Singular Origin Research Articles

ON PHASE TRANSITIONS ON BETHE LATTICES

Starting from some recent rigorous results about correlation functions of statistical model on tree structures, we analyze the nature of phase transitions occurring on Bethe lattices, showing the lack of long range order and the purely geometrical origin of the thermodynamic singularities. This approach gives a very simple formula for the critical temperature for any model with compact symmetry group and immediately leads to the value 1 for the critical exponent γ. The “geometrical” critical behavior only partially coincides with the mean field solution and violates the usual scaling relations.

Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations

A simple, general and numerically stable approach for avoiding the singularities which generally occur when atoms or interaction sites are created or annihilated in free energy calculations based on computer simulations is presented. The origin of such singularities and numerical instabilities occurring in Monte Carlo or molecular dynamics simulations is discussed, as is the limited accuracy of the techniques currently used to avoid such difficulties.

Electron instability, electrical conductivity, and the electret effect in insulators

The origin of dielectric singularity is examined by calculating the electrostatic energy of a cylinder containing a periodic negative-charge density and periodically repeating planes containing positive charges. When the planes deviate from their initial positions, the cells acquire dipole moments, and the energy is a function of the deviations. The condition for the stability of the unpolarized state is that the charge density at the middle of a cell exceeds the mean charge over the cell. When these are equal, stability in the charge disposition is lost and conductivity arises. A three-dimensional array is considered for the polarizable ions in the polar cells, which is located between short-circuited electrodes and has cavity gaps by the electrodes. Microscopic-field calculations show that the field in a gap in general does not vanish on electronic instability. The phenomenon is compared with the electret effect.

The significance of the interstellar Li-7/Li-6 ratio

view Abstract Citations (20) References (38) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Significance of the Interstellar 7Li/ 6Li Ratio Steigman, Gary Abstract The present abundances of Li-6 and Li-7, when compared with the solar system values, can provide valuable information on stellar and cosmic-ray nucleosynthesis, stellar structure and evolution, and Galactic chemical evolution in the solar vicinity in the last 4.6 Gyr. Unfortunately, the interpretation of stellar data from observations of main-sequence stars in young clusters and of pre-main-sequence stars are clouded by large and uncertain corrections for burning of lithium and for non-LTE effects, and the interpretation of observations of interstellar Li are rendered uncertain by large and unknowable corrections for ionization and depletion onto grains and/or molecules. In this Letter it is shown that the singular origin for Population I Li-6 offers the potential for exploiting bounds to interstellar beryllium and boron to infer an upper bound to the present interstellar Li-6 abundance. Then the recent observations (Lemoine et al., 1992; Meyer et al., 1993) of the interstellar Li-7/Li-6 ratio may be utilized to bound the present abundance of Li-7. This approach is independent of any model for the evolution of Li-7. The current data suggest that the Li abundance has barely increased, and may well have decreased, in the 4.6 Gyr since the formation of the solar system. This result is inconsistent with the predictions of chemical evolution models and raises the question of the reliability of the sun as a probe of the abundances in the local ISM 4.6 Gyr ago. Publication: The Astrophysical Journal Pub Date: August 1993 DOI: 10.1086/186962 Bibcode: 1993ApJ...413L..73S Keywords: Interstellar Matter; Lithium Isotopes; Metallicity; Milky Way Galaxy; Abundance; Solar System; Astrophysics; GALAXY: ABUNDANCES; ISM: ABUNDANCES; SUN: ABUNDANCES full text sources ADS |

Bianchi-type cosmological models in Lyra’s geometry with constant deceleration parameter

The Bianchi-type cosmological models have been studied in Lyra’s geometry for a law of variation of Hubble’s parameter presented by Berman (1983) that yields constant deceleration parameter models of the universe. All the models have a singular origin (t = 0) and evolve with time. The gauge function \(t) is an arbitrary function of time.

Evaluation of field singularities by an iterative boundary‐element method

AbstractA numerical method is presented for the evaluation of field singularities of the type (1/r1‐λ) using iterative solutions of standard boundary‐element analyses in a region surrounding the origin of singularity. Results for λ are presented for both two and three‐dimensional problems, and representative asymptotic fields for these examples are discussed.

Understanding geometrical phases in quantum mechanics: An elementary example

We discuss an exact solution to the simplest nontrivial example of a geometrical phase in quantum mechanics. By means of this example: (1) we elucidate the fundamental distinction between rays and vectors in describing quantum mechanical states; (2) we show that superposition of quantal states is invalid; only decomposition is allowed—which is adequate for the measurement process. Our example also shows that the origin of singularities in the analog vector potential is to be found in the unavoidable breaking of projective symmetry caused by using the Schrodinger equation.

DETERMINATION OF THE SINGULARITIES OF THE DYSON-SCHWINGER EQUATION FOR THE QUARK PROPAGATOR

In this paper we study the analytic continuation of the Dyson-Schwinger equation into the entire complex p2 plane. It is shown that in the usual ladder approximation with a running coupling, there are two complex-conjugate branch points and one real branch point in the timelike region. The real branch point corresponds presumably to a physical mass for a quark; but it is removed by the addition of a so-called confinement term to the bare gluon propagator: with this extra term, there are at least three pairs of complex-conjugate branch points. The origin of these complex singularities is not yet clear.

EVOLUTIONARY SIGNIFICANCE OF THE LOSS OF THE CHLOROPLAST-DNA INVERTED REPEAT IN THE LEGUMINOSAE SUBFAMILY PAPILIONOIDEAE.

The distribution of a rare chloroplast-DNA structural mutation, the loss of a large inverted repeat, has been determined for 95 species representing 77 genera and 25 of the 31 tribes in the legume subfamily Papilionoideae. This mutation, which is regarded as a derived feature of singular origin within the subfamily, marks a group comprising six temperate tribes, the Galegeae, Hedysareae, Carmichaelieae, Vicieae, Cicereae, and Trifolieae, an assemblage traditionally considered to be monophyletic. This mutation also occurs in the chloroplast genome of Wisteria, a member of the tropical tribe Millettieae whose other members so far surveyed lack the mutation. These new DNA data, together with traditional evidence, support the hypothesis that Wisteria is an unspecialized member of a lineage that gave rise to the temperate tribes marked by the chloroplast-DNA mutation; the probable paraphylesis of Millettieae is revealed. Two other tribes, Loteae and Coronilleae (traditionally regarded as a derived element of the aforesaid temperate tribes) do not possess this chloroplast-DNA structural mutation and, therefore, presumably represent a distinct temperate lineage. This hypothesis is supported by additional evidence from pollen, inflorescence, and root-nodule morphology that suggests that the Loteae and Coronilleae share a more recent ancestry with tropical tribes such as Phaseoleae and Millettieae than with other temperate tribes.

Singularity removal: A refinement of resistivity modeling techniques

Modeling techniques commonly exhibit errors of 3 to 10 percent or more in the calculation of apparent resistivities over earth models for which analytic solutions are easily available. A singularity occurs in the solution of any elliptic partial differential equation for which the forcing function is not smooth. The inability to adequately represent in discrete space a discontinuous function (in this case, the delta function describing the introduction of current at a point) commonly results in numerical error near the source of a modeled singularity. Inspection of an integrated finite‐difference method for modeling the dc resistivity geophysical technique indicates much of the error encountered is of singular origin. A procedure is herein detailed by which the singularity is mathematically removed from the modeling process and reintroduced as a last step, thus preventing it from contributing to the numerical error. Using this procedure, the average error in apparent resistivity values for a model of a polar‐dipole traverse over a nonconducting sphere is reduced by 40 percent. For a dipole‐dipole traverse of a two‐layer model the error decreases by 75 percent, and in the case of a Wenner profile of a model of a vertically faulted earth, the average error is diminished by 90 percent.

Perturbative origin of an essential singularity in dimensional renormalization of quadratic divergences.

It has been shown recently that in the 1/N expansion, the minimally subtracted dimensional renormalization scheme breaks down for quadratically divergent operators. The physical dimension \ensuremath{\epsilon}=0 becomes an essential singularity, the accumulation point of an infinite sequence of poles. In this article, it is shown explicitly how these poles are generated order by order in perturbation theory.

CONFORMAL QUANTIZATION AND SPACE-TIME SINGULARITY

This work generalizes earlier results of conformal quantization1,2 that within the full range of space-times conformal to any singular space-time satisfying Einstein’s field equations for minimally coupled matter, the singular solutions form a set of zero-probability measure. A wider definition of space-time singularity that includes the curvature singularity assumed in the earlier work (op. cit.) is adapted and it is shown that the previous conclusion stands even when the present state of the universe is defined by wave functionals that are not necessarily wave packets. Within the present framework of quantum gravity therefore it seems extremely unlikely that the universe had a singular origin.

Topological Origin of the Surface Singularities in Glasses

ABSTRACTA model of CRN in two dimensions is presented, composed of equilateral but not equiangular polygons with a constant coordination number = 3; in a simplified version only pentagons, hexagons and heptagons are present in the network. We introduce the mean potential energy per atom averaged over a typical cell containing three adjacent polygons; we assume that although the thermal equilibrium is not attained for single atoms, it is attained on the level of these cells, so that we can apply the virial theorem for the cells. Then we minimize the free energy which contains the configuration entropy contribution. In terms of two variables P and δ (hexagon frequency and mean bond angle deviation) we get the surfaces of constant energy. Under stress the energy configurations cease to be one-connected, and the 0-th homotopy group is no more trivial. This can give rise to surface singularities (cracks).

Studies of liquid water by computer simulations. II. Static properties of a 3D model

A 3D model for water is presented and its static properties are thoroughly studied by Monte Carlo simulations over a wide region of temperature and density. Various kinds of molecular distribution functions are derived and from their temperature and density dependences are revealed the structure of the liquid state in detail. Relevant thermodynamic quantities are estimated as functions of temperature and pressure (or density) and main features of the observed anomalous properties of liquid water are reproduced semiquantitatively. The mechanical instability is found as the limit of supercooling and ascribed to the origin of the divergent singularities observed in supercooled water.

Autonomous development of reciprocally exchanged regeneration blastemas of normal forelimbs and symmetrical hindlimbs

AbstractNormal upper arm blastemas and blastemas derived from double posterior or double anterior thighs of A. mexicanum were reciprocally exchanged either by autografting or homografting between dark and white animals. Those grafted blastemas which survived always regenerated a morphology and pigmentation characteristics of the donor limb. Thus, upper arm blastemas on double anterior or posterior thigh stumps regenerated normal forelimbs. Double anterior blastemas on normal upper arm stumps failed to regenerate, and double posterior blastemas on normal upper arm stumps regenerated posterior half hindlimbs. These results show that the morphogenetic field of the regenerate is reflected in the composition of the limb stump, and that its pattern is expressed autonomously.Supernumerary limbs formed where posterior and anterior tissues of graft and host were opposed in 35–43% of cases where normal upper arm blastemas were grafted to symmetrical thighs. The morphology and pigmentation of the supernumeraries suggests that they are probably derived from both graft and stump, although a singular origin from either graft or stump is not ruled out in some cases.

Dynamical symmetry breaking as the origin of the pomeranchuk singularity

We consider the viewpoint that Reggeons are built out of Reggeized quarks and that an O(2) symmetry between two kinds of quarks (“heavy” and “light”) is dynamically broken by their interaction. The Goldstone boson thus generated is associated with the Pomeron, and it is argued that it naturally has a smaller slope than the other Reggeons which are ordinary bound states of the quarks.

Rotational analyticity of theSmatrix

Starting from known results of field theory, it is shown that both scattering and production amplitudes are analytic functions on the group SU(2). This analyticity is then used to simplify the derivation of high-energy bounds for scattering amplitudes of particles with spin. The origin of kinematic singularities as the result of parametrization of an analytic manifold is seen to be particularly transparent when the manifold is chosen to be SU(2). Field theory is used to show that production amplitudes are analytic in an SU(2) domain analogous to the Lehman ellipse for scattering amplitudes. Finally, unitarity is used to demonstrate that production amplitudes, when smeared over a small region of outgoing phase space, are SU(2) analytic in a larger domain analogous to the Martin ellipse.

Origin and intercept of the Pomeranchuk singularity

Assuming that the non diffractive part of exclusive cross sections contributes to the Pomeranchuk singularity in the total cross section, we derive general relations between Regge intercepts and parameters of the multiplicity distribution. A dynamical assumption on the mechanism that generates the Pomeron gives automatically an intercept near one provided that a particular correlation parameter is small.

The Young Paseal

Versatility is not inevitably the companion of genius. It is not altogether common to find a man who is at the same time a clever experimental physicist, a creative mathematician, an inventor with an eye to money-making, a gifted writer whose artistry places him among the foremost French stylists, and a religious philosopher of singular originality and ardor. Blaise Pascal was such a man. He could write an important treatise on the vacuum as well as produce those incomparable examples of controversial literature, the famous Provincial Letters. lie invented the first adding machine of practical consequence and tried (in vain) to realize a profit from its sale. In the fragment. of his projected a pology for the Christian Religion, left unfinished by his death at the early age of thirty-nine, are to be found many evidences of his mathematical genius as well as of a remarkable piety and zeal. A clear and complete picture of his early life and education would not only be of rare in terest, but it could not fail to contain many suggestions of value to the modem teacher. It is indeed a pity that such incomplete information is available. The story is soon told, but it is well worth the telling, and perhaps it holds some inspiration or lesson for our own times.