Occurrence Of Singularities Research Articles

Raving Sibyls, signifying Gods: Noise and sense in Heraclitus fragments 92 and 93

Both animals and humans make sounds. And yet, could there be something that is no more than the sound of an animal? This question opens up two domains of inquiry: the first concerns the relationship between sound and speech and the second between sound and sense, where sense designates the realm of meaning. The interesting problem posed by noise does not concern the obvious difference between noise and words but the possible one between noise and sense. While a distinction may need to be drawn between that which has meaning, even if it is a meaning to be discovered, and that which can be attributed meaning, the liminal can have a decisive quality. A snarl be it animal or human is neither fully meaningful nor mere noise. The snarl hovers at the edge. The edge is the limit condition at which claims of sense are negotiated. The comprehension of both noise and speech involves this limit. What this entails is that noise and speech are not to be understood in terms of an opposition. Identity emerges through what can be described as an operational liminality. The task therefore is to understand noise in terms of this operation. Moreover, it will be an operative quality marked by continuity and as such cannot be understood as though it were only a singular occurrence. Rather than treat this as an abstract problem, its presence in the writings of Heraclitus will be the point of focus of this paper.

The Democratic Impact of International Organizations

Democracy from Above: Regional Organization and Democratization. By Jon C. Pevehouse. Cambridge: Cambridge University Press, 2005. 262 pp., $75.00 cloth (ISBN: 0-521-84482-7), $29.99 paper (ISBN: 0-521-60658-6). In Democracy from Above , Jon C. Pevehouse looks at the impact of regional international organizations (IOs) on the domestic processes involved in the transition to and consolidation of democracy. Taking as its point of departure the observation that international factors have traditionally been neglected in democratization studies, this book is an impressive attempt to bridge insights from international relations and comparative politics in a theoretically and methodologically rigorous manner, using numerous empirical examples. Democracy from Above demonstrates Pevehouse's awareness of several ongoing debates within international relations and political science as well as his ability to discuss critically this vast body of literature. The book is situated in part within the literature on international regimes and international cooperation. In this respect, Pevehouse's approach is unabashedly neoliberal. Indeed, the book includes a critique of the realist and neorealist rejection of the role and autonomy of IOs (pp. 51–56) and hence of their capacity to exert pressure on states to democratize. Of course, Democracy from Above also speaks to the vast literature on comparative democratization. In this context, it criticizes to the so-called actor-oriented approach, which emphasizes the role of individuals and of unanticipated, singular occurrences—or path dependence—in democratization processes (for example, Karl 1990; Karl and Schmitter 1991). Pevehouse …

Viscosity contrast effects on fingering formation in rotating Hele-Shaw flows

The different finger morphologies that arise at the interface separating two immiscible fluids in a rotating Hele-Shaw cell are studied numerically. The whole range of viscosity contrast is analyzed and a variety of fingering patterns systematically introduced, including the case in which the inner fluid is less viscous than the outer one. Our numerical results demonstrate that both the magnitude and the sign of the viscosity contrast strongly affect the shape of the emerging fingers, and also their length distribution. We have also found that the occurrence and location of pinch-off singularities are remarkably modified when the inner fluid is less viscous: instead of generating an isolated detaching drop, a full finger is disconnected from the interface. Finally, we have verified that the finger competition phenomena revealed by our simulations are correctly predicted by a weakly nonlinear analysis of the pattern development, showing that such important finger competition dynamics is already set at relatively early stages of interfacial evolution.

Endangered sounds: a sound project

endangered sounds is a project that focuses on the exploration of sound marks (trade-marked sounds). the initial stage of this project was funded by arts victoria, and comprised legal searches that resulted in the listings of sound marks registered in australasia and the united states of america. this list was published on the internet with a call for volunteers to collect samples of the listed sounds internationally. the volunteer was sent a specimen tube with label and cap, and asked to collect the sound by placing the specimen tube close to the source (thereby capturing the air through which the sound travelled), securing the cap and then completing the label, documenting the time, place and nature of the sound (sound mark reg. no., sound mark description, time of capture, date of capture, location, etc.). these specimen tubes were collected and displayed in chemistry racks in the exhibition in the biennale of electronic arts, perth in 2004, illustrating the frequency and diversity of the environment into which these ‘private’, protected sounds have been released. the exhibition project consisted of:(1) a web portal listing all the sound marks listed in australasia and the usa, and negotiations are underway to expand that to include the eu.(2) a collection of sound marks in specimen tubes with caps and labels gathered internationally by people who volunteered to collect samples of sound marks in their environment.(3) a number of glass vacuum desiccator vessels containing a small loudspeaker and sound reproduction chip suspended in a vacuum, reproducing sound marks in the vacuum, notionally breaking the law, but as sound does not travel in a vacuum the gallery visitor hears no sound – what then is the jurisdiction of the sound mark?(4) a card index register of lost and deceased sounds.this project questions the legitimacy of privatising and protecting sounds that are released at random in public spaces. if i own a multi-million dollar penthouse in a city, and work night shifts, i have no recourse against the loud harley davidson or australian football league (afl) siren that wakes me from my precious sleep – both sounds are privately protected, making their recording, reproduction and broadcast illegal.while there are legal mechanisms for protection against repeat offenders, and many of us are committed to a culturally conditioned moral obligation re sound dispersion, there are no legal limits – i can call the police, but the football siren is already within legal standards and still permeates the private domain of city dwellings. the noise abatement legislation is only applicable to regular breaches of the law, and takes some time to sort out, but it does not apply to singular occurrences which, although within legislated limits, still disturb. additionally, the laws are based on amplitude and do not really address the issue of propagation. the ownership of the sound is not addressed in these legislative mechanisms – it should be; if the sound is an emblem of corporate identity, we should be able to choose not to be exposed to it, in the same way that we can place a ‘no junk mail’ sign on our letter boxes. acknowledgement of the private domain is sacrosanct in other areas of legislation, in fact heavily policed, but not addressed in discussions of the acoustic environment beyond amplitude limitations.

INHOMOGENEOUS DUST COLLAPSE WITH COSMOLOGICAL CONSTANT

We investigate the occurrence of naked singularities in the gravitational collapse of an inhomogeneous dust cloud in an expanding de Sitter background — a piece of Tolman–Bondi–de Sitter space–time. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. Our result unambiguously support the fact that the asymptotic flatness of space–time is not a necessary ingredient for the development of naked singularities.

Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I

First-order system least squares (FOSLS) is a recently developed methodology for solving partial differential equations. Among its advantages are that the finite element spaces are not restricted by the inf-sup condition imposed, for example, on mixed methods and that the least-squares functional itself serves as an appropriate error measure. This paper studies the FOSLS approach for scalar second-order elliptic boundary value problems with discontinuous coefficients, irregular boundaries, and mixed boundary conditions. A least-squares functional is defined, and ellipticity is established in a natural norm of an appropriately scaled least-squares bilinear form. For some geometries, this ellipticity is independent of the size of the jumps in the coefficients. The occurrence of singularities at interface corners, cross points, reentrant corners, and irregular boundary points is discussed, and a basis of singular functions with local support around singular points is established. A companion paper shows that the singular basis functions can be added at little extra cost and lead to optimal performance of standard finite element discretization and multilevel solver techniques, also independent of the size of coefficient jumps for some geometries.

Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part II

First-order system least squares (FOSLS) is a methodology that offers an alternative to standard methods for solving partial differential equations. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. In a companion paper [M. Berndt, T. A. Manteuffel, S. F. McCormick, and G. Starke, Analysis of first-order system least squares ({FOSLS}) for elliptic problems with discontinuous coefficients: Part I, SIAM J. Numer. Anal., 43 (2005), pp. 386--408], ellipticity of an appropriately scaled least-squares bilinear form is established in a natural norm. For some geometries this ellipticity is independent of the size of the jumps in the coefficients. The occurrence of singularities at interface corners, cross-points, reentrant corners, and irregular boundary points is discussed, and a basis of singular functions with local support around singular points is established. This paper describes a method for including discrete versions of the singular basis functions together with standard finite element spaces in a least-squares format at little additional computational cost. The singular basis functions are constructed to match the jump conditions that arise at interfaces between regions of continuity of the diffusion coefficient. Because these basis functions must be approximated in practice, the resulting discretization is by nature nonconforming. This necessitates the establishment here of a general error estimate for FOSLS L2 minimization problems discretized by nonconforming finite elements. An advantage of the FOSLS formulation is that this estimate does not involve the consistency error term usually present in bounds for other methods. Based on this general estimate, error bounds are derived for the finite element space that includes singular basis functions. Numerical tests are included that confirm these discretization error bounds. Finally, a multilevel method is developed for solving the discrete system that uses singular basis functions on all levels, and its efficiency is demonstrated by the numerical results.

Singularity Prediction for Parallel Robots for Improvement of Sensor-Integrated Assembly

The frequent occurrences of singularities inside a parallel robot's workspace and in certain cases of sensor integration non-deterministic end-effector trajectories demand a powerful online singularity prediction and a control design that is capable of displacing motion algorithms. The theory of a power-inspired index of closeness to a singularity pose for parallel kinematic manipulators is illumined and presented in this paper, supported by comparison to Grassmann geometry and experimental results achieved on a HEXA robot. An experimentally validated strategy for jerk bounded braking the end-effector while approaching a singularity and an algorithm for departing it again are presented as well.

An improved description of magnetic fringing field

A new method of describing the magnetic fringing field is proposed. While the traditional method gives the two-dimensional magnetic field distribution by terminating the summation of the Maclaurin expansions at a finite derivative order, we summed the expansions up to infinity using the complex variable method. The exact summation shows an occurrence of singularities to which no attention has been paid. Because the traditional empirical function causes many unnecessary singularities where there should not be in the two-dimensional space, we derived a new empirical function whose singularities are located where they should be. The new function can reproduce the two-dimensional field distribution seamlessly and very precisely in the full region where we need the field information.

Achronal cosmic future.

The spherically symmetric accretion of dark and phantom energy onto Morris-Thorne wormholes is considered. It is obtained that the accretion of phantom energy leads to a gradual increase of the wormhole throat radius which eventually overtakes the superaccelerated expansion of the Universe and becomes infinite at a time in the future before the occurrence of the big rip singularity. After that time, as it continues accreting phantom energy, the wormhole becomes an Einstein-Rosen bridge whose corresponding mass decreases rapidly and vanishes at the big rip.

Green's function solution of temperature field for flow in porous passages

Recently, the heat transfer in porous passages has received attention from many investigators. The Green's function solution method can serve as a powerful tool to accomplish this task of providing solutions to this type of problems with or without the effect of axial conduction. The study of heat transfer with emphasis on frictional heating, in the absence of axial conduction, is the subject of this presentation. As a simple example, consideration is given to the numerical study of the heat transfer in flow between two impermeable parallel plates. The individual effects of temperature change at the walls, frictional heating, and the combined effects are examined. The data shows that the combined effects can produce removable singularities under certain boundary conditions. To avoid the occurrence of singularities in these types of applications, certain heat transfer parameters are presented in different but basic forms.

Influence of small imperfections on the stability of plane Poiseuille flow: A theoretical model and direct numerical simulation

It is well known that the stability of plane Poiseuille flow is extremely sensitive to small imperfections that are inevitably present. In this paper, a simple model is proposed, in which the imperfections are represented by a steady but spatially periodic surface roughness and a small oscillatory pressure gradient. A steady perturbation in the form of spatially periodic suction is also considered. For both cases, the resulting steady and unsteady components interact to produce a forcing that is in resonance with the Tollmien–Schlichting (TS) wave. The latter is excited as a result, and grows in proportion to time during the initial stage. The subsequent nonlinear development of the TS wave is shown to be governed by a forced (nonlocal) amplitude equation, which provides a simple framework to link the subcritical nonlinear instability explicitly to external forcing. The validity of the amplitude equation was checked against the direct numerical simulation (DNS), carried out in the case of wall suction. The results indicate that for a fixed level of external disturbance, there exist two distinctive regimes of response: A large-amplitude regime for the Reynolds numbers above a critical value, and a small-amplitude regime below it. The large-amplitude response regime in DNS was found to correspond to the occurrence of a finite-time singularity in the solution to the amplitude equation. This observation allows the critical Reynolds number for the large-amplitude response regime to be defined as one that divides the singular and bounded solutions of the amplitude equation. Estimate based on this equation shows that presence of small imperfections may reduce the critical Reynolds number for subcritical instability to values well below 5772.22.

Adaptive Tracking Control of Underwater Vehicle-Manipulator Systems Based on the Virtual Decomposition Approach

A novel adaptive control law for the end-effector tracking problem of underwater vehicle-manipulator systems (UVMSs) is presented in this paper. By exploiting the serial-chain kinematic structure of the UVMS, the overall control problem is decomposed in a set of elementary control problems, each of them formulated with respect to a single rigid body in the system. The proposed approach results in a modular control scheme which simplifies application to UVMSs with a large number of links, reduces the required computational burden, and allows efficient implementation on distributed computing architectures. Furthermore, the occurrence of kinematic and representation singularities is overcome, respectively, by expressing the control law in body-fixed coordinates and representing the attitude via the unit quaternion. To show the effectiveness of the proposed control strategy, a simulation case study is developed for a vehicle in spatial motion carrying a six-degree-of-freedom manipulator.

Bayesian-Based Hypothesis Testing for Topology Error Identification in Generalized State Estimation

This paper develops a Bayesian-based hypothesis testing procedure to be applied in conjunction with topology error processing via normalized Lagrange multipliers. As an advantage over previous methods, the proposed approach eliminates the need of repeated state estimator runs for alternative hypothesis evaluation. The identification process assumes that the set of switching devices is partitioned into suspect and true subsets. A geometric test is devised to ensure that all devices with wrong status are included in the suspect set. In addition, the results of criticality analysis performed at substation physical level prevents the occurrence of matrix singularities, which otherwise would degrade the performance of topology error identification. The IEEE 24-bus test system represented at physical level is employed to evaluate the proposed approach, considering diverse substation layouts and distinct types of topology errors.

Tetracycline and other tetracycline-derivative staining of the teeth and oral cavity.

Tetracyclines (TCN) were introduced in 1948 as broad-spectrum antibiotics that may be used in the treatment of many common infections in children and adults. One of the side-effects of tetracyclines is incorporation into tissues that are calcifying at the time of their administration. They have the ability to chelate calcium ions and to be incorporated into teeth, cartilage and bone, resulting in discoloration of both the primary and permanent dentitions. This permanent discoloration varies from yellow or gray to brown depending on the dose or the type of the drug received in relation to body weight. Minocycline hydrochloride, a semisynthetic derivative of tetracycline often used for the treatment of acne, has been shown to cause pigmentation of a variety of tissues including skin, thyroid, nails, sclera, teeth, conjunctiva and bone. Adult-onset tooth discoloration following long-term ingestion of tetracycline and minocycline has also been reported. The remarkable side-effect of minocycline on the oral cavity is the singular occurrence of "black bones", "black or green roots" and blue-gray to gray hue darkening of the crowns of permanent teeth. The prevalence of tetracycline and minocycline staining is 3-6%. The mechanism of minocycline staining is still unknown. Most of the reviewed literature consisted of case reports; longitudinal clinical trials are necessary to provide more information on the prevalence, severity, etiology and clinical presentation of tetracycline and TCN-derivative staining in the adult population.

Spherical dust collapse in higher dimensions

We consider here whether it is possible to recover cosmic censorship when a transition is made to higher-dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as the end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear, that, in a generic higher-dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher-dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes on the nature of the initial data from which the collapse develops is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.

Possible end of the universe in a finite future from dark energy withw<−1

The occurrence of a big smash singularity which ends the universe in a finite time in the future is investigated in the context of superquintessence, i.e. dark energy with effective equation of state parameter w<-1. The simplest model of superquintessence based on a single nonminimally coupled scalar field exhibits big smash solutions which are attractors in phase space.

Quasi-Spherical Gravitational Collapse in Any Dimension

We study the occurrence and nature of naked singularities for a dust model with non-zero cosmological constant in ($n+2$)-dimensional Szekeres space-times (which possess no Killing vectors) for $n\geq 2$. We find that central shell-focusing singularities may be locally naked in higher dimensions but depend sensitively on the choice of initial data. In fact, the nature of the initial density determines the possibility of naked singularity in space-times with more than five dimensions. The results are similar to the collapse in spherically symmetric Tolman-Bondi-Lema\^{\i}tre space-times.

NAKED SINGULARITIES IN THE CHARGED VAIDYA–De SITTER SPACETIME

We study the occurrence of naked singularities in the spherically symmetric collapse of a charged null fluid in an expanding de Sitter background — a piece of charged Vaidya–de Sitter spacetime. The naked singularities are found to be gravitationally strong in Tipler's sense and thus violate the cosmic censorship hypothesis.

GRAVITATIONAL COLLAPSE OF PERFECT FLUID IN SELF-SIMILAR HIGHER DIMENSIONAL SPACE–TIMES

We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space–times. It is shown that strong curvature naked singularities could occur if the weak energy condition holds. Its implication for cosmic censorship conjecture is discussed. Known results of analogous studies in four dimensions can be recovered.