Particle Orientation Research Articles

Simple Models of Directly Measured Energy Landscapes for Different Shaped Particles in Nonuniform AC Electric Fields.

We report direct measurements of potential energy landscapes for different shaped colloidal particles interacting with nonuniform AC electric fields. Epoxy particle shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, which are all part of the superelliptical prism shape class and are chosen to systematically vary particle anisotropy and corner features. The measurement configuration consists of noninteracting single particles sedimented onto microscope slides within electric fields between parallel coplanar electrodes. Thermally sampled positions and orientations of single particles in nonuniform fields are tracked in an optical microscope, and measured potential energy landscapes are obtained via Boltzmann inversions. We develop a new analytically simple model that captures all measured energy landscapes for superelliptical prism shaped colloidal particles with electrostatic double layers. The model recovers known validated potentials for spherical and ellipsoidal particles, and therefore captures energy landscapes for a variety of different colloidal particle sizes, shapes, and materials reported in prior studies.

Eulerian multi-fluid simulations of local liquid distribution in a bed packed with cylindrical particles

Packed bed reactors (PBRs) are extensively used in chemical process industries to perform solid-catalyzed gas–liquid reactions. Their performance is significantly influenced by liquid distribution which is a strong function of particle shape and size. In the present work, we simulated the steady-state local liquid distribution, pressure drop (ΔP/L), and overall liquid holdup (〈εL〉) for the beds packed with spherical and cylindrical particles using a three-dimensional (3D) Eulerian multifluid model and validated the predictions using corresponding high-speed imaging measurements performed in pseudo-2D packed beds. We showed that the Eulerian model with existing closures significantly underpredicts the liquid distribution for the bed randomly packed with cylindrical particles. To address this, we proposed a modification in existing mechanical dispersion force (F→D) model as a function of average particle orientation angle (θ). The modification significantly improved agreement between the predictions and the corresponding measurements. Using the modified model, we showed that the increased magnitude of F→D in the lateral direction leads to higher lateral liquid spreading for cylindrical particles as compared to that for the spherical particles. Importantly, the modified model also predicted the local liquid distribution and ΔP/L for beds packed manually with cylindrical particles oriented at different θ in a satisfactory agreement with the corresponding measurements. On increasing θ, the F→D in lateral direction (i.e., perpendicular to flow) as well as liquid–solid interaction force (F→LS) in axial direction (i.e., parallel to flow) found to increase significantly. As a result, the lateral liquid spreading as well as ΔP/L decrease substantially on increasing θ.

Cryo-EM phase-plate images reveal unexpected levels of apparent specimen damage

Apoferritin (apoF) is commonly used as a test specimen in single-particle electron cryo-microscopy (cryo-EM), since it consistently produces density maps that go to 3 Å resolution or higher. When we imaged apoF with a laser phase plate (LPP), however, we observed more severe particle-to-particle variation in the images than we had previously thought to exist. Similarly, we found that images of ribulose bisphosphate carboxylase/oxygenase (rubisco) also exhibited a much greater amount of heterogeneity than expected. By comparison to simulations of images, we verified that the heterogeneity is not explained by the known features of the LPP, shot noise, or differences in particle orientation. We also demonstrate that our specimens are comparable to those previously used in the literature, based on using the final-reconstruction resolution as the metric for evaluation. All of this leads us to the hypothesis that the heterogeneity is due to damage that has occurred either during purification of the specimen or during preparation of the grids. It is not, however, our goal to explain the causes of heterogeneity; rather, we report that using the LPP has made the apparent damage too obvious to be ignored. In hindsight, similar heterogeneity can be seen in images of apoF and the 20S proteasome which others had recorded with a Volta phase plate. We therefore conclude that the increased contrast of phase-plate images (at low spatial frequencies) should also make it possible to visualize, on a single-particle basis, various forms of biologically functional heterogeneity in structure that had previously gone unnoticed.

Mass distribution impacts on particle translation and orientation dynamics in dilute flows

We present a novel model for tracking particles (based on Lagrangian particle tracking) with inhomogeneous mass distribution. Without loss of generality, the presented approach captures inhomogeneity by assuming an offset spherical inclusion in an elongated ellipsoidal particle matrix. The model is first validated on simplified flow configurations such as particles settling in vacuum or air as well as suspended in simple shear and laminar pipe flow, where we achieved an excellent agreement with the available reference results. Furthermore, we investigate the impact of the inclusion parameters on the particle motion. Finally, the deposition of inhomogeneous particles in a simplified bifurcation is analyzed. We conclude that the consideration of inhomogeneity significantly alters the translational and orientational dynamics of the particles. Consequently, we advocate for the consideration of more realistic mass distributions to increase the accuracy of modeling and predicting the motion of inhomogeneous particles in flows for real-world applications.

Orientation of inertialess spheroidal particles in turbulent channel flow with spanwise rotation

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

Particle morphology and principal stress direction dependent strength anisotropy through torsional shear testing

The major principal stress direction angle (ασ) experienced by granular soils varies widely in engineering, causing different strengths. However, how particle morphology affects the strength anisotropy behavior under different ασ remains unclear. To address this gap, this study performed drained hollow cylinder torsional shear tests under different ασ on six granular materials with distinct morphologies. Results highlight the significant dependence of peak strengths of granular materials on both particle morphology and ασ. Increasing particle shape irregularity and surface roughness leads to a considerable enhancement in peak strength, while this peak strength significantly degrades with increasing ασ. Materials with more irregular shapes were found to have a more pronounced strength anisotropy. Furthermore, the initial fabric of particle packings, derived from three-dimensional X-ray microtomography, was used to interpret microscopic mechanisms behind the morphology-dependent strength anisotropy. Irregular-shaped materials display broader preferred particle orientations and higher initial fabric anisotropy compared to relatively regular-shaped materials. This higher morphology-induced fabric anisotropy contributes to strength anisotropy, and a correlation was established for describing this trend. Additionally, an anisotropic failure criterion incorporating fabric anisotropy was developed to characterize the strength envelope for granular materials with diverse shapes.

The Ice Cloud Imager: retrieval of frozen water column properties

Abstract. The Ice Cloud Imager (ICI) aboard the second generation of the EUMETSAT Polar System (EPS-SG) will provide novel measurements of ice hydrometeors. ICI is a passive conically scanning radiometer that will operate within a frequency range of 183 to 664 GHz, helping to cover the present wavelength gap between microwave and infrared observations. Reliable global data will be produced on a daily basis. This paper presents the retrieval database to be used operationally and performs a final pre-launch assessment of ICI retrievals. Simulations are performed within atmospheric states that are consistent with radar reflectivities and represent the three-dimensional (3D) variability of clouds. The radiative transfer calculations use empirically based hydrometeor models. Azimuthal orientation of particles is mimicked, allowing for the consideration of polarisation. The degrees of freedom (DoFs) of the ICI retrieval database are shown to vary according to cloud type. The simulations are considered to be the most detailed performed to this date. Simulated radiances are shown to be statistically consistent with real observations. Machine learning is applied to perform inversions of the simulated ICI observations. The method used allows for the estimation of non-Gaussian uncertainties for each retrieved case. Retrievals of ice water path (IWP), mean mass height (Zm), and mean mass diameter (Dm) are presented. Distributions and zonal means of both database and retrieved IWP show agreement with DARDAR. Retrieval tests indicate that ICI will be sensitive to IWP between 10−2 and 101 kg m−2. Retrieval performance is shown to vary with climatic region and surface type, with the best performance achieved over tropical regions and over ocean. As a consequence of this study, retrievals from real observations will be possible from day one of the ICI operational phase.

Human Mastication Analysis-A DEM Based Numerical Approach.

Mastication is an essential and preliminary step of the digestion process involving fragmentation and mixing of food. Controlled muscle movement of jaws with teeth executes crushing, leading towards fragmentation of food particles. Understanding various parameters involved with the process is essential to solve any biomedical complication in the area of interest. However, exploring and analyzing such process flow through an experimental route is challenging and inefficient. Computational techniques such as discrete element numerical modeling can effectively address such problems. The current work employs the Discrete Element Method (DEM) as a numerical modeling technique to simulate the human mastication process. Tavares and Ab-T10 breakage models coupled with Gaudin Schumann and Incomplete Beta fragment distribution models have been implemented to analyze the fragmental distribution of food particles. The effect of particle shape (spherical, polyhedron, and faceted cylinder), size (aspect ratio), and orientation (vertical and horizontal) on breakage and fragment distribution is analyzed. To account for the elastic-plastic behavior and moisture content in food particles, modifications has been made in breakage models by incorporating numerical softening factor and adhesion force. The study demonstrates how numerical modeling techniques can be utilized to analyze the mastication process involving multiple process parameters.

Ultrafast X-ray laser-induced explosion: How the depth influences the direction of the ion trajectory

Single particle imaging using X-ray lasers is a technique aiming to capture atomic resolution structures of biomolecules in their native state. Knowing the particle's orientation during exposure is crucial for method enhancement. It has been shown that the trajectories of sulfur atoms in a Coulomb exploding lysozyme are reproducible, providing orientation information. This study explores if sulfur atom depth influences explosion trajectory. Employing a hybrid collisional-radiative/molecular dynamics model, we analyze the X-ray laser-induced dynamics of a single sulfur ion at varying depths in water. Our findings indicate that the ion spread-depth relationship depends on pulse parameters. At a photon energy of 2 keV, high-charge states are obtained, resulting in an increase of the spread with depth. However, at 8 keV photon energy, where lower charge states are obtained, the spread is essentially independent with depth. Finally, lower ion mass results in less reproducible trajectories, opening a promising route for determining protein orientation through the introduction of heavy atoms.

Ejection and deposition of mica suspension droplets under electric field

Inkjet printing of ceramic materials is a shaping process of interest for building micrometer-sized components. It consists of depositing droplets of colloidal inks according to a printing pattern designed to obtain a given final part. Improving the printed part properties, e.g., thermal or electrical, requires to tailor the printed material's local structure and orientation. Electric field is an efficient external stimulus to control particle orientation. A major challenge is to efficiently couple the effects of electric field and those of capillary, viscous, and evaporation phenomena occurring during inkjet printing. In this paper, the effect of an external electric field on the structuration of inkjet deposits is investigated. Suspensions of mica platelets dispersed in binary mixtures of chloroform and silicone oil are ejected on demand on a glass plate. An electric potential difference is applied by means of a set of electrodes below the glass substrate, separated by a small gap in order to maximize the electric field on the surface of the plate. A cartography of splat morphology and structuration for different inks as a function of applied field is performed. Promising experimental conditions display particle arrangement and limited splat deformation, whereas others lead to fingering. This paves the way to a novel additive shaping process by adding another smaller scale of structuration to inkjet printed parts.

Dependence of Protein Immobilization and Photocurrent Generation in PSI-FTO Electrodes on the Electrodeposition Parameters.

This study investigates the immobilization of cyanobacterial photosystem I (PSI) from Synechocystis sp. PCC 6803 onto fluorine-doped tin oxide (FTO) conducting glass plates to create photoelectrodes for biohybrid solar cells. The fabrication of these PSI-FTO photoelectrodes is based on two immobilization processes: rapid electrodeposition driven by an external electric field and slower adsorption during solvent evaporation, both influenced by gravitational sedimentation. Deposition and performance of photoelectrodes was investigated by UV-Vis absorption spectroscopy and photocurrent measurements. We investigated the efficiency of PSI immobilization under varying conditions, including solution pH, applied electric field intensity and duration, and electrode polarization, with the goals to control (1) the direction of migration and (2) the orientation of the PSI particles on the substrate surface. Variation in the pH value of the PSI solution alters the surface charge distribution, affecting the net charge and the electric dipole moment of these proteins. Results showed PSI migration to the positively charged electrode at pH 6, 7, and 8, and to the negatively charged electrode at pH 4.4 and 5, suggesting an isoelectric point of PSI between 5 and 6. At acidic pH, the electrophoretic migration was largely hindered by protein aggregation. Notably, photocurrent generation was consistently cathodic and correlated with PSI layer thickness, and no conclusions can be drawn on the orientation of the immobilized proteins. Overall, these findings suggest mediated electron transfer from FTO to PSI by the used electrolyte containing 10 mM sodium ascorbate and 200 μM dichlorophenolindophenol.

Spouting behavior of binary mixtures of spherocylindrical and spherical particles in a spouted bed

Gas-solid spouted bed systems involving biomass utilization have received much attention in recent years. In actual biomass industrial processes, some fine inert particles are usually added to assist the fluidization of biomass particles. However, the flow mechanisms of binary particle systems containing biomass particles in spouted beds are still poorly understood so far. In this study, spherocylindrical particles representing biomass particles and spherical particles representing inert particles were used as the objects of study. The macroscopic and microscopic flow characteristics were explored based on CFD-DEM modeling when the volume fractions of spherocylindrical particles in the binary particle mixtures were 25 %, 50 %, 75 % and 100 %, respectively. The results showed that the minimum spouting velocities (Ums) were in the range of 150–173 m/s, but did not show a correlation with the different particle systems. During fluidization in binary particle systems, separation of spherocylindrical and spherical particles occurs. There is no significant correlation between the particle systems with different volume fractions of spherocylindrical particles and particle orientation. As the volume fraction of spherocylindrical particles increases, the average bed height of the particles decreases and the translational kinetic energy of the particles decreases/rotational kinetic energy increases. Furthermore, the wall effect influences the spherocylindrical particle orientation and volume fraction, driving the spherocylindrical particles near the wall surface toward the vertical direction.

Small LEA proteins mitigate air-water interface damage to fragile cryo-EM samples during plunge freezing

Air-water interface (AWI) interactions during cryo-electron microscopy (cryo-EM) sample preparation cause significant sample loss, hindering structural biology research. Organisms like nematodes and tardigrades produce Late Embryogenesis Abundant (LEA) proteins to withstand desiccation stress. Here we show that these LEA proteins, when used as additives during plunge freezing, effectively mitigate AWI damage to fragile multi-subunit molecular samples. The resulting high-resolution cryo-EM maps are comparable to or better than those obtained using existing AWI damage mitigation methods. Cryogenic electron tomography reveals that particles are localized at specific interfaces, suggesting LEA proteins form a barrier at the AWI. This interaction may explain the observed sample-dependent preferred orientation of particles. LEA proteins offer a simple, cost-effective, and adaptable approach for cryo-EM structural biologists to overcome AWI-related sample damage, potentially revitalizing challenging projects and advancing the field of structural biology.

Directional cues affect the collective behaviour of self-propelled particles in one dimension

This study explores the effect of quenched disorder on the characteristics of self-propelled particles in one dimension. Here, particles interact with disorder which serve as directional cues. The study investigates how the density of the directional cues influences the emergence of ordering and clustering in the collection of the self-propelled particles. We introduce the microscopic model as well as corresponding coarse-grained equations of motion for the local density and the orientation of particles. Directional cues affect the macroscopic ordering in the system, the size of the ordered clusters decays algebraically with density of cues. Further, in the presence of directional cues, a big macroscopic cluster breaks into small clusters, leading to the localization of particles around it and resulting in high density around the cues.

Quasi-1D Conductive Network Composites for Ultra-Sensitive Strain Sensing.

Highly performance flexible strain sensor is a crucial component for wearable devices, human-machine interfaces, and e-skins. However, the sensitivity of the strain sensor is highly limited by the strain range for large destruction of the conductive network. Here the quasi-1D conductive network (QCN) is proposed for the design of an ultra-sensitive strain sensor. The orientation of the conductive particles can effectively reduce the number of redundant percolative pathways in the conductive composites. The maximum sensitivity will reach the upper limit when the whole composite remains only "one" percolation pathway. Besides, the QCN structure can also confine the tunnel electron spread through the rigid inclusions which significantly enlarges the strain-resistance effect along the tensile direction. The strain sensor exhibits state-of-art performance including large gauge factor (862227), fast response time (24ms), good durability (cycled 1000 times), and multi-mechanical sensing ability (compression, bending, shearing, air flow vibration, etc.). Finally, the QCN sensor can be exploited to realize the human-machine interface (HMI) application of acoustic signal recognition (instrument calibration) and spectrum restoration (voice parsing).

Ultraconfined oblate hard particles between hybrid penetrable walls.

We have investigated, by Monte Carlo simulation, the orientational structure of very thin films of a discotic liquid crystal (DLC) confined between hybrid walls of controllable penetrability, as a function of wall separation L_{z}. Our purpose was to clarify whether, as predicted by continuum theory, the preferred orientation of the DLC is uniform, changes linearly, or changes discontinuously, when L_{z} and the anchoring strengths at either wall are changed. The model consists of oblate hard Gaussian overlap (HGO) particles: each wall sees a particle as a disk of zero thickness and diameter D less than or equal to that of the actual particle σ_{0}, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This provides a particle-level mechanism to control the anchoring properties of the walls, from planar (edge-on) for D∼0 to homeotropic (face-on) for D∼σ_{0}, which can be done independently at either wall. As in our earlier work [C. Anquetil-Deck et al., J. Phys. Chem. B 124, 7709 (2020)1520-610610.1021/acs.jpcb.0c05027], which was restricted to L_{z}=6σ_{0}, depending on the values of D_{s}≡D/σ_{0} at the top (D_{s}^{t}) and bottom (D_{s}^{b}) walls, we find domains in (D_{s}^{b},D_{s}^{t}) space in which particle alignment is uniform planar (UP), uniform homeotropic (UH), or varies linearly from planar at one wall to homeotropic at the other (L), but no bistable or tristable regions are identified between these domains. Most importantly, there appears never to occur an abrupt change of the LC orientation when the walls strongly favor different anchorings, in general agreement with the scenario proposed by Velasco and co-workers [D. de las Heras et al., Phys. Rev. E 79, 011712 (2009)1539-375510.1103/PhysRevE.79.011712], but in contrast to the behavior of equivalent calamitic systems [F. Barmes et al., Phys. Rev. E 69, 061705 (2004)1539-375510.1103/PhysRevE.69.061705; Phys. Rev. E, 71, 021705 (2005)1539-375510.1103/PhysRevE.71.021705; C. Anquetil-Deck et al., Phys. Rev. E 86, 041707 (2012)1539-375510.1103/PhysRevE.86.041707]. However, for the thinnest films investigated (L_{z}=2σ_{0}), the system is unable to accommodate a rotation of the preferred particle orientation from one wall to the other and adopts instead a tilted configuration, similar to that reported earlier for Gay-Berne films in symmetric confinement [T. Gruhn et al., Thin Solid Films 330, 46 (1998)0040-609010.1016/S0040-6090(98)00799-8; Mol. Phys. 93, 681 (1998)10.1080/002689798169014] but which, as far as we know, has been missed in most earlier work.

Influence of Carbon Nanotubes in Improving the Superconducting and Structural Properties of Bulk Bi-2212 Synthesis by Thermal Treatment Method

Bi-2212 superconductor has garnered significant interest in recent years due to its potential applications in the development of superconducting wires and tapes. The effect of introducing carbon nanotubes (CNT) into the Bi-2212 system was investigated in terms of superconducting and structural properties. The results of this study indicated that the addition of CNTs had a notable effect on the phase formation of Bi-2212, with a substantial increase from 86.8% to 97.4% for the sample with a weight percentage of 0.8 wt.%. This can be attributed to the improved particle orientation brought about by the introduction of CNTs. The microstructure analysis displayed randomly distributed grains of irregular shapes, with a reduced average grain size of 1.018 μm upon the addition of 0.4 wt.% CNTs. Additionally, the inclusion of CNTs led to an increase in the Tc value, with the maximum Tc-onset recorded at 79 K for the sample containing 0.6 wt.% CNTs. In summary CNT has enhanced the structural and the superconducting properties of the Bi-2212 synthesised with thermal treatment method.

Rheology and Structure of Model Smectite Clay: Insights From Molecular Dynamics

AbstractThe low frictional strength of smectite minerals, such as montmorillonite, is thought to play a critical role in controlling the rheology and the stability of clay‐rich faults. In this study, we perform molecular dynamics simulations on a model clay system. Clay platelets are simplified as oblate ellipsoids interacting via the Gay‐Berne potential. We study the rheology and structural development during shear in this model system, which is sheared at constant strain rates for 10 strains after compression and equilibrium. We find that the system exhibits velocity‐strengthening behavior over a range of normal stresses from 1.68 to 56.18 MPa and a range of strain rates from 6.93 × 105 to 6.93 × 108/s. The relationship between shear stress and strain rate follows the Herschel‐Bulkley model. Shear localization is observed at lower strain rates despite the velocity‐strengthening friction, while homogeneous shear is realized at higher strain rates. The structure change due to shear is analyzed from various aspects: the porosity, particle orientation, velocity profile, and the parallel radial distribution function. We find that particle rearrangement and compaction dominate at the early stage of shear when the shear stress increases. The shear band starts to form in the later stage as the shear stress decreases and relaxes to a steady‐state value. The structural development at low strain rates is similar to previous experimental observations. The stacking structure is reduced during shear and restores logarithmically with time in the rest period.

Aspect-ratio-dependent void formation in active rhomboidal and elliptical particle systems.

We execute a numerical simulation of active nematics with particles interacting by an excluded-volume effect. Systems with rhomboidal particles and with elliptical particles are considered in order to investigate the effect of the direct contact of particles. In our simulation, the void regions, where the local number density is almost zero, appear in both systems when the aspect ratio of the particles is high. We focus on the relationship between the void regions and the particle orientation of the bulk. The particle number density, particle orientation, topological defects, and void regions are analyzed for different aspect ratios in both systems. The systems with rhomboidal particles have characteristic void sizes, which increase with an increase in the aspect ratio. In contrast, the distribution of the void-region size in the systems with elliptical particles is broad. The present results suggest that the void size in the systems with rhomboidal particles is determined by the correlation length of the particle orientational field around the void regions, while the void size might be determined by the system size in the systems with elliptical particles.

Three-dimensional simulation on phase change heat transfer of moving spherical particle

Investigating the motion process of paraffin particle under a mesoscopic scale is very helpful to master the heat transfer mechanism of the mushy zone in solid–liquid phase change. Prior researches predominantly focused on either particle motion or phase change, without accounting for their coupling. In this study, the three-dimensional finite element method is used to solve the motion and heat transfer of the particle, taking into account the coupling of motion and phase change. The moving grid is employed to trace the interface of moving particles and liquid using the Arbitrary Lagrangian-Euler method, which is able to calculate flow and heat transfer in fluid region and allow grid deformation in solid region. The results indicate that uneven fluid velocity around the particles results in non-uniform temperature gradients on particle’s surface. In areas with larger temperature gradient, it melts more quickly and its deformation is obvious. The maximum is located at particle orientation angle 30°. Changing the size and direction of fluid velocity will reinforce or inhibit the movement of particle. The changing time of motion direction when fluid velocity is −0.03 m/s shorten 2.7 times than when fluid velocity is −0.01 m/s. The initial temperature of the surrounding fluid has a positive relationship with the particle melting rate. The channel width affects significantly the motion and melting of particle. The initial position of particle has an important effect on it’s falling movement, and the closer is close to the wall of channel, the greater the displacement of left and right movement.