scholarly journals Parabolic-accelerating vector waves

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Bo Zhao ◽  
Valeria Rodríguez-Fajardo ◽  
Xiao-Bo Hu ◽  
Raul I. Hernandez-Aranda ◽  
Benjamin Perez-Garcia ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Optical Manipulation ◽  
Laser Material Processing ◽  
Complex Vector ◽  
New Family ◽  
Vector Beams ◽  
Vortex Beams ◽  
Transverse Polarisation ◽  
Straight Lines ◽  
General Vector

Abstract Complex vector light fields have become a topic of late due to their exotic features, such as their non-homogeneous transverse polarisation distributions and the non-separable coupling between their spatial and polarisation degrees of freedom (DoF). In general, vector beams propagate in free space along straight lines, being the Airy-vector vortex beams the only known exception. Here, we introduce a new family of vector beams that exhibit novel properties that have not been observed before, such as their ability to freely accelerate along parabolic trajectories. In addition, their transverse polarisation distribution only contains polarisation states oriented at exactly the same angle but with different ellipticity. We anticipate that these novel vector beams might not only find applications in fields such as optical manipulation, microscopy or laser material processing but also extend to others.

An Efficient Weighted Residual Time Integration Family

2021 ◽  
pp. 2150106
Author(s):  
Mohammad Rezaiee-Pajand ◽  
S. A. H. Esfehani ◽  
H. Ehsanmanesh
Keyword(s):  
Degrees Of Freedom ◽  
Time Integration ◽  
Nonlinear Damping ◽  
Implicit Methods ◽  
New Family ◽  
Error Analyses ◽  
Damping Behavior ◽  
The Family ◽  
New Strategy ◽  
Time Integration Methods

A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge–Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors’ formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are [Formula: see text] and [Formula: see text] for even and odd values of [Formula: see text], respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms.

scholarly journals Laser material processing with tightly focused cylindrical vector beams

2016 ◽  
Vol 108 (22) ◽  
pp. 221107 ◽  
Author(s):  
Rokas Drevinskas ◽  
Jingyu Zhang ◽  
Martynas Beresna ◽  
Mindaugas Gecevičius ◽  
Andrey G. Kazanskii ◽  
...  
Keyword(s):  
Material Processing ◽  
Laser Material Processing ◽  
Laser Material ◽  
Vector Beams

scholarly journals Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra

2019 ◽  
Vol 29 (06) ◽  
pp. 1037-1077 ◽  
Author(s):  
Ilona Ambartsumyan ◽  
Eldar Khattatov ◽  
Jeonghun J. Lee ◽  
Ivan Yotov
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Mixed Finite Element ◽  
Mixed Finite Elements ◽  
Higher Order ◽  
Local Velocity ◽  
New Family ◽  
Gauss Points ◽  
Theoretical Results ◽  
Optimal Formula

We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure systems. The methods are based on a new family of mixed finite elements, which are enhanced Raviart–Thomas spaces with bubbles that are curls of specially chosen polynomials. The velocity degrees of freedom of the new spaces can be associated with the points of tensor-product Gauss–Lobatto quadrature rules, which allows for local velocity elimination and leads to a symmetric and positive definite cell-based system for the pressures. We prove optimal [Formula: see text]th order convergence for the velocity and pressure in their natural norms, as well as [Formula: see text]st order superconvergence for the pressure at the Gauss points. Moreover, local postprocessing gives a pressure that is superconvergent of order [Formula: see text] in the full [Formula: see text]-norm. Numerical results illustrating the validity of our theoretical results are included.

scholarly journals A general vector analysis, with applications to electrodynamical theory

1925 ◽  
Vol 108 (747) ◽  
pp. 418-455 ◽  
Keyword(s):  
Three Dimensions ◽  
Vector Analysis ◽  
Cartesian Coordinates ◽  
Straight Line ◽  
Straight Lines ◽  
General Vector

The vector analyses in use up to the present, as a rule, are concerned with quantities which are represented by straight lines, and the space to which they are applicable is Euclidean in its properties. The straight line, AB, in space of three dimensions, is represented by a vector a, and if B has Cartesian coordinates ( x, y, z ) with respect to A, we write: a = i x + j y + k z , where i, j, k, are fundamental vectors. An account will be given of a vector analysis in which a vector is represented by δa' = Σ n i n δx n . The vector is of infinitesimal length and represents a component measured in any system of co-ordinates.

Optical manipulation characteristics of yeast cells by asymmetric dynamic vortex beams

2021 ◽  
Vol 36 (6) ◽  
pp. 841-847
Author(s):  
Ming-xue ZHAO ◽  
◽  
Liu-hao ZHU ◽  
Tong-tong SHAO ◽  
Wen-jun WEI ◽  
...  
Keyword(s):  
Yeast Cells ◽  
Optical Manipulation ◽  
Vortex Beams

A New Family of 4-DOF Parallel Mechanisms (1T-3R and 2T-2R) With Two Platforms and Its Application to a Footpad Device

2004 ◽  
Author(s):  
Jungwon Yoon ◽  
Jeha Ryu
Keyword(s):  
Degrees Of Freedom ◽  
Base Plate ◽  
Driving Mechanism ◽  
Parallel Mechanisms ◽  
Pitch Motion ◽  
Human Foot ◽  
New Family ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Kinematic Analyses

This paper proposes a new family of four degrees-of-freedom (dof) parallel mechanisms with two platforms and its application to a footpad device that can simulate the spatial motions of the human foot. The new mechanism consists of front and rear platforms, and three limbs. Two limbs with 6-dof serial joints (P-S-P-P) are attached to each platform and are perpendicular to the base plate, while the middle limb (Pe-Re-R or Pe-Pe-R) is attached to the revolute joint that connects the front and rear platforms. The middle limb is driven by the 2-dof driving mechanism that is equivalent active serial prismatic and revolute joints (Pe-Re), or prismatic and prismatic joints (Pe-Re) with two base-fixed prismatic actuators. Therefore, two new 4-dof parallel mechanisms with two platforms can generate pitch motion of each platform, and roll and heave motions (1T-3R) or pitch motion of each platform and two translational motions (2T-2R) at both platforms. Kinematic analyses of the 1T-3R mechanism were performed, including inverse and forward kinematics, and velocity analysis. Based on the 1T-3R mechanism, a footpad device was designed to generate foot trajectories for natural walking. Finally, simulations of the foot trajectories in the normal gait cycle were performed using the proposed footpad device.

scholarly journals A Chargeless Complex Vector Matter Field in Supersymmetric Scenario

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
L. P. Colatto ◽  
A. L. A. Penna
Keyword(s):  
Degrees Of Freedom ◽  
Mass Shell ◽  
Equations Of Motion ◽  
Matter Field ◽  
Complex Vector ◽  
Massive Vector ◽  
Spinor Fields ◽  
Respective Field ◽  
Component Field ◽  
Matter Fields

We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a globalU1gauge symmetry. For the aim of dealing with consistent terms without breaking the globalU1symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.

Type Synthesis of a Special Family of Remote Center-of-Motion Parallel Manipulators With Fixed Linear Actuators for Minimally Invasive Surgery

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Qinchuan Li ◽  
Jacques Marie Hervé ◽  
Pengcheng Huang
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Degrees Of Freedom ◽  
Load Capacity ◽  
Parallel Manipulators ◽  
New Family ◽  
In Series ◽  
Surgery First ◽  
Linear Actuators

Remote center-of-motion (RCM) parallel manipulators (PMs) are fit for robotized minimally invasive surgery (MIS). RCM PMs with fixed linear actuators have the advantages of high stiffness, reduced moving mass, and higher rigidity and load capacity. However, there are very few available architectures of these types of PMs. Using the Lie group algebraic properties of the set of rigid-body displacements, this paper proposes a new family of RCM PMs with fixed linear actuators for MIS. The general motion with a remote center has four degrees-of-freedom (DOF) and is produced by the in-series concatenation of a spherical S pair and a prismatic P pair and, therefore, is said to be SP equivalent. The SP-equivalent PMs can be used in minimally invasive surgery. First, the kinematic bonds of limb chains and their mechanical generators for SP-equivalent RCM PMs are presented. Limb chains with fixed linear actuators are then derived using the closure of products in subgroups. Structural conditions for constructing an SP-equivalent RCM PM with linear fixed actuators are revealed. Helical pairs are introduced to remove a local rotation and yield a 360-deg-rotation capability of the moving platform. Numerous new architectures with practical potential are presented.

scholarly journals Angular momentum separation in focused fractional vector beams for optical manipulation

2021 ◽  
Vol 29 (10) ◽  
pp. 14705
Author(s):  
Bing Gu ◽  
Yueqiu Hu ◽  
Xiaohe Zhang ◽  
Miao Li ◽  
Zhuqing Zhu ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Optical Manipulation ◽  
Vector Beams

scholarly journals The geometric phase and the geometrodynamics of relativistic electron vortex beams

2014 ◽  
Vol 470 (2163) ◽  
pp. 20130525 ◽  
Author(s):  
Pratul Bandyopadhyay ◽  
Banasri Basu ◽  
Debashree Chowdhury
Keyword(s):  
Relativistic Electron ◽  
Geometric Phase ◽  
Vortex Line ◽  
Degrees Of Freedom ◽  
Berry Phase ◽  
Scalar Particle ◽  
Propagation Direction ◽  
Dirac Monopole ◽  
Vortex Beams ◽  
Group Flow

We have studied here the geometrodynamics of relativistic electron vortex beams from the perspective of the geometric phase associated with the scalar electron encircling the vortex line. It is pointed out that the electron vortex beam carrying orbital angular momentum is a natural consequence of the skyrmion model of a fermion. This follows from the quantization procedure of a fermion in the framework of Nelson's stochastic mechanics when a direction vector (vortex line) is introduced to depict the spin degrees of freedom. In this formalism, a fermion is depicted as a scalar particle encircling a vortex line. It is here shown that when the Berry phase acquired by the scalar electron encircling the vortex line involves quantized Dirac monopole, we have paraxial (non-paraxial) beam when the vortex line is parallel (orthogonal) to the wavefront propagation direction. Non-paraxial beams incorporate spin–orbit interaction. When the vortex line is tilted with respect to the propagation direction, the Berry phase involves non-quantized monopole. The temporal variation of the direction of the tilted vortices is studied here taking into account the renormalization group flow of the monopole charge and it is predicted that this gives rise to the spin Hall effect.

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