Parallel Wedge Research Articles

Reconfiguration of Nematic Disclinations in Plane-Parallel Confinements

We study numerically the reconfiguration process of colliding m=1/2 strength disclinations in an achiral nematic liquid crystal (NLC). A Landau–de Gennes approach in terms of tensor nematic-order parameters is used. Initially, different pairs m1,m2 of parallel wedge disclination lines connecting opposite substrates confining the NLC in a plane-parallel cell of a thickness h are imposed: {1/2,1/2}, {−1/2,−1/2} and {−1/2,1/2}. The collisions are imposed by the relative rotation of the azimuthal angle θ of the substrates that strongly pin the defect end points. Pairs {1/2,1/2} and {−1/2,−1/2} “rewire” at the critical angle θc1=3π4 in all cases studied. On the other hand, two qualitatively different scenarios are observed for {−1/2,1/2}. In the thinner film regime h<hc, the disclinations rewire at θc2=5π4. The rewiring process is mediated by an additional chargeless loop nucleated in the middle of the cell. In the regime h>hc, the colliding disclinations at θc2 reconfigure into boojum-like twist disclinations.

New Features in Feko and WinProp 2019

This paper describes some of the latest features in the commercial electromagnetic software Feko (including WinProp). These include the modeling of non-ideal cable shield connections, the parallel direct adaptive cross approximation (ACA) solver, edge and wedge diffraction for the ray launching geometrical optics (RL-GO) solver, and several new features related to automotive radar.

Analisis Stratigrafi dan Identifikasi Fasies Seismik Pada Interval Syn - Rift, Daerah Kotagaro, Cekungan Sumatera Tengah

The Kotagaro area is one of the hydrocarbon field in the Central Sumatra basin one of the old giant hydrocarbon basins in Indonesia. Only Post-rift deposit are well explored in the Kotagaro are,while Synrift deposit of Pematang Group still not being explored as a reservoir, because they are not a focus in the development study. Research on synrift interval is expected to be new knowledge, especially in the Kotagaro area. This study aims to explore (new insights) regarding synrift interval by analyzing seismic facies and interpreting the depositional environments of the study area. This study used 2D and 3D seismic data and data from a well located outside the study area. Well data is used for well-seismic tie. The methods used in this study included well-seismic tie, 2D and 3D seismic interpretations the synrift intervals, generation of time structure maps and isochrones maps seismic facies analysis, and interpretation of depositional environments. Based on this analysis, the research area has four seismic facies, Chaotic Wedge (AM), Divergent Wedge (DM), Hummocky Wedge (HM), and Parallel Wedge (PM). The four seismic facies showed that the study area was deposited in the fluvial zone, alluvial fan zone, deep lacustrine zone, shallow lacustrine zone, and lacustrine shoreline zone.

Line and point defects in nonlinear anisotropic solids

In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with distributed line and point defects. In particular, we determine the stress fields of (i) a parallel cylindrically symmetric distribution of screw dislocations in infinite orthotropic and monoclinic media, (ii) a cylindrically symmetric distribution of parallel wedge disclinations in an infinite orthotropic medium, (iii) a distribution of edge dislocations in an orthotropic medium, and (iv) a spherically symmetric distribution of point defects in a transversely isotropic spherical ball.

An attraction-repulsion transition of force on wedges induced by active particles.

Effective forces between two micro-wedges immersed in an active bath are investigated using Brownian dynamics simulations. Two anti-parallel and parallel wedge-like obstacles are considered respectively, and the effective forces between two wedges rely on the wedge-to-wedge distance, the apex angle of the wedge, as well as the particle density and aspect ratio. For two anti-parallel wedges, a transition from repulsion to attraction occurs by varying the apex angle, which is also sensitive to the particle density and aspect ratio. The optimal apex angle θr* (or θa*) and particle density ρ* are characterized by the saturated trapping of active particles inside a wedge. For two parallel wedges, the effective force also experiences a transition from repulsion to attraction as the wedge-to-wedge distance increases. These results originate from the collective trapping effect which is driven by the many-body dynamics of self-propelled particles in the confinement (near the boundary) of obstacles. Our results can provide insight into controlling the motion and assembly of microscopic objects through the suspension of active particles.

Dynamics of a ±1/2 defect pair in a confined geometry: A thin hybrid aligned nematic cell**Project supported by the National Natural Science Foundation of China (Grant No. 11374087) and the Key Subject Construction Project of Hebei Province University.

Confined geometry can change the defect structure and its properties. In this paper, we investigate numerically the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry: a thin hybrid aligned nematic (HAN) cell, based on the Landau–de Gennes theory. When the cell gap d is larger than a critical value of 12ξ (where ξ is the characteristic length for order-parameter change), the pair annihilates. A pure HAN configuration without defect is formed in an equilibrium state. In the confined geometry of d ≤ 12ξ, the diffusion process is discovered for the first time and an eigenvalue exchange configuration is formed in an equilibrium state. The eigenvalue exchange configuration is induced by different essential reasons. When 10ξ < d ≤ 12ξ, the two defects coalesce and annihilate. The biaxial wall is created by the inhomogeneous distortion of the director, which results in the eigenvalue exchange configuration. When d ≤ 10ξ, the defects do not collide and the eigenvalue exchange configuration originates from the biaxial seeds concentrated at the defects.

Dynamics of a &amp;#177;1/2 Defect Pair in a Confined Geometry

This paper investigated the dynamics of a dipole of ±1/2 parallel wedge disclination lines in a confined geometry, based on Landau-de Gennes theory. The behavior of the pair depends on the competition between two kinds of forces: the attractive force between the two defects, aggravating the annihilation process, and the anchoring forces coming from the substrates, inhibiting the annihilation process. There are three states when the system is equilibrium, divided by two critical thicknesses dc1 and dc2 (existing when r0≤15ξ, r0 is the initial distance between the two defects), both changing linearly with r0. When the cell gap d＞dc1, the two defects coalesce and annihilate. The dynamics follows the function of r∝(t0-t)α during the annihilation step when d is sufficiently large, relative to r0, where r is the relative distance between the pair and t0 is the coalescence time. α decreases with the decrease of d or the increase of r0. The annihilation process has delicate structures: when r0≤15ξ and d＞dc2 or r0＞15ξand d＞dc1, the two defects annihilate and the system is uniaxial at equilibrium state; when r0≤15ξ and dc2＞d＞dc1, the two defects coalesce and annihilate, and the system is not uniaxial, but biaxial in the region where the defects collide. When d≤dc1, the defects can be stable existence.

Investigation of the laser action in a dye-doped cholesteric liquid crystal wedge cell

The wedge cell of cholesteric liquid crystal device is designed and fabricated, and doping PM580 (exciton) in the cholesteric liquid crystal, the laser emission action is studied. There appear a series of parallel wedge edges of dislocation lines and different shapes of domain in the wedge cell. The planar state of alignment is confirmed. A second harmonic Nd:YAG 532 nm laser is adopted as a pump light beam, and then one-dimensional tunable laser radiation is obtained and its wavelength interval is approximately 1 nm and tuning range is about 17 nm. In the processs of interaction between the torques of LC and the surface anchoring of direction film, the pitch elongation takes place. The positon of photonic band gap is changed, so the laser radiation wavelength can be tuned in the band edge.

Error Modeling of a Parallel Wedge Precision Positioning Stage

The parallel wedge precision positioning stage (PW-PPS) presents a novel configuration of a parallel mechanism for precision positioning applications. Based on its specific parallel configuration, the corresponding inverse and forward kinematic models were developed and used to formulate the volumetric error model of the mechanism. The error model that considers the influence of manufacturing errors is built in two steps. In the first, the structural parameter-induced errors associated with the PW-PPS's structural parameters and input variables were considered, while in the second, the joint clearance-induced errors produced by joint clearances were taken into account. The structural parameter-induced errors were modeled based on complete differential-coefficient theory, while the joint clearance-induced errors due to joint clearances were modeled based on the virtual work and deterministic method. In the latter case, the kinetostatic model and joint error contact modes were analyzed to build a joint clearance-induced error model. The relationship between the different error sources and the output pose error of the mechanism's moving platform was obtained. Finally, considering practical values for the mechanism's parameters and errors, the error distribution in the PW-PPS's workspace was evaluated to determine the distributive rules of the various error components.

Riemann–Cartan geometry of nonlinear disclination mechanics

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan’s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material.

A phase-shifting vectorial-shearing interferometer with wedge plate phase-shifter

We present a novel phase-shifting vectorial-shearing interferometer with a wedge plate phase-shifter. The interferometer is based on a modified Mach-Zehnder configuration; the common-path nature makes it capable of testing the wavefront of a short coherence-length light source, such as a laser diode. Vectorial shear (shearing in the x and y directions simultaneously) in an arbitrary direction is introduced by inserting two wedge plates orthogonally in two arms, respectively. One of the wedge plates is split into two parts (parallel part and wedge part); phase shift is produced by moving the wedge part in contact along the parallel part. The moving distance for a 2 pi phase shift is a few millimetres in specific conditions. The wedge plate phase-shifter increases the moving distance for phase shift and makes the control of phase shift relatively easy. We also discuss the lateral shear error and phase shift errors induced by wedge plates. The lateral shear error is small enough to be ignored; the phase shift error is determined mainly by the wedge angle error. Lastly, we give the experimental results of phase-shifting interference fringes in vectorial shear mode.

Simulation of the Field Emission Arrays with Parallel Wedge Emitter, Gates and Co-Planar Lens

Using the particle-in-cell (PIC) simulation code MAGIC, the wedge emitter, parallel gate and anode with and without co-planar lens have been simulated. The electron beam streamlines and the X-Vx phase space have been evaluated, which show that the co-planar lens focuses the electron. Simulation results are presented for a single FEA's cell with the anode biased at 500V and spaced 100μm from the cathode, which indicated that the electron beam width at anode is about 60.2μm for without lens FEAs, after add the lens with −70V, the electron beam width will be decrease to 8.1μm, meanwhile the maximum transverse velocity will decrease from ±1×106m/s to ±1.46×105m/s.

Scattering on Dislocations and Cosmic Strings in the Geometric Theory of Defects

We consider scattering of elastic waves on parallel wedge dislocations in the geometric theory of defects or, equivalently, scattering of point particles and light rays on cosmic strings. Dislocations are described as torsion singularities located on parallel lines, and trajectories of phonons are assumed to be the corresponding extremals. Extremals are found for arbitrary distribution of the dislocations in the monopole, dipole, and quadrupole approximation and the scattering angle is obtained. Examples of continuous distribution of wedge and edge dislocations are considered. We have found that for deficit angles close to −2 πa star located behind a cosmic string may have any even number of images, 2, 4, 6, … The close relationship between dislocations and conformal maps is elucidated in detail.

A note on double edge diffraction for parallel wedges

An extended spectral theory of the diffraction approach is used in the investigation of double-edge diffraction in the near-field region of a parallel wedge geometry illuminated by a cylindrical wave. A high-frequency approximation can be formulated in terms of a canonical double stationary phase integral. A uniform asymptotic reduction of the latter, using the method of D.S. Jones (1971), results in a compact representation involving the generalized Fresnel integral, with certain advantages in numerical applications over past representations. >

A hybrid asymptotic solution for the scattering by a pair of parallel perfectly conducting wedges

The overlapping transition regions of the double diffraction by a pair of parallel wedge edges are considered for the hybrid case where the gap between the edges is small compared to the distances from the source and the observation point (plane-wave-far-field limit) and the scatterer as a whole is large (or infinite). A closed-form asymptotic solution for the scattered field continuous at all angles of incidence and scattering is constructed for this case. The peculiar feature of this solution is a hybrid representation of the field singly diffracted by the first wedge: a part of it is described by a nonuniform, geometrical theory of diffraction (GTD) expression, while the other part is described in terms of the uniform theory of diffraction (UTD). The rest of the diffracted ray fields are described by nonuniform expressions, with singularities mutually canceling on summation. This solution is applied to the scattering by a perfectly conducting rectangular cylinder with appropriate geometrical parameters, and agreement with moment method calculation is demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic diffraction by two perfectly conducting wedges with dented edges loaded with a dielectric cylinder

A rigorous field analysis of the problem of two identical perfectly conducting parallel wedges with dented edges loaded with a dielectric cylinder, and excited by an electric or magnetic line current in the upper sector, is given in this paper. The dielectric medium is assumed to be linear, homogeneous, isotropic and free from losses, whereas the mediums of the upper and lower sectors are free space. A field equivalence theorem is used to derive, for each excitation, a system of coupled integral equations for the equivalent magnetic currents on the dielectric interfaces, which is later solved using Galerkin&apos;s method. The fields and powers transmitted into the lower sector, hence the transmission coefficients, for both polarisations are subsequently determined in terms of the equivalent magnetic currents on the lower dielectric interface. The analysis is then specialised to the problem of a slit loaded with a dielectric cylinder, as well as to the case of plane wave excitation. Sample numerical results for the dielectric-loaded double dented wedge and slit problems in the case of plane wave excitation are also given.

High-frequency electromagnetic scattering of plane waves from double wedges

The application of a high-frequency solution for the field doubly diffracted in the far zone from a pair of parallel wedges illuminated by a plane wave is described. It is shown how a spectral extension of the uniform geometrical theory of diffraction (GTD) is used to obtain closed-form expressions for the field that are valid at any incidence and observation aspects. These expressions exhibit the proper discontinuities and singularities so that they can be suitably combined with the other singly diffracted fields to provide a uniformly valid ray description of the scattering in the far zone by an obstacle which is illuminated by a plane wave. They smoothly reduce both to those derived by directly applying the uniform GTD solution for single diffraction augmented by slope diffraction and to those recently obtained for grazing illumination of the edges, in their respective regions of validity. The solutions to the scalar problems are then used to construct a dyadic diffraction coefficient for the doubly diffracted field in the ray-fixed coordinate system. Examples of triangular cylinders are considered, and numerical results are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Double diffraction by wedges in nonperfectly conducting surfaces

A high-frequency solution is obtained via an extended ray method for the field doubly diffracted in the far zone by a pair of parallel wedges with impedance faces, when they are illuminated by a plane wave perpendicularly incident on the edges. Except for a multiplying special function, this solution is expressed in closed form, which is valid for any incidence and observation aspects.

A new asymptotic high‐frequency analysis of electromagnetic scattering by a pair of parallel wedges: Closed form results

A new asymptotic analysis of the high‐frequency scattering by a pair of parallel wedges is presented, resulting in a uniform, closed‐form approximation for the doubly diffracted field. The analysis is based on an extension of the physical theory of diffraction, in which the radiation integral over the actual induced currents is replaced by the Helmholtz integral over a surface enclosing the wedges. A term‐by‐term relationship is established between the geometrical theory of diffraction ray decomposition of the scattered field and the asymptotic decomposition of the radiation integral into endpoint contributions. The closed form expressions obtained for the various endpoint contributions to the singly diffracted field are used in an extended spectral theory of diffraction analysis of the doubly diffracted field to cast the latter in the form of a steepest descent path integral satisfying the principle of reciprocity. An Ansatz based on the uniform theory of diffraction in combination with a singularity‐matching procedure is proposed to transform the initial nonuniform approximation for the doubly diffracted field into a uniform one. The latter includes terms to order k−1 and applies to all angles of incidence and scattering, including the overlapping transition regions. The limitations on this closed‐form solution are that the incident wave be approximately plane throughout the gap between the edges, the observation point be in the far scattered field, and the gap be large in terms of the wavelength.

An analysis of diffraction at edges illuminated by transition region fields

A solution is obtained for the high‐frequency scattering by a pair of parallel wedges where the edge of one wedge is illuminated by the shadow boundary field of the other. A generalized spectral extension of the uniform GTD is used to determine the contribution from the doubly diffracted ray. Expressions for the diffracted field are given for plane, cylindrical, and spherical wave illuminations. Incidence oblique to the edges is also considered. These expressions reduce to a closed form at the shadow boundaries and outside the overlapping transition regions where the results coincide with those obtained by the uniform GTD augmented by slope diffraction. The solutions to the scalar problems are then used to derive a dyadic diffraction coefficient for the doubly diffracted field, in the ray‐fixed coordinate system. The general expressions presented here directly apply to the diffraction by half planes, strips, and joined wedges (thick edges) where the number of terms involved significantly reduces.