Special Contour Research Articles

Time-inversion technique based correction of complex radome radiation beam distortion

In the electromagnetic wave radiated by radome, there often occur pointing angle deviation, beam distortion and other phenomena, due to the complex electromagnetic medium composition, special contour and complex working environments. For conventional optimization methods, harsh and complex situations increase its workload, especially in the case that the specific location parameter information is unknown. In this paper, a method with time-inversion technique for correcting the radiation beam distortion of the complex radome is proposed. With the time-inversionl method, the concrete parameters of different positions for the radome and the surrounding environment information are not necessary to be determined in advance. The derivation shows that the environmental information is eliminated adaptively by the conjugate convolution operation, and it is proved by numerical operation that the signal of maximum radiation gain in target angle is time-inversion signal. Then based on the adaptive focusing properties of time-inversion electromagnetic waves, a top wedge radome and an icing working radome are taken as the case study. The equal amplitude phase shifting serves as the control group to highlight the advantages of time-reversal. In the end, the results show that the radiation beam pointing error can be reduced from ±10° to ±0.9° within ±45° scanning range for the top wedge radome in C-band. And the annihilated main beam can be converged again for the radome in the icing state. In addition, all the improvements are in a broadband range, and the robustness of the entire radome system is enhanced by increasing target angle energy caused by the increasing the directionality of the array radiation and the narrowing the 3 dB beamwidth. This paper provides an effective method of analyzing the complex radomes and radio wave propagations in complex media.

A Water-Soluble Core for Manufacturing Hollow Injection-Molded Products.

To manufacture a complicated hollow product without any assembly process, for example, the plastic intake manifold, is difficult by the traditional injection molding method. The fusible-core technique, which uses a low-melting-point alloy as a sacrificial core, was developed to solve this problem; however, the limited selection of resin type and the huge capital investment have caused this technique to spread slowly. In this work, a novel method is established that can produce similar products without the limitation of resin type, as well as a lower-energy-consumption process. The concept of the enveloped core defined by a water-soluble core assembled with a shell is proposed herein; it provides both rigidity and toughness to resist the pressure during the injection molding process. The shape of the enveloped core equals the internal contour of the designated product. An insert molding process was introduced to cover the enveloped core with a skin layer. Cut out the end of the enveloped core and immerse it into a water bath. When the water-soluble core inside the shell is dissolved, the product with a special internal contour is accomplished. A tee-joint is presented to demonstrate how the proposed method can be utilized. The optimal ingredient of the core and processing parameters are determined by the Taguchi method. The result shows that the proposed product is molded successfully when the compressive strength of the core is larger than 2 MPa. In addition, the eccentricity measurement of internal contour of the optimal sample exhibits a 56% improvement, and the required time for the core removal is less than 154 s.

Multi-surface hydraulic valve block technique hole plug inspection from monocular image

We propose a visual inspection framework that can detect technique hole plugs on multiple surfaces of hydraulic valve block from monocular RGB image. Firstly, the pose of the valve block relative to the camera is estimated, and then the visible surfaces of the valve block are corrected. Finally, according to the size information, the image patch around the technique hole are classified to judge whether there is a plug. This paper uses the LINEMOD object pose estimation framework as the pose estimation backbone. We propose a special contour extraction method for the counterbore features of valve blocks. Sample points of a matched template are used to construct a nonlinear optimization problem to obtain the accuracy pose. The experimental results show that our method can accurately estimate the pose of the valve block, and at the same time can cooperate with a simple machine learning algorithm to complete the plug inspection.

Arabic Hand Written Character Recognition Based on Contour Matching and Neural Network

Complexity of Arabic writing language makes its handwritten recognition very complex in terms of computer algorithms. The Arabic handwritten recognition has high importance in modern applications. The contour analysis of word image can extract special contour features that discriminate one character from another by the mean of vector features. This paper implements a set of pre-processing functions over a handwritten Arabic characters, with contour analysis, to enter the contour vector to neural network to recognize it. The selection of this set of pre-processing algorithms was completed after hundreds of tests and validation. The feed forward neural network architecture was trained using many patterns regardless of the Arabic font style building a rigid recognition model. Because of the shortcomings in Arabic written databases or datasets, the testing was done by non-standard data set. The presented algorithm structure got recognition ratio about 97%.

Fast Fabrication of 1.26-Meter-Long Optic for Elliptic Cylindrical Focusing Bending Mirror

As beamline emittance reaching the diffraction limit, the demand for focusing mirrors over one meter in length is ever increasing. Bending mirrors, are competitive for its adjustable radius and high manufacture precision, whose final surface form is managed by a delicate bending of a high precision plane. A special contour plays an essential role and benefits this final touch, given that the computed torque along the length closely correlates with the corresponding width of the optics. However, it poses main challenges with severe edge effect, deformation and metrology to the fabrication of the precursor plane mirror. This paper reports on a fast processing technology for a 1.26-meter-long plane as a bending mirror with irregular shape. A smooth surface with a slope error of 0.67 urad(RMS) and 0.3nm roughness is achieved through deterministic flexible finishing of robot polishing system and annular polishing, providing a high precision and cost-effective method to meet the growing needs for long X-ray mirrors.

Isolated Arabic Hand Written Letters Recognition Based on Contour Matching and Neural Network

Complexity of Arabic writing language makes its handwritten recognition very complex in terms of computer algorithms comparing with other languages such as English and French. The Arabic handwritten recognition has high importance in modern applications. The contour analysis of word image can extract special contour features that discriminate one character from another by the mean of vector features. This paper aims to implements a set of pre-processing functions over a handwritten Arabic character, with contour analysis, to enter the contour vector to neural network to recognize it. For training part, the neural network architecture was trained using many patterns regardless of the Arabic font style building a rigid recognition model. The presented algorithm structure got recognition ratio about 97%.

Set-oriented design of interplanetary low-thrust trajectories using Earth Gravity Assist

A method by which to incorporate the Electric Delta-V Earth Gravity Assist (EDVEGA) scheme into a patched three-body approach to design an interplanetary transfer trajectory is presented in this paper. The EDVEGA scheme is a promising technique to reduce fuel consumption using Earth gravity assist and electric propulsion. In a patched three-body approach, the dimension of the problem that connects some trajectories is reduced by the use of special attainable sets. However, because of the singularity associated with Earth's center, it is difficult to connect an EDVEGA trajectory with a trajectory designed in the three-body problem. Therefore, this paper proposes a design method for an Earth–Mars transfer trajectory that combines the EDVEGA scheme with a patched three-body approach using Levi-Civita regularization and a special contour plot. Through comparison with conventional invariant manifold techniques, we demonstrate that fuel consumption is reduced by the proposed method.

Tsunami generation and associated waves in the water column and seabed due to an asymmetric earthquake motion within an anisotropic substratum

AbstractIn this paper, closed‐form integral expressions are derived to describe how surface gravity waves (tsunamis) are generated when general asymmetric ground displacement (due to earthquake rupturing), involving both horizontal and vertical components of motion, occurs at arbitrary depth within the interior of an anisotropic subsea solid beneath the ocean. In addition, we compute the resultant hydrodynamic pressure within the seawater and the elastic wavefield within the seabed at any position. The method of potential functions and an integral transform approach, accompanied by a special contour integration scheme, are adopted to handle the equations of motion and produce the numerical results. The formulation accounts for any number of possible acoustic‐gravity modes and is valid for both shallow and deep water situations as well as for any focal depth of the earthquake source. Phase and group velocity dispersion curves are developed for surface gravity (tsunami mode), acoustic‐gravity, Rayleigh, and Scholte waves. Several asymptotic cases which arise from the general analysis are discussed and compared to existing solutions. The role of effective parameters such as hypocenter location and frequency of excitation is examined and illustrated through several figures which show the propagation pattern in the vertical and horizontal directions. Attention is directed to the unexpected contribution from the horizontal ground motion. The results have important application in several fields such as tsunami hazard prediction, marine seismology, and offshore and coastal engineering. In a companion paper, we examine the effect of ocean stratification on the appearance and character of internal and surface gravity waves.

Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations

Quantum fluctuations of local quantities can be a direct signature of entanglement in an extended quantum many-body system. Hence they may serve as a theoretical (as well as an experimental) tool to detect the spatial properties of the entanglement entropy of a subsystem. In the ground state of quantum many-body systems, its scaling is typically linear in the boundary of the subsystem (area law). Here we propose a microscopic insight into the spatial structure of entanglement and fluctuations using the concept of \emph{contour}, recently introduced to decompose the bipartite entanglement entropy of lattice free fermions between two extended regions $A$ and $B$ into contributions from single sites in $A$. We generalize the notion of contour to the entanglement of any quadratic (bosonic or fermionic) lattice Hamiltonian, as well as to particle-number fluctuations. The entanglement and fluctuations contours are found to generally decay when moving away from the boundary between $A$ and $B$. We show that in the case of free fermions the decay of the entanglement contour follows closely that of the fluctuation contour. In the case of Bose-condensed interacting bosons, treated via the Bogoliubov and spin-wave approximations, such a link cannot be established -- fluctuation and entanglement contours are found to be radically different, as they lead to a logarithmically violated area law for fluctuations, and to a strict area law of entanglement. Analyzing in depth the role of the zero-energy Goldstone mode of spin-wave theory, and of the corresponding lowest-energy mode in the entanglement spectrum, we unveil a subtle interplay between the special contour and energy scaling of the latter, and universal additive logarithmic corrections to entanglement area law discussed extensively in the recent literature.

Mini UAV Design and Manufacture with Bungee Launched / Parachute Recovery

In the past ten years, the R&D of UAV (Unmanned Aerial Vehicle) is very popular and has the trend to replacing with the manned aerial vehicle due to its low-cost and high-mobility. According to the specifications, this project completes special contour and function of a mini-UAV design and passes the strict fabrication, prototyping, and aerial test processes. With the advantages of long flight endurance, speedy assembly/disassembly, simply contour, and portable, the developed mini-UAV has the capabilities of bungee launch and parachute recovery. Thus, it makes much progress in Taiwan’s mini-UAV area.

Explore the Contour Turning Circular FANUC CNC System Based on Macro Program

In the numerical control turning processing, for some of the special contour parts, G71 and G73 instructions are difficult to handle.The ball tool is often used for turning,but the programming is more complex.By the system macroinstruction of FANUC-0iCNC system, this paper writes the preparation of the outer contourloop, thus simplifying the ball tooling special parts operating procedures, and the processing efficiency is improved .

The Green’s function of a five-point discretization of a two-dimensional finite-gap Schrödinger operator: The case of four singular points on the spectral curve

We consider a regular Riemann surface of finite genus and “generalized spectral data,” a special set of distinguished points on it. From them we construct a discrete analog of the Baker-Akhiezer function with a discrete operator that annihilates it. Under some extra conditions on the generalized spectral data, the operator takes the form of the discrete Cauchy-Riemann operator, and its restriction to the even lattice is annihilated by the corresponding Schrodinger operator. In this article we construct an explicit formula for the Green’s function of the indicated operator. The formula expresses the Green’s function in terms of the integral along a special contour of a differential constructed from the wave function and the extra spectral data. In result, the Green’s function with known asymptotics at infinity can be obtained at almost every point of the spectral curve.

An Experimental Investigation during Micro Machining of E-Glass-Fibre-Epoxy Composite on Developed Electrochemical Spark Machining Setup

In the present research, specially designed square cross-section with centrally micro hole brass tool and different diameter round shape micro tools made of IS-3748 steel were used for micro electrochemical spark machining (ECSM) of electrically non conductive e-glass-fibre-epoxy composite. To analyze the influences of the various process parameters of ECSM setup, the specific numbers of experiments have been carried out on developed ECSM setup. The ECSM performance characteristics such as material removal rate, hole depth, and over-cut on hole radius during machining of e-glass-fibre-epoxy composite under varying process parametric conditions are reported in this paper. From the test results, it is found that at higher setting value of D.C. supply voltage, moderate setting value of electrolytic concentration and 180 mm gap between tool (cathode) and auxiliary electrode (anode) the material removal rate is higher. Utilizing the test results mathematical models for MRR and over-cut on hole radius have been developed to express the effect of ECSM process parameters. Different SEM photographs of the micro holes show the surface texture of the machined holes and shape of the generated special shape contour.

The Laplace transform method for Burgers' equation

AbstractThe Laplace transform method (LTM) is introduced to solve Burgers' equation. Because of the nonlinear term in Burgers' equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t, we divide the solution u(x, t) into two parts: u(x, tk) and w(x, t), tk⩽t⩽tk+1, and obtain a time‐dependent linear partial differential equation (PDE) for w(x, t). For this PDE, the LTM is applied to eliminate time dependency. The subsequent boundary value problem is solved by rational collocation method on transformed Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that the present method is effective and competitive. Copyright © 2009 John Wiley & Sons, Ltd.

Spin precession due to a non-Abelian spin-orbit gauge field

We study the spatial behavior of spin precession for traversing electrons in a two-dimensional system with both the Rashba and Dresselhaus spin-orbit (SO) couplings. Treating the two SO coupling as non-Abelian SO gauges and performing the unitary gauge transformation for the Hamiltonian, the effect of SO coupling is exactly represented by a spin-rotation operator providing a convenient framework for studying the property of ballistic spin transport. We derive the analytical expression for the spin configuration and demonstrate a classical analog of spin precession. The present approach provides a powerful means (e.g., the spin-rotation axis, the precession angle, and the cone angle) allowing concrete description of the local spin orientation. In particular, the spatial features such as the specific transport path with null spin precession and the special contour with complete cycles of spin precession can be easily identified.

High accuracy time and space transform method for advection–diffusion equation in an unbounded domain

AbstractA new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection–diffusion equation in the unbounded domain Rn is converted to one on the bounded domain [−1, 1]n, and the Laplace transform is applied to eliminate time dependency. The consequent boundary value problem is solved by collocation on Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that TSTM has exponential rate in time and space. Copyright © 2008 John Wiley & Sons, Ltd.

The Bueckner work conjugate integral for a permeable crack in piezoelectric materials

The Bueckner work conjugate integral for cracked piezoelectric materials is studied. The analysis is based on the permeable crack model to avoid the unphysically impermeable crack assumption. It is proved that the values of the Bueckner integrals are dependent on the normal electric displacement component on the crack surfaces and the coordinates of the starting point and the end point of the integral contour on the lower and upper crack faces, respectively. This means that, strictly speaking, the Bueckner integral for the permeable crack model is path-dependent unless a special condition is satisfied, i.e., the horizontal coordinates of the starting point and the end points of the integral contour are the same. The present conclusions are quite different from those derived from the impermeable crack model, where the Bueckner integral is strictly path-independent. The universal relation between the Bueckner integral and the J-integral existing in the impermeable crack model is also proved not to be always valid for the present permeable model unless the special integral contour is taken. This implies that the crack electric boundary condition in piezoelectric materials yields some significant influence on the properties of the Bueckner work conjugate integral.

Optimizing Talbot’s Contours for the Inversion of the Laplace Transform

Talbot’s method for the numerical inversion of the Laplace transform consists of numerically integrating the Bromwich integral on a special contour by means of the trapezoidal or midpoint rules. In this paper we address the issue of parameter selection in the method, for the particular situation when parabolic PDEs are solved. In the process the well‐known subgeometric convergence rate $O(\exp(-c \sqrt{N}))$ of this method is improved to the geometric rate $O(\exp(-c N))$, with N the number of nodes in the integration rule. The value of the maximum decay rate c is explicitly determined. Numerical results for two versions of the heat equation are presented. With the choice of parameters derived here, the rule of thumb is that to achieve an accuracy of $10^{-\ell}$ at any given time, the associated elliptic problem has to be solved no more than $\ell$ times.

Detailed characterization of (3×3) iodine adlayer on Pt(111) by unequal-sphere packing model

A simple unequal-sphere packing model is applied to study the iodine (3x3) adlayer on the Pt(111) surface. By using a newly introduced parameter, defined as the average adsorbate height, three characteristic adlattices, (3x3)-sym, (3x3)-asym, and (3x3)-lin, have been selected and characterized in great detail, including the exact adatom registry. The (3x3)-sym iodine adlattice, observed in many experimental studies, appears to be, on average, the closest one to the substrate surface. A special contour plot of average adsorbate height vs X and Y positions of the (3x3) iodine unit cell indicates the existence of two local minima, which are related to preferential formation of (3x3)-sym and (3x3)-asym iodine adlattices. Our model gives good agreement with experimental findings, and explains the mechanism of preferential appearance of (3x3)-sym and (3x3)-asym structures.

Analytical Result on the Supercurrent Through a Superconductor/Quantum-Dot/Superconductor Junction**The project supported by National Natural Science Foundation of China under Grant Nos. 10074001, 90103027 and by the State Key Laboratory for Mesoscopic Physics in Peking University

We present an analytical result for the supercurrent across a superconductor/quantum-dot/superconductor junction. By converting the current integration into a special contour integral, we can express the current as a sum of the residues of poles. These poles are real and give a natural definition of the Andreev bound states. We also use the exact result to explain some features of the supercurrent transport behavior.