Anisotropic Motion Research Articles

Superhydrophobic, Biocompatible and Durable Nanofiber Composite with an Asymmetric Structure for Anisotropic Strain Sensing and Body Motion Detection

Superhydrophobic, Biocompatible and Durable Nanofiber Composite with an Asymmetric Structure for Anisotropic Strain Sensing and Body Motion Detection

Анизотропное насыщение спектра ЭПР радикала DCO, стабилизированного в твердом CO при 4.2 K, и его ориентационное движение

Formyl radicals, DCO, were produced in solid CO matrix and studied by EPR using gas deposition technique on a cold substrate at 4.2 K. The radical electron spin-lattice relaxation was measured to be anisotropic. The anisotropy was found to originate from the anisotropic orientational motion of the radical with the most intensive librations performed around a z axis corresponding to the smallest moment of inertia of the molecule. It was shown that, in solid CO, the libration motion of small molecules is modeled by considering a particle rotating in the orientational potential box. A suggestion was substantiated about the complicated nature of the orientational motion of HCO in the solid CO matrix including the intensive librations and slow tunneling rotation of the molecule around the z axis.

Anisotropic saturation of the EPR spectrum of an DCO radical stabilized in solid CO at 4.2 K and its orientation motion

Formyl radicals, DCO, were produced in solid CO matrix and studied by EPR using gas deposition technique on a cold substrate at 4.2 K. The radical electron spin-lattice relaxation was measured to be anisotropic. The anisotropy was found to originate from the anisotropic orientational motion of the radical with the most intensive librations performed around a z axis corresponding to the smallest moment of inertia of the molecule. It was shown that, in solid CO, the libration motion of small molecules is modeled by considering a particle rotating in the orientational potential box. A suggestion was substantiated about the complicated nature of the orientational motion of HCO in the solid CO matrix including the intensive librations and slow tunneling rotation of the molecule around the z axis. Keywords: electron paramagnetic resonance, matrix isolation, formyl radical, anisotropy of the spin-lattice relaxation time, librations and tunneling rotation of molecules.

Hydrodynamic couplings of colloidal ellipsoids diffusing in channels

The hydrodynamic interactions (HIs) of two colloidal spheres characterized by the translation–translation (T–T) couplings have been studied under various confinements, but little is known regarding the HIs of anisotropic particles and rotational motions, which are common in nature and industry. Here, we study the T–T, rotation–rotation (R–R) and translation–rotation (T–R) hydrodynamic couplings of two colloidal ellipsoids sediment on the bottoms of channels in experiment, theory and simulation. We find that the degree of confinement and the particle shape anisotropy are critical tuning factors resulting in anomalous hydrodynamic and diffusive behaviours. The negative R–R coupling reflects the tendency of opposite rotations of two neighbouring ellipsoids. The positive T–R coupling reflects that an ellipsoid rotates away from the channel axis as another ellipsoid approaches. As the channel width increases, the positive T–T coupling changes to an abnormal negative coupling, indicating that the single-file diffusion can exist even in wide channels. By contrast, only positive T–T couplings were observed for spheres in channels. The T–T coupling increases with the aspect ratiop. The R–R coupling is the maximum at a moderatep ~ 2.8. The T–R coupling is the maximum at a moderate degree of confinement. The spatial range of HIs is longer than that of spheres and increases withp. We propose a simple model which reproduces some coupling phenomena between two ellipsoids, and it is further confirmed by low-Reynolds-number hydrodynamic simulation. These findings shed new light on anisotropic particle diffusion in porous media, transport through membranes, microfluidics and microrheology.

Reflecting time-Space Gaussian random field on compact Riemannian manifold and excursion probability

Motivated from measuring the performance of quantum computing and storage systems together with nanorheology over different shapes of devices, we introduce a reflecting time-space Gaussian random field (RGRF) on a general -parameter compact Riemannian manifold to model the quantum particle movement dynamics. The main task in studying the RGRF is to estimate an asymptotic upper bound of its excursion probability, which asymptotically converges to zero. In doing so, we establish a relationship between the RGRF and its netput Gaussian random field (GRF) via a Skorohod mapping. Then, as an intermediate step, we approximate the excursion probability of the GRF by constructing a chart oriented homeomorphism mapping between a flat manifold and a general compact Riemannian manifold. The netput GRF can be either isotropic or anisotropic. Case studies in terms of anisotropic GRFs over a flat manifold such as normalized fractional Brownian sheets (FBSs) and those over a sphere such as normalized anisotropic fractional spherical Brownian motions (FSBMs) are also presented, where an α-FSBM is introduced and its existence is proved for some constant .

Aligned stripe magnetic domains in a Pt/Co/Pt film induced by a step-terrace substrate

Pt/Co/Pt trilayers were deposited on flat and step-terrace Al2O3 substrates to study the influence of surface morphology on the perpendicular magnetic anisotropy (PMA) and magnetic domain structure. The total thickness of the Pt/Co/Pt trilayers was minimized to resemble the step-terrace morphology of the substrate, which possessed a terrace width and height in the ranges of approximately 90–165 nm and 1.8–4.2 nm. The flat surface of the Pt/Co/Pt trilayers exhibited many small-dot domains or few large-block domains, whereas the terrace surface exhibited highly aligned stripe domains parallel to the longitudinal direction of the step-terrace Al2O3 substrate. The width of the stripe domains was within a range of approximately 500–700 nm, and the length of the stripe domains exceeded a few hundred micrometers. An anisotropic domain-wall motion in the longitudinal direction of the step-terrace may be used to control the operation of a magnetic device, such as a racetrack memory.

Elliptical skyrmion moving along a track without transverse speed

It was recently demonstrated that introducing the shape anisotropy of a skyrmion is an alternative strategy for controlling the skyrmion Hall effect. For example, an elliptical skyrmion shows anisotropic motion under the applied driving force. Here, we study the fundamental properties of an elliptical skyrmion induced by uniaxial in-plane magnetic anisotropy. The dynamics of a skyrmion under various parameters, such as uniaxial in-plane magnetic anisotropy, interfacial Dzyaloshinskii-Moriya interaction, and the damping constant, are investigated, and we employ Thiele's theory and derive expressions for the velocity of the skyrmion that match very well with micromagnetic simulation results. We find that the skyrmion Hall angle can reach ${90}^{\ensuremath{\circ}}$ with the optimized angle between the in-plane easy axis and the current. Our results offer a potential application of racetrack memory based on skyrmions, and a type of racetrack configuration was designed.

Numerical experiments on turbulent entrainment and mixing of scalars

Numerical experiments on the turbulent entrainment and mixing of scalars in a incompressible flow have been performed. These simulations are based on a scale decomposition of the velocity field, thus allowing the establishment from a dynamic point of view of the evolution of scalar fields under the separate action of large-scale coherent motions and small-scale fluctuations. The turbulent spectrum can be split into active and inactive flow structures. The large-scale engulfment phenomena actively prescribe the mixing velocity by amplifying inertial fluxes and by setting the area and the fluctuating geometry of the scalar interface. On the contrary, small-scale isotropic nibbling phenomena are essentially inactive in the mixing process. It is found that the inertial mechanisms initiate the process of entrainment at large scales to be finally processed by scalar diffusion at the molecular level. This last stage does not prescribe the amount of mixing but adapts itself to the conditions imposed by the coherent anisotropic motion at large scales. The present results may have strong repercussions for the theoretical approach to scalar mixing, as anticipated here by simple heuristic arguments which are shown able to reveal the rich dynamics of the process. Interesting repercussions are also envisaged for turbulence closures, in particular for large-eddy simulation approaches where only the large scales of the velocity field are resolved.

In Situ Aliovalent Nickle Substitution and Acidic Modification of Nanowalls Promoted Proton Conductivity in InOF with 1D Helical Channel.

Proton-conductive materials have attracted increasing attention because of their broad explorations in chemical sensors, water electrolysis, fuel cells, and biological systems. Especially, metal-organic frameworks (MOFs) have been demonstrated to be extremely promising candidates as proton-exchange membrane (PEM) fuel cells. Compared with other configurations, MOFs with one-dimensional (1D) channels have the characteristics of enhancing the host-guest interaction and promoting the anisotropic motion of proton carriers in restricted volume, which are beneficial for acquiring rich proton sources and forming successive hydrogen bonds to improve proton conductivity. We are endeavored to screen and find a helical three-dimensional (3D) framework InOF-1, namely, [In2(OH)2(BPTC)]·6H2O (BPTC4- = 3,3',5,5'-biphenyl tetracarboxylate), as a typical 1D-channel MOF, which is pristinely grafted with spirally distributed -OH groups on the channel surface. Accompanied by an aliovalent substitution Ni(II) for In(III), isostructural NiOF-1 ([Ni2(BPTC)(HCOOH)2]·3H2O) is successfully prepared and massive formic acids are anchored at interior walls, which are interacted with adsorbed water molecules via the formation of stronger O-H···O bonds. This interaction between host-guest molecules and dynamics of lattice water has already led to a remarkable conductivity of InOF-1 (σ = 7.86 × 10-3 S/cm at 328 K under 95% RH). The synergistic effect of the acidic-modified nanowall, contracted volume, and enhanced adsorption of water molecules in the NiOF-1 channel contributes to a high conductivity value of 3.41 × 10-2 S/cm (at 328 K under 95% RH). Moreover, the proton conduction mechanism is further visually presented by molecular dynamic (MD) simulation. In contrast to InOF-1, aliovalent-substituted and acidic-modified NiOF-1 has a stronger host-guest interaction and more abundant hydrogen-bond networks, resulting in shorter proton migration distances and more frequent proton hopping, in agreement with the experimental results.

Noether\u2019s theorem in statistical mechanics

Noether’s calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the free energy and the power functional, for equilibrium and driven many-body systems. Translational and rotational symmetry operations yield mechanical laws. These global identities express vanishing of total internal and total external forces and torques. We show that functional differentiation then leads to hierarchies of local sum rules that interrelate density correlators as well as static and time direct correlation functions, including memory. For anisotropic particles, orbital and spin motion become systematically coupled. The theory allows us to shed new light on the spatio-temporal coupling of correlations in complex systems. As applications we consider active Brownian particles, where the theory clarifies the role of interfacial forces in motility-induced phase separation. For active sedimentation, the center-of-mass motion is constrained by an internal Noether sum rule.

A 2D Front-Tracking Lagrangian Model for the Modeling of Anisotropic Grain Growth.

Grain growth is a well-known and complex phenomenon occurring during annealing of all polycrystalline materials. Its numerical modeling is a complex task when anisotropy sources such as grain orientation and grain boundary inclination have to be taken into account. This article presents the application of a front-tracking methodology to the context of anisotropic grain boundary motion at the mesoscopic scale. The new formulation of boundary migration can take into account any source of anisotropy both at grain boundaries as well as at multiple junctions (MJs) (intersection point of three or more grain boundaries). Special attention is given to the decomposition of high-order MJs for which an algorithm is proposed based on local grain boundary energy minimisation. Numerical tests are provided using highly heterogeneous configurations, and comparisons with a recently developed Finite-Element Level-Set (FE-LS) approach are given. Finally, the computational performance of the model will be studied comparing the CPU-times obtained with the same model but in an isotropic context.

The hodograph equation for slow and fast anisotropic interface propagation.

Using the model of fast phase transitions and previously reported equation of the Gibbs–Thomson-type, we develop an equation for the anisotropic interface motion of the Herring–Gibbs–Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship ‘velocity—Gibbs free energy’, Klein–Gordon and Born–Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater. 47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation.This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Lagrangian three-dimensional transport and dispersion by submesoscale currents at an upper-ocean front

The three-dimensional transport pathways, the time and space scales of vertical transport, and the dispersion characteristics (single-, pair- and multi-particle statistics) of submesoscale currents at an upper-ocean front are investigated using material points (tracer particles) that advect with the local fluid velocity. Coherent vortex filaments and eddies, generated and sustained during the evolution of baroclinic instability, dominate submesoscale (0.1 - 10 km) dynamics. These coherent structures play a crucial role in the particle transport and dispersion, which we quantify here. Particles in the central frontal region organize into vertically inclined lobes with anticyclonic circulation, each associated with a coherent eddy with cyclonic rotation. Furthermore, the coherent filaments associated with heavy/light edges of the front transfer particles from the edges to the lobes by downwelling/upwelling. This flux of new particles into the central region causes the particles circulating in the lobes to adjust, which leads to slumping of the front. The particle motion in the vertical shows multiple time scales – a fast time scale with O(10m) vertical displacement within an hour and a slower near-inertial time scale, comparable to the intrinsic time scale of the growing instability. The fast O(1h) time scale is also seen in the decorrelation of vertical velocity and the tapering of the initial ballistic growth of relative particle dispersion. The overall slumping process is slower than what one might anticipate from the large magnitude of vertical velocity in the filaments since it requires a sustained correlation over time between the lateral and the vertical motion. By tracking clouds of particles, we show that their centers of mass downwell/upwell over 1−2 inertial time periods, after which an adjustment follows with a sub-inertial time scale. The shape change in clusters of four particles reveals filamentogenesis, i.e. deformation into thin, needle-like structures by the coherent, anisotropic motions of the submesoscale, which occurs as a rapid process that is complete within approximately an hour.

Anisotropic diffusion of membrane proteins at experimental timescales.

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2Dr)-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.

Investigation of an additively manufactured pentamode material using non-contact vibration transmissibility measurements

Pentamodal (PM) metamaterials are one potential means to enable concepts from transformation acoustics in underwater applications because they can be designed to support anisotropic longitudinal wave motion over wide frequency bands while simultaneously being impedance matched to water [Su et al., J. Acoust. Soc. Am. 141(6), (2017)]. In three dimensions, PM materials can be fabricated using additive manufacturing (AM) to create elastic lattice structures whose microstructure can be tailored to produce the desired anisotropic sound speed and impedance in a target frequency band. This work presents measurements of the vibrational response of a PM block designed to display anisotropic stiffness. The sample measures approximately 100x100x85 mm and is constructed from titanium using direct metal laser sintering. Measurements were made on a sample mounted on an electro-dynamic shaker providing base excitation between 0.05 and 20i kHz. A scanning laser Doppler vibrometer measured out-of-plane surface velocity with normals both parallel and orthogonal to the excitation axis. The finite extent of the sample introduces geometric asymmetry associated with domain truncation, which is observable in the vibrational modes. Measurements were made for various sample orientations and compared to full-featuredfinite element models. Simulation-experiment comparisons and other findings will be presented and discussed. [Work supported by ONR.]

Bioinspired Two-Dimensional Structure with Asymmetric Wettability Barriers for Unidirectional and Long-Distance Gas Bubble Delivery Underwater.

Gas bubble manipulations in liquid have long been a concern because of their vital roles in various gas-related fields. To deal with the weakness in long-distance gas transportation of previous works, we took inspiration from the ridgelike structure on Nepenthes pitcher's peristome and successfully prepared a two-dimensional superaerophilic surface decorated with asymmetric aerophobic barriers capable of unidirectional and long-distance gas bubble delivery. For the first time, this process was investigated by in situ bubble-releasing experiments recorded by a high-speed camera and finite element modeling, which demonstrates a kinetic process regulated by the anisotropic motion resistance arising from the patterns. Furthermore, the Nepenthes alata-inspired two-dimensional surface (NATS) was integrated into a water electrolysis system for H2 directional transportation and efficient collection. As a result, the NATS design was proved to be a potential solution for facile manipulation of gas bubbles and provides a simple, adaptive, and reliable strategy for long-range gas transport underwater.

Probing the Properties of Gaia-CRF2 Quasars at the Faintest Magnitudes

Gaia data release 2 (DR2) provides the best non-rotating optical frame aligned with the radio frame (ICRF) thanks to the inclusion of about half-million quasars in the five-parameter astrometric solution. We cross-match with Gaia DR2 the quasars from Large Quasar Astrometric Catalogue, Sloan Digital Sky Survey and LAMOST, obtaining 208,743 new sources (denominated as KQCG), and most of them are fainter than G = 19. Given their crucial diagnostic role for characterizing the properties of the celestial reference frame, we aim to probe more accurately the properties of the reference frame at the faintest magnitudes. Combining them with the quasars already identified in DR2, we estimate the moving mean of parallaxes and proper motions. The features of the proper motion are analyzed by means of vectorial spherical harmonics; the scalar field of parallaxes is expanded into spherical harmonics to investigate their spatial correlation, which reveals an angular scale of systematics of ≈18° with a rms amplitude of 13 μas. The global moving mean of the parallaxes and proper motions are calculated. The amplitude of proper motion bias can be up to ∼10 μas yr−1 in some sky regions for both components, and these biases seem to be related to the patterns of the scanning law. The reference frame exhibits a (−6, −5, −5) ± 1 μas yr−1 spin in the northern hemisphere and a spin of (0, +1, +3) ± 1 μas yr−1 in the southern one, which may be caused by the star contamination. The quadrupolar anisotropy of the proper motion filed is analyzed, where a significant quadrupolar signal (the largest component’s amplitude is up to −15 μas yr−1) is found.

Confined Brownian Motion Tracked With Motion Blur: Estimating Diffusion Coefficient and Size of Confining Space

Mesoscopic environments and particles diffusing in them are often studied by tracking such particles individually while their Brownian motion explores their environment. Environments may be, e.g., a domain in a cell membrane, an interior compartment of a cell, or an engineered nanopit. Particle trajectories are typically determined from time-lapse recorded movies. These are recorded with sufficient exposure time per frame to be able to detect and localize particles in each frame. Since particles move during this exposure time, particles image with motion blur. This motion blur can compromise estimates of diffusion coefficients and the size of the confining domain if not accounted for correctly. We do that here. We give explicit and exact expressions for the variance of measured positions and the mean-squared displacement of a Brownian particle confined in, respectively, a 1D box, a 2D box, a 2D circular disc, and a 3D sphere. Our expressions are valid for all exposure times, irrespective of the size of the confining space and the value of the diffusion coefficient. They apply also in the common case where the exposure time is smaller than the time-lapse due, e.g., to “dead time” caused by the readout process in the camera. These expressions permit determination of diffusion coefficients and domain sizes for given movies for the simple geometries we consider. More important, the trends observed in our exact results when parameter values are varied are valid also for more complex geometries for which no exact analytical solutions exist. Wherever the underlying physics is the same, the exact quantitative description of its consequences provided here is portable as a qualitative and semi-quantitative understanding of its consequences in general. The results may also be useful for other types of reflected Brownian motion than those occurring in single-particle tracking, e.g., in nuclear magnetic resonance imaging techniques. For use in that particular context, we briefly discuss the effects of confinement on anisotropic Brownian motion imaged with motion blur.

Convergence of nonlocal geometric flows to anisotropic mean curvature motion

We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blow-up limit from them. As a consequence, we prove that the viscosity solutions to the rescaled nonlocal geometric flows locally uniformly converge to the viscosity solution to the anisotropic mean curvature motion. The result is achieved by combining a compactness argument and a set-theoretic approach related to the theory of De Giorgi's barriers for evolution equations.

Towards accurate and precise positions of hydrogen atoms bonded to heavy metal atoms.

A comparison of five X-ray structures of transition-metal-bound hydride complexes, successfully refined using Hirshfeld Atom Refinement (HAR) against low resolution X-ray diffraction data (including the positions and ADPs of all hydrogen atoms), with neutron structures shows that using aspherical atomic scattering factors instead of spherical ones results in systematic elongation of metal-hydrogen bonds, which in the case of the highest-quality data leads to excellent agreement of the X-ray and the neutron-derived bond lengths.