Nonzero Velocity Research Articles

Sub-cycle strong-field tunneling dynamics in solids

Tunneling ionization is a crucial process in the interaction between strong laser fields and matter which initiates numerous nonlinear phenomena including high-order harmonic generation, photoelectron holography, etc. Both adiabatic and nonadiabatic tunneling ionization are well understood in atomic systems. However, the tunneling dynamics in solids, especially nonadiabatic tunneling, has not yet been fully understood. Here, we study the sub-cycle resolved strong-field tunneling dynamics in solids via a complex saddle-point method. We compare the instantaneous momentum at the moment of tunneling and the tunneling distances over a range of Keldysh parameters. Our results demonstrate that for nonadiabatic tunneling, tunneling ionization away from Γ point is possible. When this happens the electron has a nonzero initial velocity when it emerges in the conduction band. Moreover, consistent with atomic tunneling, a reduced tunneling distance as compared to the quasi-static case is found. Our results provide remarkable insight into the basic physics governing the sub-cycle electron tunneling dynamics with significant implications for understanding subsequent strong-field nonlinear phenomena in solids.

A fully well-balanced hydrodynamic reconstruction

Abstract The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is to derive a scheme that exactly preserves these stationary solutions, as well as the commonly preserved lake at rest steady solution. These moving steady states are solution to a nonlinear equation. We emphasize that the method proposed here never requires solving this nonlinear equation; instead, a suitable linearization is derived. To address this issue, we propose an extension of the well-known hydrostatic reconstruction. By appropriately defining the reconstructed states at the interfaces, any numerical flux function, combined with a relevant source term discretization, produces a well-balanced scheme that preserves both moving and non-moving steady solutions. This eliminates the need to construct specific numerical fluxes. Additionally, we prove that the resulting scheme is consistent with the homogeneous system on flat topographies, and that it reduces to the hydrostatic reconstruction when the velocity vanishes. To increase the accuracy of the simulations, we propose a well-balanced high-order procedure, which still does not require solving any nonlinear equation. Several numerical experiments demonstrate the effectiveness of the numerical scheme.

Comparison of Floating Offshore Wind Turbine Tower Deflection Mitigation Methods Using Nonlinear Optimal-Based Reduced-Stroke Tuned Vibration Absorber

Tower fatigue and strength are crucial operational concerns of floating offshore wind turbines (FOWTs) due to the escalation of the vibration phenomena observed on these structures as compared to land-based ones. FOWT towers are excited by wave and wind polyperiodic disturbances yielding continual transient states of structural vibration that are challenging for vibration mitigation systems. Thus, the paper investigates a novel implementation of nonlinear optimal-based vibration control solutions for the full-scale, tension leg platform (TLP)-based, NREL 5MW wind turbine tower-nacelle model with a 10-ton tuned vibration absorber (TVA), equipped with a magnetorheological (MR) damper, located at the nacelle. The structure is subjected to excessive wave and wind excitations, considering floating platform motions derived from model experiments in a wave tank. The MR damper operates simultaneously with an electromagnetic force actuator (forming a hybrid TVA) or independently (a semiactive TVA). The study includes both actuators’ nonlinearities and dynamics, whereby the former are embedded in the Hamilton-principle-based nonlinear control solutions. The TVA is tuned either to the NREL 5MW tower-nacelle 1st bending mode frequency (TVA-TN) or to the TLP surge frequency (TVA-TLP). The optimal control task was redeveloped concerning the TVA stroke and transient vibration minimisation, including the implementation of the protected structure’s acceleration and relative displacement terms, as well as the nonzero velocity term in the quality index. The regarded model is embedded in a MATLAB/Simulink environment. On the basis of the obtained results, the TVA-TN solution is by far superior to the TVA-TLP one. All the regarded TVA-TN solutions provide a tower deflection safety factor of ca. 2, while reference systems without any vibration reduction solutions or with a passive TVA-TLP are at risk of tower structural failure as well as the hybrid TVA-TLP system. The obtained TVA stroke reductions of 25.7%/22.0% coincide with 3.6%/10.3% maximum tower deflection reductions for the semiactive/hybrid TVA-TN case (respectively) with regard to the previously developed approaches. Moreover, these reductions are obtained due to the sole control algorithm enhancement; thus, no additional resources are necessary, while this attainment is accompanied by a reduction in the required MR damper force. The lowest obtained TVA stroke amplitude of 1.66 m is guaranteed by the newly introduced semiactive control. Its hybrid equivalent ensures 8% lower primary structure deflection amplitude and reduced nacelle acceleration levels thanks to the utilisation of the force actuator of the relatively low power (ca. 6 kW); the trade-off is an increased TVA stroke amplitude of 2.19 m, which, however, is the lowest among all the tested hybrid solutions. The analysed reference passive TVA systems, along with a modified ground-hook hybrid solution, can hardly be implemented in the nacelle (especially along the demanding side–side direction). The latter, being the well-proven hybrid solution for steady-state tower deflection minimisation, yielded unsatisfactory results. The achievements of the study may be used for an effective design of a full-scale vibration reduction system for the TLP-based floating wind turbine structure.

Collisional space-charge-limited current with monoenergetic velocity: From Child–Langmuir to Mott–Gurney

All theories coupling electron emission theories ultimately approach the space-charge-limited current (SCLC) in vacuum, given by the Child–Langmuir (CL) law, for sufficiently high voltage, or the Mott–Gurney (MG) law for finite electron mobility and high (but not infinite) voltage. These analyses demonstrate the presence of an SCLC regime that cannot be described by either CL or MG. Here, we derive an exact solution for SCLC for general electron mobility and nonzero velocity. We recover the traditional CL with nonzero initial velocity at high voltage. For low mobility (or infinite collision frequency), we derive corrections to the MG law that depend on the ratio of initial velocity to the product of collision frequency and gap distance or initial velocity to drift velocity for low and high voltage, respectively. Increasing collisionality decreases the correction to SCLC for nonzero velocity, indicating that these corrections are less important for low-mobility materials (e.g., solids) than high-mobility materials (e.g., air or vacuum). For a given gap distance (collision frequency), increasing the collision frequency (gap distance) increases the voltage necessary to make the gap appear more like vacuum. These results provide a generalized SCLC for both collisionality and initial velocity when assessing the transitions between electron emission mechanisms.

Anomalous phase diagram of the elastic interface with nonlocal hydrodynamic interactions in the presence of quenched disorder.

We investigate the influence of quenched disorder on the steady states of driven systems of the elastic interface with nonlocal hydrodynamic interactions. The generalized elastic model (GEM), which has been used to characterize numerous physical systems such as polymers, membranes, single-file systems, rough interfaces, and fluctuating surfaces, is a standard approach to studying the dynamics of elastic interfaces with nonlocal hydrodynamic interactions. The criticality and phase transition of the quenched generalized elastic model are investigated numerically and the results are presented in a phase diagram spanned by two tuning parameters. We demonstrate that in the one-dimensional disordered driven GEM, three qualitatively different behavior regimes are possible with a proper specification of the order parameter (mean velocity) for this system. In the vanishing order parameter regime, the steady-state order parameter approaches zero in the thermodynamic limit. A system with a nonzero mean velocity can be in either the continuous regime, which is characterized by a second-order phase transition, or the discontinuous regime, which is characterized by a first-order phase transition. The focus of this research is to investigate the critical scaling features near the pinning-depinning threshold. The behavior of the quenched generalized elastic model at the critical depinning force is explored. Near the depinning threshold, the critical exponent is obtained numerically.

Explicit and implicit large eddy simulations of variable-density low-speed flows

The application of the Non-oscillatory Forward-in-Time (NFT) class of solvers to facilitate conventional explicit Large Eddy Simulations (LES) and implicit LES (ILES) of low-speed turbulent flow encompassing substantial local density variations is explored. Schemes solving two different sets of Low Mach Number (LMN) equations are proposed with the aim of capturing variable-density effects arising from either a non-isothermal distribution in single-species flow or compositional variation occurring in a binary-species mixing under isothermal conditions. Both schemes employ the semi-implicit NFT integrators based on the Multidimensional Positive Definite Advection Transport Algorithm and a non-symmetric Krylov subspace solver for the variable-coefficient Poisson problems arising from different treatments applied to the non-zero velocity divergence term in the two sets of the LMN equations. The developments are successfully validated using three diverse test cases, differentially heated cavity flow, non-isothermal free-jets, and a helium plume. The reported simulations show that both the dynamic Smagorinsky model in LES and ILES subgrid-scale treatments yield similar accuracy in capturing turbulent effects for the considered flows.

Evaluation of Deuterium Oxide Deposition Velocity over a Forest Environment.

Field experiments were performed to evaluate the deposition velocity of tritium oxide within a forest environment at the Savannah River Site near Aiken, SC. Field releases were designed to guide selection of deposition velocity values for use in safety-basis modeling. Six releases of deuterium oxide were conducted in 2020 and 2021 with corresponding air samples during and following each release. Samples were analyzed to determine the deuterium-to-hydrogen ratio in water and converted to concentrations of deuterium in the air during the experiment. Measurements were compared to prior model simulations to evaluate model performance and deposition velocity estimates. Field releases demonstrated vertical and horizontal mixing of a plume in a forest. Predicted deposition velocities ranged from 2.4 to 5.4 cm s -1 on average. In all cases, model simulations underpredicted deuterium concentration by 1 to 2 orders of magnitude, indicating the model does not sufficiently mix the plume into the forest. While the model underestimated the transfer of material downward through the forest, it does suggest that the model's estimates are conservative for making downwind dose estimates because of lower plume depletion, leading to higher concentration and dose estimates. While the field releases do not cover all possible meteorological conditions, we conclude it is appropriate to use a non-zero deposition velocity when performing safety-basis modeling of tritium oxide based on conservatism within the model. A recommendation of 1.0 cm s -1 as a deposition velocity is made, which is beyond the 95 th percentile value estimated from the prior modeling study.

An experimental investigation on salt-finger convection

This work investigates the vertical and horizontal characteristic velocities of salt-finger convection over different density ratios by experimentally adding various concentrations of salty, hot water into cold, fresh water in a water tank. salt fingers are visualized by dye and its displacement over time is obtained by recording and analysing video. These experiments effectively generate the phenomena resembling salt-finger micro-structure in the ocean. The vertical velocity is significantly increased by lowering the density ratio corresponding to a larger salinity difference between the top and bottom showing a stronger destabilizing effect. Tilted fingers that resemble the experimental and oceanography observations are also observed. We also observe a non-zero horizontal velocity implying the presence of staircases. Finger widths obtained from the experiments are compared with that predicted from the linear stability analysis, which is within the same order of magnitude.

Investigation of surface inclination effect during dropwise condensation of flowing saturated steam

When a pure vapor condenses over a surface, it can form a continuous liquid film or a multitude of discrete droplets, thus realizing the so-called dropwise condensation (DWC). In the literature, most of the experimental data refer to DWC on vertical condensing surfaces with quiescent vapor. However, in many applications, the condensing vapor usually has a non-zero flow velocity with a consequent effect on the sliding motion of droplets. Moreover, the drag force due to vapor velocity may be the only mechanism for liquid removal on a horizontal surface or in space applications. A systematic investigation of the effects of vapor drag and surface inclination on the heat transfer and droplet population during DWC is needed and is addressed in the present paper.Here, DWC of flowing steam is experimentally studied on sol-gel silica-based coated aluminium substrates at three different inclinations: vertical, inclined at 45°, and horizontal. Heat transfer coefficient (HTC) and droplet population measurements are performed in a wide range of heat flux (260–610 kW m−2) and average vapor velocity (3.3–13.8 m s−1). When decreasing the tilt angle, from vertical to horizontal, due to the lower contribution of the gravity force, the average droplet size increases, and a strong HTC reduction is observed above all at low vapor velocities. Because of the vapor drag force, the HTC increases with steam velocity and, at the highest mass velocity, the HTC is independent from the surface inclination. A model for the droplet departing radius in the presence of vapor velocity, initially proposed by the present authors for the sole case of vertical surfaces, is here modified to account also for the effect of surface inclination and then assessed against the present experimental data. Hence, we propose to predict the heat flux during DWC by coupling the new equation for the departing radius with the available models of heat transfer through a single droplet and drop-size distribution. The developed calculation method is found to provide satisfactory predictions of the HTC for the whole range of vapor velocity, heat flux and surface inclination.

Trajectory tracking control of nonholonomic wheeled mobile robots using only measurements for position and velocity

This paper studies the trajectory tracking control of nonholonomic wheeled mobile robots, and only measurements for Cartesian position and velocity are used. A full-order observer is proposed to estimate the unmeasurable attitude and filter the position signal. Its effectiveness relies on the persistent excitation (PE) condition of non-zero linear velocity. Using the observer states, we design a local tracking controller that guarantees: (a) the linear velocity input is positive, and (b) the position tracking error is convergent to zero locally asymptotically. Experiments performed on a robot built in-house illustrate the control algorithm.

Smooth symmetric transonic isothermal flows with nonzero angular velocity

In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary conditions at the inner and outer circle. By solving the one side boundary problem, we obtain that there exist accelerating or decelerating smooth transonic flows in an annulus. Moreover, the structural stability of these smooth symmetric transonic flows with nonzero angular velocity are further investigated. Furthermore, we examine the transonic solutions with shocks as well via prescribing suitable boundary conditions on the inner and outer circle.

Contribution of Deep Vertical Velocity to Deficiency of Sverdrup Transport in the Low-Latitude North Pacific

Abstract Deep vertical velocity is a critical factor causing deficiencies in Sverdrup theory. However, few studies have focused on its influence in the low-latitude western Pacific. Through multiple analyses of observational, reanalysis, and simulation data, this study explored the contribution of deep nonzero vertical velocity to the Sverdrup transport inaccuracy in the low-latitude North Pacific. The vertical velocities inducing relatively small non-Sverdrup transport exist within 1500–2500 m, which exhibit similar patterns with opposite values to the south and north of 13°N. The zonally integrated meridional volume transport associated with these vertical velocities displays nonnegligible dipolar zonal bands west of approximately 150°W. The positive and negative transport bands, centered at 11° and 17°N, can reach an amplitude of approximately 8.0 Sv (1 Sv ≡ 106 m3 s−1) when integrated from the eastern boundary to 140°E. On average, such integrated meridional transport makes up roughly half of the prominent Sverdrup transport discrepancies in the central-western Pacific. Further investigation indicated that the spatial pattern of these vertical velocities is modulated by ocean topography and deep meridional currents. Moreover, a near-global test suggested that the meridional non-Sverdrup transport related to deep vertical velocity is widespread and undergoes remarkable multidecadal variation. This study reveals the disruptive role of deep vertical velocity in disturbing the Sverdrup balance and emphasizes the consideration of its long-term variation when diagnosing wind-driven circulation changes using Sverdrup theory.

Triple collision orbits with nonzero initial velocities

Triple collision orbits with nonzero initial velocities

Machine learning interatomic potentials as efficient tools for obtaining reasonable phonon dispersions and accurate thermal conductivity: A case study of typical two-dimensional materials

The accurate description of phonon dispersion of two-dimensional (2D) materials demonstrates significance in many research fields of condensed matter physics. In this paper, we systematically calculate the phonon spectra and transport properties of six representative 2D materials (encompassing single-element and binary compounds with flat, buckled, and puckered backbone geometries) by means of density functional theory (DFT) and two machine learning interatomic potentials [MLIPs, on-the-fly machine learning potential (FMLP), and moment tensor potential (MTP)]. The results show that the acoustic out-of-plane flexural (ZA) dispersion of the 2D materials are always and easily exhibiting non-quadratic dispersion phenomena near the center of the Brillouin zone by using the pure DFT calculation method. This phenomenon contradicts physics and reflects intuitively from the non-zero group velocity at Γ point. However, no matter which MLIP (FMLP/MTP) the calculation is based on, it could solve such behavior perfectly, where the ZA mode conforms to the quadratic dispersion relationship in the long-wavelength limit. Our results further demonstrate that compared to the pure DFT calculation, the FMLP and MTP method could quickly and relatively accurately obtain the lattice thermal conductivities of graphene, silicene, phosphorene, SiC, MoS2, and GeS. The findings presented in this work provide a solution about the pseudophysical phenomenon of ZA dispersions in 2D materials with the pure DFT calculation, which will greatly facilitate research areas such as phonon thermal transport, flexural mechanics, and electron–acoustic coupling.

Stationary state of harmonic chains driven by boundary resetting

We study the nonequilibrium steady state of an ordered harmonic chain of N oscillators connected to two walls which undergo diffusive motion with stochastic resetting. The intermittent resetting of the walls effectively emulates two nonequilibrium reservoirs that exert temporally correlated forces on the boundary oscillators. These reservoirs are characterized by the diffusion constants and resetting rates of the walls. We find that, for any finite N, the velocity distribution of the bulk oscillators remains non-Gaussian, as evidenced by a non-zero bulk kurtosis that decays . We calculate the spatio-temporal correlation of the velocity of the oscillators both analytically as well as using numerical simulation. The signature of the boundary resetting is present at the bulk in terms of the two-time velocity correlation of a single oscillator and the equal-time spatial velocity correlation. For the resetting driven chain, the two-time velocity correlation decay as at the large time, and there exists a non-zero equal-time spatial velocity correlation when . A non-zero average energy current will flow through the system when the boundary walls reset to their initial positions at different rates. This average energy current can be computed exactly in the thermodynamic limit. Numerically we show that the distribution of the instantaneous energy current at the boundary is independent of the system size. However, the distribution of the instantaneous energy current in the bulk approaches a stationary distribution in the thermodynamic limit.

On the gravitational fall of a non-spherical particle in a quiescent fluid medium

Closed-form analytical solutions have been derived for the gravitational fall of a non-spherical particle in a quiescent fluid. The Boussinesq-Basset-Oseen equation accounting for history force and particle slip effects was applied to derive the particle motion equation, using a sphericity-dependent drag law for transitional flow in the range 0.001<Re≤100000 and valid for sphericities >0.50. The derived closed-form solutions were validated with published experimental data and the accuracy was verified using published approximate analytical solutions and numerical results. The closed-form solutions were found to agree with experiments and produced more accurate results than other published approximate analytical solutions. Also, the effects of sphericity, Basset force and particle slip on the particle motion were investigated and discussed. The present analytical solutions are applicable to zero and non-zero initial velocity, steady and unsteady motion, and the corresponding displacements and accelerations. Additionally, new settling velocity formula valid for non-spherical particles was derived.

Uniform space-charge-limited current for a two-dimensional planar emitter with nonzero monoenergetic initial velocity

While characterizing space-charge-limited current (SCLC) is important for numerous applications, no analytical solutions for SCLC with monoenergetic initial velocity exist for two-dimensional (2D) geometries. Here, we derive approximate closed-form solutions for uniform SCLC with monoenergetic emission of electrons in a 2D planar diode, where emission is restricted to a long patch of width W for electrodes separated by a distance D. We also derive a semiempirical approach for estimating the SCLC for these cases by treating the geometric and velocity correction factors as multiplicative corrections to the SCLC for a one-dimensional vacuum diode given by the Child–Langmuir (CL) law. We show that the SCLC for a finite patch with nonzero velocity can exceed the CL law by three orders of magnitude. The theoretically calculated SCLCs for various emission widths and initial velocities in the 2D diode agree well with particle-in-cell simulations using the over-injection method in XOOPIC; they agree with the semiempirical relationship for lower initial velocities. In the limit of high initial velocity, the geometry and velocity corrections to the CL law cannot be decoupled, invalidating the assumption of the semiempirical approach and causing it to diverge from the theoretical solution and XOOPIC simulations. These results provide valuable estimates for determining the onset of virtual cathode formation for photocathodes and thermionic cathodes, which operate in the over-injection regime to avoid beam quality degradation.

Information in feedback ratchets.

Feedback control uses the state information of the system to actuate on it. The information used implies an effective entropy reduction of the controlled system, potentially increasing its performance. How to compute this entropy reduction has been formally shown for a general system and has been explicitly computed for spatially discrete systems. Here, we address a relevant example of how to compute the entropy reduction by information in a spatially continuous feedback-controlled system. Specifically, we consider a feedback flashing ratchet, which constitutes a paradigmatic example for the role of information and feedback in the dynamics and thermodynamics of transport induced by the rectification of Brownian motion. A Brownian particle moves in a periodic potential that is switched on and off by a controller. The controller measures the position of the particle at regular intervals and performs the switching depending on the result of the measurement. This system reaches a long-time dynamical regime with a nonzero mean particle velocity, even for a symmetric potential. Here, we calculate the efficiency at maximum power in this long-time regime, computing all the required contributions. We show how the entropy reduction can be evaluated from the entropy of the non-Markovian sequence of control actions, and we also discuss the required sampling effort for its accurate computation. Moreover, the output power developed by the particle against an external force is investigated, which-for some values of the system parameters-is shown to become larger than the input power provided by the switching of the potential. The apparent efficiency of the ratchet thus becomes higher than one, if the entropy reduction contribution is not considered. This result highlights the relevance of including the entropy reduction by information in the thermodynamic balance of feedback-controlled devices, specifically when writing the second principle. The inclusion of the entropy reduction by information leads to a well-behaved efficiency over all the range of parameters investigated.

On the Child–Langmuir law in one, two, and three dimensions

We consider the limiting current from an emitting patch whose size is much smaller than the anode–cathode spacing. The limiting current is formulated in terms of an integral equation. It is solved iteratively, first to numerically recover the classical one-dimensional Child–Langmuir law, including Jaffe's extension to a constant, nonzero electron emission velocity. We extend to two-dimensions in which electron emission is restricted to an infinitely long stripe with infinitesimally narrow stripe width so that the emitted electrons form an electron sheet. We next extend to three-dimensions in which electron emission is restricted to a square tile (or a circular patch) with an infinitesimally small tile size (or patch radius) so that the emitted electrons form a needlelike line charge. Surprisingly, for the electron needle problem, we only find the null solution for the total line charge current, regardless of the assumed initial electron velocity. For the electron sheet problem, we also find only the null solution for the total sheet current if the electron emission velocity is assumed to be zero, and the total maximum sheet current becomes a finite, nonzero value if the electron emission velocity is assumed to be nonzero. These seemingly paradoxical results are shown to be consistent with the earlier works of the Child–Langmuir law of higher dimensions. They are also consistent with, or perhaps even anticipated by, the more recent theories and simulations on thermionic cathodes that used realistic work function distributions to account for patchy, non-uniform electron emission. The mathematical subtleties are discussed.

Quantized vortex nucleation in collisions of superfluid nanoscopic helium droplets at zero temperature.

We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40m/s, respectively, induced by the long-range van der Waals attraction between the droplets.