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At least 919 records · Page 51

Robonaut 2 - IVA Experiments On-Board ISS and Development Towards EVA Capability

Robonaut 2 (R2) has completed its fixed base activities on-board the ISS and is scheduled to receive its climbing legs in early 2014. In its continuing line of firsts, the R2 torso finished up its on-orbit activities on its stanchion with the manipulation of space blanket materials and performed multiple tasks under teleoperation control by IVA astronauts. The successful completion of these two IVA experiments is a key step in Robonaut's progression towards an EVA capability. Integration with the legs and climbing inside the ISS will provide another important part of the experience that R2 will need prior to performing tasks on the outside of ISS. In support of these on-orbit activities, R2 has been traversing across handrails in simulated zero-g environments and working with EVA tools and equipment on the ground to determine manipulation strategies for an EVA Robonaut. R2 made significant advances in robotic manipulation of deformable materials in space while working with its softgoods task panel. This panel features quarter turn latches that secure a space blanket to the task panel structure. The space blanket covers two cloth cubes that are attached with Velcro to the structure. R2 was able to open and close the latches, pull back the blanket, and remove the cube underneath. R2 simulated cleaning up an EVA worksite as well, by replacing the cube and reattaching the blanket. In order to interact with the softgoods panel, R2 has both autonomously and with a human in the loop identified and localized these deformable objects. Using stereo color cameras, R2 identified characteristic elements on the softgoods panel then extracted the location and orientation of the object in its field of view using stereo disparity and kinematic transforms. R2 used both vision processing and supervisory control to successfully accomplish this important task. Teleoperation is a key capability for Robonaut's effectiveness as an EVA system. To build proficiency, crewmembers have attempted increasingly difficult tasks using R2 inside the Station. After donning motion capture equipment and a virtual reality visor, Expedition 34/35 flight engineer Tom Marshburn began operations with simple hand movements. Having gained confidence, Marshburn guided R2's arms in a leader-follower exercise with crewmate Chris Cassidy. He was also able to use the hand to grab a tumbling roll of tape, a task only demonstrable in microgravity. Later efforts saw Cassidy handle softgoods through shared control with ground operators, mimicking an activity previously achieved using only autonomy. Robotic climbing through the ISS on handrails requires both precision motion and compliant grasps in order to both position grippers on handrails/seat track and prevent large internal forces. R2 climbs using actively controlled compliance and torque limiting to meet both the precision and softness requirements. During a step, the attached leg is controlled to be strong and stiff in order to maintain precision trajectory tracking. The swing leg is controlled to be stiff but weak to minimize unintentional impact forces while maintaining precision. During a simulated dual limb grasp (as shown in Figure 1), the R2 controller maintains one limb rigid and one limb soft to prevent large internal forces from building up. R2's grippers also use a form of force control to limit grip force while not fully closed on either a handrail or seat track thus limiting unintentional forces on cables/objects that may be present in R2's translational path. The on-board torso R2 safety system relies on a single end-effector velocity limit to prevent potential impact forces from exceeding Station maximum load requirements. R2's mobile configuration required modifications to the velocity limiting safety function due to its large, dynamic inertia. R2's legs maneuver the robot's mass creating configuration dependent, joint-relative inertias. A single all-encompassing velocity limit to cover worst case inertia is prohibitively low. The upgraded R2 control and safety systems solve this problem using momentum limiting, momentum control, and kinetic energy minimization. Momentum and kinetic energy take the robot mass into account relieving low velocity restrictions on low inertia end-effectors while ensuring that the overall mass of R2 is limited from hazardous velocities. The momentum of R2's five safety nodes (each of the four end-effectors and the body) is monitored and compared to a single momentum limit. If any of the five nodes exceeds the safety limit, the motor power is removed and the robot comes to a stop. Momentum control/limiting also provides a simple, reliable method to integrate hand held tools into the safety system by providing the tool mass to the control system thus automatically reducing the allowable velocity of the end-effector with the tool. Work on the ground continues to build the skill set for an EVA Robonaut. Recent experiments (Figure 2) demonstrate how a teleoperator can use R2 to manipulate a tether hook, an important safety precaution on spacewalks. Another task displayed Robonaut's ability to pull back a protective jacket over a hose and search for damage, as well as inspect a quick-disconnect fitting for debris. Demonstrations such as these are indicative of EVA work done on ISS, specifically seen during a series of spacewalks over 2012 and 2013 where astronauts searched for an ammonia leak in one of the external cooling loops. Through experiments both on ISS and on the ground, R2 is evolving and providing the information needed to plan out the upgrades that will make an EVA Robonaut an effective tool. With the addition of legs, R2 will start climbing inside the space station and supply invaluable information on how the climbing strategies and task stabilization techniques must be refined. Ground R2 systems will continue to work with additional EVA tools and equipment in preparation for onboard IVA testing and future EVA applications.

Diftler, Myron↗

Synergistic Evolution of Segmental Motion and Cooperative Relaxation within the Amorphous Phase of Organic Mixed Ionic-Electronic Conductors

Organic mixed ionic-electronic conductors (OMIECs) facilitate a variety of electrochemical processes and feature a heterogeneous microstructure composed of both crystalline and amorphous phases. However, structural evolution in amorphous regions during electrochemical doping remains poorly understood, limiting our understanding of mixed conduction mechanisms. Here, in this work, we develop operando chip calorimetry to probe amorphous phase evolution in poly­(3,4-ethylenedioxythiophene):poly­(styrenesulfonate) (PEDOT:PSS) under swelling and electrochemical (de)­doping. Our results reveal that amorphous regions providing ionic transport pathways and those within electronic transport channels undergo heterogeneous, yet synergistic, evolution during electrochemical modulation. The cooperative interplay between segmental motion and relaxation maintains ionic conductivity and intergrain electronic transport upon electrowetting and doping, while facilitating efficient ion hopping and adaptable chain conformations during dedoping. Such synergies are more pronounced in loose structures featuring a fibrillar morphology, which exhibit lower glass transition temperatures (T g ) and higher fragility (m). High-throughput robotic screening further establishes a strong correlation between elevated m/T g ratios and enhanced mixed conduction. These findings elucidate the role of the amorphous phase in the synthesis of OMIECs and underscore the potential of operando chip calorimetry in uncovering structure–property relationships in electroactive polymers.

amorphous phase↗

Insights of Boundary Layer Turbulence Over the Complex Terrain of Central Himalaya from GVAX Field Campaign

Limited observations hinder understanding of turbulent characteristics in mountainous terrain resulting from heating or cooling of slopes, wind, vertical motions, and heat or moisture advection, which disperse aerosols and other pollutants over the region. In this study, the 1290 MHz radar wind profiler data are utilized to compute the boundary layer height (BLH), the refractive index structure constant (C n 2 ), and the energy dissipation rate (ε) over the central Himalayan site for the period of November 2011 to March 2012, from the intense Ganges Valley Aerosol Experiment (GVAX) field measurements. The radar wind profiler (RWP) based estimation of BLH and ε is validated against the radiosonde, representing the effectiveness of the datasets for further investigation. The strong seasonal variation of log C n 2 and log ε, with average values of ≈ -12 m -2/3 and -2 m 2 s -3 , respectively, is associated with the mountain-induced local circulations and stability in the atmospheric boundary layer. The weak stratification during weak flow is found to be responsible for deep mixing, particularly in the nocturnal boundary layer in spring. Furthermore, the level of cloud cover significantly impacts the strength of turbulence, with the highest cloud cover resulting in a substantial increase in log C n 2 (approximately -11 m -2/3 ) due to intense updraft and downdraft motions compared to clear skies. Additionally, the distribution of aerosol loading across the site, coupled with the behavior of BLH, atmospheric stability, and orographic-induced circulations, implies distinctive seasonal mechanisms for transporting aerosols toward the mountains. This study offers valuable insights into the diurnal and seasonal patterns of turbulent mixing and the mechanisms behind the transport of pollutants through boundary layer processes over the region.

54 ENVIRONMENTAL SCIENCES↗

Antiphase-Boundary-Engineered Domain Switching in a (110)-Oriented BiFeO 3 Film

A ferroelectric domain wall memory device exploits the presence (or absence) of domain walls as the basis for information storage. Although structural defects strongly influence ferroelectric domain wall nucleation and growth, this correlation is far from being fully understood. For example, a single defect can play opposing roles: it can act as a nucleation site to initiate domain switching or, conversely, serve as a pinning center inhibiting domain wall motion. This is particularly the case for antiphase boundaries (APBs), whose influence on switching remains relatively unexplored despite being ubiquitous in oxide perovskite ferroelectrics. Here, we use aberration-corrected scanning transmission microscopy and in situ transmission electron microscopy under an applied bias to extensively characterize the influence of an APB on the switching behavior in a (110)-oriented BiFeO 3 thin film. We demonstrate that deterministic nucleation occurs in the proximity of a vertically oriented APB, following which domain growth occurs laterally in a symmetric fashion. Atomic-scale structural analysis reveals that the shear operation vector for the APB is 1/2[110]; this half-unit-cell shift extends over a few nanometers, implying that the APB plane is inclined toward the imaging direction. The symmetric switching observation is attributed to local inhomogeneous lattice strain and a reduction of polarization caused by the APB. These results demonstrate that an extended structural defect can be used as an active switching element rather than a stumbling block in reprogrammable domain-wall-based devices. Ultimately, this will expand the capabilities of ferroelectric thin films for future electronic devices based on ferroelectric domain walls.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phonon-enhanced nonlinearities in hexagonal boron nitride

Abstract Polar crystals can be driven into collective oscillations by optical fields tuned to precise resonance frequencies. As the amplitude of the excited phonon modes increases, novel processes scaling non-linearly with the applied fields begin to contribute to the dynamics of the atomic system. Here we show two such optical nonlinearities that are induced and enhanced by the strong phonon resonance in the van der Waals crystal hexagonal boron nitride (hBN). We predict and observe large sub-picosecond duration signals due to four-wave mixing (FWM) during resonant excitation. The resulting FWM signal allows for time-resolved observation of the crystal motion. In addition, we observe enhancements of third-harmonic generation with resonant pumping at the hBN transverse optical phonon. Phonon-induced nonlinear enhancements are also predicted to yield large increases in high-harmonic efficiencies beyond the third.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observation of the Electromagnetic Field Effect via Charge-Dependent Directed Flow in Heavy-Ion Collisions at the Relativistic Heavy Ion Collider

The deconfined quark-gluon plasma (QGP) created in relativistic heavy-ion collisions enables the exploration of the fundamental properties of matter under extreme conditions. Noncentral collisions can produce strong magnetic fields on the order of 10 18 G , which offers a probe into the electrical conductivity of the QGP. In particular, quarks and antiquarks carry opposite charges and receive contrary electromagnetic forces that alter their momenta. This phenomenon can be manifested in the collective motion of final-state particles, specifically in the rapidity-odd directed flow, denoted as v 1 ( y ) . Here, we present the charge-dependent measurements of d v 1 / d y near midrapidities for π ± , K ± , and p ( p ¯ ) in Au + Au and isobar ( Ru 44 96 + Ru 44 96 and Zr 40 96 + Zr 40 96 ) collisions at s NN = 200 GeV , and in Au + Au collisions at 27 GeV, recorded by the STAR detector at the Relativistic Heavy Ion Collider. The combined dependence of the v 1 signal on collision system, particle species, and collision centrality can be qualitatively and semiquantitatively understood as several effects on constituent quarks. While the results in central events can be explained by the u and d quarks transported from initial-state nuclei, those in peripheral events reveal the impacts of the electromagnetic field on the QGP. Our data put valuable constraints on the electrical conductivity of the QGP in theoretical calculations. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

IUE spectroscopic investigation of interacting binary systems

The IUE observations of binaries consisting of at least one early type star, to the Algol systems, and to W Serpentis systems are discussed. The OB close binaries almost invaribly show a stellar wind. The difference between an unevolved early type system and a slightly evolved system is difficult to discern observationally and probably not meaningful in terms of Roche lobes. the zeta Aur stars show complex gas motions and shocks. Many of the Algol systems show peculiarities in their ultraviolet continua and the resonance lines, particularly Si IV, are of abnormal and variable strength. Emission lines were detected in several systems during the total eclipse. The W Ser stars are characterized by numerous strong emission lines in their ultraviolet spectra. It appears that these systems may be related to beta Lyrae as they seem to be in a phase of rapid mass transfer and their spectra show similarities to that of beta Lyrae.

Mccluskey, G. E., Jr.↗

A cloud model simulation of space shuttle exhaust clouds in different atmospheric conditions

A three-dimensional cloud model was used to characterize the dominant influence of the environment on the Space Shuttle exhaust cloud. The model was modified to accept the actual heat and moisture from rocket exhausts and deluge water as initial conditions. An upper-air sounding determined the ambient atmosphere in which the cloud could grow. The model was validated by comparing simulated clouds with observed clouds from four actual Shuttle launches. The model successfully produced clouds with dimensions, rise, decay, liquid water contents and vertical motion fields very similar to observed clouds whose dimensions were calculated from 16 mm film frames. Once validated, the model was used in a number of different atmospheric conditions ranging from very unstable to very stable. In moist, unstable atmospheres simulated clouds rose to about 3.5 km in the first 4 to 8 minutes then decayed. Liquid water contents ranged from 0.3 to 1.0 g kg-1 mixing ratios and vertical motions were from 2 to 10 ms-1. An inversion served both to reduce entrainment (and erosion) at the top and to prevent continued cloud rise. Even in the most unstable atmospheres, the ground cloud did not rise beyond 4 km and in stable atmospheres with strong low level inversions the cloud could be trapped below 500 m. Wind shear strongly affected the appearance of both the ground cloud and vertical column cloud. The ambient low-level atmospheric moisture governed the amount of cloud water in model clouds. Some dry atmospheres produced little or no cloud water. One case of a simulated TITAN rocket explosion is also discussed.

Chen, C.↗

Dynamics of the outgoing turbulent boundary layer in a Mach 5 unswept compression ramp interaction

Wall pressure fluctuations have been measured under the unsteady separation shock and on the ramp face in an unswept Mach 5 compression ramp interaction. The freestream Reynolds number was 51.0 x 10 to the 6th/m, and the incoming turbulent boundary layer developed on the tunnel floor under approximately adiabatic wall temperature conditions. Standard data-acquisition methods, as well as real-time and posttest conditional sampling techniques were used. The results show that the mean and rms pressure levels are strong functions of separation shock position. At all stations on the ramp, from the corner to where the pressure reaches the theoretical inviscid value, the pressure signals have two dominant components: a low frequency component characteristic of the global unsteadiness, which correlates with the separation shock motion, and a higher frequency component associated with turbulence. The former is the major contributor to the overall signal variance.

Gramann, Richard A.↗

Barotropic instability with divergence - Theory and applications to Venus

IR images of Venus reveal a curious double-lobed hot spot in the polar region. Elson (1982) has suggested that this dipole represents a barotropic instability associated with a high-latitude jet. Unfortunately, the classical theory of barotropic instability cannot predict temperature variations. This paper generalizes the theory to include horizontal divergence, vertical motions, and temperature variations, and applies it to the stratosphere of Venus. The fastest-growing barotropic instability in the nominal model matches the observed dipole in period and horizontal temperature pattern. The accompanying wind variations are comparable to the speed of the mean jet, indicating strong nonlinear effects. It is concluded that the Venus dipole may represent the self-limited stage of a barotropic instability with divergence.

Dobrovolskis, Anthony R.↗

An Analysis of the Torsion-Rotation-Vibration Rotational Spectrum of the Lowest In-Plane Bend and First Excited Torsional State of the C(3V) Internal Rotor C2H5CN

C2H5CN (Propionitrile or ethyl cyanide) is a well known interstellar species abundantly observed in hot cores during the onset of star formation. The onset of star formation generally results in elevated temperature, which thermally populates may low lying vibrational states such as the 206/cm in-plane bend and the 212/cm first excited torsional state in C2H5CN. Unfortunately, these two states are strongly coupled through a complex series of torsion-vibration-rotation interactions, which dominate the spectrum. In order to understand the details of these interactions and develop models capable of predicting unmeasured transitions for astronomical observations in C2H5CN and similar molecules, several thousand rotational transitions in the lowest excited in-plane bend and first excited torsional state have been recorded, assigned and analyzed. The analysis reveals very strong a- and b-type Coriolis interactions and a number of other smaller interactions and has a number of important implications for other C3V torsion-rotation-vibration systems. The relative importance and the physical origins of the coupling among the rotational, vibrational and torsional motions will be presented along with a full spectroscopic analysis and supporting astronomical observations.

Pearson, J. C.↗

The Transition from Hydrogen Bonding to Ionization in (HCI)n(NH3)n and (HCI)n(H2O)n Clusters: Consequences for Anharmonic Vibrational Spectroscopy

Anharmonic vibrational frequencies and intensities are calculated for 1:1 and 2:2 (HCl)(sub n)(NH3)(sub n) and (HCl)(sub n)(H2O)(sub n) complexes, employing the correlation-corrected vibrational self-consistent field method with ab initio potential surfaces at the MP2/TZP computational level. In this method, the anharmonic coupling between all vibrational modes is included, which is found to be important for the systems studied. For the 4:4 (HCl)(sub n)(H2O)(sub n) complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Just as the (HCl)(sub n)(NH3)(sub n) structure switches from hydrogen-bonded to ionic for n=2, the (HCl)(sub n)(H2O)(sub n) switches to ionic structure for n=4. For (HCl)2(H2O)2, the lowest energy structure corresponds to the hydrogen-bonded form. However, configurations of the ionic form are separated from this minimum by a barrier of less than an O-H stretching quantum. This suggests the possibility of experiments on ionization dynamics using infrared excitation of the hydrogen-bonded form. The strong cooperative effects on the hydrogen bonding, and concomitant transition to ionic bonding, makes an accurate estimate of the large anharmonicity crucial for understanding the infrared spectra of these systems. The anharmonicity is typically of the order of several hundred wave numbers for the proton stretching motions involved in hydrogen or ionic bonding, and can also be quite large for the intramolecular modes. In addition, the large cooperative effects in the 2:2 and higher order (HCl(sub n)(H2O)(sub n) complexes may have interesting implications for solvation of hydrogen halides at ice surfaces.

Chaban, Galina M.↗

High-resolution IUE observations of interstellar absorption lines in the Vela supernova remnant

Ultraviolet spectra of 45 stars in the vicinity of the Vela supernova remnant were recorded by the short-wavelength echelle spectrograph aboard the International Ultraviolet Explorer (IUE). Over one-third of the stars show interstellar absorption lines at large radial velocities (greater than 60 km/s). The mapping of these high-velocity components in the sky suggests the motions are chaotic, rather than from a coherent expansion of the remnant material. In accord with earlier conclusions from Copernicus data, the gas at high velocity exhibits higher than normal ionization and shows substantially less depletion of nonvolatile elements than normal interstellar material at low velocities. Relatively strong lines from neutral carbon in the two excited fine-structure states indicate that the neutral clouds within the remnant have had their pressures enhanced by the passage of the blast wave from the supernova. Also, the remnant seems to show a significant enhancement in the abundances of low-velocity Si IV, C IV, and N V over those found in the general interstellar medium.

Jenkins, E. B.↗

Morphological changes in the NGC 6251 jet

The giant radio galaxy NGC 6251 is a particularly good object for observational tests of relativistic jet models. Due to its high declination and approximately 0.5 Jy radio nucleus, high-quality Very Long Baseline Interferometry (VLBI) images of the central regions of the source can be made with northern hemisphere arrays. In addition, the large-scale radio morphology strongly suggests that the radio axis lies close to the plane of the sky, so Doppler boosting should be less extreme than in the core-dominated superluminal sources. Earlier 18 cm VLBI observations of NGC 6251 revealed an unexpectedly large jet/counterjet brightness ratio and small transverse motion of a feature in the parsec-scale jet. These early results are difficult to reconcile with the simplest symmetric relativistic jet models. In this paper we present a third-epoch 18 cm VLBI image of the parsec-scale radio jet in NGC 6251, and compare jet morphology over a 5 year time span. The jet shows a minor brightness peak at nearly the same distance from the core as the '25 mas knot' seen in the first- and second-epoch VLBI images. This feature is much less pronounced in the third epoch, and a relatively bright, new knot has appeared approximately 12 mas from the core. If this new component had a constant brightness during the 5 years separating the first and third observing epochs, then it must have moved away from the core with an apparent speed of at least 1.2c (compared with an upper limit of 0.23c for motion of the 25 mas knot). However, we cannot yet rule out a local brightening of the inner jet in favor of a new moving component. We determine a lower limit for the jet/couterjet brightness ratio of 100:1 within 6 mas of the core. We also present a new Very Large Array (VLA) image of the kpc-scale jet with 3 sec resolution, made from data obtained during the VLBI observations. The rate of decrease in jet surface brightness from parsec to kiloparsec scales is similar to jets in known superluminal radio sources.

Jones, Dayton L.↗

Navier-Stokes Computations on Full Wing-Body Configuration with Oscillating Control Surfaces

Unsteady Navier-Stokes simulations have been performed for vortical flows over an "arrow-wing" configuration of a supersonic transport in the transonic regime. Computed steady pressures and integrated force coefficients with and without control surface deflection at a moderate angle of attack are compared with experiment. For unsteady cases, oscillating trailing-edge control surfaces are modeled by using moving grids. Response characteristics between symmetric and antisymmetric oscillatory motions of the control surfaces on the left and right wings are studied. The antisymmetric case produces higher lift than the steady case with no deflection and the unsteady symmetric case produces higher lift than the antisymmetric case. The detailed analysis of the wake structure revealed a strong interaction between the primary vortex and the wake vortex sheet from the flap region when the flap is deflected up.

Obayashi, Shigeru↗

Role of Ocean Currents and Bottom Pressure Variability on Seasonal Polar Motion

Changes in the ocean angular momentum (OAM) components about the equatorial axes, either due to fluctuations in currents or bottom pressure (mass redistribution), can induce movements of the Earth's pole of rotation, commonly referred to as polar motion or wobble. Output from a 1 deg resolution ocean model is used to calculate the effective equatorial OAM functions chi(sub 1, sup O) and chi(sub 2, sup O), corresponding to polar motion excitation about the equatorial axis pointing to the Greenwich and 90 deg E meridians, respectively. Time series of chi(sup O) are combined with similar atmospheric series chi(sup A), computed from the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalyses, to interpret the observed low-frequency polar motion excitation for the period 1985-1996. Results indicate that the oceans are a very important excitation source for the Chandler (approximately 433 days), annual, and semiannual wobbles, providing for much better amplitude and phase agreement with the observed excitation at these periods, in comparison with what is obtained when only the atmosphere is considered. Both oceanic mass and motion terms are found to be important but with mass signals having somewhat larger amplitudes. The role of regional variability in ocean currents and bottom pressure in contributing to chi(sup O) signals is quantified. Midlatitude regions (approximately 30 deg - 70 deg) figure prominently as places of strong local oceanic excitation signals. The North Pacific basin is found to be generally important for chi(sup O) excitation, while the Southern Ocean is important for both chi(sub 1, sup O) and chi(sub 2, sup O). The largest positive covariances of local with global chi(sup O) signals occur in the Kuroshio region near the western boundary of the North Pacific for chi(sub 1, sup O) and southwest of Australia for chi(sub 2, sup O).

Ponte, Rui M.↗

Morphological Changes in the NGC 6251 Jet

The giant radio galaxy NGC 6251 is a particularly good object for observational tests of relativistic jet models. Due to its high declination and similar 0.5 Jy radio nucleus, high quality VLBI images of the central regions of the source can be made with northern hemisphere arrays. In addition, the large-scale radio morphology strongly suggests that the radio axis lies close to the plane of the sky, so Doppler boosting should be less extreme than in the core-dominated superluminal sources. Earlier 18-cm VLBI observations of NGC 6251 revealed an unexpectedly large jet/counterjet brightness ratio and small transverse motion of a feature in the parsec-scale jet. These early results are difficult to reconcile with the simplest symmetric relativistic jet models.

Wehrle, A. E.↗

Brownian motion of electrons in time-dependent magnetic fields.

The behavior of a weakly ionized plasma in slowly varying time-dependent magnetic fields is studied through an extension of Williamson's stochastic theory. In particular, attention is focused on the properties of electron diffusion in the plane perpendicular to the direction of the magnetic field, when the field strength is large. It is shown that, in the strong field limit, the classical 1/B-squared dependence of the perpendicular diffusion coefficient is obtained for two models in which the field B(t) is monotonic in t and for two models in which B(t) possesses at least one turning point.

Iverson, G. J.↗