Inertial Dynamics Research Articles

Continuous Newton-like Inertial Dynamics for Monotone Inclusions

In a Hilbert framework ℌ, we study the convergence properties of a Newton-like inertial dynamical system governed by a general maximally monotone operator A ℌ: → 2ℌ. When A is equal to the subdifferential of a convex lower semicontinuous proper function, the dynamic corresponds to the introduction of the Hessian-driven damping in the continuous version of the accelerated gradient method of Nesterov. As a result, the oscillations are significantly attenuated. According to the technique introduced by Attouch-Peypouquet (Math. Prog. 2019), the maximally monotone operator is replaced by its Yosida approximation with an appropriate adjustment of the regularization parameter. The introduction into the dynamic of the Newton-like correction term (corresponding to the Hessian driven term in the case of convex minimization) provides a well-posed evolution system for which we will obtain the weak convergence of the generated trajectories towards the zeroes of A. We also obtain the fast convergence of the velocities towards zero. The results tolerate the presence of errors, perturbations. Then, we specialize our results to the case where the operator A is the subdifferential of a convex lower semicontinuous function, and obtain fast optimization results.

Bi-level multi-objective model for existing link capacity expansion problem across urban transportation network considering travel time reliability: presenting dynamic particle swarm algorithm

Urban transportation network design and traffic control problems fall within the scope of infrastructural engineering sciences which become increasingly more important in ever-growing societies of today. In highly populated old cities where establishing new links are facing many human-related, social, economic, and political problems, a workaround for addressing traffic problems is to expand the capacity of existing links, so as to not only control the traffic, but also reduce the urban environmental pollutions caused by vehicles stuck in traffic and decrease the time wasted in traffic to accelerate routines of the society. In the present research, an urban transportation network design model is presented with the aim of enhancing travel time reliability by expanding the capacity of existing network links at minimum possible cost. A significant assumption taken in the present study is that demands in normal condition and peak traffic hours are treated separately, so as to prevent possible problems by congestion management. In the present study, the uncertainty associated with demand for travel, travel time, and the flow passing through different links are taken into consideration. Travel time reliability calculations are carried out assuming that the demand for travel and travel time follow lognormal distributions. In order to solve this bi-level model, particle swarm optimization algorithm was used. Incorporation of the inertial coefficients dynamics, personal learning, and communal learning into the algorithm contributes to the convergence of this algorithm for solving the bi-level model.

Clustering of Marine‐Debris‐ and Sargassum‐Like Drifters Explained by Inertial Particle Dynamics

AbstractDrifters designed to mimic floating marine debris and small patches of pelagic Sargassum were satellite tracked in four regions across the North Atlantic. Though subjected to the same initial conditions at each site, the tracks of different drifters quickly diverged after deployment. We explain the clustering of drifter types using a recent Maxey‐Riley theory for surface ocean inertial particle dynamics applied on multidata‐based mesoscale ocean currents and winds from reanalysis. Simulated trajectories of objects at the air‐sea interface are significantly improved when represented as inertial (accounting for buoyancy and size), rather than as perfectly Lagrangian (fluid following) particles. Separation distances between simulated and observed trajectories were substantially smaller for debris‐like drifters than for Sargassum‐like drifters, suggesting that additional consideration of its physical properties relative to fluid velocities may be useful. Our findings can be applied to model variability in movements and distribution of diverse objects floating at the ocean surface.

Inertial spin dynamics in ferromagnets

The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps. Inertial dynamics are observed in a ferromagnet. Specifically, a nutation is seen on top of the usual spin precession that has a lifetime on the order of 10 picoseconds.

Constructional and functional anatomy of Ediacaran rangeomorphs

AbstractEdiacaran rangeomorphs were the first substantially macroscopic organisms to appear in the fossil record, but their underlying biology remains problematic. Although demonstrably heterotrophic, their current interpretation as osmotrophic consumers of dissolved organic carbon (DOC) is incompatible with the inertial (high Re) and advective (high Pe) fluid dynamics accompanying macroscopic length scales. The key to resolving rangeomorph feeding and physiology lies in their underlying construction. Taphonomic analysis of three-dimensionally preserved Charnia from the White Sea identifies the presence of large, originally water-filled compartments that served both as a hydrostatic exoskeleton and semi-isolated digestion chambers capable of processing recalcitrant substrates, most likely in conjunction with a resident microbiome. At the same time, the hydrodynamically exposed outer surface of macroscopic rangeomorphs would have dramatically enhanced both gas exchange and food delivery. A bag-like epithelium filled with transiently circulated seawater offers an exceptionally efficient means of constructing a simple, DOC-consuming, multicellular heterotroph. Such a body plan is broadly comparable to that of anthozoan cnidarians, minus such derived features as muscle, tentacles and a centralized mouth. Along with other early bag-like fossils, rangeomorphs can be reliably identified as total-group eumetazoans, potentially colonial stem-group cnidarians.

Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology.

A Dynamic Model for Concentric Tube Robots

Existing static and kinematic models of concentric tube robots are based on the ordinary differential equations of a static Cosserat rod. In this paper, we provide the first dynamic model for concentric tube continuum robots by adapting the partial differential equations of a dynamic Cosserat rod to describe the coupled inertial dynamics of precurved concentric tubes. This generates an initial-boundary-value problem that can capture robot vibrations over time. We solve this model numerically at high time resolutions using implicit finite differences in time and arc length. This approach is capable of resolving the high-frequency torsional dynamics that occur during unstable "snapping" motions and provides a simulation tool that can track the true robot configuration through such transitions. Further, it can track slower oscillations associated with bending and torsion as a robot interacts with tissue at real-time speeds. Experimental verification of the model shows that this wide range of effects is captured efficiently and accurately.

Active phase field crystal systems with inertial delay and underdamped dynamics

.Active matter systems often are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic systems but also for many mesoscopic ones particle mass can become relevant for the dynamics. For such systems we recently proposed an underdamped continuum model which captures translationally inertial dynamics via two contributions. First, convection and second a damping time scale of inertial motion. In this paper, we ask how both of these features influence the collective behavior compared to overdamped dynamics by studying the example of the active phase field crystal model. We first focus on the case of suppressed convection to study the role of the damping time. We quantify that the relaxation process to the steady collective motion state is considerably prolonged with damping time due to the increasing occurrence of transient groups of circularly moving density peaks. Finally, we illustrate the fully underdamped case with convection. Instead of collective motion of density peaks we then find a coexistence of constant high and low density phases reminiscent of motility-induced phase separation.Graphical abstract

Laboratory verification of the buoyancy dependence of the carrying flow in a Maxey–Riley theory for inertial ocean dynamics

We present results from laboratory experiments conducted in an air–water stream flume facility that provide controlled observational support for the buoyancy dependence of the drag-induced carrying flow velocity in a recent Maxey–Riley theory for inertial particle motion in the ocean.

Drivers and barriers for Industry 4.0 readiness and practice: empirical evidence from small and medium-sized manufacturers

The technological development e.g. in terms of Industry 4.0 is moving rapidly enabling manufacturing companies with new possibilities for digital transformations to offer products and services to current and new markets at competitive costs. A mixed-method approach is used to investigate the drivers and barriers for Industry 4.0 readiness and practice among Danish small and medium-sized manufacturers. Data is based on a questionnaire-survey among 190 manufacturers about their readiness for digitalized manufacturing and their actual practice in this area. A main finding is that it is the managers’ lack of perceiving Industry 4.0 drivers, not their perceptions of high Industry 4.0 barriers that obstruct SMEs’ development of Industry 4.0 readiness and their application of Industry 4.0 technologies. Using these insights provide four more nuanced interpretations of the significance of the Industry 4.0 challenges faced by the four case companies. The finding that SMEs seem to engage positively with Industry 4.0 barriers, when there is perceived a business case to do so, has important consequences for our understanding of the inertial dynamics surrounding SMEs’ Industry 4.0 application, and consequently for guiding policy initiatives to promote Industry 4.0 adaptation among SMEs.

Ordenamiento territorial, agua subterránea y participación sociopolítica en Bacalar, Quintana Roo, México

A partir de un estudio interdisciplinario sobre la participación sociopolítica en la formulación del Programa de Ordenamiento Ecológico Local (POEL) de Bacalar, analizamos las motivaciones y dificultades para considerar la "vocación natural” de este territorio, es decir, la capacidad que tiene para sustentar las actividades de los diversos seres vivos que lo habitan, partiendo del hecho de que se trata de un sistema kárstico. Para incluir dicha consideración, el equipo de investigación implementó una estrategia de investigación-acción (IA) que consistió en elaborar un modelo de conectividad hidrogeológica y sumarse a las gestiones para la configuración de este instrumento de política pública. Desde un enfoque socioambiental, la investigación incluyó técnicas etnográficas como entrevistas, observación participante y diario de campo. Los resultados muestran que algunas de las representaciones territoriales de los actores son incompatibles con las características del sistema kárstico y plantean la necesidad de una política participativa, orientada a la construcción de una visión común del territorio mediante procesos de socialización del conocimiento entre los actores y los sectores involucrados. Entre las limitantes de la IA se encontró que, a pesar de lograr la convergencia de sectores, se mantuvo la dinámica inercial que hasta ahora ha impedido la entrada en vigor del POEL en un espacio cada vez más codiciado y en riesgo para el ecosistema y quienes lo habitan.

Rototaxis: Localization of active motion under rotation

The ability to navigate in complex, inhomogeneous environments is fundamental to survival at all length scales, giving rise to the rapid development of various subfields in bio-locomotion such as the well established concept of chemotaxis. In this work, we extend this existing notion of taxis to rotating environments and introduce the idea of roto-taxis to bio-locomotion. In particular, we explore both overdamped and inertial dynamics of a model synthetic self-propelled particle in the presence of constant global rotation, focusing on the particle's ability to localize near a rotation center as a survival strategy. We find that in the overdamped regime, the swimmer is in general able to generate a self restoring active torque that enables it to remain on stable epicyclical-like trajectories. On the other hand, for underdamped motion with inertial effects, the intricate competition between self-propulsion and inertial forces, in conjunction with the rototactic torque leads to complex dynamical behavior with non-trivial phase space of initial conditions which we reveal by numerical simulations. Our results are relevant for a wide range of setups, from vibrated granular matter on turntables to microorganisms or animals swimming near swirls or vortices.

A tailored, electronic textile conformable suit for large-scale spatiotemporal physiological sensing in vivo

The rapid advancement of electronic devices and fabrication technologies has further promoted the field of wearables and smart textiles. However, most of the current efforts in textile electronics focus on a single modality and cover a small area. Here, we have developed a tailored, electronic textile conformable suit (E-TeCS) to perform large-scale, multimodal physiological (temperature, heart rate, and respiration) sensing in vivo. This platform can be customized for various forms, sizes and functions using standard, accessible and high-throughput textile manufacturing and garment patterning techniques. Similar to a compression shirt, the soft and stretchable nature of the tailored E-TeCS allows intimate contact between electronics and the skin with a pressure value of around ~25 mmHg, allowing for physical comfort and improved precision of sensor readings on skin. The E-TeCS can detect skin temperature with an accuracy of 0.1 °C and a precision of 0.01 °C, as well as heart rate and respiration with a precision of 0.0012 m/s2 through mechano-acoustic inertial sensing. The knit textile electronics can be stretched up to 30% under 1000 cycles of stretching without significant degradation in mechanical and electrical performance. Experimental and theoretical investigations are conducted for each sensor modality along with performing the robustness of sensor-interconnects, washability, and breathability of the suit. Collective results suggest that our E-TeCS can simultaneously and wirelessly monitor 30 skin temperature nodes across the human body over an area of 1500 cm2, during seismocardiac events and respiration, as well as physical activity through inertial dynamics.

Soviet Musical Avant-Garde in the Context of Time (in the mid. 1950s – 1980s): Historical and Cultural Studies and Philosophical Aspects

Introduction. Interest in the work of avant-garde artists does not wane as they move away from the 20th century. This is due to the fact that the musical avant-garde, becoming a sign of the time, reflected the most important trends of the outgoing era. In the paper, the Soviet musical avant-garde is considered in the historical, cultural and philosophical aspect in the context of the historical era, which determines the novelty of the study. An aspect of novelty is the analysis of music as a sphere of intercultural communication.Methodology and sources. The research methodology is based on the analysis of sources and literature, taking into account interdisciplinary approaches. A special role in the understanding of the theoretical aspects of the problem play the work of musicologists Yu. N. Kholopova, V. N. Kholopova, V. S. Price, R. L. Pospelova, A. I. Demchenko. Among the sources highlighted in cinema, photo- and phonodocuments, which depicts a vivid image of the era. The interviews with composers, which presents a wide canvas of social and musical life (A. Schnittke, A. Ivashkina entry and volkonskii, recording E. Dubinets) are of considerable interest. Historical, comparative, systematic and semiotic methods of analysis were used. Applies a comprehensive approach (formation and civilization methods of research and the Annales school). This allows for a new approach to the historical era of the middle1950s – 1980s.Results and discussion. Postwar culture is examined as a single space, in which a special role was played by the impulses of the “thaw”. They gave cultural phenomena such inertial dynamics, which preserves the spiritual maturity of society and produced changes of the 1990s, the results of the study show that in contrast to the political and socio-economic processes, cultural life in these years continued to feel the pulses of the “thaw”. Retaining the inertial dynamics of development, cultural processes have been far from stagnation, which casts doubt on the overall rating this time as the “era of stagnation”. This allows you to put a discussion question on the revision of the political clichés in relation to the period of the middle 1960s – 1980s in the Soviet Union as the “era of stagnation”.Conclusion. Soviet avant-garde, expressing the spirit of the time, represents the unique phenomenon in which reflected global trends, and the uniqueness of national culture. Experience avant-garde shows that cultural processes of the epoch middle 1950s – 1980s had a high development dynamics. The study of this period, especially in its spiritual sphere, requires interdisciplinary approaches and the use of modern, including foreign methods. Interest methods of the Annales school in its historical retrospect and the “new cultural history”.

Mapping diffusivity of narrow channels into one dimension.

The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, a molecular-dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks confined to long, narrow, structureless channels with hard walls in the no-passing regime. We show that the diffusion coefficient obtained from the mean-squared displacement can be mapped onto the exact results for the diffusion of the strictly-one-dimensional hard rod system through an effective occupied volume fraction obtained from either the equation of state or a geometric projection of the particle interaction diameters.

Current-Induced Dynamics and Chaos of Antiferromagnetic Bimerons.

A magnetic bimeron is a topologically nontrivial spin texture carrying an integer topological charge, which can be regarded as the counterpart of the skyrmion in easy-plane magnets. The controllable creation and manipulation of bimerons are crucial for practical applications based on topological spin textures. Here, we analytically and numerically study the dynamics of an antiferromagnetic bimeron driven by a spin current. Numerical simulations demonstrate that the spin current can create an isolated bimeron in the antiferromagnetic thin film via the dampinglike spin torque. The spin current can also effectively drive the antiferromagnetic bimeron without a transverse drift. The steady motion of an antiferromagnetic bimeron is analytically derived and is in good agreement with the simulation results. Also, we find that the alternating-current-induced motion of the antiferromagnetic bimeron can be described by the Duffing equation due to the presence of the nonlinear boundary-induced force. The associated chaotic behavior of the bimeron is analyzed in terms of the Lyapunov exponents. Our results demonstrate the inertial dynamics of an antiferromagnetic bimeron, and may provide useful guidelines for building future bimeron-based spintronic devices.

Fractal catastrophes

We analyse the spatial inhomogeneities (‘spatial clustering’) in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to configuration space. Folds of a smooth phase-space manifold give rise to catastrophes (‘caustics’) in this projection. When the inertial particle dynamics is damped by friction, however, the phase-space manifold converges towards a fractal attractor. It is believed that caustics increase spatial clustering also in this case, but a quantitative theory is missing. We solve this problem by determining how projection affects the distribution of finite-time Lyapunov exponents (FTLEs). Applying our method in one spatial dimension we find that caustics arising from the projection of a dynamical fractal attractor (‘fractal catastrophes’) make a distinct and universal contribution to the distribution of spatial FTLEs. Our results explain a projection formula for the spatial fractal correlation dimension, and how a fluctuation relation for the distribution of FTLEs for white-in-time Gaussian force fields breaks upon projection. We explore the implications of our results for heavy particles in turbulence, and for wave propagation in random media.

Newton-like Inertial Dynamics and Proximal Algorithms Governed by Maximally Monotone Operators

The introduction of the Hessian damping in the continuous version of Nesterov's accelerated gradient method provides, by temporal discretization, fast proximal gradient algorithms where the oscillations are significantly attenuated. We will extend these results to the maximally monotone case. We rely on the technique introduced by Attouch and Peypouquet [Math. Program., 174 (2019), pp. 391--432], where the maximally monotone operator is replaced by its Yosida approximation with an appropriate adjustment of the regularization parameter. In a general Hilbert framework, we obtain the weak convergence of the iterates to equilibria, and the rapid convergence of the discrete velocities to zero. By specializing these algorithms to convex minimization, we obtain the convergence rate $o(1/k^2)$ of the values, and the rapid convergence of the gradients toward zero.

Convergence Rates of Damped Inertial Dynamics under Geometric Conditions and Perturbations

In this article a family of second-order ODEs associated with the inertial gradient descent is studied. These ODEs are widely used to build trajectories converging to a minimizer $x^*$ of a functio...

Space-time symmetry of brownian motors controlled by a dichotomous process

Studying the symmetry of different systems allows one to formulate a variety of conclusions regarding their properties without knowing the detailed information about a particular system. The models of Brownian motors (ratchets) relate the spatial-temporal dependence of the potential energy of Brownian particles and the resulting ratchet effect. In this article, we use the symmetry description of ratchet systems to study the mechanisms of the influence of the spatial and (or) temporal asymmetry of a nanosystem on the average velocity of Brownian motors of the two main types - with fluctuating periodic potential energy and fluctuating force (the so-called pulsating and forced (or tilted) ratchets). We consider the overdamped motion of a Brownian particle in an unbiased force field, which is described by a periodic stepwise coordinate function, that undergoes dichotomous changes with time. The use of symmetry transformations and symmetry properties of Brownian motors made it possible to obtain compact analytical representations of the average velocity of pulsating and forced ratchets as a function of the parameters of the spatial and temporal asymmetries of the force fields. The fundamental difference between the dependences of the average velocity of the Brownian motors of these two types on the asymmetry parameters is revealed. For the pulsating Brownian motors, the directed motion of nanoparticles is absent in a spatially symmetric system regardless of the presence of temporal asymmetry; the motion appears in the presence of spatial asymmetry, and it is possible to obtain the motor stopping points by tuning the temporal asymmetry parameter of the control process. For the forced Brownian motors, it is the temporal asymmetry that permits the ratchet effect in spatially symmetric systems. For this reason, stopping points as a result of competition of spatial and temporal asymmetries are easier to realize precisely for the motors with fluctuating forces (forced ratchets). The results presented in this article were obtained by analyzing only general symmetry properties, without involving hidden symmetries of ratchet systems, therefore the results are also valid for inertial dynamics.