Singular Regions Research Articles

Skeletonization of ribbon-like shapes based on regularity and singularity analyses

A major problem with traditional skeletonization algorithms is that their results do not always conform to human perceptions since they often contain unwanted artifacts. This paper presents an indirect skeletonization method to reduce these artifacts. The method is based on analyzing regularities and singularities of shapes. A shape is first partitioned into a set of triangles using the constrained Delaunay triangulation technique. Then, regular and singular regions of the shape are identified from the partitioning. Finally, singular regions are stabilized to produce a better result. Experiments show that skeletons obtained from the proposed method closely resemble human perceptions of the underlying shapes.

Singular full-field stresses in composite laminates with open holes

A method of the superposition of a hybrid and displacement approximation was developed to provide the accurate stress fields in a multilayered composite laminate, including the singular neighborhood of the ply interface and the hole edge. Asymptotic analysis was used to derive the hybrid stress functions. The displacement approximation is based on the polynomial B-spline functions. The method provides the determination of the coefficient of the singular term along with convergent stress components including the singular regions. Reissner’s variational principle was employed. Simple [45/−45] s and quasi-isotropic IM7/5250 [45/90/−45/0] s laminates were analyzed. Uniaxial loading and residual stress calculation (quasi-isotropic laminate) were considered. A convergence study showed that accurate values of the coefficient of the singular term of the asymptotic stress expansion could be obtained with coarse out-of-plane and in-plane subdivisions. The interaction between the singular terms on the neighboring interfaces was found to be important for the convergence with coarse subdivisions. Converged transverse interlaminar stress components as a function of the distance from the hole edge, were shown for all examples.

Inclusive Jet Production in γp and γγ Processes: Direct and Resolved Photon Cross Sections in Next-To-Leading Order QCD

The production of jets in low Q2 ep scattering (photoproduction) and in low Q2 ey+ey− scattering (γγ scattering) allows for testing perturbative QCD and for measuring the proton and photon structure functions. This requires exact theoretical predictions for one- and two-jet cross sections. We describe the theoretical formalism, giving sufficient details, for calculating the direct and resolved processes in γp and γγ reactions in next-to-leading order QCD. We present the complete analytical results for the Born terms, the virtual, and the real corrections. To separate singular and regular regions of phase space we use the phase space slicing method with an invariant mass cut-off. In this way, all soft and collinear singularities are either canceled or absorbed into the structure functions. Using a flexible Monte Carlo program, we evaluate the cross sections numerically and perform various tests and comparisons with other calculations. We consider the scale dependence of our results and compare them to data from the experiments H1 and ZEUS at HERA and OPAL at LEP.

Silicon-induced faceting of vicinal GaAs(001)

This article presents in situ x-ray diffraction studies of the evolution of the morphology of 0.5°-miscut vicinal GaAs(001) surfaces during and following undoped and silicon-doped growth using organometallic vapor-phase epitaxy. Undoped growth leads to ordered monolayer steps. However, growth in the presence of silicon destabilizes this surface morphology and triggers faceting. Coarsening of the facet size proceeds even after the growth has stopped and results in large singular regions of GaAs(001) surface separated by step bunches. Dosing the surface with silicon without growing material does not trigger faceting. Growth of undoped GaAs on faceted surfaces recovers the initial state of ordered monolayer steps.

Asymptotically exact stresses in laminates with a rigid fastener

A method of superposition of a hybrid and displacement approximation has been extended to provide accurate stress fields in a multilayered composite laminate including the singular neighborhood of the ply interface and the edge of a hole containing a rigid fastener. Asymptotic analysis was used to derive the hybrid stress functions. Multiple singular terms at each interface were incorporated. The displacement approximation is based on polynomial B-spline functions. The method provides determination of the coefficient of the singular term along with convergent stress components, including the singular regions. Reissner's variational principle was employed. Coefficients of the singular term of the asymptotic expansion were determined for a [45/-45] s laminate under bearing loading introduced through a rigid fastener.

Motion Control Strategy for Robot Manipulators in the Neighbourhood of Singularities

This work presents a control strategy applied to robot manipulators operating close to kinematic singularities. Considering the robot to be in contact with the environment, a PD controller is iInplelnented with inverse dynamics compensation to control the robot manipulator. In order to accomlTIodate the forces originated froln the interaction with the environment, the control systelTI includes an impedance loop that modifies the robot's references accordingly. In the vicinity of a singularity, the algorithm generates a fictitious force to which a second impedance function is applied. This causes a small deviation to the original robot trajectory to avoid the singularity region. The algoritlun is based on the minimwn singular value of the Jacobian matrix in order to generate the module and direction of the fictitious force. This strategy is applied to a teleoperation system without time delay

Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms

This paper presents a study of kinematic and force singularities in parallel manipulators and closed-loop mechanisms and their relationship to accessibility and controllability of such manipulators and closed-loop mechanisms. Parallel manipulators and closed-loop mechanisms are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace are obtained by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques in Cartesian space. The regions in the workspace which violate the small time local controllability (STLC) and small time local accessibility (STLA) condition are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie algebra. We show that for fully actuated manipulators when the number of actuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator does not meet the STLC requirement. For the case where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and non-STLC regions in the workspace of a parallel manipulator and closed-loop mechanism can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and non-STLC/non-STLA regions of parallel manipulators and closed-loop mechanisms belonging to the above mentioned classes.

Functional renormalization description of the roughening transition

We reconsider the problem of the static thermal roughening of an elastic manifold at the critical dimension $d=2$ in a periodic potential, using a perturbative Functional Renormalization Group approach. Our aim is to describe the effective potential seen by the manifold below the roughening temperature on large length scales. We obtain analytically a flow equation for the potential and surface tension of the manifold, valid at all temperatures. On a length scale $L$, the renormalized potential is made up of a succession of quasi parabolic wells, matching onto one another in a singular region of width $\sim L^{-6/5}$ for large $L$. We also obtain numerically the step energy as a function of temperature, and relate our results to the existing experimental data on $^4$He. Finally, we sketch the scenario expected for an arbitrary dimension $d<2$ and examine the case of a non local elasticity which is realized physically for the contact line.

Supersymmetric domain wall world from D=5 simple gauged supergravity

We address a supersymmetric embedding of domain walls with asymptotically anti-deSitter (AdS) space-times in five-dimensional simple, N=2 U(1) gauged supergravity theory constructed by Gunaydin, Townsend and Sierra. These conformally flat solutions interpolate between supersymmetric AdS vacua, satisfy the Killing spinor (first order) differential equations, and the four-dimensional world on the domain wall is a flat world with N=1 supersymmetry. Regular solutions in this class have the energy density related to the cosmological constants of the supersymmetric AdS vacua. An analysis of such solutions is given for the example of one (real, neutral) vector supermultiplet with the most general form of the prepotential. There are at most two supersymmetric AdS vacua that are in general separated by a singularity in the potential. Nevertheless the supersymmetric domain wall solution exists with the scalar field interpolating continuously across the singular region.

Analysis of singular regions in bonded joints

Singular regions in bonded joints with geometric and material stress singularities are studied by expressing the displacement and stress fields in the neighborhood of the singularity by means of eigenfunction expansions which are in terms of unknown coefficients. These coefficients are found by matching displacements with those from a finite element analysis at points remote from the singularity. Expressions for the eigenfunction expansions are given explicitly for bonded joints with and without fillets (closed and open wedges). The results are not limited to stress intensity factors at the point of singularity, but can include stress values at any point near the singularity. It was found that two singular terms exist in all cases, and that, for joints with adhesive fillets and E 1/E 2>7, failure is governed by the term associated with the second lowest eigenvalue, while the lowest eigenvalue controls the failure of joints without fillets. It was also found that the calculation of stresses using only the singular terms provided a good approximation to the actual stresses over a distance of about one-fifth the adhesive thickness. The method was also used in conjunction with the Erdogan–Sih maximum stress failure criterion to determine the initial angle of crack propagation for bonded joints with and without fillets. This revealed that the direction of the maximum principal stress in the adhesive, which is also the direction of crack propagation, for joints with fillets remains essentially constant beyond a very small region near the point of singularity, while for joints without fillets crack propagation always occurs in a direction parallel to the adhesive/adherend interface.

TEST OF THE EMPIRICAL GREEN'S FUNCTION DECONVOLUTION ON VRANCEA (ROMANIA) SUBCRUSTAL EARTHQUAKES

Vrancea is one of the few singular seismic regions of the world where intermediate-depth earthquakes are permanently generated (around 10 events/month with M L > 3) within an extremely confined focal volume. This particularity and the relatively large number of short-period waveforms recorded by the Romanian local network provides us the opportunity to test the performance of the empirical Green's function technique in retrieving the source time function and source directivity of the Vrancea earthquakes. Three earthquakes that occurred on March 11, 1983 (M L = 5.4), April 12, 1983 (M L = 5.1) and August 7, 1984 (M L = 5.1) in the lower part of the subducting lithosphere (h ≍ 150 km) were analyzed. A set of 28 adjacent events (3.0 < M L < 4.4) which occurred between 1981 and 1997 were selected as corresponding empirical Green's functions. To test the confidence of the retrieved source time function, we compare the deconvolved pulses using Green's functions of different sizes and recorded simultaneously by short-period and broad-band instruments. Our tests show that the durations of the source time function is well-constrained and is not affected by the limited frequency range of the short-period instruments, or by the relative difference in the focal mechanism between the main event and Green's event. The apparent duration of the source time function outlines source directivity effects, and when these effects are sufficiently strong, they can identify the real fault plane. Relatively short source duration and correspondingly high stress drop values are in agreement with other previous results emphasizing a specific seismic regime in the lower part of the Vrancea subducting lithosphere.

A neural network strategy for end-point optimization of batch processes

The traditional way of operating batch processes has been to utilize an open-loop “golden recipe”. However, there can be substantial batch to batch variation in process conditions and this open-loop strategy can lead to non-optimal operation. In this paper, a new approach is presented for end-point optimization of batch processes by utilizing neural networks. This strategy involves the training of two neural networks; one to predict switching times and the other to predict the input profile in the singular region. This approach alleviates the computational problems assocaiated with the classical Pontryagin's approach and the nonlinear programming approach. The efficacy of this scheme is illustrated via simulation of a fed-batch fermentation.

The Structure of the Extreme Schwarzschild-de Sitter Space-time

The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global structure of this space-time is here analyzed in detail. Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented. The permitted geodesic motions are also analyzed. By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram. The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.

The deformed two-dimensional black hole

A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal. The singularity present in the classical geometry is resolved by the deformation, so that propagation of a wave-packet can be continued through the classically singular region, ultimately reaching another asymptotically “flat” region.

More process simulation in singular regions

The behavior of Newton-based equation-solving methods in regions containing saddle points is studied. It is shown that saddle points can cause Newton's method to settle into periodic or aperiodic orbits or diverge. To improve reliability and computational efficiency, a quadratic acceleration technique is used in the context of a complex domain trust region method together with approximate eigendecomposition in these and other singular regions. The quadratic acceleration technique gives rapid convergence to saddle points while the approximate eigenvalue-eigenvector decomposition provides a path from any saddle point to a solution. A numerical example for a binary mixture with retrograde behavior is used to illustrate the key features of the algorithm.

A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds. Part 2: Experimental

Using the epoxy-aluminum wedge specimens defined and analyzed in Part 1, we measure the number of cycles required to initiate an interfacial fatigue crack near the apex, where the stress field is predicted to be singular. The eigenvalue, λ, and the generalized stress intensity factor, Q, are varied via the wedge angle, and via the beam deflection, respectively. Crack initiation is detected using a strain gage bonded near the tip of the wedge. Following the methodology developed in Part 1, the fatigue data are then used to construct a fatigue initiation criterion characteristic of the bimaterial interface. This criterion is a 3-D surface, with the ordinate representing the generalized stress intensity factor and the two horizontal axes representing the number of cycles to initiation and the eigenvalue, respectively. Three key assumptions of the model are found to be satisfied in the specimens tested herein: (1) geometric imperfections at the apex are smaller than the singular region, (2) the plastic zones near the apex are also smaller than the singular region, and (3) the locus of initiation is near interfacial. Finally, a thermomechanical analysis indicates that the residual thermal stresses generated during the fabrication process make a significant contribution to the critical stress intensity factor. With high Tg adhesives and under unfavorable conditions (high modulus, high CTE, poor adhesion), we predict that the residual stresses alone could be sufficient to cause debond initiation.

Nonlinear anomalies of conducting media with conical microconstrictions

An investigation is made of the divergence of the higher moments of the field in conducting structures with conical singular regions. Calculations are made of the critical values of the parameters which determine the nonlinear anomalies of a medium.

Energy constraints in forced recirculating MHD flows

We are concerned here with forced steady recirculating flows which are laminar, two-dimensional and have a high Reynolds number. The body force is considered to be prescribed and independent of the flow, a situation which arises frequently in magnetohydrodynamics. Such flows are subject to a strong constraint. Specifically, the body force generates kinetic energy throughout the flow field, yet dissipation is confined to narrow singular regions such as boundary layers. If the flow is to achieve a steady state, then the kinetic energy which is continually generated within the bulk of the flow must find its way to the dissipative regions. Now the distribution of u2/2 is governed by a transport equation, in which the only cross-stream transport of energy is diffusion, v∇2 (u2/2). It follows that there are only two possible candidates for the transport of energy to the dissipative regions: the energy could be diffused to the shear layers, or else it could be convected to the shear layers through entrainment of the streamlines. We investigate both options and show that neither is a likely candidate at high Reynolds number. We then describe numerical experiments for a model problem designed to resolve these issues. We show that, at least for our model problem, no stable steady solution exists at high Reynolds number. Rather, as soon as the Reynolds number exceeds a modest value of around 10, the flow becomes unstable via a supercritical Hopf bifurcation.

Green’s functions for inhomogeneous weakly anisotropic media

Summary Formulae for the zeroth-order principal term plus the first-order additional term of the qP- and qS-wave Green’s functions in the so-called quasi-isotropic (QI) approximation are derived for an unbounded inhomogeneous weakly anisotropic medium. The basic idea of this approximation is to seek the asymptotic solution of the elastodynamic equation as an expansion with respect to two small parameters of the same order: the small parameter used in the standard ray method and a parameter characterizing differences of tensors of elastic parameters of a weakly anisotropic medium and of a nearby ‘background’ isotropic medium. As a result, the procedure of constructing the Green’s functions is split into two steps: (1) calculation of rays, traveltimes, the geometrical spreading and polarization vectors in the background isotropic medium; (2) calculation of corrections of traveltimes, amplitudes and polarization vectors due to the deviation of the weakly anisotropic medium from the isotropic background. Application of the QI approximation to qP-wave propagation leads to useful simplified formulae found earlier by the application of the perturbation methods. Application of the QI approximation to qS-wave propagation leads to formulae of basic importance. The zeroth-order QI approximation removes the well-known problems of the standard ray method for anisotropic media and gives regular solutions for regions in which the differences between the phase velocities of qS waves in the direction of propagation are small. This is the case for weakly anisotropic media as well as for singular regions of qS waves such as in the vicinities of kiss and intersection singularities, for example. In such situations, frequency-dependent amplitudes of the qS waves in the zeroth-order QI approximation are obtained by a νmerical solution of two coupled first-order ordinary differential equations along a ray in the background isotropic medium. When a medium is strongly anisotropic and/or high frequencies are considered, approximate closed-form solutions of the two coupled differential equations have the form of the ray solutions describing two decoupled qS waves. The standard ray method for anisotropic media can substitute the QI approximation in such regions. On the other hand, in the limit of infinitely weak anisotropy, the formulae for the QI approximation smoothly converge to formulae for isotropic media. Thus the QI approximation represents a link between ray formulae for anisotropic and isotropic media. The formulae for the zeroth-order QI approximation are regular everywhere except for singular regions of the ray method for isotropic media. The accuracy of the QI approximation can be increased by considering the first-order additional terms of the QI approximation. The two coupled differential equations are equivalent to the equations of the coupling ray theory (CRT) based on a simplification of a coupling volume integral. Use of a vectorial framework along rays in the background medium that is different in the QI approximation from that used in the CRT avoids some problems of the CRT approach. The QI approximation including the first-order additional terms is expected to yield results of comparable quality to or better quality than those of the CRT. The equivalence of the zeroth-order QI approximation to the CRT promises acceptable results of the QI approximation not only in weakly anisotropic media but also in singular regions of qS waves.

The Details of Combustion of Ammonium Perchlorate Propellants: Leading Edge Flame Detachment

The transition from particle flamelet burning to premixed flame burning of ammonium perchlorate (AP)/hydrocarbon (HC) binder propellants is identified with detachment of the oxidizer/fuel (O/F) flamelet from the stoichiometric tip of the diffusion field over the AP particle. The conditions (pressure, particle area, local stoichiometry) for detachment are revealed by singular regions of the burning rate versus pressure curves for selected bimodal propellants.