Time-relevant stability of 2D systems

For many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems ‘time-relevant’. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system. We also give an LMI characterization of time-relevant stability involving only constant matrices.     

基于相对距离的D2D通信模式选择方案

D2D(Device-to-Device)通信技术是一种能够降低基站负载率和提高系统资源利用率的新型近场通信技术。本文根据D2D接收端与蜂窝端的相对距离关系,分别讨论了传统蜂窝系统以及引入中继技术后的模式选择问题,给出了一种基于蜂窝用户与D2D用户地理位置关系的模式选择方案。仿真数据验证了D2D系统采用复用模式的概率与设定的系统信干噪比阈值成反比关系,表明引入中继技术后的D2D系统采用复用模式的概率大大增加,意味着在混合网络中加入中继节点能够有效地提高系统的频谱利用率。     

Conditions for internal stability of 2D systems

The numerical range (the field value) of a matrix is generalised for two matrices and via this extension new stability conditions for 2D systems are derived.     

Robust stability and stabilisation of 2D discrete state-delayed systems

In this paper, we first present sufficient stability and robust stability conditions for discrete linear state-delayed 2D systems in terms of linear matrix inequalities. All results are obtained with Fornasini–Marchesini delay model but appropriate transformation to the corresponding Roesser form is provided as well. Generalisation to the multiple state-delayed case is also given. Then the stabilisation and robust stabilisation using static state feedback are studied. Stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities. An numerical example is used to illustrate the effectiveness of the approach.     

二维线性连续系统稳定性的新判据

提出了一个检验二维线性连续系统稳定性的新算法。该算法基于多项式判别系统理论,可以对系统稳定与否作出完备的判断,克服了传统频域方法需要取大量频率点进行检验且只能提供近似结论的不足。更重要的是,此算法可以用于分析含参数系统的稳定裕度。实际案例显示了该算法的有效性。     

2-D stability test via 1-D stability robustness analysis

A new two-dimensional stability test is proposed, based on the stability robustness analysis of a relevant 1-D system family. A linear algebra type algorithm for numerical implementation of the test is also described. Two examples then follow, to illustrate the use of the algorithm and the feasibility of the proposed test.     

基于隐私度和稳定度的D2D数据共享伙伴选择机制

设备到设备（D2D）数据共享已经成为一种很有前途的卸载蜂窝网络流量的解决方案,但数据共享伙伴的隐私脆弱性和服务不稳定性影响着共享服务的质量。针对这个问题,提出一种基于隐私度和稳定度的D2D数据共享伙伴选择机制（PSUS）。首先对提供者的隐私信息进行抽象和概括,根据提供者的隐私偏好和历史共享记录构建隐私度量的方法,得出提供者在不同共享服务中的隐私度;然后基于隐私度来设计数据共享过程,提供者在隐私偏好约束下缓存数据并在隐私度低的时候参与共享服务以满足提供者的隐私要求;最后在已满足隐私要求的提供者的基础上,设计一种多指标评价法来评估提供者的服务稳定性以选择稳定的共享伙伴。通过性能分析,证明所提机制的可行性。     

1D and 2D structured mass-spring models with preload

In this paper, the objective is to enrich the existing 1D and 2D mass-spring models with physical accuracy as well as visual realism. It is found that using nonzero preloads on the springs is a necessary condition for the models to approximate their continuum counterparts. First, the parameters of the 1D mass-spring model of a beam are derived based on pure bending and axial action. It is proved that the mass-spring model with this set of parameter has correct characteristics of resistance against lateral displacement, which is one of the most important aspects of the accuracy of the 1D mass-spring model. Then, the method is extended to the 2D mass-spring models of the continuum plate with two different mesh structures. The mass-spring model with equilateral triangle meshes is shown to be physically more accurate than that with rectangular meshes. Finally, the physical accuracy that the mass-spring models with preload can achieve is investigated under different load conditions by comparison with the finite element method (FEM) to demonstrate the efficacy of our approach.     

1D selection of 2D objects in head-worn displays

In current desktop user interfaces, selection is usually accomplished easily with a mouse or a similar two-dimensional locator. In wearable computing, however, controlling two dimensions simultaneously gets significantly harder: a change in one dimension results easily in an undesired change in the other dimension as well when the user is occupied with a parallel task – such as walking. We present a way to overcome this problem by applying one-dimensional selection for graphical user interfaces in head-worn displays. Our new interaction technique allows a wearable computer user to perform object selection tasks easily and accurately. The technique is based on a visible circle on the screen. The user controls the circle, altering its radius with a one-dimensional valuator. The midpoint of the circle is in the middle of the screen. The object currently on the perimeter of the circle is highlighted and can be selected. Our preliminary usability evaluation, applying our custom evaluation method designed especially for walking users, indicates that the proposed technique is usable also when walking.     

von Neumann stability analysis of first-order accurate discretization schemes for one-dimensional (1D) and two-dimensional (2D) fluid flow equations

In literature, the von Neumann stability analysis of simplified model equations, such as the wave equation, is typically used to determine stability conditions for the non-linear partial differential fluid flow equations (Navier–Stokes and Euler). However, practical experience suggests that such simplistic stability conditions are grossly inadequate for computations involving the system of coupled flow equations. The goal of this paper is to determine stability conditions for the full system of fluid flow equations – the Euler equations are examined, as any conditions derived for the Euler equations will apply to the Navier–Stokes (NS) equations in the limit of convection-dominated flows. A von Neumann stability analysis is conducted for the one-dimensional (1D) and two-dimensional (2D) Euler equations. The system of equations is discretized on a staggered grid using finite-difference discretization techniques; the use of a staggered grid allows equivalence to finite-volume discretization. By combining the different discretization techniques, ten solution schemes are formulated – eight solution schemes are considered for the 1D Euler equations, and two schemes for the 2D Euler equations. For each scheme, error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum-allowable CFL (Courant–Friedrichs–Lewy) number as a function of Mach number. The predictions are verified for selected schemes using the Riemann problem at incompressible and compressible Mach numbers. Very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, which offer a viable alternative to complicated mathematical expressions often reported in published literature, and should benefit everyday CFD (Computational Fluid Dynamics) users. The stability regions are used to discuss the effect of time integration (explicit vs. implicit), density bias in continuity equation and momentum convection term linearization on stability. A comparison of the predicted stability limits for 1D and 2D Euler equations with commonly-used stability conditions arising from the wave equation shows that the stability thresholds for the Euler equations lie well below those predicted by the wave equation analysis; in addition, the 2D Euler stability limits are more restrictive as compared to 1D Euler limits. Since the present analysis accounts for the full system of fluid flow (Euler) equations, the derived stability conditions can be used by CFD practitioners to estimate a timestep or CFL number to guide the stability of their computations.     

Boundary Element Tearing and Interconnecting Methods

In this paper we introduce the Boundary Element Tearing and Interconnecting (BETI) methods as boundary element counterparts of the well-established Finite Element Tearing and Interconnecting (FETI) methods. In some practical important applications such as far field computations, handling of singularities and moving parts etc., BETI methods have certainly some advantages over their finite element counterparts. This claim is especially true for the sparse versions of the BETI preconditioners resp. methods. Moreover, there is an unified framework for coupling, handling, and analyzing both methods. In particular, the FETI methods can benefit from preconditioning components constructed by boundary element techniques. The first numerical results confirm the efficiency and the robustness predicted by our analysis.     

EMOD2D—a program in C++ for finite difference modelling of magnetotelluric TM mode responses over 2D earth

A program, EMOD2D, in C++, is developed to compute the apparent resistivities of two-dimensional geological structures for magnetotelluric (MT) H-polarization case, using finite difference technique. Five C++ classes with member functions are designed to compute apparent resistivitiy values. The program utilizes object oriented programming features such as multiple inheritance, encapsulation to allow the user to easily deploy and modify the given classes. This program has been used to study the responses of various ore deposit models. This modelling study is relevant to: (i) search for mineral deposits underlying conductive or resistive overburden, (ii) understand the response pattern for the ore body with different depths and conductivities, and (iii) study the response pattern for the ore body when it is in contact and without contact with the overburden. The program is compiled on Borland C++.     

Miniaturized 1D beam switching and 2D printed Yagi-Uda antenna arrays

This article presents a multi-board arrangement of printed Yagi-Uda antennas that can be configured into 1D and 2D arrays. First, a 1 × 4 collinear array is designed and fed with a metamaterial Butler matrix (BM) network to provide beam switching at four azimuthal directions. Slow-wave concept is used in designing the hybrid, crossover and delay sections of BM to achieve a footprint reduction of 67%. The 1 × 4 collinear array with the feed network achieves 8.42–11.7 dBi gain and 21.7–25.7 degrees half power beam width (HPBW) in horizontal plane for the four switched beam patterns at 5.8 GHz in simulations. Second, measurement results of the fabricated 1 × 4 collinear array with its miniaturized feed network confirm a range of 22–27 degrees in HPBW in the horizontal plane. Finally, parasitic structures are designed to reduce antenna coupling and a 3-shelf holder is proposed to stack the 1 × 2 printed Yagi antenna subarray boards in compact 2D planar array configurations. Simulations of the 2 × 4-array demonstrate achieving 13.09 dBi peak gain at 5.8 GHz along with reduction of the HPBW by 24.7 degrees in horizontal plane in comparison with the 1 × 4-array prototype.     

Two-way ambiguity in 2D projective reconstruction from threeuncalibrated 1D images

We show that there is, in general, a two-way ambiguity for 2D projective reconstruction from three uncalibrated 1D views, independent of the number of point correspondences. The two distinct projective reconstructions are exactly related by a quadratic transformation with the three camera centers as fundamental points. Unique 2D reconstruction is possible only when the three camera centers are aligned. By Carlsson duality (1995), there is a dual two-way ambiguity for 2D projective reconstruction from six point correspondences, independent of the number of 1D views. The theoretical results are demonstrated on numerical examples     

Delay-dependent stability and stabilisation of continuous 2D delayed systems with saturating control

This paper deals with the stabilisation problem of continuous two-dimensional (2D) delayed systems, in the presence of saturations on the control signals. For this, a new delay decomposition approach is proposed to deal with the stability and stabilisation issues. The idea is that the range of variation of each delay is divided into segments, and a specific Lyapunov– Krasovskii functional is used that contains different weight matrices in each segment. Then, based on this approach, new delay-dependent stability and stabilisation criteria for continuous 2D delayed systems are derived. These criteria are less conservative and include some existing results as special cases. Some numerical examples are provided to show that a significant improvement is achieved using the proposed approach.     

Phase diagrams for 2D and 3D spin 1 Ising model

We present the study of phase of phase diagrams in spin 1 Ising model for honeycomb, square and simple-cubic lattices using the one-spin cluster approximation. They show re-entrant behaviour in certain ranges of concentration p and different α.     

Lacunarity analysis of raster datasets and 1D, 2D,and 3D point patterns

Spatial scale plays an important role in many fields. As a scale-dependent measure for spatial heterogeneity, lacunarity describes the distribution of gaps within a set at multiple scales. In Earth science, environmental science, and ecology, lacunarity has been increasingly used for multiscale modeling of spatial patterns. This paper presents the development and implementation of a geographic information system (GIS) software extension for lacunarity analysis of raster datasets and 1D, 2D, and 3D point patterns. Depending on the application requirement, lacunarity analysis can be performed in two modes: global mode or local mode. The extension works for: (1) binary (1-bit) and grey-scale datasets in any raster format supported by ArcGIS and (2) 1D, 2D, and 3D point datasets as shapefiles or geodatabase feature classes. For more effective measurement of lacunarity for different patterns or processes in raster datasets, the extension allows users to define an area of interest (AOI) in four different ways, including using a polygon in an existing feature layer. Additionally, directionality can be taken into account when grey-scale datasets are used for local lacunarity analysis. The methodology and graphical user interface (GUI) are described. The application of the extension is demonstrated using both simulated and real datasets, including Brodatz texture images, a Spaceborne Imaging Radar (SIR-C) image, simulated 1D points on a drainage network, and 3D random and clustered point patterns. The options of lacunarity analysis and the effects of polyline arrangement on lacunarity of 1D points are also discussed. Results from sample data suggest that the lacunarity analysis extension can be used for efficient modeling of spatial patterns at multiple scales.     

Parallel 1D and 2D vector quantizers using a Kohonen neural network

The process of reconstructing an original image from a compressed one is a difficult problem, since a large number of original images lead to the same compressed image and solutions to the inverse problem cannot be uniquely determined. Vector quantization is a compression technique that maps an input set of k-dimensional vectors into an output set of k-dimensional vectors, such that the selected output vector is closest to the input vector according to a selected distortion measure. In this paper, we show that adaptive 2D vector quantization of a fast discrete cosine transform of images using Kohonen neural networks outperforms other Kohonen vector quantizers in terms of quality (i.e. less distortion). A parallel implementation of the quantizer on a network of SUN Sparcstations is also presented.     

Intrinsic nonlinear multiscale image decomposition: A 2D empirical mode decomposition-like tool

Many works have been achieved for analyzing images with a multiscale approach. In this paper, an intrinsic and nonlinear multiscale image decomposition is proposed, based on partial differential equations (PDEs) and the image frequency contents. Our model is inspired from the 2D empirical mode decomposition (EMD) for which a theoretical study is quite nonexistent, mainly because the algorithm is based on heuristic and ad hoc elements making its mathematical study hard. This work has three main advantages. Firstly, we prove that the 2D sifting process iterations are consistent with the resolution of a nonlinear PDE, by considering continuous morphological operators to build local upper and lower envelopes of the image extrema. In addition to the fact that now differential calculus can be performed on envelopes, the introduction of such morphological filters eliminates the interpolation dependency that also terribly suffers the method. Also, contrary to former 2D empirical modes, precise mathematical definition for a class of functions are now introduced thanks to the nonlinear PDE derived from the consistency result, and their characterization on the basis of Meyer spaces. Secondly, an intrinsic multiscale image decomposition is introduced based on the image frequency contents; the proposed approach almost captures the essence and philosophy of the 2D EMD and is linked to the well known Absolutely Minimizing Lipschitz Extension model. Lastly, the proposed multiscale decomposition allows a reconstruction of images. The filterbank capability of the new multiscale decomposition algorithm is shown both on synthetic and real images, and results show that our proposed approach improves a lot on the 2D EMD. Moreover, the complexity of the proposed multiscale decomposition is very reduced compared to the 2D EMD by avoiding the surface interpolation approach, which is the core of all 2D EMD algorithms and is very time consuming. For that purpose also, our work will then be a great benefit; especially, in higher dimension spaces.     

LC GRIN lens mode with wide viewing angle for rotatable 2D/3D tablet

To widen the vertical and horizontal angular ranges where the lens performs well, the off‐axis performance of a liquid crystal gradient index (LC GRIN) lens is analyzed by the combined simulation system of an LC director simulator and a ray‐tracing simulator. We found that the angular difference between an LC alignment direction and an electrode array direction of the LC GRIN lens is one of significant parameters, and detailed conditions of structure are established. The measurement result shows that the developed structure reduces the degradation ratio in a luminance profile from 61% to 3.2%. We have applied a user tracking system for the rotatable 3D display, equipped with a detection of a panel orientation and a face position. As a result, we have developed a rotatable 2D/3D tablet whose 3D viewing azimuth angle is over 30° in both landscape and portrait orientations.