KIRCHHOFF FORMULA WITH LINE INTEGRAL FORM AND ITS APPLICATIONS

In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave.

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.

A monolithic distributed phase shifter based on right-handed nonlinear transmission lines at 30 GHz

The epitaxial material, device structure, and corresponding equivalent large signal circuit model of GaAs planar Schottky varactor diode are successfully developed to design and fabricate a monolithic phase shifter, which is based on right-handed nonlinear transmission lines and consists of a coplanar waveguide transmission line and periodically distributed GaAs planar Schottky varactor diode. The distributed-Schottky transmission-line-type phase shifter at a bias voltage greater than 1.5 V presents a continuous 0°–360° differential phase shift over a frequency range from 0 to 33 GHz. It is demonstrated that the minimum insertion loss is about 0.5 dB and that the return loss is less than-10 dB over the frequency band of 0–33 GHz at a reverse bias voltage less than 4.5 V. These excellent characteristics, such as broad differential phase shift, low insertion loss, and return loss, indicate that the proposed phase shifter can entirely be integrated into a phased array radar circuit.

Broadband microwave frequency doubler based on left-handed nonlinear transmission lines

A bandwidth microwave second harmonic generator is successfully designed using composite right/left-handed non- linear transmission lines （CRLH NLTLs） in a GaAs monolithic microwave integrated circuit （MMIC） technology. The structure parameters of CRLH NLTLs, e.g. host transmission line, rectangular spiral inductor, and nonlinear capacitor, have a great impact on the second harmonic performance enhancement in terms of second harmonic frequency, output power, and conversion efficiency. It has been experimentally demonstrated that the second harmonic frequency is deter- mined by the anomalous dispersion of CRLH NLTLs and can be significantly improved by effectively adjusting these structure parameters. A good agreement between the measured and simulated second harmonic performances of Ka-band CRLH NLTLs frequency multipliers is successfully achieved, which further validates the design approach of frequency multipliers on CRLH NLTLs and indicates the potentials of CRLH NLTLs in terms of the generation of microwave and millimeter-wave signal source.

A 3-Node Co-Rotational Triangular Finite Element for Non-Smooth,Folded and Multi-Shell Laminated Composite Structures

Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.

LIC color texture enhancement algorithm for ocean vector field data based on HSV color mapping and cumulative distribution function

Texture-based visualization method is a common method in the visualization of vector field data.Aiming at adding color mapping to the texture of ocean vector field and solving the ambiguity of vector direction in texture image,a new color texture enhancement algorithm based on the Line Integral Convolution(LIC)for the vector field data is proposed,which combines the HSV color mapping and cumulative distribution function calculation of vector field data.This algorithm can be summarized as follows:firstly,the vector field data is convoluted twice by line integration to get the gray texture image.Secondly,the method of mapping vector data to each component of the HSV color space is established.And then,the vector field data is mapped into HSV color space and converted from HSV to RGB values to get the color image.Thirdly,the cumulative distribution function of the RGB color components of the gray texture image and the color image is constructed to enhance the gray texture and RGB color values.Finally,both the gray texture image and the color image are fused to get the color texture.The experimental results show that the proposed LIC color texture enhancement algorithm is capable of generating a better display of vector field data.Furthermore,the ambiguity of vector direction in the texture images is solved and the direction information of the vector field is expressed more accurately.

GPU Accelerated Marine Data Visualization Method

The study of marine data visualization is of great value. Marine data, due to its large scale, random variation and multiresolution in nature, are hard to be visualized and analyzed. Nowadays, constructing an ocean model and visualizing model results have become some of the most important research topics of ‘Digital Ocean'. In this paper, a spherical ray casting method is developed to improve the traditional ray-casting algorithm and to make efficient use of GPUs. Aiming at the ocean current data, a 3D view-dependent line integral convolution method is used, in which the spatial frequency is adapted according to the distance from a camera. The study is based on a 3D virtual reality and visualization engine, namely the VV-Ocean. Some interactive operations are also provided to highlight the interesting structures and the characteristics of volumetric data. Finally, the marine data gathered in the East China Sea are displayed and analyzed. The results show that the method meets the requirements of real-time and interactive rendering.

ARBITRARILY HIGH-ORDER ENERGY-CONSERVING METHODS FOR HAMILTONIAN PROBLEMS WITH QUADRATIC HOLONOMIC CONSTRAINTS

In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.

Integrated optical delay lines:a review and perspective[Invited]

Optical delay lines（ODLs） are one of the key enabling components in photonic integrated circuits and systems.They are widely used in time-division multiplexing, optical signal synchronization and buffering, microwave signal processing, beam forming and steering, etc. The development of integrated photonics pushes forward the miniaturization of ODLs, offering improved performances in terms of stability, tuning speed, and power consumption. The integrated ODLs can be implemented using various structures, such as single or coupled resonators, gratings, photonic crystals, multi-path switchable structures, and recirculating loop structures.The delay tuning in ODLs is enabled by either changing the group refractive index of the waveguide or changing the length of the optical path. This paper reviews the recent development of integrated ODLs with a focus on their abundant applications and flexible implementations. The challenges and potentials of each type of ODLs are pointed out.

THE E^(1)_(3) TYPE OF CUBIC SYSTEMS WITH TWO INTEGRAL STRAIGHT LINES

The existence and uniqueness of limit cycle for the E 1 3 type of cubic systems with two integral straight lines has been studied in this paper. It is found that the system has no limit cycle when the two integral straight lines intersect each other; it has a unique limit cycle when the two integral straight lines are paralleled. The sufficient and necessary conditions are also given to guarantee the existence of the unique limit cycle.

An adaptive LIC based geographic flow field visualization method by means of rotation distance

Geographic visualization is essential for explaining and describing spatiotemporal geographical processes in flow fields.However,due to multi-scale structures and irregular spatial distribution of vortices in complex geographic flow fields,existing two-dimensional visualization methods are susceptible to the effects of data accuracy and sampling resolution,resulting in incomplete and inaccurate vortex information.To address this,we propose an adaptive Line Integral Convolution(LIC)based geographic flow field visualization method by means of rotation distance.Our novel framework of rotation distance and its quantification allows for the effective identification and extraction of vortex features in flow fields effectively.We then improve the LIC algorithm using rotation distance by constructing high-frequency noise from it as input to the convolution,with the integration step size adjusted.This approach allows us to effectively distinguish between vortex and non-vortex fields and adaptively represent the details of vortex features in complex geographic flow fields.Our experimental results show that the proposed method leads to more accurate and effective visualization of the geographic flow fields.

Regulation and Control of Electromagnetic Field in Radio-Frequency Circuits and Systems

Since the first demonstrations of radio-frequency(RF)circuits,the physics of the electromagnetic(EM)field and its regulation and control with codesigned circuits,have become essential competencies of RF circuit designers.Leveraging advanced regulation or control methods,numerous high-performance circuits have been developed at RF and millimeter-wave(mm-wave)frequencies.Three main methods of electromagnetic regulation have been widely utilized,namely,the separation of electric and magnetic coupling paths,the manipulation of electromagnetic energy through the coupling of multiple tanks or multiple resonators,and the regulation of electromagnetic fields in air cavities or meta-substrates.The separated coupling paths of electric and magnetic fields provide guidance for designing a high-performance filter topology with a quasielliptical response through additional zeros.The manipulation of the EM field through electrical and magnetic intercouplings of multitanks or multiresonators,such as are used in oscillators,power amplifiers(PAs),etc.,results in remarkable power efficiency,size reduction,and wide bandwidth.The regulation of electromagnetism through an air cavity,patterned substrate,or metasubstrate reduces dielectric losses and size,especially when using a substrate integrated suspended line(SISL)platform.Many excellent circuits have been reported based on SISL with low loss,high integration,and self-packaging.Here,we present state-of-the-art cases that demonstrate the benefits of EM field regulation and control.

QUALITIVE THEORY OF THE QUADRATIC DIFFERENTIAL SYSTEMS (I)

Qualitative properties of critical points, integral lines and limit cycles are studied. Interesting relations between quantities characterizing local properties and those characterizing global properties are obtained.

Real-Time Image and Video Artistic Style Rendering System Based on GPU

Aiming at the practical engineering application of video stylization,in this paper, a GPU-based video art stylization algorithm is proposed, and areal-time video art stylization rendering system is implemented. The four mostcommon artistic styles including cartoon, oil painting, pencil painting and watercolorpainting are realized in this system rapidly. Moreover, the system makesgood use of the GPU’s parallel computing characteristics, transforms the videostylized rendering algorithm into the texture image rendering process, acceleratesthe time-consuming pixel traversal processing in parallel and avoids the loop processingof the traditional CPU. Experiments show that the four art styles achievedgood results, and the system has a good interactive experience.