Singular Regions Research Articles

Boundary element analysis of the stress field at the singularity lines in three-dimensional bonded joints under thermal loading

The stress distribution near a point on the stress singularity line of dissimilar materials in three-dimensional joints under thermal loading are investigated using BEM based on Rongved’s fundamental solutions. Stress distributions for the material combinations in the singularity region, in the no singularity region, and in the boundary between them on the Dundurs composite plane are investigated. The influences of thermal expansion coefficients, loading conditions and dimensions on the stress distribution in three-dimensional joints composed of two blocks are examined. The stress intensity factors in threedimensional joints under a uniform change in temperature are proportional to the temperature variation, 1T, and depend on the difference in the thermal expansion coefficients. Furthermore, the level of the stress distributions around the stress singularity lines also increases significantly as the length of one side in the parallel cross section to the interface decreases. Stress singularities at the interface in the bonded joints of dissimilar materials are induced by mechanical loading or thermal loading. Thermal stresses are caused by differences in elastic properties and thermal expansion coefficients in dissimilar materials joints. The stress singularities exist not only at the vertex in three-dimensional joints of dissimilar materials but also along the intersection of the interface with its free surfaces. The cross line has been referred to as the stress singularity line. Li et al. [1992] reported the results of stress analysis for dissimilar materials using three-dimensional BEM based on Kelvin’s fundamental solutions. In the analysis, the interface must be divided using very fine meshes along the stress singularity lines, and hugely memory- and time-consuming procedures are required for accurate analysis. Then, Koguchi [1997] investigated the stress singularity in three-dimensional bonded joints using three-dimensional BEM based on Rongved’s fundamental solutions. Rongved’s fundamental solutions [Rongved 1955] satisfy boundary conditions at the interface. Therefore, the number of nodes and elements necessary for accurate analysis decreases, because the BEM based on Rongved’s fundamental solutions does not require the interface area of dissimilar materials joints to be divided into elements. Koguchi et al. [2003] also used the fundamental solution for two-phase transversely isotropic materials to investigate the stress singularity fields in three-dimensional bonded joints using three-dimensional BEM. Furthermore, Prukvilailert and Koguchi [2005] reported on stress singularity analysis around a point on the stress singularity line in three-dimensional bonded joints using three-dimensional BEM based on Rongved’s fundamental solutions. However, this previous research focused only on the stress

A state event detection algorithm for numerically simulating hybrid systems with model singularities

This article describes an algorithm for detecting the occurrence of events, which signify discontinuities in the first derivative of the state variables, while simulating a set of nonsmooth differential equations. Such combined-discrete continuous systems arise in many contexts and are often referred to as hybrid systems, switched systems, or nonsmooth systems. In all cases, the state events are triggered at simulated times which generate states corresponding to the zeros of some algebraic “event” function. It has been noted that all existing simulators are prone to failure when these events occur in the neighborhood of model singularities---regions of the state space where the right-hand side of the differential equation is undefined. Such model singularities are often the impetus for using nonsmooth models in the first place. This failure occurs because existing algorithms blindly attempt to interpolate across singular regions, checking for possible events after the fact. The event detection algorithm described here overcomes this limitation using an approach inspired by feedback control theory. A carefully constructed extrapolation polynomial is used to select the integration step size by checking for potential future events, avoiding the need to evaluate the differential equation in potentially singular regions. It is shown that this alternate approach gives added functionality with little impact on the simulation efficiency.

Self-energy corrections to anisotropic Fermi surfaces

The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper-oxide superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is nontrivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.

Bounded differential games guidance law for dual-controlled missiles

A new guidance law tailored for an interceptor missile having forward and aft controls is proposed. The guidance law is derived using a differential games formulation with bounded controls. For the derivation, the interceptor closed-loop dynamics is represented by two first-order bi-proper transfer functions. Possible game-space structures are investigated, including a new one with two closed singular regions. The effect of the direct lift associated with the canard and tail controls is investigated, and it is proved that zero miss distance can always be guaranteed for some initial conditions. It is also shown that for the tail control a switching surface at some constant time before interception exists in the game-space, resulting from its nonminimum-phase nature.

Fibonacci grids: A novel approach to global modelling

Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude–longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges); (iv) ease of parallelization. One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as ‘Fibonacci grids’. These grids possess virtually uniform and isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of this type of grid in shallow-water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional weather prediction or climate models. © Crown copyright, 2006. Royal Meteorological Society

Singular sources in Demiański–Newman spacetimes

The analysis of singular regions in the NUT solutions carried out in the recent paper (Manko and Ruiz 2005 Class. Quantum Grav. 22 3555) is now extended to Demiański–Newman (DN) vacuum and electrovacuum spacetimes. We show that the effect which produces the NUT parameter in a more general situation remains essentially the same as in the purely NUT solutions: it introduces the semi-infinite singularities of infinite angular momenta and positive or negative masses depending on the interrelations between the parameters; the presence of the electromagnetic field endows the singularities additionally with electric and magnetic charges. The exact formulae describing the mass, charges and angular momentum distributions in the Demiański–Newman solutions are obtained, and concise general expressions Pn = (m + iν)(ia)n, Qn = (q + ib)(ia)n for the entire set of the corresponding Beig–Simon multipole moments are derived. These moments correspond to a unique choice of the integration constant in the expression of the metric function ω which is different from the original choice made by Demiański and Newman.

Segmentation of discrete vector fields

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Semiclassical propagator and van Vleck determinant in a mixed position–momentum space

In this paper a semiclassical propagator in a mixed position–momentum space is derived in the formalism of Maslov's multi-dimensional semiclassical theory. The corresponding mixed van Vleck determinant is also given explicitly. The propagator can be used to locally fix semiclassical divergences in singular regions of configuration space. It is shown that when a semiclassical propagator is transformed from one representation to another, its form is invariant.

PVT Growth at High Temperatures

Physical vapor transport (PVT) growth method was used to grow bulk crystals of AlN and thick epitaxial SiC films on on-axis Si-face 4H-SiC(0001) substrates from the powder source materials. Both bulk and thick film crystals were characterized by scanning electron microscopy (SEM), which showed a surface morphology did not have any observable growth defects or cracking. We observed nice hexagonal growth morphology a typical characteristic of diffusion-limited growth. River-patterns free from micro bubbles and micro voids were observed on the as grown surface. An XRD rocking curve measured the FWHM as 51.0 arc seconds and a reciprocal space map showed a singular intense region that is attributed to the high quality homoepitaxial SiC film. A similar value was observed for small AlN crystals also.

Bifurcation analysis and control in Turbo decoding algorithm

Turbo Codes can approach the Shannon limit very closely with the help of its special iterative decoding algorithm. This paper establishes a nonlinear dynamic system to analyze the relationship between Turbo decoding output and the number of iterations. Here, the number of iterations is taken as the time axis, decoding output as the state variable, SNR and information bits N as system parameters. It is shown that with SNR increasing, the decoding algorithm undergoes three stages, namely the indecisive fix-point, singular region and unequivocal fix-point. Bifurcations occur during the transformation from the indecisive fix-point to the singular region. It is first proposed that fold, period doubling and Neimark-Sacker bifurcation all have the possibility to occur, depending on the value of N. In the singular region, phase trajectories may appear as period-two, period-three, quasiperiod and chaos. This paper first observed and confirmed the existence of period-three and chaos. Singular region deteriorates the performance of Turbo codes under low SNR. This paper proposes a time-delay feedback control method to stablize the fix-point. Simulation results show that this method achieves 0.1—0.3 dB improvement for Turbo codes under low SNR condition.

Investigation of structure and energy of edge dislocation in bcc iron

Based on the theory of dislocations, we have constructed the four models of the 〈100〉{010}, 〈100〉{011}, 1/2〈111〉{011} and 1/2〈111〉{112} edge dislocations in bcc Fe using the molecular dynamics method, and the formation energy, core energy and core radius of the dislocations have been calculated respectively. The calculated results indicated that the formation energies of 〈100〉{010} and 〈100〉{011} edge dislocations are higher than those of 1/2〈111〉{011} and 1/2〈111〉{112} edge dislocations. This shows that the formation of 1/2〈111〉 edge dislocation is easier than that of 〈100〉 edge dislocation. However, the core radii of 〈100〉{010} and 〈100〉{011} edge dislocations are smaller than those of 1/2〈111〉{011} and 1/2〈111〉{112} edge dislocations. This shows that the atomic numbers locating at the singular region in the 1/2〈111〉 edge dislocation are greater than those in 〈100〉 edge dislocation. Therefore, the motion of 1/2〈111〉 edge dislocation is easier than that of 〈100〉 edge dislocation.

Task reconstruction method for real-time singularity avoidance for robotic manipulators

The kinematic (KS) and algorithmic singularities (AS) in controlling robotic manipulators have been investigated intensively because they are not predictable or difficult to avoid. The problem with handling these singularities is an unnecessary performance reduction in the non-singular region and the difficulty in performance tuning. In this paper, we propose a method of avoiding KS and AS by applying a task reconstruction approach while maximizing the task performance by calculating singularity measures. The proposed method is implemented by removing the component approaching the singularity calculated by using a singularity measure in real-time. The outstanding feature of the proposed task reconstruction (TR) method is that it is based on a local TR as opposed to the local joint reconstruction of many other approaches. This method has a dynamic task priority assignment feature which ensures system stability under singular regions due to the change of task priority. The TR method enables us to increase the task controller gain to improve the task performance, whereas this increase can destabilize the system for conventional algorithms in real experiments. In addition, the physical meaning of tuning parameters is very straightforward. Hence, we can maximize task performance even near the singular region while simultaneously obtaining the singularity-free motion. The advantage of the proposed method is experimentally tested by using a 7-d. o. f. spatial manipulator and the result shows that the new method improves the performance several times over the existing algorithms.

Coarse-Grid Processing Based Load Balancing for Maximizing the Performance of Parallel 3D LIC for Large Vector Field Visualization

Despite its proven usefulness for vector field visualization, LIC requires large amounts of processing power and memory. Parallel processing is an effective approach for computational intensive problems, however in the case of LIC it can suffer from workload imbalance depending on the distribution and orientation of the vectors elements in a given vector field. Specifically, elements of the boundary and singularity regions have the potential to cause workload imbalance, therefore affecting the parallel processing performance. In this paper, we propose and evaluate a coarse-grid pre-processing based load balancing method for minimizing this undesirable performance loss. By utilizing the same LIC algorithm in both pre-processing and final LIC computation stages, we can avoid redundant computations and minimize the impact of the pre-processing stage on the total LIC computation time. Since this method does not influence the original LIC algorithm, it is expected to work along with other enhancements proposed for LIC. We verified the effectiveness of the proposed method for maximizing the performance of parallel 3D LIC.

Effect of material gradation on K-dominance of fracture specimens

This work describes the effect of material gradation (parallel to the crack plane) on stress intensity factors and K-dominance, i.e. the dominance of the singular region, of fracture specimens; SE(T), SE(B) and C(T). The extent of K-dominance is investigated by comparing the actual stress field with the Williams’ asymptotic stress field. Linear-elastic finite element analyses are performed using graded elements which incorporate graded material properties at the element level. Material gradation and crack geometry are systematically varied to perform the parametric study. Results reveal that the effect of material gradation on K I is most pronounced when a short crack is located on the stiffer side of the fracture specimen. For a given specimen and crack geometry, the extent of K-dominance yields a curve with a peak point at a certain material gradation. Results of the present study provide valuable insight into the K-dominance of FGMs.

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random $S=1$ antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, $z$, and $z=1$ signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.

Capture Conditions in a Pursuit-Evasion Game between Players with Biproper Dynamics1

Capture conditions in a planar pursuit-evasion game between a guided missile and its aerial target, each having either forward control or tail control, are derived analytically. The adversaries closed-loop maneuver dynamics are represented by first-order biproper transfer functions. A distinction is made between open and closed capture zones in the reduced-order game space. It is shown that locating the control surface forward, instead of aft, provides considerable advantages with regard to the existence and size of different capture zones. A new game space decomposition with two singular regions is also presented and the conditions for its existence are given.

The tachyon at the end of the universe

We show that a tachyon condensate phase replaces the spacelike singularity in certain cosmological and black hole spacetimes in string theory. We analyze explicitly a set of examples with flat spatial slices in various dimensions which have a winding tachyon condensate, using worldsheet path integral methods from Liouville theory. In a vacuum with no excitations above the tachyon background in the would-be singular region, we analyze the production of closed strings in the resulting state in the bulk of spacetime. We find a thermal result reminiscent of the Hartle-Hawking state, with tunably small energy density. The amplitudes exhibit a self-consistent truncation of support to the weakly-coupled small-tachyon region of spacetime. We argue that the background is accordingly robust against back reaction, and that the resulting string theory amplitudes are perturbatively finite, indicating a resolution of the singularity and a mechanism to start or end time in string theory. Finally, we discuss the generalization of these methods to examples with positively curved spatial slices.

Crustal velocity and Moho structure beneath the Gulf of Corinth, Greece

The Gulf of Corinth (GOC), Greece is a continental rift with high rates of seismicity and extensional strain. How this strain is accommodated in the crust and whether there are variations in the mechanism along strike remain open questions, in part because of a lack of wide-angle reflection/refraction studies that constrain crustal velocity structure. In 2001, an extensive multichannel seismic survey was conducted within the GOC, one component of which included the wide-angle recording of sources from within the gulf at stations on land surrounding the gulf. In this paper we use wide-angle data in two separate, but allied, studies to constrain crustal velocities and depth to the Moho. A 2-D inversion of refraction and reflection traveltimes along an axial profile through the GOC constrains the shallow crustal velocity structure, images the Moho at 29 km depth in the east, dipping to 39 km in the west, and images the eastward subducting African slab beneath the western GOC at a depth of 74 km. The 1-D average of the 2-D velocity model was used in a tomographic inversion of PmP reflection times to solve for depth to the Moho throughout the Corinth region. This model shows generally thick, isostatically compensated crust (≥37 km) beneath the Hellenide Mountains, except immediately south of the GOC, and a singular region of thin crust (<30 km) beneath the Perahora Peninsula at the eastern end of the gulf. A comparison with Moho depths derived from gravity inversion shows a general agreement with crust thickening from east to west, but a number of differences in detail. The 3-D crustal thickness variations are more complex than those predicted by either pure shear or simple shear models of continental extension and suggest significant pre-rift structural variability.

A procedure to correct the effects of a relative delay between the quadrature components of radar signals at base band

Abstract. The real and imaginary parts of baseband signals are obtained from a real narrow-band signal by quadrature mixing, i.e. by mixing with cosine and sine signals at the narrow band's selected center frequency. We address the consequences of a delay between the outputs of the quadrature mixer, which arise when digital samples of the quadrature baseband signals are not synchronised, i.e. when the real and imaginary components have been shifted by one or more samples with respect to each other. Through analytical considerations and simulations of such an error on different synthetic signals, we show how this error can be expected to afflict different measurements. In addition, we show the effect of the error on actual incoherent scatter radar data obtained by two different digital receiver systems used in parallel at the EISCAT Svalbard Radar (ESR). The analytical considerations indicate a procedure to correct the error, albeit with some limitations due to a small singular region. We demonstrate the correction procedure on actually afflicted data and compare the results to simultaneously acquired unafflicted data. We also discuss the possible data analysis strategies, including some that avoid dealing directly with the singular region mentioned above.

Interface Effects and Coherent Waves in Porous Elastic Media

Results concerning the behavior of interfaces in the presence of multiple scattering are obtained here for the first time. To characterize interface effects, we consider an elastic slab of finite thickness containing a random distribution of circular cylindrical cavities. Using elasticity theory, and taking first-order multiple scattering effects between cavities into account, we obtain two new results. First, inside the slab, within one cavity-diameter from the two slab boundaries, the coherent displacement is strongly inhomogeneous (with singular first and second derivatives). Second, inside the slab, away from the preceding singular regions, the coherent displacement is governed by a complex-valued wavenumber (which is independent of slab thickness). Exhaustive analytical work, together with time-consuming finely-tuned numerical work, has been performed, which has allowed us to evaluate the complex-valued wavenumber. We plot the corresponding speed and attenuation as functions of frequency for various cavity densities. This work will help researchers improve the precision of ultrasound technologies in materials engineering or biomaterials engineering.