit several dynamical states and transitions between them can be controlled by the level of self-propulsion.

Nutation resonance in ferromagnets

The inertial dynamics of magnetization in a ferromagnet is investigated theoretically. The analytically derived dynamic response upon microwave excitation shows two peaks: ferromagnetic and nutation resonances. The exact analytical expressions of frequency and linewidth of the magnetic nutation resonance are deduced from the frequency dependent susceptibility determined by the inertial Landau-Lifshitz-Gilbert equation. The study shows that the dependence of nutation linewidth on the Gilbert precession damping has a minimum, which becomes more expressive with increase of the applied magnetic field.

Pore-Scale Transport and Two-Phase Fluid Structures in Fibrous Porous Layers: Application to Fuel Cells and Beyond

We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three-dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics, and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regime at intermediate times, where liquid is transported along a gradually increasing number of preferential flow paths of the size of one–two pores, and a third regime at longer times, where liquid, after having reached the outlet, is exclusively flowing along such flow paths and the two-phase fluid structures are stabilised. We observe that the fibrous layer presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics, and counteract the stabilising viscous force. Liquid transport is indeed affected by the presence of microstructure-induced capillary pressures acting adversely to the flow, leading to capillary fingering transport mechanism and unstable front displacement, even in the absence of hydrophobic treatments of the porous material. We propose a macroscopic model based on an effective contact angle that mimics the effects of the such a dynamic capillary pressure. Finally, we underline the significance of the results for the optimal design of face masks in an effort to mitigate the current COVID-19 pandemic.

First-order optimization algorithms via inertial systems with Hessian driven damping

In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both viscous and Hessian-driven dampings. The geometrical damping driven by the Hessian intervenes in the dynamics in the form $$\nabla ^2 f (x(t)) \dot{x} (t)$$ . By treating this term as the time derivative of $$ \nabla f (x (t)) $$ , this gives, in discretized form, first-order algorithms in time and space. In addition to the convergence properties attached to Nesterov-type accelerated gradient methods, the algorithms thus obtained are new and show a rapid convergence towards zero of the gradients. On the basis of a regularization technique using the Moreau envelope, we extend these methods to non-smooth convex functions with extended real values. The introduction of time scale factors makes it possible to further accelerate these algorithms. We also report numerical results on structured problems to support our theoretical findings.

Nonlinear dynamics of inertial particles in the ocean: from drifters and floats to marine debris and Sargassum

Buoyant, finite-size or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey-Riley equation. Derived from first principles - a result of over a century of research since the pioneering work by Sir George Stokes - the Maxey-Riley equation is a Newton-type-law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper we present an overview of recent efforts to port the Maxey-Riley framework to oceanography. These involved: 1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; 2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air-sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and 3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight on the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey-Riley equation forms, which represent singular perturbation problems involving slow and fast variables.