Axis Of Ellipse Research Articles

Adiabatic theory of generation and rescattering of vortex electrons in strong-field ionization by elliptically polarized pulses

The adiabatic theory of strong-field ionization is extended to the specific configuration in which ionization occurs from a vortex orbital in an axially symmetric target by an elliptically polarized pulse with small ellipticity and the major axis of the polarization ellipse directed along the vortex axis of the initial state. Generation of vortex electrons in the continuum, their propagation in the laser field, and subsequent rescattering on the parent ion are described. Adiabatic asymptotics of the rescattering parts of the solution to the time-dependent Schr\"odinger equation and the ionization amplitude are obtained. On the basis of these results, the factorization formula giving the photoelectron momentum distribution (PEMD) in the vicinity of a backward rescattering caustic is derived. Our interest in the present configuration stems from the fact that, because of the nonzero ellipticity of the field, liberated vortex electrons arrive for rescattering with a nonzero impact parameter. The corresponding scattering amplitude generalizes the recently introduced vortex scattering amplitude characterizing head-on vortex-target rescattering in the linear polarization case [O. I. Tolstikhin and T. Morishita, Phys. Rev. A 99, 063415 (2019)]. Using the factorization formula, one can extract the absolute value of this generalized scattering amplitude from the observable PEMD, which opens a new window for target structure imaging in strong-field physics. The theory is illustrated by calculations for two atomic targets, ${\mathrm{He}}^{+}(2p,m=1)$ and $\mathrm{Xe}(5p,m=1)$. We show that in the case of the initial $\ensuremath{\pi}$ orbital and nonzero ellipticity not only the absolute values of two head-on scattering amplitudes with $m=0$ and 1, but also their phase difference as functions of the scattering angle can be extracted from the PEMD.

Analysis of Current at a Continuous Observation Station in the Shallow Water of the Northern Outer Shelf of the East China Sea

In this paper, multi-layer current data continuously observed in November 2021 was studied by statistical analysis, spectral analysis, and harmonic analysis in the shallow water area of the northern outer shelf of the East China Sea. The results showed that: during observation, the average velocity was 30.5cm/s, and the maximum velocity was 78.1cm/s. The velocity from 30cm/s to 40cm/s accounts for the largest proportion, and the maximum direction frequency was eastward, up to 12.4%. The stationary flow direction is northward and changes from northeast to northwest with the increase of depth. The current is a regular semi-diurnal current, and the current ellipse rotates clockwise. The major axis of the M2 tidal current ellipse ranges from 12.9cm/s to 37.7cm/s, and firstly increases, then keeps constant, and finally decreases with the increase of depth. This study fills in the blank of the autumn hydrodynamic data and can provide a reference for studying hydrodynamics in the Kuroshio affected area.

Small and large oscillatory shear behaviors of gelatin/starch system regulated by amylose/amylopectin ratio

This work explores the influence of starch amylose/amylopectin ratio on the gel-related features of gelatin/starch system using small and large amplitude oscillation shear methods. The higher self-aggregation and self-entanglement ability of amylose reduced the miscibility of gelatin and starch, and increases zero-shear viscosity (ŋ0) and reduces sol-gel transition temperature (Tgel) by enhancing the difficulty of molecule movement and thus the difficulty of gel formation. The gelatin/amylopectin-rich system has higher gel hardness and wider linear viscoelastic region, which are related to the higher integrity and uniformity of network structure. The gelatin/amylose-rich system shows enhanced ability to resist deformation against external shear forces (suggested by higher storage and complex modulus) under small amplitude oscillatory shear (SAOS), which is ascribed to the larger rigidity and entanglement degree of amylose. At strain amplitude up to 50% (middle amplitude oscillatory shear, MAOS), gelatin/amylose-rich system exhibits reduced structure recovery ability (reflected by larger semi-minor axis of ellipse, and lower strain amplitude for inflexion of elastic stress) under MAOS, but enhances restructuring capacity at strains of 500% and 1000% (large amplitude oscillatory shear, LAOS) (indicated by occurrence of secondary loop) than gelatin/amylopectin-rich system. Those seemingly contradictory phenomena are correlated with the preference of hydrogen bond forming ability among amylose rather than with gelatin. This weakens interactions between amylose and gelatin and thus inhibits recovery of bulk structure under MAOS, but is favor for the formation of amylose aggregations, which is helpful for the local structure restructuring and thus enhances structure restructuring capacity under LAOS. The results help us comprehensively understand the gel-related properties of gelatin/starch system and are valuable for rational design of gelatin/starch systems with improved gel-related features.

On the Polarization Dependence of Two-Photon Processes including X-ray Scattering

The polarization dependence of the cross sections of two-photon transitions including X-ray scattering was analyzed. We developed the regular approach to the derivation of the polarization parameters of photoprocesses. Our approach is based on the tensor representation of the photon density matrix, which is written in terms of the unit vectors directed along the major axis of the polarization ellipse (ϵˆ) and the photon propagation (kˆ). Explicit expressions for the product of two photon density matrices were derived. As an example, the parametrization of the polarization dependence of the X-ray scattering by closed-shell atoms is given both in terms of (i) scalar products of photon vectors ϵˆ1,2, kˆ1,2 and (ii) X-ray Stokes parameters. We discuss the applicability of the atomic scattering for the measurement of the polarization of X-rays.

Virtual Stiffness: A Novel Biomechanical Approach to Estimate Limb Stiffness of a Multi-Muscle and Multi-Joint System

In recent years, different groups have developed algorithms to control the stiffness of a robotic device through the electromyographic activity collected from a human operator. However, the approaches proposed so far require an initial calibration, have a complex subject-specific muscle model, or consider the activity of only a few pairs of antagonist muscles. This study described and tested an approach based on a biomechanical model to estimate the limb stiffness of a multi-joint, multi-muscle system from muscle activations. The "virtual stiffness" method approximates the generated stiffness as the stiffness due to the component of the muscle-activation vector that does not generate any endpoint force. Such a component is calculated by projecting the vector of muscle activations, estimated from the electromyographic signals, onto the null space of the linear mapping of muscle activations onto the endpoint force. The proposed method was tested by using an upper-limb model made of two joints and six Hill-type muscles and data collected during an isometric force-generation task performed with the upper limb. The null-space projection of the muscle-activation vector approximated the major axis of the stiffness ellipse or ellipsoid. The model provides a good approximation of the voluntary stiffening performed by participants that could be directly implemented in wearable myoelectric controlled devices that estimate, in real-time, the endpoint forces, or endpoint movement, from the mapping between muscle activation and force, without any additional calibrations.

Plasmonic vortices for tunable manipulation of target particles, using arrays of elliptical holes in a gold layer

Here, we numerically prove that light with linear polarization can be coupled to surface plasmon polaritons at an elliptical hole perforated in a gold layer to generate plasmonic vortex (PV). Benefiting from the smooth variation of the minor to major ellipse axes, a gradual variation in the phase profile of the generated PV is achieved. Regarding this, three types of independent arrays of elliptical holes are presented, which can produce uniform and high quality PVs with different topological charges at the center of the arrays. The first array can produce PV with topological charges of + 1 and − 1, depending on the polarization orientation of the incident light. In the second one, the topological charge of the PV can be switched between 0 and + 2, by switching the polarization direction of the incident light. In the third array, a robust PV with topological charge of + 1 is generated independent of possible tolerances in the polarization orientation. In order to use the generated PVs for plasmonic tweezing application, there are side fringes around the central vortex of the arrays that should be eliminated. To produce a single vortex, we propose metal-insulator-metal (MIM) structures, screening excessive fringes and allowing the central PVs to leak out. It is also demonstrated by simulation that target particles, such as gold and polystyrene spheres of subwavelength dimensions, can be efficiently manipulated by our MIM designs, suitable for different applications including local mixing, and applying switchable torque or force to target particles to explore their complete elastic characteristics.

Manipulated deformation of lipid bilayer vesicles in magnetic fields

ABSTRACTWe have extended the Helfrich’s spontaneous curvature model of the equilibrium vesicle by adding the interaction between magnetic field and the constituent molecules to supply an explaination in principle of the emerging manipulated deformation of a magnetic vesicles such as the reversibly deformation of artificial stomatocyte. The small deformation can be measured by birefringence. Here, we present the derivations of formulas in detailed to reveal the perturbation of deformation ψ under two cases. New features, for example, a ‘phase transition’ of shape will occur with increasing of B from B1∗ to B2∗ for Δχ<0, in which the major axis of ellipse was rotated by 90°, have been revealed. It is worthy for experimenter to demonstrate the ‘phase transition’. The significance of imaginary relation (B1∗<B<B2∗) is also waiting to be uncovered.

Modification of root architecture of rice by guard cell and rhizosphere halotolerant bacteria under saline stress

A significant global issue for agriculture is soil salinity. Rice, being one of the most salt-sensitive cereals, is greatly affected by salinity. High salt concentrations have a detrimental impact on root growth of rice. Halotolerant bacteria are known to alleviate salinity stress and have been shown to alter the root morphology of some plants. This possible alteration effect of halotolerant bacteria on rice is not well known. In this study, the halotolerant bacterial strains Enterobacter cloacae GCH3, Acinetobacter sp. GCH4, Acinetobacter calcoaceticus RSH6 and Bacillus tequilensis RSH8 were used to evaluate the early alterations of rice root architecture. These bacteria were inoculated into rice seedlings growing in culture tubes under gnotobiotic conditions, and root architecture variables of developing roots were assessed periodically using non-destructive 2-dimensional imaging and processing in both normal and salt stress conditions. The images were analyzed and processed to obtain 20 root architecture variables in which, the variables such as maximum number of roots, network solidity, number of lateral roots, network surface area, root thickness, area, volume and bushiness were significantly increased with time course due to halotolerant bacterial inoculation than uninoculated control. The root and shoot biomass was also found to be increased by bacterial inoculation. Number of connecting components, median number of roots, specific root length and major ellipse axes were negatively impacted by halotolerant bacteria. Enterobacter cloacae GCH3 and Bacillus tequilensis RSH8 excelled in most of the traits in improving the root architecture of rice under saline conditions which can promote the early growth stages of root and protect the plant from saline stress effects.

Optimal Geometries for AOA Localization in the Bayesian Sense

This paper considers the optimal sensor placement problem for angle-of-arrival (AOA) target localization in the 2D plane with a Gaussian prior. Optimal sensor locations are analytically determined for a single AOA sensor using the D- and A-optimality criteria and an approximation of the Bayesian Fisher information matrix (BFIM). Optimal sensor placement is shown to align with the minor axis of the prior covariance error ellipse for both optimality criteria. The approximate BFIM is argued to be valid for a sufficiently small prior covariance compared with the target range. Optimal sensor placement results obtained for Bayesian target localization are extended to manoeuvring target tracking. For sensor trajectory optimization subject to turn-rate constraints, numerical search methods based on the D- and A-optimality criteria as well as a new closed-form projection algorithm that aims to achieve alignment with the minor axis of the prior error ellipse are proposed. It is observed that the two optimality criteria generate significantly different optimal sensor trajectories despite having the same optimal sensor placement for the localization of a stationary target. Analysis results and the performance of the sensor trajectory optimization methods are demonstrated with simulation examples. It is observed that the new closed-form projection algorithm achieves superior tracking performance compared with the two numerical search methods.

Alignment dependence of photoelectron momentum distributions for diatomic molecule N2 in strong elliptical laser fields

The ionization dynamics of aligned N2 molecules are studied in strong elliptical laser fields experimentally and theoretically. The alignment-dependent photoelectron momentum distribution of N2 is measured for highlighting the molecular structure contribution by comparing to that of Ar measured synchronously. Our results show that the ionization of N2 depends strongly on the alignment of molecules, relative to the main axis of the polarization ellipse of the laser. In particular, the most-probable electron-emission angle which is often used in attosecond measurement changes remarkably when changing the relative angle between the molecular axis and the major axis of laser fields. The alignment-dependent rotation angles have been well reproduced by our theoretical calculations. We show that the interplay between molecular structure and the laser fields plays an important role in the rotation angles based on the strong-field approximation analysis and this interaction also influences remarkably on the photoelectron angle distribution of aligned N2.

Research on the Bearing Sliding Loss Based on Time-Varying Contact Angle between Ball and Raceway

Based on the mechanical model, the friction loss between the ball and the raceway along the major axis of the contact ellipse is analyzed. The result shows that this part of the loss accounts for about 13.67% of the overall loss, which is mainly determined by the ball sliding length and cannot be ignored. The effects of the radial force, torque, rotational speed and groove curvature ratio on the sliding are all studied. Compared with other factors, radial force has the greatest influence on the sliding loss. As bearing speed gradually grows, the sliding on the inner raceway gradually increases while it gradually decreases on the outer raceway. Compared to the outer raceway curvature ratio, the sliding length is less sensitive to changes in the curvature ratio of the inner raceway. The paper provides theoretical guidance for the design and application of low-friction bearings.

ТЕХНОЛОГИЧЕСКИЕ ВОЗМОЖНОСТИ ЯЧЕИСТОГО РЕЛЬЕФА ДЛЯ ОБЕСПЕЧЕНИЯ ЭКСПЛУАТАЦИОННЫХ СВОЙСТВ ЦИЛИНДРИЧЕСКИХ ПОВЕРХНОСТЕЙ ТЕХНОЛОГИЧЕСКИХ АГРЕГАТОВ

The work is aimed to study the cylindrical surfaces of parts with a cellular shape surfaces, which is an elliptical paraboloid with unequal positive parameters. The hypothesis of the study is the high potential of using a cellular relief, associated with a decrease in the running-in wear of technological units, while providing the hydrodynamic bearing capacity of the lubricating layer with the shape of the relief. The objectives of the study are reduced to a parametric analysis of the behavior of the lubricating layer in a gap with a relief cell using the construction of an analytical model based on the theory of hydrodynamic lubrication. In addition, the computer fluid dynamic simulation in the ANSYS Fluent software, where the SST turbulence model is adopted to close the transport equations k–ω. It is found that the maximum hydrodynamic bearing capacity occurs at a cell depth of 0.128 mm and falls on 21/25 of the major axis of the cell ellipse. It is shown by both models, which verified their acceptable accuracy. The maximum lifting hydrodynamic pressure on one cell is also calculated, which amounted to 3 kPa. The results of parametric analysis state a significant potential for using a cellular relief to ensure the operational properties of cylindrical surfaces.

Research on desktop object grasping based on ellipse fitting

The grasping operation task in service scenes faces several problems including too many kinds of objects and a large amount of training data. This paper focuses on the grasping strategy and pose detection in desktop object grasping tasks. A grasping strategy is given based on the combination of desktop normal vector detection, object category detection, and grasping pose detection. The grasping pose is calculated by ellipse fitting on the depth map. An optimal function is designed to evaluate the possibility of the object sliding along the ellipse axis and the stability of the grasping height. The most reliable grasping pose is selected. Finally, experiments were carried out with a six-degree-of-freedom manipulator, and the proposed grasping method achieved effective grasping of desktop objects without prior knowledge of the object.

Superposition of two orthogonal transpressions: An example from the oblique convergent margin adjoining the Tan–Lu Fault Zone, eastern China

Deformation in oblique convergent margins, especially non-plane deformation in décollement belts within such a margin, is not fully understood. The northern Zhangbaling tectonic belt represents an oblique convergent margin to the east of the NNE–SSW-striking Tan–Lu Fault Zone that separates the Yangtze Block to the east from the North China Craton to the west, and it provides a good opportunity to understand deformation in the margin. The tectonic belt consists of a fold-and-thrust belt in the east and a low-angle ductile décollement belt in the west. The fold-and-thrust belt in the marginal cover rocks indicates a pure shear-dominated deformation, and the fold axes rotated with the long axis of the horizontal finite strain ellipse. The underlying décollement belt was involved in a non-plane deformation owing to the superposition of wrenching along the Tan–Lu Fault Zone and horizontal décollement shearing. The horizontal décollement shearing dominated in the development of the flat-lying foliation, whereas the wrenching mostly dominated in the development of stretching lineations. Top-to-the-SSW sense of shear dominates in the central to southern parts of the décollement belt, whereas top-to-the-SSE sense of shear is widely present in the northern part of the belt and locally in other parts. Partitioning of the non-plane deformation is shown by kinematic partitioning within the originally flat-lying décollement belt, and it is different from the strain partitioning in a transpressional zone involved in plane deformation. The structural and geochronological data for the oblique convergent margin are consistent with sinistral faulting of the initial Tan–Lu Fault Zone during the Triassic.

What does the quantitative morphological diversity of starch grains in terrestrial orchids indicate?

Starches granules vary in structure and morphologies in the orchids as well as other plant sources that starch is industrially valuable. This article aims to provide information on the variability of starch grain based on quantitative size and shape descriptive features using regression and discriminant analysis and to develop an easy method related to starch morphology giving perspective for various disciplines. All measurements of 26 species belonging to three different tribes were obtained using polarized light and scanning electron microscopy. Results show significant differences in size descriptive (e.g., perimeter, the major axis of the fit ellipse, minimum caliper diameter) and shape descriptive (e.g., circularity, hilum position) features, suggesting that taxonomic assignment of orchids starch granules to a higher category could enable to the testing of the industrially desired product and protect orchid biodiversity. HIGHLIGHTS: Studies on detailed morphology and morphometry of orchid starch using polarized light microscopy and scanning electron microscopy. Relation and effect of size descriptive on shape descriptive features (circularity and hilum position) of the starch grains. Described size and shape pattern of starch granules, and confirmed the usefulness of quantitative data sets for easily and effectively assessing the variation of the orchid.

Thermal Effects in Slender EHL Contacts

This study deals with experimental and numerical analysis of the thermal effects of slender elastohydrodynamically lubricated (EHL) contacts under high sliding. Thereby, the entrainment direction is along the major axis of the contact ellipse. Film thickness measurements were carried out on an optical EHL tribometer with a glass disk and steel roller. Numerical EHL solutions were obtained with consideration for non-Newtonian rheology and thermal effects. The results show that thermal effects can result in a strong viscosity wedge diverting oil flow to the contact sides. For high positive sliding, in which the glass disk moves faster, the influence of entrainment speed on minimum film thickness is almost negligible, while the film thickness shows a continuous decrease in gap length direction.

Study on the propagation characteristics of elliptical Airy vortex beam

The propagation characteristics of elliptical Airy vortex beams (EAVB) with different elliptical parameter and topological charges are demonstrated experimentally and numerically. Besides, the relationship between elliptical parameter and detection probability of the orbital angular momentum(OAM) is analyzed numerically. The results show that elliptical parameter has a significant impact on the OAM spectral distribution and the propagation characteristics of the EAVB. The EAVB possess an elliptical shaped transverse pattern in the main lobe surrounded by a series of rings and has the line of intensity nulls in the focal plane. It also has two focal planes during the propagation, and the distance between the two focal plane becomes shorter with the increase of elliptical parameter. The long axis of the intensity ellipse of the EVAB rotates 90°between the second focal plane and the first focal plane. There is a linear relationship between OAM detection probability and the elliptical parameter. The experimental results are in good agreement with theory, which will be helpful for the application of EAVB in optical trapping and optical communication.

Adhesive contacts of rough elliptical punches

We numerically study adhesive contact between an elastic half-space and a rigid punch with elliptic shape and superimposed roughness. Simulation is carried out using the Fast Fourier Transform-assisted Boundary Element Method for JKR-type adhesive contact. Both regular roughness (in form of a two-dimensional wave) and random fractal roughness are studied. It is confirmed that the main governing parameter determining different modes of adhesion is the Johnson parameter. For under-critical values of the Johnson parameter (large enough amplitude of roughness), the adhesive force increases with the normal force during compression stage, until it reaches a plateau. The evolution of the contact area during the pull-off shows different configurations depending on the roughness and the pre-loading. For large Johnson parameters the detachment begins from the ends of the major axis of the ellipse and propagates to the center of the contact. In a narrow interval near the critical Johnson parameter, the detachment can also start from the center of ellipse or from the ends of minor axis, if the pre-loading is not too large (so that the complete compact contact is not established). The maximum pull-off force (force of adhesion) is also a function of the Johnson parameter. Enhanced adhesion is observed when the maximum pull-off force is larger than that for a flat-ended punch. In experiment, steel flat indenters with different elliptical shapes are indented into soft rubber sheets. It is observed that the detachment begins from the edge of minor axis of ellipse in all cases, contrary to the results of numerical simulation and analytical theory.

Study of gain and trajectories in elliptical electron beam considering a planar wiggler and self fields and ion-channel in free electron laser

In this study, the relativistic electron beam with an elliptical cross-section is introduced instead of the relativistic electron beam with a circular cross-section in free-electron laser (FEL). Influences of ion-channel guiding, axial magnetic field, Planar Wiggler Magnetic Field (PWMF) and self-fields on trajectories of the elliptical relativistic electron beam have also been investigated. At first, it was assumed that the PWMF is applied along the minor axis of the beam cross-section ellipse. In the second case, the PWMF was applied along the major axis of beam cross-section ellipse, the results of which were compared for the two cases. Effects of elliptical cross-section demotions and elliptical electron beam density on electron trajectory have been studied. The results were compared in the limit that the elliptical electron beam is converted to a circular electron beam, which has also been graphically presented. Moreover, a limit case in which the elliptical beam is converted into a sheet beam was studied. Furthermore, a formula was obtained for the small signal gain in a FEL with elliptical electron beam. The obtained gain for a FEL, together with a relativistic electron beam with an elliptical cross section was compared to the maximum gain for a FEL together with a relativistic electron beam with a circular cross section. It is shown that increasing the ratio of the semi-major to semi-minor axes of the beam cross-section causes the gain rate of the FEL to increases. We investigated a study of electron trajectories and dispersion equation in relativistic electron beam with elliptical cross section under the influence of electromagnetic wave wiggler and axial magnetic field considering ion-channel guiding and self fields in Appendix A.

Numerical computation of preimage domains for spiral slit regions and simulation of flow around bodies.

In this paper, we propose the iterative numerical methods to calculate the conformal preimage domains for the specified logarithmic spiral slit regions and develop the applications of conformal mappings in the simulations of the flow around bodies. Firstly, we postulate that the boundaries of the preimage domains mapped onto logarithmic spiral slits are ellipses. The lengths of the long axes of ellipses and the coordinates of the centers are calculated using our iterative methods. Secondly, each type of the presented iterative method calculates numerical conformal mappings via solving the boundary integral equation with the generalized Neumann kernel. Finally, numerical examples show the convergence and availability of our iterative methods and display the simulations of the flow around the bodies as an application.