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Dynamic variables of drop impact such as force, drag, pressure, and stress distributions are key to understanding a wide range of natural and industrial processes. While the study of drop impact kinematics has been in constant progress for decades thanks to high-speed photography and computational fluid dynamics, research on drop impact dynamics has only peaked in the last 10 years. Here, we review how recent coordinated efforts of experiments, simulations, and theories have led to new insights on drop impact dynamics. Particularly, we consider the temporal evolution of the impact force in the early- and late-impact regimes, as well as spatiotemporal features of the pressure and shear-stress distributions on solid surfaces. We also discuss other factors, including the presence of water layers, air cushioning, and nonspherical drop geometry, and briefly review granular impact cratering by liquid drops as an example demonstrating the distinct consequences of the stress distributions of drop impact.

A Free Energy Lattice Boltzmann Method has been developed to characterize dominant forces and regimes involved in the capillary rise imbibition process. The comparison of the capillary rise behavior at the initial stages, reveals significant differences between numerical and theoretical models. This is attributed to the simplifying assumptions, ignoring the entrance region, dynamic contact angle, and inertial term in the theoretical model. By relaxing these assumptions in numerical formulations, the proposed model prevails the theoretical model limitations and shows closer results to the experimental records. However, as the capillary tube size decreases, the capillary force overcomes the inertia and the theoretical and numerical curves converge. Comparing the numerical curves and the experimental results indicates that the dynamics of the capillary ascent predicted by the present model is similar to the dry tube data. It should be mentioned that the inertial regime, the viscous regime, and the gravity-viscous regime can be considered as the successive regimes involved. Further investigations reveal a transition regime at the beginning of the process, which appears due to singular pressure loss. Therefore, the capillary rise phenomenon develops during these regimes as h ~ t2, h ~ t, h ~ t1/2 and relaxing to a constant value, respectively. Finally, for better understanding of the phenomenon, sensitivity analysis on the dominant forces has been performed.

Controlling the drop impact behaviors plays an important role in both designing surface functional materials and improving industrial techniques. Here, the impact dynamics of nanodroplets on "V-shaped" substrates is studied, which is manifested as asymmetrical spreading and retraction behaviors that could be weakened by increasing the angles of the "V" shape, accompanied by the evolution of the shape from leaf-like, stripe-like, to dumbbell-like at v = 20 A/ps. When v increases to 40 A/ps, the previously deposited nanodroplets could be transformed to a rebound one at α = 60 and 90°, which is ascribed to the combined effect of the confinement conditions and the extrusion force. Furthermore, an impact behavior map as a function of impact velocity and angle is depicted, which suggests that a decrease in angles or an increase in the impact velocity is likely to cause the nanodroplets to rebound. More importantly, the results give visible evidence that compared to the flat substrates, the V-shaped structure is advantageous for achieving a fast-rebound behavior even at a low speed of impact, which should be good news for practical applications in many multidisciplinary fields, such as self-cleaning, anti-icing/fogging, pollution prevention, energy storage, and so forth.

In this study, a new controller to prevent the yaw instability and rollover of a three-wheeled vehicle has been proposed. This controller offers the most obvious opportunity for affecting the vehicle's lateral dynamics performance on the full range of nonlinearities during various operating boundaries. The active combined controller has been designed based on sliding mode control method using an active roll system and an active braking system to dominate the uncertainties of the nonlinear dynamic model. Firstly, to avoid rollover of the three-wheeled vehicle, the roll angle was considered as the control objective, and the anti-roll bar was employed as an actuator to produce the roll moment. Secondly, to increase the maneuverability and lateral dynamics enhancement, an active braking system was designed. In the control system, the yaw rate and the lateral velocity were regarded as the control variables to track their references. Moreover, to verify the performance of the mentioned combined controller, another control system has been designed using the linearization feedback control method. Then, computer simulation has been carried out with a 12 degrees of freedom dynamic model of the three-wheeled vehicle called the delta. Furthermore, a nonlinear tire model has been utilized to compute the longitudinal and the lateral forces. Next, the comparative simulation results confirmed the effectiveness of the robust control system to raise the vehicle's maneuverability and its rollover stability in comparison with the linearization feedback control method, especially when the three-wheeled vehicle is subjected to critical conditions.

In the paper, a combined model of traction and ball bearings dynamics is established, considering the interaction among the cage, races, and balls. A curve-fitted traction model, which can be used to analyze the effect of the geometry of the bearing and parameters of the lubricant, is applied. The traction that is affected by certain parameters is analyzed; then, the effect of the traction on ball bearings is investigated. The displacements of balls and contact angles are different under different surface roughness. The changes in displacements of balls and contact angles are obtained with different roughness, load, and velocities. The amplitudes of axial displacement of balls are bigger with the roughness being higher. The amplitudes of ball-inner contact angles increase with greater roughness, and the amplitudes of ball-outer race contact angles decrease with greater roughness. The simulated vibration results of ball bearings under different levels agree with the actual by the model.

In this paper, we study the geometric quantum discord dynamics of the double quantum dot charge qubit in the non-Markovian environment. We apply the non-perturbative non-Markovian quantum state diffusion method to obtain the exact master equation of the double quantum dot system coupled to two independent non-zero temperature electronic baths. Then, we use this master equation to investigate the effects of non-Markovianity, inter-dot coupling strength and bath temperature on the dynamics of geometric quantum discord. Our studies show that the geometric quantum discord of a double quantum dot system can be modified and enhanced in some cases via these factors.

The dynamics of water droplets on fiber layers are investigated by fiber-scale simulation using volume of fluid (VOF) method. The effects of fiber spaces, contact angles at fibers and numbers of layers on droplet dynamics are investigated. Force analysis for the pinned and moving droplets on fiber layers shows that the resistant forces from the wetted fibers at the edge positions rather than middle positions are the dominant force to control the droplet mobility. Force analysis for droplets on the dual-layers fiber layer are also conducted. The results show that the second layer contributes little to hinder the droplet directly due to the insignificant resistant force they provided. However, the second fiber layer enhances the total resistant force from the first layer. Furthermore a simplified model is used to compare with the fiber model. The results indicate that the simplified model can also be used to predict the droplet mobility once the contact angle is given.

In the second part of this series, we propose a physics-based model for describing the temperature dependence of TiO x -based memristors, both switching and static. We show that the current–voltage ( ${I}$ – ${V}$ ) characteristics of memristor in the nonswitching regime, indicating a Schottky emission mechanism, can be described by minor modifications to the Schottky current equation. This leads to a physics-based static ${I}$ – ${V}$ compact model. Simultaneously, we show that the temperature dependence of the switching dynamics model parameters naturally emerges as a mere scaling factor from the static ${I}$ – ${V}$ model. This is a computationally efficient approach, which does not require any additional parameters to extend the switching dynamics model for incorporating thermal dependence.

In conventional Finite Element – Lagrangian methods, the dynamics model of a flexible robot is usually formulated based on a critical assumption that the kinetic energy of an element is approximately calculated with an integral of mass point energy. Since the energy integral is implicit, the formulation of the dynamics model is also very complex and implicit. Hence, this paper develops a new mathematical approach for the dynamic modelling of a general flexible/rigid robot. The proposed method is more comprehensive and efficient in comparison with the previous ones because it no longer requires the calculation of the symbolic integrals and the implicit expressions of the elemental and global mass matrices. Besides, the proposed approach is applicable for both the flexible robots and the hybrid flexible/rigid robots. To validate the proposed method, numerical simulations and experimental results are presented.

The control of coalescence and motion of droplets play a significant role in advanced technology and our daily life, and one of the most important approaches is surface design. Here, the microtextured surfaces decorated with wrinkled substrates are designed and studied for coalescence behaviors. The simulation results show that the coalescence speed would be slower on such surfaces due to the downward movement of the droplets induced by the penetration of atoms into the grooves that delays their movement along the coalescence direction, which is considered as a restriction effect. With the increase of the angles and the interval distance of wrinkled structures, the coalescence time becomes longer and the coalescing process becomes unfavorable, resulting from the enhanced restriction effect. More importantly, a composite substrate possessing the original and sub-wrinkled structures has been designed to tune the coalescence dynamics. The results of this work may not only help shed light on understanding the coalescence behaviors on the wrinkled substrates but also propose a feasible method for controlling the liquid coalescence behavior, which is expected to provide some useful implications for practical applications.

Direct numerical simulations of a turbulent channel with liquid infused surfaces made of longitudinal micro-ridges have been performed to study the effect of texture geometry and interface deformat...

The nonlinear absorption of two-dimensional (2 D) Nb2CTx (MXene) nanosheets were investigated by using nanosecond Z-scan measurements in 532 nm under different laser intensities. It was found that,...

A data-driven framework is presented for building magneto-elastic machine-learning interatomic potentials (ML-IAPs) for large-scale spin-lattice dynamics simulations. The magneto-elastic ML-IAPs are constructed by coupling a collective atomic spin model with an ML-IAP. Together they represent a potential energy surface from which the mechanical forces on the atoms and the precession dynamics of the atomic spins are computed. Both the atomic spin model and the ML-IAP are parametrized on data from first-principles calculations. We demonstrate the efficacy of our data-driven framework across magneto-structural phase transitions by generating a magneto-elastic ML-IAP for α-iron. The combined potential energy surface yields excellent agreement with first-principles magneto-elastic calculations and quantitative predictions of diverse materials properties including bulk modulus, magnetization, and specific heat across the ferromagnetic–paramagnetic phase transition.

A differential mechanism is an essential component in the majority of automotive applications. Its vitality stems from the fact that it allows a wheel-drive vehicle to take a curve safely. On the other hand, it can ratchet up the vibration in the wheel-drive vehicle due to the excessive gear tooth deflection from applied torque. Some gear tooth modifications can increase or decrease the level of vibration in the mechanism. So far, very little attention has been paid to the effects of the uncertain geometric deviation of the tooth profile and uncertain crowning parameters on the dynamic performance of the mechanism. This study aims to investigate the impacts of these uncertain parameters on the gear systems’ dynamic performance. To this end, the nonlinear interval model of the differential mechanism is proposed. The mesh stiffness for straight bevel gear is modelled through the potential energy method and slice theory, while bearing stiffness elements are calculated at each time step. A refined computational algorithm is proposed to deal with any gear system with multiple interval variables. The scanning method is used as a reference method in this paper. The main outcomes of this study are that the crowning design can slightly reduce the vibration in the mechanism, and the profile errors can increase its vibration level excessively. Besides, the results derived from the refined algorithm show similarities to those determined by the scanning method, and the study shows that the refined algorithm can handle any gear system with uncertain static or time-varying parameters.

In the framework of the classical equations for the magnetization dynamics and the collective variables approximation, the dynamics of magnetic vortices in two-dimensional ferromagnets with the easy-plane anisotropy and spatially inhomogeneous exchange interaction is considered. In the case of a wide straight line of the interface between magnetic media with different but slightly different exchange interaction, the dependence of the magnetic vortex velocity on its distance to the structure defect and position inside the interface domain is obtained.

A complete phenomenological description for the relaxation dynamics of the Ising ferromagnets in the presence of external magnetic field h is given by using the pair approximation. To study the relaxation dynamics, we calculate two characteristic times (denoted as τS, τF ) using the rate constants which satisfy the Onsager reciprocity theorem. Temperature/magnetic field variations of τS and τF are investigated. We have shown that the extrema of the curves obtained for τS when h 6= 0 determine the loci of correlation length maxima or the Widom lines. The results are compared with those of response functions and thermodynamic curvature. We observe that they exactly match that for the magnetic susceptibility. 000713033100009

Macroscopic nonlinearity and hysteresis observed in the piezoelectric and dielectric responses of ferroelectric materials to external stimuli are commonly attributed to localized displacements of domain walls (DWs). The link between the macroscopic response and microscopic DW dynamics is provided by the well-known Rayleigh relations, extensively used to quantify the electrical and electromechanical behavior of ferroelectric ceramics and thin films under subswitching conditions. In this chapter, I will present an intriguing case where DWs exhibit enhanced electrical conductivity with respect to the bulk conductivity. By combining experimental data and modeling, it will be shown that the local conductivity, related to accumulation of charged points defect at DWs, does not only affect DW dynamics through DW-defect pinning interactions, as we may expect, but goes beyond it by affecting the macroscopic nonlinearity and hysteresis in a more complex manner. The major characteristics and implications of the underlying nonlinear Maxwell-Wagner piezoelectric relaxation, triggered by the presence and dynamics of conducting DWs, will be presented, reviewed and discussed in the framework of systematic multiscale analyses on BiFeO3 ceramics. The result may have implications in the development of promising BiFeO3-based compositions for high-temperature piezoelectric applications.

Magnetic dynamics of iron oxyhydroxide akaganeite nanoparticles, functional building blocks of the newest generation iron deficiency drug Ferinject, has been studied. While magnetism of the involved nanoparticles relies in general on bulk properties of akaganeite, the low temperature magnetic dynamics of Ferinject differs a lot from large number of other iron-oxides-based intravenous drugs in pharmaceutical practice. Clear separation of the high-temperature (Curie) and the low-temperature (spin-freezing) regimes has been identified. Instead of standard single superparamagnetic blocking temperature we show that the spin freezing relies on the two dominant and superimposed relaxations, characterizing the temperature ranges 50–100 K and 4.2–10 K, respectively. Complex magnetic dynamics is interpreted to rely on presence of the two assemblies of nanoparticles differing significantly in their average sizes. Bimodal distribution of particle sizes has been confirmed using atomic force microscopy. The knowledge of the drug’s physicochemical characteristics has been thus significantly improved.

A magnetic monopole in spin ice is a novel quasiparticle excitation in condensed matter physics, and we found that the ac frequency dependent magnetic susceptibility $\chi(\omega)$ in the two-dimensional (2D) spin ice (so-called kagom\'{e} ice) of Dy$_2$Ti$_2$O$_7$ shows a single scaling form. This behavior can be understood in terms of the dynamical scaling law for 2D Coulomb gas (CG) systems [Phys. Rev. B 90, 144428 (2014)], characterized by the charge correlation length $\xi (\propto1/\sqrt{\omega_1})$, where $\omega_{1}$ is a characteristic frequency proportional to the peak position of the imaginary part of $\chi(\omega)$. It is a generic behavior among a wide variety of models such as the vortex dynamics of 2D superconductors, 2D superfluids, classical XY magnets, and dynamics of melting of Wigner crystals., Comment: 5 pages, 4 figures, Supplemental Material

Drop coalescence occurs through the rapid growth of a liquid bridge that connects the two drops. At early times after contact, the bridge dynamics is typically self-similar, with details depending on the geometry and viscosity of the liquid. In this paper we analyse the coalescence of two-dimensional viscous drops that float on a quiescent deep pool; such drops are called liquid lenses. The analysis is based on the thin-sheet equations, which were recently shown to accurately capture experiments of liquid lens coalescence. It is found that the bridge dynamics follows a self-similar solution at leading order, but, depending on the large-scale boundary conditions on the drop, significant corrections may arise to this solution. This dynamics is studied in detail using numerical simulations and through matched asymptotics. We show that the liquid lens coalescence can involve a global translation of the drops, a feature that is confirmed experimentally.

Description, Equilibrium gels formed by the reversible association of limited-valence colloids display a remarkable spatially uniform dynamics., Gels of DNA nanostars, besides providing a compatible scaffold for biomedical applications, are ideal model systems for testing the physics of equilibrium colloidal gels. Here, using dynamic light scattering and photon correlation imaging (a recent technique that, by blending light scattering and imaging, provides space-resolved quantification of the dynamics), we follow the process of gel formation over 10 orders of magnitude in time in a model system of tetravalent DNA nanostars in solution, a realization of limited-valence colloids. Such a system, depending on the nanostar concentration, can form either equilibrium or phase separation gels. In stark contrast to the heterogeneity of concentration and dynamics displayed by the phase separation gel, the equilibrium gel shows absence of aging and a remarkable spatially uniform dynamics.

The phenomena of microlayer formation and its dynamic characteristics during the nucleate pool boiling regime have been widely investigated in the past. However, experimental works on real-time microlayer dynamics during nucleate flow boiling conditions are highly scarce. The present work is an attempt to address this lacuna and is concerned with developing a fundamental understanding of microlayer dynamics during the growth process of a single vapour bubble under nucleate flow boiling conditions. Boiling experiments have been conducted under subcooled conditions in a vertical rectangular channel with water as the working fluid. Thin-film interferometry combined with high-speed cinematography have been adopted to simultaneously capture the dynamic behaviour of the microlayer along with the bubble growth process. Transients associated with the microlayer have been recorded in the form of interferometric fringe patterns, which clearly reveal the evolution of the microlayer beneath the growing vapour bubble, the movement of the triple contact line and the growth of the dryspot region during the bubble growth process. While symmetric growth of the microlayer was confirmed in the early growth phase, the bulk flow-induced bubble deformation rendered asymmetry to its profile during the later stages of the bubble growth process. The recorded fringe patterns have been quantitatively analysed to obtain microlayer thickness profiles at different stages of the bubble growth process. For Re = 3600, the maximum thickness of the almost wedge-shaped microlayer was obtained as δ ~ 3.5 μm for a vapour bubble of diameter 1.6 mm. Similarly, for Re = 6000, a maximum microlayer thickness of δ ~ 2.5 μm was obtained for a bubble of diameter 1.1 mm.

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter $D$ ), in which current ( $U_c$ ), wave velocity ( $U_w$ ) and period ( $T$ ) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as $U_w/U_c$ increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number $KC=U_wT/D$ and $U_c/U_w$ increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on $U_c/U_w$ and $KC$ . For large roughness elements, bottom friction is well represented by a friction factor ( $f_w$ ) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with $KC$ and $U_c/U_w$ .

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ( $\textit {Re}$ ). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} , the LEV stability is mainly driven by viscous diffusion. At $200 , the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$ , the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$ . In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$ -independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low- $\textit {Re}$ revolving wings.

In this paper, we investigate two different constant-coefficient nonlinear evolution equations, namely the Schamel Burgers equation and the Schamel equation. These models also have a great deal of potential for studying ion-acoustic waves in plasma physics and fluid dynamics. The primary goal of this paper is to establish closed-form solutions and dynamics of analytical solutions to the Schamel Burgers and the Schamel equations, which are special examples of the well-known Schamel–Korteweg-de Vries (S-KdV) equation. We derive completely novel solutions to the considered models using a variety of computation programmes and a newly proposed extended generalized [Formula: see text] expansion approach. The newly formed solutions, which include hyperbolic and trigonometric functions as well as rational function solutions, have been produced. The annihilation of three-dimensional shock waves, periodic waves, single soliton, singular soliton, and combo soliton, multisoliton as well as their three-dimensional and contour plots are used to show the dynamical representations of the acquired solutions. These results demonstrate that the proposed extended technique is efficient, reliable and simple.

The structural relaxation slows down drastically upon approaching the glass transition, accompanied by the significant growth of dynamic heterogeneity. The fundamental question of elusiveness and interest is whether there exists an underlying quantitative relationship between structural relaxation and dynamic heterogeneity. Here, we reveal that which is related to the reduced mean square displacements to overcome the energy barriers of activated jumps, instead of the kinetic fragility m, is the genuine key parameter connecting dynamic heterogeneity with structural relaxation for varying types of glass formers. Furthermore, based on the dependence of dynamic heterogeneity on the Debye–Waller factor we obtained a direct quantitative relation between dynamic heterogeneity and structural relaxation is built for different glass-forming liquids. More importantly, a scaling collapse of structural relaxation and dynamic heterogeneity is achieved by the important parameter . These results are of fundamental and critical importance for developing a unified theory of glassy dynamics.

Unlike single-network hydrogel whose thermodynamic equilibrium of all phases is governed by one single rule, double-network (DN) hydrogel is incorporated of two coexisting phases, which are separated from each other due to the differences in their mechanoresponsive responses. However, the resonance differences and multipartite dynamics of coexisting phases in these DN hydrogels have not been fully understood. This paper reports a new methodology to use a rheological model in combination of Arrhenius principle and Kirkwood approximation, to characterize the differences in mechanoresponsive resonances and viscoelastic behaviors of coexisting phases in the DN hydrogel. Their multipartite dynamics has been identified to originate from mechanical stretching, mechanochemical coupling and chemical kinetics of the ductile network, original brittle network and self-healed brittle network, respectively. Furthermore, molecular dynamics simulation and finite-element analysis have been conducted to verify the proposed model and explore the toughening mechanism, which is determined not only by the mechanochemical coupling, but also by the self-healing kinetics. Finally, effectiveness of proposed model has been well verified using the experimental results of DN hydrogels reported in literature.

International audience; Foams are inherently unstable objects, that age and disappear over time. The main cause of foam aging is Ostwald ripening: smaller air bubbles within the foam empty their gas content into larger ones. One strategy to counter Ostwald ripening consists in creating armored bubbles, where solid particles adsorbed at the air/liquid interface prevent bubbles from shrinking below a given size. Here, we study the efficiency of coating air bubbles with fat crystals to prevent bubble dissolution. A monoglyceride, monostearin, is directly crystallized at the air/oil interface. Experiments on single bubbles in a microfluidic device show that the presence of monostearin fat crystals slows down dissolution, with an efficiency that depends on the crystal size. Bubble ripening in the presence of crystals exhibits intermittent dissolution dynamics, with phases of arrest, when crystals jam at the interface, followed by phases of dissolution, when monostearin crystals are ejected from the interface. In the end, crystals do not confer enough mechanical strength to the bubbles to prevent them from fully dissolving.

In this paper, we present a systematic treatment of a [Formula: see text] qubit in the presence of a time-dependent external flux. A gauge-invariant Lagrangian and the corresponding Hamiltonian are obtained. The effect of the flux noise on the qubit relaxation is obtained using the perturbation theory. Under a time-dependent drive of sinusoidal form, the survival probability, and transition probabilities have been studied for different strengths and frequencies. The driven qubit is shown to possess coherent oscillations among two distinct states for a weak to moderate strength close to resonant frequencies of the unperturbed qubit. The parameters can be chosen to prepare the system in its ground state. This feature paves the way to prolong the lifetime by combining ideas from weak measurement and quantum Zeno effect. We believe that this is an important variation of a topologically protected qubit which is tunable.

Actively driven colloids demonstrate complex out-of-equilibrium dynamics often rivaling self-organized patterns and collective behavior observed in living systems. Recent studies revealed the emergence of steady macroscopic states with multiple interacting vortices in an unconfined environment that emerge from the coupling between microscale particle rotation and translation. Yet, insights into the microscopic behavior during the vortex emergence, growth, and formation of a multi-vortical state remain lacking. Here, we investigate in experiments and simulations how the microscale magnetic roller behavior leads to the emergence of seed vortices, their aggregation or annihilation, and the formation of stable large-scale vortical structures. We reveal that the coupling of roller-induced hydrodynamic flows guides the local self-densifications and self-organization of the micro-rollers into seed vortices. The resulting multi-vortical state is sensitive to the external magnetic field amplitude and allows tuning the rollers' number density in a vortex and its characteristic size.

We study a model describing relaxation dynamics of point vortices, from quasi-stationary state to the stationary state. It takes the form of a mean field equation of Brownian point vortices derived from Chavanis, and is formulated by our previous work as a limit equation of the patch model studied by Robert-Someria. This model is subject to the micro-canonical statistic laws; conservation of energy, that of mass, and increasing of the entropy. We study the existence and nonexistence of the global-in-time solution. It is known that this profile is controlled by a bound of the negative inverse temperature. Here we prove a rigorous result for radially symmetric case. Hence E/M2 large and small imply the global-in-time and blowup in finite time of the solution, respectively. Where E and M denote the total energy and the total mass, respectively.

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.

A new method is proposed to obtain Gross–Pitaevskii equation by the chain of Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) quantum kinetic equations. In that sense, we investigate the dynamics of a quantum system including infinite number of identical particles which interact via a (special) pair potential on the form of Dirac delta-function.

An investigation of spin waves interacting with antiferromagnetic spin textures is meaningful for future spintronic and magnonic-based memory and logic applications. In this work, we numerically study the skyrmion dynamics driven by circularly polarized spin waves in antiferromagnets and propose a method of suppressing the Hall motion. It is demonstrated that the application of two circularly polarized spin waves with opposite chirality allows the skyrmion motion straightly along the intersection line of the two spin wave sources. The skyrmion speed depending on these parameters of the spin waves and system is estimated, and a comparison with other methods is provided. Furthermore, two depinning behaviors of the skyrmion related to the strengths of the defect are also observed in the simulations. Thus, the proposed method could be used in precisely modulating the skyrmion dynamics, contributing to skyrmion-based memory device design.

This paper comprises the different types of optical soliton solutions of an important Triki–Biswas model equation with beta-time derivative. The beta derivative is considered as a generalized version of the classical derivative. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation that describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel beta derivative operator and three efficient integration schemes. During this work, a sequence of new optical solitons is produced that may have an importance in optical fiber systems. These solutions are verified and numerically simulated through soft computation.

We investigated here the influence of the lateral and normal Casimir force on the actuation dynamics between sinusoidal corrugated surfaces undergoing both normal and lateral displacements. The calculations were performed for topological insulators and phase change materials that are of high interest for device applications. The results show that the lateral Casimir force becomes stronger by increasing the material conductivity and the corrugations toward similar sizes producing wider normal separation changes during lateral motion. In a conservative system, bifurcation and Poincaré portrait analysis shows that larger but similar in size corrugations and/or higher material conductivity favor stable motion along the lateral direction. However, in the normal direction, the system shows higher sensitivity on the optical properties for similar in size corrugations leading to reduced stable operation for higher material conductivity. Furthermore, in non-conservative systems, the Melnikov function with the Poincaré portrait analysis was combined to probe the possible occurrence of chaotic motion. During lateral actuation, systems with more conductive materials and/or the same but high corrugations exhibit lower possibility for chaotic motion. By contrast, during normal motion, chaotic behavior leading to stiction of the moving components is more likely to occur for systems with more conductive materials and similar in magnitude corrugations.

The Lie symmetry method is used to obtain a variety of closed-form wave solutions for the extended (3[Formula: see text]+[Formula: see text]1)-dimensional Jimbo–Miwa (JM) Equation, which describes certain interesting higher-dimensional waves in ocean studies, marine engineering, and other fields. By applying the Lie symmetry technique, we explicitly investigate all the possible vector fields, commutation relations of the considered vectors, and various symmetry reductions of the equation. Based on three stages of Lie symmetry reductions, the JM equation is reduced to several nonlinear ordinary differential equations (NLODEs). Consequently, abundant closed-form wave solutions are achieved, including arbitrary functional parameters. Evolutionary dynamics of some analytic wave solutions are demonstrated through three-dimensional plots based on numerical simulation. Consequently, singular soliton, kink waves, periodic oscillating wave profiles, combined singular soliton profiles, curved-shaped multiple solitons, and periodic multiple solitons with parabolic wave profiles are demonstrated by taking advantage of symbolic computation work. The obtained analytical wave solutions, which include arbitrary independent functions and other constants of the governing equation, could be used to enrich the advanced dynamical behaviors of solitary wave solutions. Furthermore, the study of conservation laws is investigated via the Ibragimov technique for Lie point symmetries.

In this study, we investigate two nonlinear Schrödinger equations (NLSEs) which point out the evolution of disturbances in dynamics. The first one is the nonlinear Heisenberg ferromagnetic spin chain equation of (2+1)-dimensional and the second one is (1+1)-dimensional cubic NLSE that govern the dynamics of modulated compressional dispersive Alfvén (CDA) envelope. The ([Formula: see text]-expansion method is adopted to carry out this target in a straightforward way. A diversity of new hyperbolic and periodic solitary wave solutions are acquired. The obtained solutions with some constraint conditions show the validity and effectiveness of the method.

In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system. On slender offshore structures, the loading due to waves is normally calculated by applying a force which consists of two parts: a linear “inertia/mass force” and a non-linear “drag force” that is proportional to the square of the velocity of the particles in the wave, multiplied by the direction of the wave particle motion. This is the so-called Morison load model. The loading function can be expanded in a Fourier series, and the drag force contribution exhibits higher order harmonic loading terms, potentially in resonance with the natural frequencies of the system. Currents are implemented as constant velocity terms in the loading function. The paper highlights the motion of structures due to non-linear resonant motion in an offshore environment with high wave intensity. It is shown that “burst”/“ringing” type motions could be triggered by the drag force during resonance situations.