Geometry of Spin: Clifford Algebraic Approach
Indian Academy of Sciences (India)
of Pauli matrices follow from the underlying algebra. Clif- ford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formal- ism has lot of applications in every field where spin plays an important role. Introduction.
Geometry of Spin: Clifford Algebraic Approach
Indian Academy of Sciences (India)
Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a ...
Spin Gauge Theory of Gravity in Clifford Space
International Nuclear Information System (INIS)
Pavsic, Matej
2006-01-01
A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: 'extra dimensions' are in C-space. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1) x SU(2) x SU(3) gauge group. The representation space for the latter group is provided by 16-component generalized spinors composed of four usual 4-component spinors, defined geometrically as the members of four independent minimal left ideals of Clifford algebra
Geometry of Spin: Clifford Algebraic Approach
Indian Academy of Sciences (India)
intuitive way to understand quantum theory of spin, and is a natural formalism to study ... Pauli matrices define two-dimensional representation of. Euclidean signature (all of ..... In the process he introduced quaternion al- gebra which has three ...
Clifford algebras, spinors, spin groups and covering groups
International Nuclear Information System (INIS)
Magneville, C.; Pansart, J.P.
1991-03-01
The Dirac equation uses matrices named Υ matrices which are representations of general algebraic structures associated with a metric space. These algebras are the Clifford algebras. In the first past, these algebras are studied. Then the notion of spinor is developed. It is shown that Majorana and Weyl spinors only exist for some particular metric space. In the second part, Clifford and spinor groups are studied. They may be interpreted as the extension of the notion of orthogonal group for Clifford algebras and their spaces for representation. The rotation of a spinor is computed. In the last part, the connexion between the spinor groups and the Universal Covering Groups is presented [fr
Climate and weather across scales: singularities and stochastic Levy-Clifford algebra
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2016-04-01
There have been several attempts to understand and simulate the fluctuations of weather and climate across scales. Beyond mono/uni-scaling approaches (e.g. using spectral analysis), this was done with the help of multifractal techniques that aim to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations of these equations (Royer et al., 2008, Lovejoy and Schertzer, 2013). However, these techniques were limited to deal with scalar fields, instead of dealing directly with a system of complex interactions and non trivial symmetries. The latter is unfortunately indispensable to answer to the challenging question of being able to assess the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013) or to fully address the question of the relevance of quasi-geostrophic turbulence and to define an effective, fractal dimension of the atmospheric motions (Schertzer et al., 2012). In this talk, we present a plausible candidate based on the combination of Lévy stable processes and Clifford algebra. Together they combine stochastic and structural properties that are strongly universal. They therefore define with the help of a few physically meaningful parameters a wide class of stochastic symmetries, as well as high dimensional vector- or manifold-valued fields respecting these symmetries (Schertzer and Tchiguirinskaia, 2015). Lovejoy, S. & Schertzer, D., 2013. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge U.K. Cambridge Univeristy Press. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.81-83. Royer, J.F. et al., 2008. Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario. C.R. Geoscience, 340(431-440). Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327-336. Schertzer, D
Castro, C
2003-01-01
A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini which was based on the Kerr-Newman metric solutions of the Einstein-Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza-Klein compactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed by a discussion on the geometrical derivation of the fine structure constant by Wyler, Smith, Gonzalez-Martin and Smilga. To finalize, the renormalization of electric charge is discussed and some remarks are made pertaining the modifications of the charge-scale relationship, when the spin of the polyparticle changes with scale, that may cast some light into the alleged Astrophysical variations of the fine structure constant.
International Nuclear Information System (INIS)
Dimakis, A.
1983-01-01
The algebraic structure of the real Clifford algebras (CA) of vector spaces with non-degenerated scalar product of arbitrary signature is studied, and a classification formula for this is obtained. The latter is based on three sequences of integer numbers from which one is the Radon-Harwitz sequence. A new representation method of real CA is constructed. This leads to a geometrical representation of real Clifford algebras in which the representation spaces are subspaces of the CA itself (''spinor spaces''). One of these spinor spaces is a subalgebra of the original CA. The relation between CA and external algebras is studied. Each external algebra with a scalar product possesses the structure of a CA. From the geometric representation developed here then follows that spinors are inhomogeneous external forms. The transformation behaviour of spinors under the orthogonal, as well as under the general linear group is studied. By means of these algebraic results the spinor connexion and the covariant Dirac operator on a differential manifold are introduced. In the geometrical representation a further in ternal SL(2,R) symmetry of the Dirac equation (DE) is shown. Furthermore other equivalent formulations of the DE can be obtained. Of special interest is the tetrade formulation of the DE. A generalization of the DE is introduced. The equations of motion of the classical relativistic spin particle are derived by means of spinors and CA from a variational principle. From this interesting formal analogies with the supersymmetric theories of the spin particle result. Finally the DE in the curved space-time is established and studied in the tetrade formulation. Using the methods developed here a new exact solution of the coupled Einstein-Curtan-Dirac theory was found (massice ''Ghost-Dirac fields''). (orig.) [de
A spin-liquid with pinch-line singularities on the pyrochlore lattice.
Benton, Owen; Jaubert, L D C; Yan, Han; Shannon, Nic
2016-05-26
The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7.
Lounesto, Pertti
1993-01-01
This volume contains a facsimile reproduction of Marcel Riesz's notes of a set of lectures he delivered at the University of Maryland, College Park, between October 1957 and January 1958, which has not been formally published to date This seminal material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this book by notes which Riesz dictated to E Folke Bolinder in the following year and which were intended to be a fifth chapter of the Riesz lecture notes In addition, Riesz's work on Clifford algebra is put into an historical perspective in a separate review by P Lounesto As well as providing an introduction to Clifford algebra, this volume will be of value to those interested in the history of mathematics
Directory of Open Access Journals (Sweden)
Bošković Aleksandar
2007-01-01
Full Text Available The paper presents some concepts of the recently deceased American anthropologist Clifford Geertz, putting them into the specific context of his rich and interesting career, influences that he had, as well as some reactions to his ideas. A particular attention is placed upon the concept of culture, as the key concept in the 20th century American anthropology.
Directory of Open Access Journals (Sweden)
María Carolina Spinel G.
1990-01-01
Con esta base, en posteriores artículos de divulgación, presentaremos algunas aplicaciones que muestren la ventaja de su empleo en la descripción de sistema físico. Dado el amplio conocimiento que se tiene de los espacios vectoriales. La estructura y propiedades del algebra de Clifford suele presentarse con base en los elementos de un espacio vectorial. En esta dirección, en la sección 2 se define la notación y se describe la estructura de un algebra de Clifford Gn, introduciendo con detalle las operaciones básicas entre los elementos del álgebra. La sección 3 se dedica a describir una base tensorial de Gn.
International Nuclear Information System (INIS)
Todorov, Ivan
2010-12-01
Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [M84] and includes historical notes and biographical data on past participants in the story. (author)
Srivastava, Madhur; Freed, Jack H
2017-11-16
Regularization is often utilized to elicit the desired physical results from experimental data. The recent development of a denoising procedure yielding about 2 orders of magnitude in improvement in SNR obviates the need for regularization, which achieves a compromise between canceling effects of noise and obtaining an estimate of the desired physical results. We show how singular value decomposition (SVD) can be employed directly on the denoised data, using pulse dipolar electron spin resonance experiments as an example. Such experiments are useful in measuring distances and their distributions, P(r) between spin labels on proteins. In noise-free model cases exact results are obtained, but even a small amount of noise (e.g., SNR = 850 after denoising) corrupts the solution. We develop criteria that precisely determine an optimum approximate solution, which can readily be automated. This method is applicable to any signal that is currently processed with regularization of its SVD analysis.
Coulomb singularities in scattering wave functions of spin-orbit-coupled states
International Nuclear Information System (INIS)
Bogdanski, P.; Ouerdane, H.
2011-01-01
We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl= 0, ±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.
International Nuclear Information System (INIS)
Dalmazi, D; Sa, F L
2010-01-01
Here we study the partition function zeros of the one-dimensional Blume-Emery-Griffiths model close to their edge singularities. The model contains four couplings (H, J, Δ, K) including the magnetic field H and the Ising coupling J. We assume that only one of the three couplings (J, Δ, K) is complex and the magnetic field is real. The generalized zeros z i tend to form continuous curves on the complex z-plane in the thermodynamic limit. The linear density at the edges z E diverges usually with ρ(z) ∼ |z - z E | σ and σ = -1/2. However, as in the case of complex magnetic fields (Yang-Lee edge singularity), if we have a triple degeneracy of the transfer matrix eigenvalues a new critical behavior with σ = -2/3 can appear as we prove here explicitly for the cases where either Δ or K is complex. Our proof applies for a general three-state spin model with short-range interactions. The Fisher zeros (complex J) are more involved; in practice, we have not been able to find an explicit example with σ = -2/3 as far as the other couplings (H, Δ, K) are kept as real numbers. Our results are supported by numerical computations of zeros. We show that it is absolutely necessary to have a non-vanishing magnetic field for a new critical behavior. The appearance of σ = -2/3 at the edge closest to the positive real axis indicates its possible relevance for tricritical phenomena in higher-dimensional spin models.
Clifford Algebras and magnetic monopoles
International Nuclear Information System (INIS)
Recami, E.
1987-01-01
It is known that the introduction of magnetic monopolies in electromagnetism does still present formal problems from the point of view of classical field theory. The author attempts to overcome at least some of them by making recourse to the Clifford Algebra formalism. In fact, while the events of a two-dimensional Minkowski space-time M(1,1) are sufficiently well represented by ordinary Complex Numbers, when dealing with the events of the four-dimensional Minkowski space M(1,3)identical to M/sub 4/ one has of course to look for hypercomplex numbers or, more generally, for the elements of a Clifford Algebra. The author uses the Clifford Algebras in terms of ''multivectors'', and in particular by Hestenes' language, which suits space-time quite well. He recalls that the Clifford product chiγ is the sum of the internal product chi . γ and of the wedge product chiΛγ
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
Energy Technology Data Exchange (ETDEWEB)
Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr [University Paris-Est, Ecole des Ponts ParisTech, Hydrology Meteorology and Complexity HM& Co, Marne-la-Vallée (France)
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Directory of Open Access Journals (Sweden)
Richard Handler
2008-01-01
Full Text Available En la primavera de 1991, Adam Kuper, por entonces director de Current Anthropology, y por derecho propio destacado historiador de la disciplina antropológica, me pidió realizar una entrevista a Clifford Geertz. Acepté encantado y ese mismo verano viajé a Princeton, Nueva Jersey, donde transcurrí aproximadamente tres horas con Geertz en su oficina, en el Instituto de Estudios Avanzados. Geertz me dio una cordial bienvenida y habló conmigo sin tapujos, dándome (como podrá comprobar el lector un claro y completo relato de su carrera (para una completa y exacta versión, los lectores pueden consultar ahora su autobiografía en After the Fact: Two Countries, Four Decades, one Anthropolgist, Harvard University Press, 1995. De la transcripción de la entrevista realicé un manuscrito, donde limpié las repeticiones y dubitaciones de la conversación, pero manteniendo fielmente la charla, tal y como tuvo lugar. Se lo mandé a Geertz, que propuso algunas correcciones pero que por lo demás aceptó todo.
Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field
Carmelo, J. M. P.; Sacramento, P. D.; Machado, J. D. P.; Campbell, D. K.
2015-10-01
We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents {{\\zeta}τ}(k) controlling the singularities for both the longitudinal ≤ft(τ =l\\right) and transverse ≤ft(τ =t\\right) dynamical structure factors for the whole momentum range k\\in ]0,π[ , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.
Clifford theory for group representations
Karpilovsky, G
1989-01-01
Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpos
Linear operators in Clifford algebras
International Nuclear Information System (INIS)
Laoues, M.
1991-01-01
We consider the real vector space structure of the algebra of linear endomorphisms of a finite-dimensional real Clifford algebra (2, 4, 5, 6, 7, 8). A basis of that space is constructed in terms of the operators M eI,eJ defined by x→e I .x.e J , where the e I are the generators of the Clifford algebra and I is a multi-index (3, 7). In particular, it is shown that the family (M eI,eJ ) is exactly a basis in the even case. (orig.)
The many faces of Maxwell, Dirac and Einstein equations a Clifford bundle approach
Rodrigues, Jr, Waldyr A
2016-01-01
This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solut...
Li, Dafa
2018-06-01
We construct ℓ -spin-flipping matrices from the coefficient matrices of pure states of n qubits and show that the ℓ -spin-flipping matrices are congruent and unitary congruent whenever two pure states of n qubits are SLOCC and LU equivalent, respectively. The congruence implies the invariance of ranks of the ℓ -spin-flipping matrices under SLOCC and then permits a reduction of SLOCC classification of n qubits to calculation of ranks of the ℓ -spin-flipping matrices. The unitary congruence implies the invariance of singular values of the ℓ -spin-flipping matrices under LU and then permits a reduction of LU classification of n qubits to calculation of singular values of the ℓ -spin-flipping matrices. Furthermore, we show that the invariance of singular values of the ℓ -spin-flipping matrices Ω 1^{(n)} implies the invariance of the concurrence for even n qubits and the invariance of the n-tangle for odd n qubits. Thus, the concurrence and the n-tangle can be used for LU classification and computing the concurrence and the n-tangle only performs additions and multiplications of coefficients of states.
International Nuclear Information System (INIS)
Castro, Carlos
2006-01-01
We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D 4 - D 5 - E 6 - E 7 - E 8 model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith's model to the full Clifford-space is presented when we write explicitly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan, and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E 8 x E 8 Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford (16) group
Obstructions to Clifford system extensions of algebras
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
group character, and then we give a classification of Clifford systems in terms of suitable low-dimensional ... Introduction. The problem of ... Clifford's theory axiomatically, and which can be referred to for general background. In §2, we state a ...
Xiu-Xing, Zhang; Fu-Li, Li
2012-01-01
We study the classical correlation (CC) and quantum discord (QD) between two spin subgroups of the Lipkin-Meshkov-Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartition, we find that the classical correlations and all the quantum correlations including the QD, the entanglement of formation (EoF) and the logarithmic negativity (LN) are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartition, however, ...
An introduction to Clifford algebras and spinors
Vaz, Jayme
2016-01-01
This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and i...
International Nuclear Information System (INIS)
Zhang, Xiu-xing; Li, Fu-li
2013-01-01
By using the lowest order expansion in the number of spins, we study the classical correlation (CC) and quantum correlations (QCs) between two spin subgroups of the Lipkin–Meshkov–Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartitions, we find that the CC and all the QCs are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartitions, however, the CC is still divergent but the QCs remain finite at the critical point. The present result shows that the CC is very robust but the QCs are much frangible to the environment disturbance.
Singh, R. R. P.; Young, A. P.
2017-08-01
We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.
2006-01-01
10. novembril toimub TLÜ-s Ameerika kultuurantropoloogi Clifford Geertzi mälestusõhtu, kus esinevad rektor Rein Raud, TLÜ Eesti Humanitaarinstituudi antropoloogia keskuse dotsent Lorenzo Cañás Bottos ja kultuuriteooria lektor Marek Tamm
Clifford Algebra Implying Three Fermion Generations Revisited
International Nuclear Information System (INIS)
Krolikowski, W.
2002-01-01
The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √p 2 → Γ (N) ·p works, leading to a sequence N=1, 2, 3, ... of Dirac-type equations, where four Dirac-type matrices Γ (N) μ are embedded into a Clifford algebra via a Jacobi definition introducing four ''centre-of-mass'' and (N - 1) x four ''relative'' Dirac-type matrices. These define one ''centre-of-mass'' and N - 1 ''relative'' Dirac bispinor indices. Secundo, the ''centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while N - 1 ''relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ''relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1, 3, 5 in the case of N odd, and two with N = 2, 4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3 x 3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is m τ = 1776.80 MeV, when the input of experimental m e and m μ is used. (author)
Clifford Algebra Implying Three Fermion Generations Revisited
Krolikowski, Wojciech
2002-09-01
The author's idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure √ {p2} → {Γ }(N)p works, leading to a sequence N = 1,2,3, ... of Dirac-type equations, where four Dirac-type matrices {Γ }(N)μ are embedded into a Clifford algebra via a Jacobi definition introducing four ``centre-of-mass'' and (N-1)× four ``relative'' Dirac-type matrices. These define one ``centre-of-mass'' and (N-1) ``relative'' Dirac bispinor indices. Secundo, the ``centre-of-mass'' Dirac bispinor index is coupled to the Standard Model gauge fields, while (N-1) ``relative'' Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to ``relative'' Dirac indices. This allows only for three Dirac-type equations with N = 1,3,5 in the case of N odd, and two with N = 2,4 in the case of N even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac 3x3 mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is mτ = 1776.80 MeV, when the input of experimental me and mμ is used.
A sequence of Clifford algebras and three replicas of Dirac particle
International Nuclear Information System (INIS)
Krolikowski, W.; Warsaw Univ.
1990-01-01
The embedding of Dirac algebra into a sequence N=1, 2, 3,... of Clifford algebras is discussed, leading to Dirac equations with N=1 additional, electromagnetically ''hidden'' spins 1/2. It is shown that there are three and only three replicas N=1, 3, 5 of Dirac particle if the theory of relativity together with the probability interpretation of wave function is applied both to the ''visible'' spin and ''hidden'' spins, and a new ''hidden exclusion principle''is imposed on the wave function (then ''hidden'' spins add up to zero). It is appealing to explore this idea in order to explain the puzzle of three generations of lepton and quarks. (author)
Agama dalam Tentukur Antropologi Simbolik Clifford Geertz
Directory of Open Access Journals (Sweden)
Yusri Mohamad Ramli
2012-06-01
Full Text Available Clifford Geertz can be regarded as one of the most influential figures in religious studies, particularly in the field of anthropology. His unique symbolic anthropology approach had attracted researchers because of his emphasis on deductive reasoning in explaining the meaning of religion and in viewing cultural values that exist in religion. Research based on the content analysis of his works found that Clifford Geertz thought very strongly influenced by Ibn Khaldun as both of them emphasize on the practical reality of religious phenomena in the society. These symbols are then making a cultural system of what we call religion.
Clifford algebra in finite quantum field theories
International Nuclear Information System (INIS)
Moser, M.
1997-12-01
We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)
Multiqubit Clifford groups are unitary 3-designs
Zhu, Huangjun
2017-12-01
Unitary t -designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers, little is known about unitary t -designs with t ≥3 in the literature. We show that the multiqubit Clifford group in any even prime-power dimension is not only a unitary 2-design, but also a 3-design. Moreover, it is a minimal 3-design except for dimension 4. As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer states forms a 3-design. In addition, our study is helpful in studying higher moments of the Clifford group, which are useful in many research areas ranging from quantum information science to signal processing. Furthermore, we reveal a surprising connection between unitary 3-designs and the physics of discrete phase spaces and thereby offer a simple explanation of why no discrete Wigner function is covariant with respect to the multiqubit Clifford group, which is of intrinsic interest in studying quantum computation.
Physical Holonomy, Thomas Precession, and Clifford Algebra
International Nuclear Information System (INIS)
Urbantke, H.
1988-01-01
After a general discussion of the physical significance of holonomy group transformations, a relation between the transports of Fermi-Walker and Levi-Civita in Special Relativity is pointed out. A well-known example -the Thomas-Wigner angle - is rederived in a completely frame-independent manner using Clifford algebra. 14 refs. (Author)
Monogenic functions with parameters in Clifford analysis
International Nuclear Information System (INIS)
Le Hung Son.
1990-02-01
In this paper we study some properties of monogenic functions taking values in a Clifford algebra and depending on several parameters. It is proved that the Hartogs extension theorems are valid for these functions and for the multi-monogenic functions, which contain solutions of many important systems of partial differential equations in Theoretical Physics. (author). 4 refs
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
A Clifford analysis approach to superspace
International Nuclear Information System (INIS)
Bie, H. de; Sommen, F.
2007-01-01
A new framework for studying superspace is given, based on methods from Clifford analysis. This leads to the introduction of both orthogonal and symplectic Clifford algebra generators, allowing for an easy and canonical introduction of a super-Dirac operator, a super-Laplace operator and the like. This framework is then used to define a super-Hodge coderivative, which, together with the exterior derivative, factorizes the Laplace operator. Finally both the cohomology of the exterior derivative and the homology of the Hodge operator on the level of polynomial-valued super-differential forms are studied. This leads to some interesting graphical representations and provides a better insight in the definition of the Berezin-integral
The Extended Relativity Theory in Clifford Spaces
Castro, C
2004-01-01
A brief review of some of the most important features of the Extended Relativity theory in Clifford-spaces ( $C$-spaces) is presented whose " point" coordinates are noncommuting Clifford-valued quantities and which incoporate the lines, areas, volumes, .... degrees of freedom associated with the collective particle, string, membrane, ... dynamics of the $p$-loop histories (closed p-branes) living in target $D$-dimensional spacetime backgrounds. $C$-space Relativity naturally incoporates the ideas of an invariant length (Planck scale), maximal acceleration, noncommuting coordinates, supersymmetry, holography, superluminal propagation, higher derivative gravity with torsion and variable dimensions/signatures that allows to study the dynamics of all (closed ) p-branes, for all values of $ p $, in a unified footing. It resolves the ordering ambiguities in QFT and the problem of time in Cosmology. A discussion of the maximal-acceleration Relativity principle in phase-spaces follows along with the study of the inva...
Clifford G. Shull and Bertram N. Brockhouse
International Nuclear Information System (INIS)
2003-01-01
In 1994, the Nobel Prize for Physics was shared by two researchers whose common characteristic, apart from the drive to work an their genius, is modesty and discretion. That may have been why the Swedish institution took forty years to appreciate the work which brought the prestigious award to them, Clifford G. Shull and Bertram N. Brockhouse, who received their respective awards for development of neutron diffraction technique and neutron spectroscopy. (Author)
Clifford coherent state transforms on spheres
Dang, Pei; Mourão, José; Nunes, João P.; Qian, Tao
2018-01-01
We introduce a one-parameter family of transforms, U(m)t,t > 0, from the Hilbert space of Clifford algebra valued square integrable functions on the m-dimensional sphere, L2(Sm , dσm) ⊗Cm+1, to the Hilbert spaces, ML2(R m + 1 ∖ { 0 } , dμt) , of solutions of the Euclidean Dirac equation on R m + 1 ∖ { 0 } which are square integrable with respect to appropriate measures, dμt. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, U(1) :L2(S1 , dσ1) ⟶ HL2(C ∖ { 0 } , dμ) , to higher dimensional spheres in the context of Clifford analysis. In Clifford analysis it is natural to replace the analytic continuation from Sm to SCm as in (Hall, 1994; Stenzel, 1999; Hall and Mitchell, 2002) by the Cauchy-Kowalewski extension from Sm to R m + 1 ∖ { 0 } . One then obtains a unitary isomorphism from an L2-Hilbert space to a Hilbert space of solutions of the Dirac equation, that is to a Hilbert space of monogenic functions.
Clifford algebras, noncommutative tori and universal quantum computers
Vlasov, Alexander Yu.
2001-01-01
Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presente...
GENERALIZED p-FORMS ELECTRODYNAMICS IN CLIFFORD SPACES
Castro, C
2003-01-01
Using Clifford algebraic methods we describe how to generalize Maxwell theory of Electrodynamics asociated with ordinary point-charges to a generalized Maxwell theory in Clifford spaces involving extended-charges and p-forms of arbitrary rank. Clifford algebras contain the appropriate algebraic-geometric features to implement the principle of polydimensional transformations (branes of different dimensionality are rotated into each other) that could possibly lead to a proper formulation of string and M theory.
On alphabetic presentations of Clifford algebras and their possible applications
Toppan, F.; Verbeek, P.W.
2009-01-01
In this paper, we address the problem of constructing a class of representations of Clifford algebras that can be named “alphabetic (re)presentations.” The Clifford algebra generators are expressed as m-letter words written with a three-character or a four-character alphabet. We formulate the
Canonical forms for single-qutrit Clifford+T operators
Glaudell, Andrew N.; Ross, Neil J.; Taylor, Jacob M.
2018-01-01
We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for ...
International Nuclear Information System (INIS)
Blinder, S M
2003-01-01
It is shown how point charges and point dipoles with finite self-energies can be accommodated in classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors the physical reality of vacuum polarization. Our results reduce to conventional electrodynamics for scales large compared to the classical electron radius r 0 ∼ 2.8 x 10 -15 m. A classical simulation for a structureless electron is proposed, with the appropriate values of mass, spin and magnetic moment
Kultuurantropoloog Clifford Geertzi mälestusõhtu
2006-01-01
Tallinna Ülikoolis peetakse homme Ameerika kultuurantropoloogi Clifford Geertzi mälestusõhtut, esinevad rektor Rein Raud, Eesti Humanitaarinstituudi dotsent Lorenzo Cañás Bottos ja kultuuriteooria lektor Marek Tamm
The naked spinor a rewrite of Clifford algebra
Morris, Dennis
2015-01-01
This book is about spinors. The whole mathematical theory of spinors is within Clifford algebra, and so this book is about Clifford algebra. Spinor theory is really the theory of empty space, and so this book is about empty space. The whole of Clifford algebra is rewritten in a much simpler form, and so the whole of spinor theory is rewritten in a much simpler form. Not only does this book make Clifford algebra simple and obvious, but it lifts the fog and mirrors from this area of mathematics to make it clear and obvious. In doing so, the true nature of spinors is revealed to the reader, and, with that, the true nature of empty space. To understand this book you will need an elementary knowledge of linear algebra (matrices) an elementary knowledge of finite groups and an elementary knowledge of the complex numbers. From no more than that, you will gain a very deep understanding of Clifford algebra, spinors, and empty space. The book is well written with all the mathematical steps laid before the reader in a w...
On Special Functions in the Context of Clifford Analysis
Malonek, H. R.; Falcão, M. I.
2010-09-01
Considering the foundation of Quaternionic Analysis by R. Fueter and his collaborators in the beginning of the 1930s as starting point of Clifford Analysis, we can look back to 80 years of work in this field. However the interest in multivariate analysis using Clifford algebras only started to grow significantly in the 70s. Since then a great amount of papers on Clifford Analysis referring different classes of Special Functions have appeared. This situation may have been triggered by a more systematic treatment of monogenic functions by their multiple series development derived from Gegenbauer or associated Legendre polynomials (and not only by their integral representation). Also approaches to Special Functions by means of algebraic methods, either Lie algebras or through Lie groups and symmetric spaces gained by that time importance and influenced their treatment in Clifford Analysis. In our talk we will rely on the generalization of the classical approach to Special Functions through differential equations with respect to the hypercomplex derivative, which is a more recently developed tool in Clifford Analysis. In this context special attention will be payed to the role of Special Functions as intermediator between continuous and discrete mathematics. This corresponds to a more recent trend in combinatorics, since it has been revealed that many algebraic structures have hidden combinatorial underpinnings.
The investigation of platonic solids symmetry operations with clifford algebra
International Nuclear Information System (INIS)
Kilic, A.
2005-01-01
The geometric algebra produces the new fields of view in the modern mathematical physics, definition of bodies and rearranging for equations of mathematics and physics. The new mathematical approaches play an important role in the progress of physics. After presenting Clifford algebra and quarantine's, the symmetry operations with Clifford algebra and quarantine's are defined. This symmetry operations are applied to a Platonic solids, which are called as tetrahedron, cube, octahedron, icosahedron and dodecahedron. Also, the vertices of Platonic solids presented in the Cartesian coordinates are calculated
Castro, C
2004-01-01
We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R ) and complexified Clifford Cl_C ( 4 ) algebra related to Twistors. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl ( 1 ,7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M, F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, Brandt's action related the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries) followed by a...
On the representation of generalized Dirac (Clifford) algebras
International Nuclear Information System (INIS)
Srivastava, T.
1981-10-01
Some results of Brauer and Weyl and of Jordan and Wigner on irreducible representations of generalized Dirac (Clifford) algebras have been proved, adopting a new and simple approach which (i) makes the whole subject straightforward for physicists and (ii) simplifies the demonstration of the fundamental theorem of Pauli. (author)
"Summer Schedule" and "The Fishin' Season": Cartoons by Clifford Berryman
Blackerby, Christine
2008-01-01
For 53 years, Clifford K. Berryman was a political cartoonist for "The Washington Post" and "The Washington Evening Star". He drew thousands of cartoons commenting on the congressional and presidential candidates, campaigns, issues, and elections of the first half of the twentieth century. Berryman was a Washington institution, and his decades of…
SIC POVMs and Clifford groups in prime dimensions
International Nuclear Information System (INIS)
Zhu Huangjun
2010-01-01
We show that in prime dimensions not equal to 3, each group covariant symmetric informationally complete positive operator valued measure (SIC POVM) is covariant with respect to a unique Heisenberg-Weyl (HW) group. Moreover, the symmetry group of the SIC POVM is a subgroup of the Clifford group. Hence, two SIC POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension 3, each group covariant SIC POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC POVM is a subgroup of at least one of the Clifford groups of these HW groups, respectively. There may exist two or three orbits of equivalent SIC POVMs for each group covariant SIC POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC POVMs in dimension 3, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC POVMs by regrouping of the fiducial vectors from different SIC POVMs which may or may not be on the same orbit of the extended Clifford group.
Antropologie tussen wetenschap en kunst : Essays over Clifford Geertz
Kuiper, Yme; Bakker, Jan Willem; Miedema, Jelle
1987-01-01
Clifford Geertz (*1926) is one of the most influential anthropologists of his generation. His most famous monographs and collection of essays are The Religion of Java, Agricultural Involution, Islam Observed, The Interpretation of Cultures, Local Knowledge, Negara: The Balinese Theatre State in
Friedmann-like cosmological models without singularity
International Nuclear Information System (INIS)
Kuchowicz, B.
1978-01-01
The Einstein-Cartan theory of gravitation ('general relativity with spin') provides a specific spin-spin contact interaction of matter, in addition to the usual long-range gravity. This new interaction enables us to prevent singularities in cosmological models. it is shown how this mechanism works in the case when the standard Einstein-Cartan equations are valid at a micro-physical level, and some spin-spin terms remain from the averaging procedure for randomly distributed spins. In contrast with the case of aligned spin distributions, it is possible to take over the isotropic and spatially homogeneous (i.e., Friedmannian) models into the Einstein-Cartan theory. These models can be made free from singularity, thanks to the self-interaction of spinning fluid. (author)
Riemann surfaces, Clifford algebras and infinite dimensional groups
International Nuclear Information System (INIS)
Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.
1990-01-01
We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)
AGAMA DAN INTEGRASI SOSIAL DALAM PEMIKIRAN CLIFFORD GEERTZ
Directory of Open Access Journals (Sweden)
Mahli Zainudin Tago
2017-03-01
Full Text Available Artikel ini menelaah hasil penelitian Clifford Geertz tentang keberagamaan masarakat di Mojokuto Jawa Timur. Tema yang diusung dalam artikel ini adalah interelasi antara agama dan masyarakat serta interaksi sosial antara berbagai kelompok sosial yang ada di Mojokuto Jawa Timur. Dari kajian terhadap interrelasi agama dan masyarakat dapat dipahami seberapa jauh pengaruh agama terhadap prilaku relegiousitas masyarakat Jawa, termasuk pengaruh budaya lokal terhadap agama itu sendiri, yang menurut pengamatan Clifford Geertz melahirkan ”Agama Jawa”. Sementara dari kajian terhadap interaksi dari berbagai kelompok sosial dapat dipahami bahwa, agama, di samping memiliki fungsi integrasi (kohesi sosial juga menjadi penyebab terjadinya konflik dalam masyarakat. Ketiga varian agama Jawa; santri, priyayi, dan abangan meskipun secara kualitas berbeda dan saling mengklaim bahwa komunitasnya yang paling baik dan benar namun ketiganya masih memperlihatkan nuansa tradisi Jawa. Bahkan, kaum santri yang ketat sekalipun dalam batas-batas tertentu pada kenyataannya masih mentolerir tradisi jawa.
Lie algebras for the Dirac-Clifford ring
International Nuclear Information System (INIS)
Mignaco, J.A.; Linhares, C.A.
1992-01-01
It is shown in a general way that the Dirac-Clifford ring formed by the Dirac matrices and all their products, for all even and odd spacetime dimensions D, span the cumulation algebras SU(2 D/2 ) for even D and SU(2 (D- 1 )/2 ) + SU(2 (D-1)/2 ) for odd D. Some physical consequences of these results are discussed. (author)
Algebraic structures in generalized Clifford analysis and applications to boundary value problems
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José Játem
2015-12-01
Full Text Available The present article has a threefold purpose: First it is a survey of the algebraic structures of generalized Clifford-type algebras and shows the main results of the corresponding Clifford-type analysis and its application to boundary value problems known so far. Second it is aimed to implement algorithms to provide the fast and accurate computation of boundary value problems for inhomogeneous equations in the framework of the generalized Clifford analysis. Finally it is also aimed to encourage the development of a generalized discrete Clifford analysis.
Clifford Continuous Wavelet Transforms in Ll0,2 and Ll0,3
International Nuclear Information System (INIS)
Bernstein, S.
2008-01-01
We consider Clifford-valued functions defined on R n . From the viewpoint of square integrable group representations a continuous wavelet transform is an irreducible continuous unitary representation of the affin group on the real line but also on R n . We will demonstrate that different Clifford continuous wavelet transforms can be obtained inside the calculus with similar properties than the real valued transform. Nevertheless, the Clifford wavelet transform is neither just a special vector transform nor just a wavelet transform applied to each component of the Clifford-valued function.
Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory
International Nuclear Information System (INIS)
Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.
2017-11-01
This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.
Initial singularity and pure geometric field theories
Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.
2018-01-01
In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.
Preventing singularities in the Einstein-Cartan cosmology
International Nuclear Information System (INIS)
Kuchowicz, B.
1977-01-01
The singularity in expanding cosmological models is an undesirable consequence of general relativity. It may be removed in the Einstein-Cartan theory of gravitation which is an extension of general relativity (''general relativity with spin''). In the Einstein-Cartan theory there appears a characteristic spin-spin interaction which counteracts the contraction of matter above a certain critical density, and thus prevents any singularity. Generalizations of homogeneous cosmological models may contain either locally aligned spins (along an asymmetry axis) or randomly distributed spins (and then only the mean spin density square is macroscopically meaningful). In both cases the singularity can be removed, if only the spin density does increase at a sufficiently fast rate with the contraction of matter. (author)
Kocia, Lucas; Love, Peter
2017-12-01
We show that qubit stabilizer states can be represented by non-negative quasiprobability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two—producing an exterior, or Grassmann, algebra—which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is noncontextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order ℏ0 with a finite number of terms. The T gate, which extends the Clifford gate set to one capable of universal quantum computation, requires a semiclassical expansion of the propagator to order ℏ1. We compare this approach to previous quasiprobability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasiprobability distributions from the odd d -dimensional case to d =2 qubits, which describe the noncontextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.
Joyce Clifford the Scholar: In Her Own Words.
Fulmer, Terry; Gibbons, M Patricia
2015-01-01
Dr Joyce H. Clifford was world renowned for her excellence in nursing administration and leadership. The purpose of this article is to examine her complete body of published scholarship and analyze her papers as a method of understanding her intellectual progression as a leader in the discipline, as well as to document how her conceptualization of professional practice and the practice environment advanced nursing practice and patient and family care. Using the qualitative method of narrative inquiry, a systematic analysis of her papers was conducted to describe the evolution of her scholarship and her impact on the discipline and patient care. We reviewed all known existing papers, categorized them into 3 stages, and discuss them here. Using quotes from her work, we have added her voice to the compelling professional practice issues she addressed in her lifetime.
Magnetic monopoles without strings by Kaehler-Clifford algebra
International Nuclear Information System (INIS)
Maia, A. Jr.; Recami, E.; Rodrigues, W.A. Jr.; Rosa, M.A.F.
1990-01-01
In place of Dirac monopoles with string, this paper presents monopoles without string on the basis of a generalized potential, the sum of a vector A and a pseudovector γB potential. By having recourse to the (graded) Clifford algebra which allows adding together tensors of different ranks (e.g., scalars + pseudoscalars + vectors + pseudovectors + . . .), in a previous paper we succeeded in constructing a Lagrangian and Hamiltonian formalism for interacting monopoles that can be regarded as satisfactory from various points of view. In the present note, after having completed that formalism, the authors put forth a purely geometrical interpretation of it within the Kahler algebra on differential forms, essential ingredients being the natural introduction of a generalized curvature and the Hodge decomposition. The authors thus pave the way for the extension of monopoles without string to non-abelian gauge groups. The analogies of this approach with supersymmetric theories are apparent
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Quantum evolution across singularities
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg
2008-01-01
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space)
Ishii, Shihoko
2014-01-01
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...
On supergroups with odd Clifford parameters and non-anticommutative supersymmetry
International Nuclear Information System (INIS)
Kuznetsova, Z.
2007-01-01
We investigate super groups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anti commutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for super groups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest non-trivial example is given by the N = 2 SQM with a real (1, 2, 1) multiplet and a cubic potential. The action is real. Depending on the overall sign ('Euclidean' or 'Lorentzian') of the deformation, a Bender-Boettcher pseudo-hermitian Hamiltonian is encountered when solving the equation of motion of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out. (author)
A Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies
Lu, Wei
2017-09-01
We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu-Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.
Charles Clifford en la exposición de la Photographic Society de Londres en 1854
Directory of Open Access Journals (Sweden)
Rachel Bullough Ainscough
2013-07-01
Full Text Available En 1854, el fotógrafo Charles Clifford expuso por primera vez en la exposición de la Photographic Society en Londres doce vistas de lugares y monumentos españoles. La selección de las fotografías no se debía a la casualidad sino a otros factores como la limitada extensión geográfica de la primera parte de la obra de Clifford, sus gustos particulares y su interés en temas históricos y el conservacionismo. En el artículo se aborda el tema de la primera visión de Clifford en el contexto de su obra y la transmisión de esta visión a una audiencia británica.
Properties of kinematic singularities
Energy Technology Data Exchange (ETDEWEB)
Coley, A A [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada); Hervik, S [Department of Mathematics and Natural Sciences, University of Stavanger, N-4036 Stavanger (Norway); Lim, W C [Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany); MacCallum, M A H, E-mail: aac@mathstat.dal.c, E-mail: sigbjorn.hervik@uis.n, E-mail: wclim@aei.mpg.d, E-mail: m.a.h.maccallum@qmul.ac.u [School of Mathematical Sciences, Queen Mary University of London, E1 4NS (United Kingdom)
2009-11-07
The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.
Nonlinear singular elliptic equations
International Nuclear Information System (INIS)
Dong Minh Duc.
1988-09-01
We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs
International Nuclear Information System (INIS)
Berry, M.V.
2002-01-01
For illumination with white light, the spectra near a typical isolated phase singularity (nodal point of the component wavelengths) can be described by a universal function of position, up to linear distortion and a weak dependence on the spectrum of the source. The appearance of the singularity when viewed by a human observer is predicted by transforming the spectrum to trichromatic variables and chromaticity coordinates, and then rendering the colours, scaled to constant luminosity, on a computer monitor. The pattern far from the singularity is a white that depends on the source temperature, and the centre of the pattern is flanked by intensely coloured 'eyes', one orange and one blue, separated by red, and one of the eyes is surrounded by a bright white circle. Only a small range of possible colours appears near the singularity; in particular, there is no green. (author)
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
Directory of Open Access Journals (Sweden)
Gabriel Martínez-Niconoff
2012-01-01
Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.
International Nuclear Information System (INIS)
Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis
2004-01-01
We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture
Directory of Open Access Journals (Sweden)
Hans Schonemann
1996-12-01
Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].
Numerical method of singular problems on singular integrals
International Nuclear Information System (INIS)
Zhao Huaiguo; Mou Zongze
1992-02-01
As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily
Some properties of generalized biregular functions with values in a Clifford algebra
International Nuclear Information System (INIS)
Le Hung Son; Tran Quyet Thang.
1992-09-01
In this paper some properties of holomorphic functions such as the Identity Theorem, the Maximum Modulus Principle, the Hartogs Extension Theorem are proved for a class of more general functions taking values in a Clifford algebra than the regular and biregular functions. (author). 7 refs
Extension problem for generalized multi-monogenic functions in Clifford analysis
International Nuclear Information System (INIS)
Tran Quyet Thang.
1992-10-01
The main purpose of this paper is to extend some properties of multi-monogenic functions, which is a generalization of monogenic functions in higher dimensions, for a class of functions satisfying Vekua-type generalized Cauchy-Riemann equations in Clifford Analysis. It is proved that the Hartogs theorem is valid for these functions. (author). 7 refs
Clifford algebras and the minimal representations of the 1D N-extended supersymmetry algebra
International Nuclear Information System (INIS)
Toppan, Francesco
2008-01-01
The Atiyah-Bott-Shapiro classification of the irreducible Clifford algebra is used to derive general properties of the minimal representations of the 1D N-Extended Supersymmetry algebra (the Z 2 -graded symmetry algebra of the Supersymmetric Quantum Mechanics) linearly realized on a finite number of fields depending on a real parameter t, the time. (author)
The Concept of Person in American Anthroplogy : The Cultural Perspective of Clifford Geertz
Kuiper, Yme; Kippenberg, Hans G.; Kuiper, Yme B.; Sanders, Andy F.
1990-01-01
The 'meanings-and-symbols' anthropologist Clifford Geertz wrote one of the most influential articles in anthropology: 'Religion as a Cultural System'. Some years later he published his collection of essays 'The Interpretation of Culture', that had a great impact on the humanities in the late 20th
Singularities in FLRW spacetimes
het Lam, Huibert; Prokopec, Tomislav
2017-12-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2017-01-01
We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...
Supersymmetry in singular spaces
Bergshoeff, Eric
2002-01-01
We discuss supersymmetry in spaces with a boundary, i.e. singular spaces. In particular, we discuss the situation in ten and five dimensions. In both these cases we review the construction of supersymmetric domain wall actions situated at the boundary. These domain walls act as sources inducing a
Singularities in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept
Charged singularities: repulsive effects
Energy Technology Data Exchange (ETDEWEB)
De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia
1980-07-01
The repulsive phenomena which a particle experiences in the vicinity of a naked singularity are investigated in the Kerr-Newman space-time. The aim is to extend the knowledge of this fact to charged solutions and to have a direct indication of how, in these situations, the gravitational and electrostatic interactions are competing.
Papapetrou's naked singularity is a strong curvature singularity
International Nuclear Information System (INIS)
Hollier, G.P.
1986-01-01
Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)
Evidence for maximal acceleration and singularity resolution in covariant loop quantum gravity.
Rovelli, Carlo; Vidotto, Francesca
2013-08-30
A simple argument indicates that covariant loop gravity (spin foam theory) predicts a maximal acceleration and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Singular potentials in quantum mechanics
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Koo, E. Ley
1995-10-01
This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs
Singularities: the Brieskorn anniversary volume
National Research Council Canada - National Science Library
Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M
1998-01-01
...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...
M theory and singularities of exceptional holonomy manifolds
International Nuclear Information System (INIS)
Acharya, Bobby S.; Gukov, Sergei
2004-12-01
M theory compactifications on G 2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory. (author)
String theory and cosmological singularities
Indian Academy of Sciences (India)
Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics.
Holographic complexity and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Barbón, José L.F. [Instituto de Física Teórica IFT UAM/CSIC,C/ Nicolás Cabrera 13, Campus Universidad Autónoma de Madrid,Madrid 28049 (Spain); Rabinovici, Eliezer [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2016-01-15
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
Are naked singularities really visible
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; De Felice, F [Alberta Univ., Edmonton (Canada); Nobili, L [Padua Univ. (Italy). Ist. di Fisica
1978-12-09
The question whether a Kerr naked singularity is actually visible from infinity is investigated; it is shown that in fact any signal which could be emitted from the singularity is infinitely red-shifted. This implies that naked singularities would be indistinguishable from a black hole.
Holographic complexity and spacetime singularities
International Nuclear Information System (INIS)
Barbón, José L.F.; Rabinovici, Eliezer
2016-01-01
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
Application of geometric algebra to electromagnetic scattering the Clifford-Cauchy-Dirac technique
Seagar, Andrew
2016-01-01
This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green's functions, double integrals, vector calculus and the combined field integral equation (CFIE). Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. The ultimate outcome is an integral formulation that lends itself to a more direct and efficient solution than conventionally is the case, and applies without exception to all types...
Magnetic monopoles without string in the Kaehler-Clifford algebra: a geometrical interpretation
International Nuclear Information System (INIS)
Maia Junior, A.; Recami, E.; Rodrigues Junior, W.A.; Rosa, M.A.F.
1989-01-01
In substitution for Dirac monopoles with string (and for topological monopoles) we have recently introduced monopoles without string on the basis of a generalized potential, the sum of a vector A and a pseudo-vector sub(γ5)B potential. By making recourse to the Clifford bundle C (τ M,g) [ T sub(x) M,g) = IR sup(1,3); C (T sub(x) M,g) = IR sub(1,3)], which just allows adding together for each x ε M tensors of different ranks, in a previous paper we succeeded in constructing a lagrangian and hamiltonian formalism for interacting monopoles and charges that can be regarded as satisfactory from various points of view. In the present note, after having completed our formalism, we put forth a purely geometrical interpretation of it within the Kaehler-Clifford bundle K (τ sup(*) M
Fault-tolerant quantum computing in the Pauli or Clifford frame with slow error diagnostics
Directory of Open Access Journals (Sweden)
Christopher Chamberland
2018-01-01
Full Text Available We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing solutions, for instance it does not require active error correction and results in a reduced error-correction overhead when error diagnostics is much slower than the gate time. In addition, we adapt our protocol to cases where the underlying error correction strategy chooses the optimal correction amongst all Clifford gates instead of the usual Pauli gates. The resulting Clifford frame protocol is of independent interest as it can increase error thresholds and could find applications in other areas of quantum computation.
Regular Functions with Values in Ternary Number System on the Complex Clifford Analysis
Directory of Open Access Journals (Sweden)
Ji Eun Kim
2013-01-01
Full Text Available We define a new modified basis i^ which is an association of two bases, e1 and e2. We give an expression of the form z=x0+ i ^z0-, where x0 is a real number and z0- is a complex number on three-dimensional real skew field. And we research the properties of regular functions with values in ternary field and reduced quaternions by Clifford analysis.
Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions
Yaşar, Banu Yılmaz; Özarslan, Mehmet Ali
2016-01-01
In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\\i}ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions. Applied Mathematics and Computation, 2014, 226 : 484-491] is defined. Several potentially useful properties of the unified family such as generating function, integral representation, Laplace transform and Mellin tran...
Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)
International Nuclear Information System (INIS)
Dubinskii, Yu A; Osipenko, A S
2000-01-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented
Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)
Dubinskii, Yu A.; Osipenko, A. S.
2000-02-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.
On magnetic monopoles (without a string) and the Clifford bundle formalism
International Nuclear Information System (INIS)
Recami, E.; Rodrigues, W.A. Jr.
1990-07-01
By adopting the Clifford Bundle language, we recently put forth a satisfactory lagrangian formalism for electromagnetism with magnetic monopoles without a string. Here, by taking advantage of the welcome opportunity of some recent comments by E. Comay (and while answering them), we ''complete'' that formalism. In particular, we show how the Lorentz forces and the motion equations, for both electric and magnetic charges, can be derived from the generalized Maxwell equations: without any further recourse to a variational principle. (author). 18 refs
Belinski, Vladimir
2018-01-01
Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...
Deformations of surface singularities
Szilárd, ágnes
2013-01-01
The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter
2007-01-01
We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....
International Nuclear Information System (INIS)
Habis, M.; Robichon, F.; Demonet, J.F.
1996-01-01
Of late ten years, neurologists are studying the brain of the dyslectics. The cerebral imagery (NMR imaging, positron computed tomography) has allowed to confirm the anatomical particularities discovered by some of them: asymmetry default of cerebral hemispheres, size abnormally large of the white substance mass which connect the two hemispheres. The functional imagery, when visualizing this singular brain at work, allows to understand why it labors to reading. (O.M.)
A toy model for higher spin Dirac operators
International Nuclear Information System (INIS)
Eelbode, D.; Van de Voorde, L.
2010-01-01
This paper deals with the higher spin Dirac operator Q 2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight (5/2, 3/2, 1/2,..., 1/2). . This operator acts as a toy model for generalizations of the classical Rarita-Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.
CSIR Research Space (South Africa)
Roux, FS
2013-09-01
Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...
Cosmological models without singularities
International Nuclear Information System (INIS)
Petry, W.
1981-01-01
A previously studied theory of gravitation in flat space-time is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models there exist at the beginning of the universe-in contrast to Einstein's theory-very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal to zero and cosmological constant ALPHA >= O. (author)
Plane waves with weak singularities
International Nuclear Information System (INIS)
David, Justin R.
2003-03-01
We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)
EDITORIAL: The plurality of optical singularities
Berry, Michael; Dennis, Mark; Soskin, Marat
2004-05-01
electric (or magnetic) polarization ellipse is purely circular (C lines) or purely linear (L lines). The patterns of ellipse-fields are different for purely paraxial and fully three-dimensional fields. White-light diffraction generates richly coloured vortices—the colours of dark light. The description of these chromatic effects, and also those associated with polarization singularities, leads to new applications of coherence theory. For non-monochromatic light, it is natural to seek singularities of the full electromagnetic field, rather than of the electric or magnetic field separately. Such electromagnetic singularities are the Riemann-Silberstein vortices; these are relativistically covariant nodal lines of a complex scalar field constructed from the electromagnetic field. Optical fields have dynamical aspects, particularly those associated with angular momentum. Although angular momentum is not inevitably associated with optical singularities, in practice the two phenomena can occur together. Orbital angular momentum is associated with the spatial structure of light, and in beams with optical vortices it can be used to rotate particles in the field. Spin angular momentum is associated with the polarization structure of the light. There are tricky questions associated with the angular momentum of light in a refracting medium, echoing the Abraham-Minkowski controversy about linear momentum. In optically nonlinear materials (leading to second-harmonic generation, for example), new classes of phenomena can occur, such as, for example, dynamical interaction between vortex lines, whose stability needs to be considered. At a more fundamental level, it is important to investigate quantum effects associated with optical singularities, and a start has been made. The dark centre of an optical vortex can be regarded as a window onto the vacuum fluctuations of quantum optics, with the quantum core emerging as a distinct entity when the classical light is intense. And for light
Residues and duality for singularity categories of isolated Gorenstein singularities
Murfet, Daniel
2009-01-01
We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.
A. V. Volyar
2002-01-01
The present review is devoted to the optical vortex behavior both in free space and optical fibers. The processes of the vortex transformations in perturbed optical fibers are analyzed on the base of the operator of the spin – orbit interaction in order to forecast the possible ways of manufacturing the vortex preserving fibers and their applications in supersensitive optical devices.
Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
Pavsic, Matej
2005-01-01
The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Eucl...
On the generalized Hankel±Clifford transformation of arbitrary order
Indian Academy of Sciences (India)
Е5Ж where C Y ЕxyЖИЕxyЖЕ З Жa2 J └ Е2. БББББ xy p. Ж is a generalized Bessel±Clifford function of first kind of order Е └ Ж, satisfying the differential equation xyHH └ Е З └ 1ЖyHЗ. Е x└1 З 1Жy И 0, which can be inverted by formulae. Proc. Indian Acad. Sci. (Math. Sci.), Vol. 110, No. 3, August 2000, pp. 293±304.
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
Local unitary versus local Clifford equivalence of stabilizer and graph states
International Nuclear Information System (INIS)
Zeng, Bei; Chung, Hyeyoun; Cross, Andrew W.; Chuang, Isaac L.
2007-01-01
The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU-equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [Phys. Rev. A 71, 062323 (2005)]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence (LU LC) to include all stabilizer states represented by graphs with cycles of length neither 3 nor 4. To compare our result with Van den Nest et al.'s, we show that any stabilizer state of distance δ=2 is beyond their criterion. We then further prove that LU LC holds for a more general class of stabilizer states of δ=2. We also explicitly construct graphs representing δ>2 stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with 2 m -1 (m≥4) vertices using quantum error-correcting codes which have non-Clifford transversal gates
Naked singularities are not singular in distorted gravity
Energy Technology Data Exchange (ETDEWEB)
Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)
2014-07-15
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Naked singularities are not singular in distorted gravity
Garattini, Remo; Majumder, Barun
2014-07-01
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Naked singularities are not singular in distorted gravity
International Nuclear Information System (INIS)
Garattini, Remo; Majumder, Barun
2014-01-01
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity
Higher spin resolution of a toy big bang
Krishnan, Chethan; Roy, Shubho
2013-08-01
Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three-dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS3, the solutions are invariantly characterized by their holonomies. We show that the dS3 quotient singularity can be desingularized by an SL(3,C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT2 dual to dS3 in the sense of dS/CFT.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
Spin-spin correlations in the tt'-Hubbard model
International Nuclear Information System (INIS)
Husslein, T.; Newns, D.M.; Mattutis, H.G.; Pattnaik, P.C.; Morgenstern, I.; Singer, J.M.; Fettes, W.; Baur, C.
1994-01-01
We present calculations of the tt'-Hubbard model using Quantum Monte Carlo techniques. The parameters are chosen so that the van Hove Singularity in the density of states and the Fermi level coincide. We study the behaviour of the system with increasing Hubbard interaction U. Special emphasis is on the spin-spin correlation (SSC). Unusual behaviour for large U is observed there and in the momentum distribution function (n(q)). (orig.)
Singularity resolution in quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Van Hove singularities revisited
International Nuclear Information System (INIS)
Dzyaloshinskii, I.
1987-07-01
Beginning with the work of Hirsch and Scalapino the importance of ln 2 -Van Hove singularity in T c -enhancement in La 2 CuO 4 -based compounds was realized, which is nicely reviewed by Rice. However, the theoretical treatment carried out before is incomplete. Two things were apparently not paid due attention to: interplay of particle-particle and particle-hole channels and Umklapp processes. In what follows a two-dimensional weak coupling model of LaCuO 4 will be solved exactly in the ln 2 -approximation. The result in the Hubbard limit (one bare charge) is that the system is unstable at any sign of interaction. Symmetry breaking moreover is pretty peculiar. Of course, there are separate singlet superconducting pairings in the pp-channel (attraction) and SDW (repulsion) and CDW (attraction) in the ph-channel. It is natural that Umklapps produce an SDW + CDW mixture at either sign of the interaction. What is unusual is that both the pp-ph interplay and the Umklapps give rise to a monster-coherent SS + SDW + CDW mixture, again at either sign of the bare charge. In the general model where all 4 charges involved are substantially different, the system might remain metallic. A more realistic approach which takes into account dopping in La-M-Cu-O and interlayer interaction provides at least a qualitative understanding of the experimental picture. 10 refs, 5 figs
Dual Vector Spaces and Physical Singularities
Rowlands, Peter
Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.
Directory of Open Access Journals (Sweden)
Mohadeseh Kanafchian
2017-04-01
In this paper, we first give a brief introduction into chaotic image encryption and then we investigate some important properties and behaviour of the logistic map. The logistic map, aperiodic trajectory, or random-like fluctuation, could not be obtained with some choice of initial condition. Therefore, a noisy logistic map with an additive system noise is introduced. The proposed scheme is based on the extended map of the Clifford strange attractor, where each dimension has a specific role in the encryption process. Two dimensions are used for pixel permutation and the third dimension is used for pixel diffusion. In order to optimize the Clifford encryption system we increase the space key by using the noisy logistic map and a novel encryption scheme based on the Clifford attractor and the noisy logistic map for secure transfer images is proposed. This algorithm consists of two parts: the noisy logistic map shuffle of the pixel position and the pixel value. We use times for shuffling the pixel position and value then we generate the new pixel position and value by the Clifford system. To illustrate the efficiency of the proposed scheme, various types of security analysis are tested. It can be concluded that the proposed image encryption system is a suitable choice for practical applications.
Directory of Open Access Journals (Sweden)
Marija Krstić
2016-03-01
Full Text Available Gordana Gorunović. Antropologija Kliforda Gerca. Kulturna teorija i interpretativna analiza kultura. 2010. Beograd: Srpski genealoški centar i Odeljenje za etnologiju i antropologiju Filozofskog fakulteta. str. 286. [The Anthropology of Clifford Geertz. Cultural Theory and the Interpretative Analysis of Cultures
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.
Local and nonlocal space-time singularities
International Nuclear Information System (INIS)
Konstantinov, M.Yu.
1985-01-01
The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established
New insights in the standard model of quantum physics in Clifford algebra
Daviau, Claude
2013-01-01
Why Clifford algebra is the true mathematical frame of the standard model of quantum physics. Why the time is everywhere oriented and why the left side shall never become the right side. Why positrons have also a positive proper energy. Why there is a Planck constant. Why a mass is not a charge. Why a system of particles implies the existence of the inverse of the individual wave function. Why a fourth neutrino should be a good candidate for black matter. Why concepts as “parity” and “reverse” are essential. Why the electron of a H atom is in only one bound state. Plus 2 very remarkable identities, and the invariant wave equations that they imply. Plus 3 generations and 4 neutrinos. Plus 5 dimensions in the space and 6 dimensions in space-time…
Kaluza-Klein-Carmeli Metric from Quaternion-Clifford Space, Lorentz' Force, and Some Observables
Directory of Open Access Journals (Sweden)
Christianto V.
2008-04-01
Full Text Available It was known for quite long time that a quaternion space can be generalized to a Clifford space, and vice versa; but how to find its neat link with more convenient metric form in the General Relativity theory, has not been explored extensively. We begin with a representation of group with non-zero quaternions to derive closed FLRW metric [1], and from there obtains Carmeli metric, which can be extended further to become 5D and 6D metric (which we propose to call Kaluza-Klein-Carmeli metric. Thereafter we discuss some plausible implications of this metric, beyond describing a galaxy’s spiraling motion and redshift data as these have been done by Carmeli and Hartnett [4, 5, 6]. In subsequent section we explain Podkletnov’s rotating disc experiment. We also note possible implications to quantum gravity. Further observations are of course recommended in order to refute or verify this proposition.
Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group
International Nuclear Information System (INIS)
Katzgraber, Helmut G.; Bombin, H.; Andrist, Ruben S.; Martin-Delgado, M. A.
2010-01-01
We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.
About the velocity operator for spinning particles in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Salesi, Giovanni [Universita Statale di Catania (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Catania (Italy); Recami, Erasmo; Rodrigues Junior, Waldyr A. [Universidade Estadual de Campinas, SP (Brazil). Dept. de Matematica Aplicada
1995-12-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into sensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector. (author). 19 refs.
About the velocity operator for spinning particles in quantum mechanics
International Nuclear Information System (INIS)
Salesi, Giovanni; Recami, Erasmo; Rodrigues Junior, Waldyr A.
1995-12-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into sensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector. (author). 19 refs
On the singularities of solutions to singular perturbation problems
International Nuclear Information System (INIS)
Fruchard, A; Schaefke, R
2005-01-01
We consider a singularly perturbed complex first order ODE εu ' Φ(x, u, a, ε), x, u element of C, ε > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot
On the singularities of solutions to singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Fruchard, A [Laboratoire de Mathematiques, Informatique et Applications, Faculte des Sciences et Techniques, Universite de Haute Alsace, 4 rue des Freres Lumiere, 68093 Mulhouse cedex (France); Schaefke, R [Departement de Mathematiques, Universite Louis Pasteur, 7 rue Rene-Descartes, 67084 Strasbourg cedex (France)
2005-01-01
We consider a singularly perturbed complex first order ODE {epsilon}u ' {phi}(x, u, a, {epsilon}), x, u element of C, {epsilon} > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot.
Rickards, Lesley
2018-02-01
This short note provides comments and a response to the paper published in Earth Systems and Environment by Albert Parker and Clifford D. Ollier (Volume 1, December 2017) entitled "Is the Sea Level Stable at Aden, Yemen?"
Is the cosmological singularity compulsory
International Nuclear Information System (INIS)
Bekenstein, J.D.; Meisels, A.
1980-01-01
The cosmological singularity is inherent in all conventional general relativistic cosmological models. There can be no question that it is an unphysical feature; yet there does not seem to be any convervative way of eliminating it. Here we present singularity-free isotropic cosmological models which are indistinguishable from general relativistic ones at late times. They are based on the general theory of variable rest masses that we developed recently. Outside cosmology this theory simulates general relativity well. Thus it provides a framework incorporating those features which have made geneal relativity so sucessful while providing a way out of singularity dilemma. The cosmological models can be made to incorporate Dirac's large numbers hypothesis. G(now)/G(0)approx.10 -38
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
Energy Technology Data Exchange (ETDEWEB)
Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)
2017-12-15
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
Singularities in geodesic surface congruence
International Nuclear Information System (INIS)
Cho, Yong Seung; Hong, Soon-Tae
2008-01-01
In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.
Singular perturbation of simple eigenvalues
International Nuclear Information System (INIS)
Greenlee, W.M.
1976-01-01
Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem
Singularity Theory and its Applications
Stewart, Ian; Mond, David; Montaldi, James
1991-01-01
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.
Ambient cosmology and spacetime singularities
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Singular moduli and Arakelov intersection
International Nuclear Information System (INIS)
Weng Lin.
1994-05-01
The value of the modular function j(τ) at imaginary quadratic arguments τ in the upper half plane is usually called singular moduli. In this paper, we use Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as the degenerate one of Gross and Zagier on Heegner points and derivatives of L-series in their paper [GZ1], and is parallel to the result in [GZ2]. (author). 2 refs
Singularities in minimax optimization of networks
DEFF Research Database (Denmark)
Madsen, Kaj; Schjær-Jacobsen, Hans
1976-01-01
A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the li......A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used...
String theory and cosmological singularities
Indian Academy of Sciences (India)
recent times, string theory is providing new perspectives of such singularities which .... holes appear as stacks of a large number of D-branes wrapped in internal .... results into a well-known measure factor which makes the wave function into a.
Charged singularities: the causality violation
Energy Technology Data Exchange (ETDEWEB)
De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia
1980-12-01
A search is made for examples of particle trajectories which, approaching a naked singularity from infinity, make up for lost time before going back to infinity. In the Kerr-Newman metric a whole family of such trajectories is found showing that the causality violation is indeed a non-avoidable pathology.
Interval matrices: Regularity generates singularity
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří; Shary, S.P.
2018-01-01
Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016
Computation at a coordinate singularity
Prusa, Joseph M.
2018-05-01
Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar
Remarks on gauge variables and singular Lagrangians
International Nuclear Information System (INIS)
Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.
1977-01-01
The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.
Branch-cut singularities in thermodynamics of Fermi liquid systems.
Shekhter, Arkady; Finkel'stein, Alexander M
2006-10-24
The recently measured spin susceptibility of the two-dimensional electron gas exhibits a strong dependence on temperature, which is incompatible with the standard Fermi liquid phenomenology. In this article, we show that the observed temperature behavior is inherent to ballistic two-dimensional electrons. Besides the single-particle and collective excitations, the thermodynamics of Fermi liquid systems includes effects of the branch-cut singularities originating from the edges of the continuum of pairs of quasiparticles. As a result of the rescattering induced by interactions, the branch-cut singularities generate nonanalyticities in the thermodynamic potential that reveal themselves in anomalous temperature dependences. Calculation of the spin susceptibility in such a situation requires a nonperturbative treatment of the interactions. As in high-energy physics, a mixture of the collective excitations and pairs of quasiparticles can effectively be described by a pole in the complex momentum plane. This analysis provides a natural explanation for the observed temperature dependence of the spin susceptibility, both in sign and in magnitude.
The plays of Lillian Hellman, Clifford Odets and William Inge on Slovene stages
Directory of Open Access Journals (Sweden)
Mateja Slunjski
2002-12-01
Full Text Available After the Second World War, Slovene theatres started to include in their repertoires more and more American authors and their plays. Their choice were varied, from serious dramas by Eugene O'Neill, Tennessee Williams and Arthur Miller, to comedies by Norman Krasna and John Van Druten dependant mostly on the availability of the texts. In the immediate postwar years the theatres liked to present playwrights with progressive ideas in their plays, such as Lillian Hellman and her "The Little Foxes", which was successfully produced at three Slovene theatres, while her "The Children's Hour" received negative reviews. In the fifties, three theatres chose two plays by Clifford Odets, "Golden Boy" and "Country Girl", mainly because of his socially critical ideas and his admiration of humanity. His plays were rather well received; however, the critics doubted his literary genius. William Inge and his plays, "Come Back, Little Sheba", "Picnic" and "Bus Stop", chosen mainly because of the warmth with which the author depicted the tragedy and the beauty of life, were produced at three Slovene theatres. The author received rather wide-ranging opinions from the critics. Some thought him to be an unoriginal depicter of dull American life, while others praised his lyricism and new dramatic techniques.
Clifford Geertz y el ensamble de un proyecto antropológico crítico
Directory of Open Access Journals (Sweden)
Carlos del Cairo
2008-01-01
Full Text Available La obra del antropólogo Clifford Geertz (1926-2006 transformó las convenciones de la escritura etnográfica a mediados de los años sesenta. Su proyecto antropológico catalogado como interpretativo, simbólico o hermenéutico, estuvo en constante ensamblaje, como él mismo lo definió, y fue considerado revolucionario por muchos, reaccionario por algunos o problemático y bastante frágil, por otros. En este artículo destacamos el sentido y la pertinencia de algunos de los planteamientos teóricos y empíricos de Geertz para el pensamiento social contemporáneo. También exploramos algunas de las críticas más incisivas a su obra, que enuncian las fisuras de sus planteamientos, caracterizados por ser cuestionadores y, a la vez, vehementemente cuestionados por la tradición positivista y postmodernista en antropología.
Analysis of singularity in redundant manipulators
International Nuclear Information System (INIS)
Watanabe, Koichi
2000-03-01
In the analysis of arm positions and configurations of redundant manipulators, the singularity avoidance problems are important themes. This report presents singularity avoidance computations of a 7 DOF manipulator by using a computer code based on human-arm models. The behavior of the arm escaping from the singular point can be identified satisfactorily through the use of 3-D plotting tools. (author)
Energy conditions and spacetime singularities
International Nuclear Information System (INIS)
Tipler, F.J.
1978-01-01
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete
Multidimensional singular integrals and integral equations
Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S
1965-01-01
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals
Fundamental solutions of singular SPDEs
International Nuclear Information System (INIS)
Selesi, Dora
2011-01-01
Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.
Why the Singularity Cannot Happen
Modis, Theodore
2012-01-01
The concept of a Singularity as described in Ray Kurzweil's book cannot happen for a number of reasons. One reason is that all natural growth processes that follow exponential patterns eventually reveal themselves to be following S-curves thus excluding runaway situations. The remaining growth potential from Kurzweil's ''knee'', which could be approximated as the moment when an S-curve pattern begins deviating from the corresponding exponential, is a factor of only one order of magnitude grea...
Black holes, singularities and predictability
International Nuclear Information System (INIS)
Wald, R.M.
1984-01-01
The paper favours the view that singularities may play a central role in quantum gravity. The author reviews the arguments leading to the conclusion, that in the process of black hole formation and evaporation, an initial pure state evolves to a final density matrix, thus signaling a breakdown in ordinary quantum dynamical evolution. Some related issues dealing with predictability in the dynamical evolution, are also discussed. (U.K.)
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
Singularities in Free Surface Flows
Thete, Sumeet Suresh
Free surface flows where the shape of the interface separating two or more phases or liquids are unknown apriori, are commonplace in industrial applications and nature. Distribution of drop sizes, coalescence rate of drops, and the behavior of thin liquid films are crucial to understanding and enhancing industrial practices such as ink-jet printing, spraying, separations of chemicals, and coating flows. When a contiguous mass of liquid such as a drop, filament or a film undergoes breakup to give rise to multiple masses, the topological transition is accompanied with a finite-time singularity . Such singularity also arises when two or more masses of liquid merge into each other or coalesce. Thus the dynamics close to singularity determines the fate of about-to-form drops or films and applications they are involved in, and therefore needs to be analyzed precisely. The primary goal of this thesis is to resolve and analyze the dynamics close to singularity when free surface flows experience a topological transition, using a combination of theory, experiments, and numerical simulations. The first problem under consideration focuses on the dynamics following flow shut-off in bottle filling applications that are relevant to pharmaceutical and consumer products industry, using numerical techniques based on Galerkin Finite Element Methods (GFEM). The second problem addresses the dual flow behavior of aqueous foams that are observed in oil and gas fields and estimates the relevant parameters that describe such flows through a series of experiments. The third problem aims at understanding the drop formation of Newtonian and Carreau fluids, computationally using GFEM. The drops are formed as a result of imposed flow rates or expanding bubbles similar to those of piezo actuated and thermal ink-jet nozzles. The focus of fourth problem is on the evolution of thinning threads of Newtonian fluids and suspensions towards singularity, using computations based on GFEM and experimental
Materialism in Clifford Odets' Golden Boy and Edward Albee's The American Dream
Directory of Open Access Journals (Sweden)
Nadia Ali Akbar
2017-07-01
Full Text Available The degration in the modern pattern of heroism during the 20th century America started with the advent of science and materialistic look of life. Modern scientific studies proposed that "man is alone, absolutely alone in a universe in which his very appearance is a cosmic accident" tending, at his best, towards an animal ancestor. Man was not cared for by spiritual or moral providence. The over soul, which the American hero was supposed to melt in, was replaced by the machine which ironically metamorphosed his significance. Modern American's pursuit of worldly gains was ultimately made at the expense of his essential spiritual and moral priorities as any material gain must be balanced against a spiritual loss. This fact is made concrete in the dehumanized character of Joe, the protagonist of Clifford Odets's Golden Boy (1937, through his aggressive anti-social behaviour. He is characterized by a lack of community. Golden Boy shows how the Americans are increasingly enervated by economic strains, racist tensions and political intimidation. Almost everywhere was the lost sense of community, a sense of inner defeat and lost self-esteem. The lost sense of community was very harmful as the Americans started looking for survival at the expense of society itself; social and economic injustices arose. Odets introduces such a motif in the character of Joe. Edward Albee (1928 is one of the significant American dramatists of the 20th century, uses the dramatic forms that were prominent on the postwar European stage to articulate an unsetting vision of the United States. He wrote about the emptiness of American cultures and the uncertainties of human existence. His work castigated what he sees as a blindly materialistic society devoid of any real sense of values and national purpose. He is against the materialism in the society which goes along with consumerism. The characters in The American Dream (1961 are materialistic. Mommy represents women's addiction
Directory of Open Access Journals (Sweden)
Miloš Milenković
2016-02-01
Full Text Available Drawing on the explanation already offered for the confusion of positivism with realism in the epistemological imagination of the author and founder of postmodern anthropology, the paper analyzes the moral implications of dealing with problems characteristic of the philosophy of science by literary-theoretical means. The transdisciplinary migration of "realism" from literary theory to social science methodology has produced a whole new history of anthropology. The history of pre-postmodern anthropology constructed in this manner can be said to fit the register of some sort of comparative-cultural theory of retroactive moral judgement, complementing postmodern anthropology as a general theory of writing by political subjects, so that the theoretical-methodological dilemmas of postmodern anthropology do not constitute proof of the legitimacy of a holistic interpretation of the discipline’s founders’ intentions, but rather lead to neo-pyrrhonic, formalistic endeavours to uphold, by respecting academic trappings, the academic authority of the discipline whose subject, method and purpose, as a rule, even colleagues from adjacent departments for various reasons fail to understand. In the paper, evidence for this is derived from Clifford's writing of Malinowski, and the moral implications of the unfortunate analogy between the writing of political subjects and the writing of disciplinary founders are followed through. The paper then goes on to explain that the critique of the possibilities of misuse, particularly through political instrumentalization, of anthropological fictions as evidence of Others did not have to come at the cost of sacrificing the semblance of continuity in the establishment of anthropology as a proper academic discipline.
Mathematical models with singularities a zoo of singular creatures
Torres, Pedro J
2015-01-01
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
On important precursor of singular optics (tutorial)
Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.
2018-01-01
The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].
Symmetry generators in singular theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1989-01-01
It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Singularities of Type-Q ABS Equations
Directory of Open Access Journals (Sweden)
James Atkinson
2011-07-01
Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.
The geometry of warped product singularities
Stoica, Ovidiu Cristinel
In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.
The dominant balance at cosmological singularities
International Nuclear Information System (INIS)
Cotsakis, Spiros; Barrow, John D
2007-01-01
We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Dressing up a Kerr naked singularity
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Nobili, L [Padua Univ. (Italy). Ist. di Fisica
1979-06-11
The evolution of a naked singularity surrounded by an accreting disk of matter is studied; two kinds of disks are considered: the standard thin-disk model and the thick barytropic model, for several initial conditions. It is shown that any Kerr naked singularity slows down in a finite time to a maximal Kerr black hole. The final mass, the luminosity and the time of evolution of the singularity are evaluated.
Transition currents in diagonal spin basis
International Nuclear Information System (INIS)
Rogalev, R.N.
1996-01-01
Scalar and pseudoscalar densities, vector, pseudovector and tensor currents are expressed in terms of momentum and spin vectors of the corresponding particles in an explicitly covariant way. The obtained expressions are free of singularities and make it possible to draw a number of identities, which relate axial-vector, vector and tensor currents to each other. 8 refs
Arian Zad, Hamid; Ananikian, Nerses
2017-11-01
We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.
Naked singularity, firewall, and Hawking radiation.
Zhang, Hongsheng
2017-06-21
Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.
Spacetime averaging of exotic singularity universes
International Nuclear Information System (INIS)
Dabrowski, Mariusz P.
2011-01-01
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
Coupled singular and non singular thermoelastic system and double lapalce decomposition methods
Hassan Gadain; Hassan Gadain
2016-01-01
In this paper, the double Laplace decomposition methods are applied to solve the non singular and singular one dimensional thermo-elasticity coupled system and. The technique is described and illustrated with some examples
Valenzuela, Sergio O; Saitoh, Eiji; Kimura, Takashi
2012-01-01
In a new branch of physics and technology called spin-electronics or spintronics, the flow of electrical charge (usual current) as well as the flow of electron spin, the so-called 'spin current', are manipulated and controlled together. This book provides an introduction and guide to the new physics and application of spin current.
Papapetrou's naked singularity is a strong curvature singularity
Energy Technology Data Exchange (ETDEWEB)
Hollier, G.P.
1986-11-01
Following Papapetrou (1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)), a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture.
The Semantics of Plurals: A Defense of Singularism
Florio, Salvatore
2010-01-01
In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…
Geometrical spin symmetry and spin
International Nuclear Information System (INIS)
Pestov, I. B.
2011-01-01
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Stable singularities in string theory
International Nuclear Information System (INIS)
Aspinwall, P.S.; Morrison, D.R.; Gross, M.
1996-01-01
We study a topological obstruction of a very stringy nature concerned with deforming the target space of an N=2 non-linear σ-model. This target space has a singularity which may be smoothed away according to the conventional rules of geometry, but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten. (orig.). With 3 figs
Directory of Open Access Journals (Sweden)
Elvio Alccinelli
2001-07-01
Full Text Available En este artículo pretendemos mostrar que le conjunto de las economías singulares, si bien pequeño desde el punto de vista de la topología y/o desde el punto de vista de la teoría de la medida, tiene importantes efectos en el desarrollo de los regímenes económicos. Es el responsable de los cambios abruptos en los estados de equilibrio y de la multiplicidad de tales estados. Permite además establecer a partir de los tipos de singularidades posibles, una partición del conjunto de economías según tenga lugar uno u otro tipo de singularidad cuya presencia o no, caracteriza el comportamiento posible de la economía en cuestión.
Quantum transitions through cosmological singularities
Energy Technology Data Exchange (ETDEWEB)
Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)
2017-07-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Coulomb branches with complex singularities
Argyres, Philip C.; Martone, Mario
2018-06-01
We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.
Quantum transitions through cosmological singularities
International Nuclear Information System (INIS)
Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick
2017-01-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
Building Reproducible Science with Singularity Containers
CERN. Geneva
2018-01-01
Michael Bauer first began working with containers at GSI national lab in Darmstadt, Germany, in 2017 while taking a semester off of school at the University of Michigan. Michael met Greg Kurtzer, project lead of Singularity, during his time at GSI and he began contributing heavily to the Singularity project. At the start of summer 2017, Greg hired Michael to work at the ...
Reasons for singularity in robot teleoperation
DEFF Research Database (Denmark)
Marhenke, Ilka; Fischer, Kerstin; Savarimuthu, Thiusius Rajeeth
2014-01-01
In this paper, the causes for singularity of a robot arm in teleoperation for robot learning from demonstration are analyzed. Singularity is the alignment of robot joints, which prevents the configuration of the inverse kinematics. Inspired by users' own hypotheses, we investigated speed and dela...
The Geometry of Black Hole Singularities
Directory of Open Access Journals (Sweden)
Ovidiu Cristinel Stoica
2014-01-01
Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.
Singularities in the nonisotropic Boltzmann equation
International Nuclear Information System (INIS)
Garibotti, C.R.; Martiarena, M.L.; Zanette, D.
1987-09-01
We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs
Cold atoms in singular potentials
International Nuclear Information System (INIS)
Denschlag, J. P.
1998-09-01
We studied both theoretically and experimentally the interaction between cold Li atoms from a magnetic-optical trap (MOT) and a charged or current-carrying wire. With this system, we were able to realize 1/r 2 and 1/r potentials in two dimensions and to observe the motion of cold atoms in both potentials. For an atom in an attractive 1/r 2 potential, there exist no stable trajectories, instead there is a characteristic class of trajectories for which atoms fall into the singularity. We were able to observe this falling of atoms into the center of the potential. Moreover, by probing the singular 1/r 2 potential with atomic clouds of varying size and temperature we extracted scaling properties of the atom-wire interaction. For very cold atoms, and very thin wires the motion of the atoms must be treated quantum mechanically. Here we predict that the absorption cross section for the 1/r 2 potential should exhibit quantum steps. These quantum steps are a manifestation of the quantum mechanical decomposition of plane waves into partial waves. For the second part of this work, we realized a two dimensional 1/r potential for cold atoms. If the potential is attractive, the atoms can be bound and follow Kepler-like orbits around the wire. The motion in the third dimension along the wire is free. We were able to exploit this property and constructed a novel cold atom guide, the 'Kepler guide'. We also demonstrated another type of atom guide (the 'side guide'), by combining the magnetic field of the wire with a homogeneous offset magnetic field. In this case, the atoms are held in a potential 'tube' on the side of the wire. The versatility, simplicity, and scaling properties of this guide make it an interesting technique. (author)
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane; Natarajan, S.; Rabczuk, T.
2013-01-01
This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient ...
DEFF Research Database (Denmark)
Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel
2008-01-01
An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...
Biclustering via Sparse Singular Value Decomposition
Lee, Mihee
2010-02-16
Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.
One dimensional systems with singular perturbations
International Nuclear Information System (INIS)
Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P
2011-01-01
This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.
Noncrossing timelike singularities of irrotational dust collapse
International Nuclear Information System (INIS)
Liang, E.P.T.
1979-01-01
Known naked singularities in spherical dust collapse are either due to shell-crossing or localized to the central world line. They will probably be destroyed by pressure gradients or blue-shift instabilities. To violate the cosmic censorship hypothesis in a more convincing and general context, collapse solutions with naked singularities that are at least nonshell-crossing and nonlocalized need to be constructed. Some results concerning the probable structure of a class of nonshellcrossing and nonlocalized timelike singularities are reviewed. The cylindrical dust model is considered but this model is not asymptotically flat. To make these noncrossing singularities viable counter examples to the cosmic censorship hypothesis, the occurrence of such singularities in asymptotically flat collapse needs to be demonstrated. (UK)
On the probabilistic structure of quasi-free states of a Clifford algebra
International Nuclear Information System (INIS)
Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.
1975-07-01
It is proved that the correlation functions of a non-relativistic Fermi field given by a quasi-free state are directly related to the values of the characteristic function of a probability measure over the phase space of a classical spin system [fr
Minimal solution for inconsistent singular fuzzy matrix equations
Directory of Open Access Journals (Sweden)
M. Nikuie
2013-10-01
Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.
Quantum cosmology and late-time singularities
International Nuclear Information System (INIS)
Kamenshchik, A Yu
2013-01-01
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behavior of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born–Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models. (topical review)
International Nuclear Information System (INIS)
Nguyen Thanh Van
2006-12-01
This paper deals with the initial value problem of the type φw / φt = L (t, x, w, φw / φx i ) (1) w(0, x) = φ(x) (2) where t is the time, L is a linear first order operator in a Clifford Analysis and φ is a generalized monogenic function. We give sufficient conditions on the coefficients of operator L under which L is associated to differential equations with anti-monogenic right-hand sides. For such operator L the initial problem (1),(2) is solvable for an arbitrary generalized monogenic initial function φ and the solution is also generalized monogenic for each t. (author)
Cultura e Sociedade Internacional: uma conjunção possível entre Clifford Geertz e Hedley Bull
Directory of Open Access Journals (Sweden)
Hugo Arend
2005-02-01
Full Text Available Este artigo objetiva a aproximação dos estudos de Hedley Bull e de Clifford Geertz no que respeita o lugar e a dimensão da cultura em seus pensamentos. Considero, primeiramente, o lugar da cultura no pensamento de Bull, para, logo após, apontar quais de seus traços podemser enriquecidos pelos estudos de Geertz, e, a partir daí, problematizar e dimensionar o lugar da cultura para o estudo das relações internacionais, tomando como foco o conceito de intersubjetividade, latente em ambos os teóricos. Ao final, realizo um estudo de caso, interpretando a forma como foram estruturados os discursos de George W. Bush, Tony Blair e José Maria Aznar para dar legitimidade à invasão do Iraque, a 16 de março de 2003.
Directory of Open Access Journals (Sweden)
Thiemo Breyer
2013-06-01
Full Text Available The paper investigates the phenomenon of foreignness and its understanding in ethnographic and philosophical context. The role of a phenomenologicalhermeneutic conception of text and action in bridging the gap between the native’s and the observer’s points of view with respect to the description of cultural phenomena is elucidated by way of comparing the theories of anthropologist Clifford Geertz and philosopher Paul Ricoeur. Hidden links between the two authors, who make sparse references to one another, but should be connected more thoroughly, are followed. The methods of “thick description” (Geertz and of taking the “text as a model” (Ricoeur for understanding social and cultural performances are analysed to attain a new notion of culture as context.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
Transmutation of singularities in optical instruments
Energy Technology Data Exchange (ETDEWEB)
Tyc, Tomas [Institute of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno (Czech Republic); Leonhardt, Ulf [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS (United Kingdom)], E-mail: tomtyc@physics.muni.cz
2008-11-15
We propose a method for eliminating a class of singularities in optical media where the refractive index goes to zero or infinity at one or more isolated points. Employing transformation optics, we find a refractive index distribution equivalent to the original one that is nonsingular but shows a slight anisotropy. In this way, the original singularity is 'transmuted' into another, weaker type of singularity where the permittivity and permeability tensors are discontinuous at one point. The method is likely to find applications in designing and improving optical devices by making them easier to implement or to operate in a broad band of the spectrum.
Quantum dress for a naked singularity
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Marc Casals
2016-09-01
Full Text Available We investigate semiclassical backreaction on a conical naked singularity space–time with a negative cosmological constant in (2+1-dimensions. In particular, we calculate the renormalized quantum stress–energy tensor for a conformally coupled scalar field on such naked singularity space–time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak cosmic censorship.
Cirant, Marco; Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ctor
2016-01-01
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Cirant, Marco
2016-11-22
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Singularities in cosmologies with interacting fluids
International Nuclear Information System (INIS)
Cotsakis, Spiros; Kittou, Georgia
2012-01-01
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for ‘phantom’ matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding to a logarithmic branch point that resembles a cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.
Singularities: the state of the art
International Nuclear Information System (INIS)
Clarke, C.J.S.; Schmidt, B.G.
1977-01-01
A brief, but precise and unified account is given of the results that have been rigorously established at the time of writing concerning the existence and nature of singularities in classical relativity. (author)
Technological Singularity: What Do We Really Know?
Directory of Open Access Journals (Sweden)
Alexey Potapov
2018-04-01
Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
Topological Signals of Singularities in Ricci Flow
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Paul M. Alsing
2017-08-01
Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.
Asymptotic safety, singularities, and gravitational collapse
International Nuclear Information System (INIS)
Casadio, Roberto; Hsu, Stephen D.H.; Mirza, Behrouz
2011-01-01
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
Stable computation of generalized singular values
Energy Technology Data Exchange (ETDEWEB)
Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)
1996-12-31
We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.
On Borel singularities in quantum field theory
International Nuclear Information System (INIS)
Chadha, S.; Olesen, P.
1977-10-01
The authors consider the effective one-loop Lagrangian in a constant electric field. It is shown that perturbation theory behaves as n factorial giving rise to singularities in the Borel plane. Comparing with the known exact result it is shown how to integrate these singularities. It is suggested that renormalons in QED and QCD should be integrated in a similar way. A speculation is made on a possible interpretation of this integration. (Auth.)
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
Observational constraints on cosmological future singularities
Energy Technology Data Exchange (ETDEWEB)
Beltran Jimenez, Jose [Aix Marseille Univ, Universite de Toulon CNRS, CPT, Marseille (France); Lazkoz, Ruth [Euskal Herriko Unibertsitatea, Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Bilbao (Spain); Saez-Gomez, Diego [Faculdade de Ciencias da Universidade de Lisboa, Departamento de Fisica, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Salzano, Vincenzo [University of Szczecin, Institute of Physics, Szczecin (Poland)
2016-11-15
In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)
Observational constraints on cosmological future singularities
International Nuclear Information System (INIS)
Beltran Jimenez, Jose; Lazkoz, Ruth; Saez-Gomez, Diego; Salzano, Vincenzo
2016-01-01
In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)
Naked singularities and cosmic censorship: comment on the current situation
International Nuclear Information System (INIS)
Seifert, H.J.
1979-01-01
The current discussion is mainly concerned with how, or indeed, whether space-times possessing naked singularities can be ruled out as being too unrealistic or not being singular at all. The present position is summarized, with references, under the following headings: the Hawking-Penrose existence theorems, hydrodynamical singularities and the strength of naked singularities. (UK)
Valenzuela, Sergio O; Saitoh, Eiji; Kimura, Takashi
2017-01-01
Since the discovery of the giant magnetoresistance effect in magnetic multilayers in 1988, a new branch of physics and technology, called spin-electronics or spintronics, has emerged, where the flow of electrical charge as well as the flow of electron spin, the so-called “spin current,” are manipulated and controlled together. The physics of magnetism and the application of spin current have progressed in tandem with the nanofabrication technology of magnets and the engineering of interfaces and thin films. This book aims to provide an introduction and guide to the new physics and applications of spin current, with an emphasis on the interaction between spin and charge currents in magnetic nanostructures.
Pettinato, Giuseppe; Vanden Berg-Foels, Wendy S; Zhang, Ning; Wen, Xuejun
2014-01-01
We report a technology to form human embryoid bodies (hEBs) from singularized human embryonic stem cells (hESCs) without the use of the p160 rho-associated coiled-coil kinase inhibitor (ROCKi) or centrifugation (spin). hEB formation was tested under four conditions: +ROCKi/+spin, +ROCKi/-spin, -ROCKi/+spin, and -ROCKi/-spin. Cell suspensions of BG01V/hOG and H9 hESC lines were pipetted into non-adherent hydrogel substrates containing defined microwell arrays. hEBs of consistent size and spherical geometry can be formed in each of the four conditions, including the -ROCKi/-spin condition. The hEBs formed under the -ROCKi/-spin condition differentiated to develop the three embryonic germ layers and tissues derived from each of the germ layers. This simplified hEB production technique offers homogeneity in hEB size and shape to support synchronous differentiation, elimination of the ROCKi xeno-factor and rate-limiting centrifugation treatment, and low-cost scalability, which will directly support automated, large-scale production of hEBs and hESC-derived cells needed for clinical, research, or therapeutic applications.
Vozková, Markéta
2011-01-01
1 ABSTRACT The aim of this text is to provide an analysis of the phenomenon of spin doctoring in the Euro-Atlantic area. Spin doctors are educated people in the fields of semiotics, cultural studies, public relations, political communication and especially familiar with the infrastructure and the functioning of the media industry. Critical reflection of manipulative communication techniques puts spin phenomenon in historical perspective and traces its practical use in today's social communica...
Cosmologies with quasiregular singularities. II. Stability considerations
International Nuclear Information System (INIS)
Konkowski, D.A.; Helliwell, T.M.
1985-01-01
The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R 1 x T 3 and R 3 x S 1 flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added
Generalized teleparallel cosmology and initial singularity crossing
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg [Center for Theoretical Physics, the British University in Egypt, Suez Desert Road, Sherouk City 11837 (Egypt)
2017-02-01
We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.
Antropologia e filosofia: estética e experiência em Clifford Geertz e Walter Benjamin
Directory of Open Access Journals (Sweden)
Relivaldo Pinho de Oliveira
2012-06-01
Full Text Available Este artigo estuda as concepções de estética e experiência de Clifford Geertz e Walter Benjamin como possibilidades argumentativas e metodológicas para pensar a realidade e suas formas estéticas. Utiliza-se para isso as discussões metodológicas de Geertz, especialmente a respeito do lugar da estética e de sua relação com os demais âmbitos do humano, que encetaram uma nova forma de concebê-los para a etnografia e antropologia de modo geral, e os estudos de Benjamin a respeito da estética como expressão fisionômica de uma época, de determinada realidade, especialmente os que se referem sobre a modernidade. Constata-se essa possibilidade a partir da observação de que a estética e a experiência, nos autores, são tomadas como dimensões da realidade que se relacionam, não de modo mecânico, e sim como âmbitos que atravessam a realidade, os artefatos estéticos, os discursos, e esses assim devem ser observados.This article study the conceptions of aesthetics and experience of Clifford Geertz and Walter Benjamin as argumentative and methodological possibilities for thinking reality and its aesthetic forms. Uses for this Geertz's methodological discussions, especially regarding the place of aesthetics and its relation to other spheres of the human, which has embarked on a new way of conceiving them to ethnography and anthropology in general, and studies Benjamin about the aesthetics and physiognomical expression of an era, a certain reality, especially those concerning about modernity. There is that possibility from the observation that the aesthetics and experience, in the authors, are taken as the dimensions of reality are related, not mechanically, but as areas that cross the reality, the aesthetic artifacts, the speeches, and so these must be observed.
International Nuclear Information System (INIS)
Anton, Gisela
1990-01-01
The idea of the intrinsic angular momentum, or 'spin', of a particle has played an essential part in fundamental physics for more than 60 years, and its continuing importance was underlined at the 9th International Symposium on High Energy Spin Physics, held in September in Bonn.
Energy Technology Data Exchange (ETDEWEB)
Anton, Gisela
1990-12-15
The idea of the intrinsic angular momentum, or 'spin', of a particle has played an essential part in fundamental physics for more than 60 years, and its continuing importance was underlined at the 9th International Symposium on High Energy Spin Physics, held in September in Bonn.
Energy Technology Data Exchange (ETDEWEB)
D' Ariano, G M [Quantum Optics and Information Group, INFM Udr Pavia, Dipartimento di Fisica ' Alessandro Volta' and INFM, Via Bassi 6, 27100 Pavia (Italy); Maccone, L [Quantum Optics and Information Group, INFM Udr Pavia, Dipartimento di Fisica ' Alessandro Volta' and INFM, Via Bassi 6, 27100 Pavia (Italy); Paini, M [Quantum Optics and Information Group, INFM Udr Pavia, Dipartimento di Fisica ' Alessandro Volta' and INFM, Via Bassi 6, 27100 Pavia (Italy)
2003-02-01
We propose a tomographic reconstruction scheme for spin states. The experimental set-up, which is a modification of the Stern-Gerlach scheme, can be easily performed with currently available technology. The method is generalized to multiparticle states, analysing the spin-1/2 case for indistinguishable particles. Some Monte Carlo numerical simulations are given to illustrate the technique.
International Nuclear Information System (INIS)
D'Ariano, G M; Maccone, L; Paini, M
2003-01-01
We propose a tomographic reconstruction scheme for spin states. The experimental set-up, which is a modification of the Stern-Gerlach scheme, can be easily performed with currently available technology. The method is generalized to multiparticle states, analysing the spin-1/2 case for indistinguishable particles. Some Monte Carlo numerical simulations are given to illustrate the technique
Partons and the EMC spin effect
International Nuclear Information System (INIS)
Bass, S.D.
1992-03-01
We focus on the patron model and the role of the axial anomaly in polarised deep inelastic scattering. We show that the axial anomaly is relevant to each of the higher moments of the spin dependent structure function g 1 (x) and not just the first moment. This result implies that the factorisation of mass singularities is not sufficient to define the parton model in spin dependent quantum chromodynamics (QCD). (It is certainly a necessary condition.) We also need to consider the locality of the photon parton interaction. The anomaly is observed over all x in the (EMC)g 1 (x) data. (author)
Role of Van Hove singularities and momentum-space structure in high-temperature superconductivity
International Nuclear Information System (INIS)
Radtke, R.J.; Levin, K.; Schuettler, H.; Norman, M.R.
1993-01-01
There is a great deal of interest in attributing the high critical temperatures of the cuprates to either the proximity of the Fermi level to a Van Hove singularity or to structure of the superconducting pairing potential in momentum space far from the Fermi surface; the latter is particularly important for spin-fluctuation-mediated pairing mechanisms. We examine these ideas by calculating the critical temperature T c for model Einstein-phonon- and spin-fluctuation-mediated superconductors within both the standard, Fermi-surface-restricted Eliashberg theory and the exact Eliashberg theory, which accounts for the full momentum structure of the pairing potential and the energy dependence of the density of states. Our computations employ band structures chosen to model both the La 2 Sr 2-x CuO 4 and YBa 2 Cu 3 O 7-δ families. For our spin fluctuation calculations, we take the dynamical susceptibility to be the pairing potential and examine two models of this susceptibility in the cuprates. We compare and contrast these models with available magnetic neutron-scattering data, since these data provide the most direct constraints on the susceptibility. We conclude that a model constrained by neutron-scattering measurements will not yield the observed 90-K T c 's regardless of the strength of the electron-spin fluctuation coupling, even when the Van Hove singularity and momentum-space structure are accounted for; moreover, when transport constraints are applied to this type of model, we expect T c ∼10 K, as was found in an earlier paper. We also find that the Van Hove singularity enhances T c much less effectively than weak-coupling calculations would suggest
Calogero-Sutherland system with two types interacting spins
Kharchev, S.; Levin, A.; Olshanetsky, M.; Zotov, A.
2017-08-01
We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin approach and prove complete integrability of the system by constructing the Lax pair and the classical r-matrix with the spectral parameter on a singular curve.
Phantom cosmology without Big Rip singularity
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)
2012-03-23
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Radioanatomy of the singular nerve canal
Energy Technology Data Exchange (ETDEWEB)
Muren, C. [Dept. of Diagnostic Radiology, Sabbatsbergs Hospital, Stockholm (Sweden); Wadin, K. [University Hospital, Uppsala (Sweden); Dimopoulos, P. [University Hospital, Uppsala (Sweden)
1991-08-01
The singular canal conveys vestibular nerve fibers from the ampulla of the posterior semicircular canal to the posteroinferior border of the internal auditory meatus. Radiographic identification of this anatomic structure helps to distinguish it from a fracture. It is also a landmark in certain surgical procedures. Computed tomography (CT) examinations of deep-frozen temporal bone specimens were compared with subsequently prepared plastic casts of these bones, showing good correlation between the anatomy and the images. The singular canal and its variable anatomy were studied in CT examinations of 107 patients. The singular canal could be identified, in both the axial and in the coronal planes. Its point of entry into the internal auditory meatus varied considerably. (orig.)
Enveloping branes and brane-world singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios; Cotsakis, Spiros [CERN-Theory Division, Department of Physics, Geneva 23 (Switzerland); Klaoudatou, Ifigeneia [University of the Aegean, Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, Samos (Greece)
2014-12-01
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well. (orig.)
Phantom cosmology without Big Rip singularity
International Nuclear Information System (INIS)
Astashenok, Artyom V.; Nojiri, Shin'ichi; Odintsov, Sergei D.; Yurov, Artyom V.
2012-01-01
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time (“phantom energy” without “Big Rip” singularity) and (ii) energy density tends to constant value with time (“cosmological constant” with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Global embeddings for branes at toric singularities
Balasubramanian, Vijay; Braun, Volker; García-Etxebarria, Iñaki
2012-01-01
We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.
Holographic subregion complexity for singular surfaces
Energy Technology Data Exchange (ETDEWEB)
Bakhshaei, Elaheh [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Mollabashi, Ali [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)
2017-10-15
Recently holographic prescriptions were proposed to compute the quantum complexity of a given state in the boundary theory. A specific proposal known as 'holographic subregion complexity' is supposed to calculate the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cut-off, due to the singularities of a family of surfaces including a kink in (2 + 1) dimensions and cones in even dimensional field theories. We also find examples of new divergent terms such as squared logarithm and negative powers times the logarithm of the UV cut-off parameter. (orig.)
Singularity hypotheses a scientific and philosophical assessment
Moor, James; Søraker, Johnny; Steinhart, Eric
2012-01-01
Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.
Bovier, Anton
2007-01-01
Spin glass theory is going through a stunning period of progress while finding exciting new applications in areas beyond theoretical physics, in particular in combinatorics and computer science. This collection of state-of-the-art review papers written by leading experts in the field covers the topic from a wide variety of angles. The topics covered are mean field spin glasses, including a pedagogical account of Talagrand's proof of the Parisi solution, short range spin glasses, emphasizing the open problem of the relevance of the mean-field theory for lattice models, and the dynamics of spin glasses, in particular the problem of ageing in mean field models. The book will serve as a concise introduction to the state of the art of spin glass theory, usefull to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
Energy Technology Data Exchange (ETDEWEB)
Anon.
1989-01-15
The recent 8th International Symposium on High Energy Spin Physics at the University of Minnesota in Minneapolis, Minnesota, opened with a bang when L. Pondrom (Wisconsin), donning a hard hat borrowed from construction workers, ventured that 'spin, the notorious inessential complication of hadronic physics, is finally telling us what real QCD (quantum chromodynamics, the field theory of quarks and gluons) looks like.' He was referring to an animated discussion on the meaning of the recent spin oriented (polarized) scattering results from the European Muon Collaboration (EMC) at CERN and reported at the Symposium by R. Garnet (Liverpool) and P. Schuler (Yale) which show that the proton spin is not simply a reflection of the spins of its constituent quarks.
Singularities in four-body final-state amplitudes
International Nuclear Information System (INIS)
Adhikari, S.K.
1978-01-01
Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering
Invariant functionals in higher-spin theory
Directory of Open Access Journals (Sweden)
M.A. Vasiliev
2017-03-01
Full Text Available A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F⁎(B(x in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space–time points of the factors of B(x, which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.
Endpoint singularities in unintegrated parton distributions
Hautmann, F
2007-01-01
We examine the singular behavior from the endpoint region x -> 1 in parton distributions unintegrated in both longitudinal and transverse momenta. We identify and regularize the singularities by using the subtraction method, and compare this with the cut-off regularization method. The counterterms for the distributions with subtractive regularization are given in coordinate space by compact all-order expressions in terms of eikonal-line operators. We carry out an explicit calculation at one loop for the unintegrated quark distribution. We discuss the relation of the unintegrated parton distributions in subtractive regularization with the ordinary parton distributions.
Characteristic classes, singular embeddings, and intersection homology.
Cappell, S E; Shaneson, J L
1987-06-01
This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.
Cosmic censorship and the strengths of singularities
International Nuclear Information System (INIS)
Newman, R.P.
1986-01-01
This paper considers the principal definitions concerning limiting curvature strength on geodesics, and on non-spacelike geodesics in particular. They are formulated in terms of focussing conditions. Two definitions suggest themselves, and these are given in terms of a concept of a generalized Jacobi field. An historical survey is presented on some important developments concerning examples of naked singularities. The historical context is recalled in which these models, and cosmic censorship in general, have arisen. It is the author's opinion that one can expect to obtain theoretical limitations on the strengths of any naked singularities which do occur
Field theory of the spinning electron: I - Internal motions
International Nuclear Information System (INIS)
Salesi, Giovanni; Recami, Erasmo; Universidade Estadual de Campinas, SP
1994-05-01
One of the most satisfactory picture of spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic electron, that relates the electron spin with the so-called Zitterbewegung (zbw). The BZ theory has been recently studied in the Lagrangian and Hamiltonian symplectic formulations, both in flat and in curved space-time. The BZ motion equations constituted the starting point for two recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra formalism. In this letter, by employing on the contrary the ordinary tensorial language, we first write down a meaningful (real) equation of motion, describing particle classical paths, quite different from the corresponding (complex) equation of the standard Dirac theory. As a consequence, we succeed in regarding the electron as an extended-type object with a classically intelligible structure (thus overcoming some long-standing, well-known problems). Second, we make explicit the kinematical properties of the 4-velocity field v μ , which also result to be quite different from the ordinary ones, valid for scalar particles. At last, we analyze the inner zbw motions, both time-like and light-like, as functions of the initial conditions (in particular, for the case of classical uniform motions, the z component of spin s is shown to be quantized). In so doing, we make explicit the strict correlation existing between electron polarization and zbw kinematics. (author). 9 refs
Field theory of the spinning electron: I - Internal motions
Energy Technology Data Exchange (ETDEWEB)
Salesi, Giovanni [Universita Statale di Catania (Italy). Dipt. di Fisica; Recami, Erasmo [Universita Statale di Bergamo, Dalmine, BG (Italy). Facolta di Ingegneria]|[Universidade Estadual de Campinas, SP (Brazil). Dept. de Matematica Aplicada
1994-05-01
One of the most satisfactory picture of spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic electron, that relates the electron spin with the so-called Zitterbewegung (zbw). The BZ theory has been recently studied in the Lagrangian and Hamiltonian symplectic formulations, both in flat and in curved space-time. The BZ motion equations constituted the starting point for two recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra formalism. In this letter, by employing on the contrary the ordinary tensorial language, we first write down a meaningful (real) equation of motion, describing particle classical paths, quite different from the corresponding (complex) equation of the standard Dirac theory. As a consequence, we succeed in regarding the electron as an extended-type object with a classically intelligible structure (thus overcoming some long-standing, well-known problems). Second, we make explicit the kinematical properties of the 4-velocity field v{sup {mu}}, which also result to be quite different from the ordinary ones, valid for scalar particles. At last, we analyze the inner zbw motions, both time-like and light-like, as functions of the initial conditions (in particular, for the case of classical uniform motions, the z component of spin s is shown to be quantized). In so doing, we make explicit the strict correlation existing between electron polarization and zbw kinematics. (author). 9 refs.
Spin-Orbit Coupling and Magnetism in Multilayer Graphene
van Gelderen, R.
2013-01-01
The topics covered in this work are - spin-density-wave instabilities in monolayer graphene doped to the van Hove singularity. Nesting of the Fermi surface and a diverging density of states are often ingredients for charge and/or magnetic instabilities. For highly doped monolayer graphene these
Caspers, W J
1989-01-01
This book is about spin systems as models for magnetic materials, especially antiferromagnetic lattices. Spin-systems are well-defined models, for which, in special cases, exact properties may be derived. These special cases are for the greater part, one- dimensional and restricted in their applicability, but they may give insight into general properties that also exist in higher dimension. This work pays special attention to qualitative differences between spin lattices of different dimensions. It also replaces the traditional picture of an (ordered) antiferromagnetic state of a Heisenberg sy
International Nuclear Information System (INIS)
Baktybaev, K.; Koilyk, N.; Ramankulov, K.
2006-01-01
Full text: Collective Schrodinger equations are applied to describe low-energy spectra of even-even nuclei [1]. Spectra for even-odd nuclei are calculated by coupling the single particle degrees of freedom to the collective degree of freedom of the core nucleus, which is of even-even type. The collective spin has a value of 3/2. This leads to the assumption that the linearized equation may be applied to describe nuclei with spin 3/2 in the ground state. Good description of the low energy spectra and electromagnetic transition probabilities can be obtained only with introduction of spin-dependent potentials, which apart from coordinates and momenta also depend on the matrices of the Clifford algebra arising in the linearization,. The interacting boson-fermion models (IBFM) [2] represent another approach to describe spectra of even-odd nuclei. For even-odd nuclei with spin 3/2 in the ground state one uses so-called j=3/2 - IBFM, which is also denoted as the U B (6)xU F (4) IBFM. In this paper we establish the relation between the matrices of the Clifford algebra, which arise in the linearization procedure, and the fermion operators of the j=3/2 IBFM. This allows us to establish a connection between the j=3/2 IBFM and spin dependent generalized collective model (SGCM). The results of the SGCM for Ir and Au nuclei are presented and compared with the results of the j=3/2 IBFM with a dynamical spin symmetry [3] present. In this respect we could apply the linearized collective Schrodinger equation and IBFM with arbitrary spin to all other even-odd nuclei. (author)
Singular Linear Differential Equations in Two Variables
Braaksma, B.L.J.; Put, M. van der
2008-01-01
The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no
Singular continuous spectrum for palindromic Schroedinger operators
International Nuclear Information System (INIS)
Hof, A.; Knill, O.; Simon, B.
1995-01-01
We give new examples of discrete Schroedinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such an x is that there is a z element of X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x element of X if X derives from a primitive substitution. For potentials defined by circle maps, x n =l J (θ 0 +nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J. (orig.)
'Footballs', conical singularities, and the Liouville equation
International Nuclear Information System (INIS)
Redi, Michele
2005-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints
Mobile communications technology: The singular factor responsible ...
African Journals Online (AJOL)
This paper investigated the factors responsible for the growth of Internet usage on the African continent. The principal finding was that increasing growth of Internet usage is also down to one singular factor: mobile communications technology. The proliferation of mobile phone usage in Africa has resulted in the sustained ...
Diamagnetism of quantum gases with singular potentials
DEFF Research Database (Denmark)
Briet, Philippe; Cornean, Horia; Savoie, Baptiste
2010-01-01
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is analytic with respect to the chemical potential and the intensity of the external magnetic...
Supersymmetric quantum mechanics under point singularities
International Nuclear Information System (INIS)
Uchino, Takashi; Tsutsui, Izumi
2003-01-01
We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
Symmetries and singularities in Hamiltonian systems
International Nuclear Information System (INIS)
Miranda, Eva
2009-01-01
This paper contains several results concerning the role of symmetries and singularities in the mathematical formulation of many physical systems. We concentrate in systems which find their mathematical model on a symplectic or Poisson manifold and we present old and new results from a global perspective.
Singular interactions supported by embedded curves
International Nuclear Information System (INIS)
Kaynak, Burak Tevfik; Turgut, O Teoman
2012-01-01
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed. (paper)
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature
Classical resolution of singularities in dilaton cosmologies
Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK
2005-01-01
For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to
Normal forms of Hopf-zero singularity
International Nuclear Information System (INIS)
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)
Normal forms of Hopf-zero singularity
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.
A Systolic Architecture for Singular Value Decomposition,
1983-01-01
Presented at the 1 st International Colloquium on Vector and Parallel Computing in Scientific Applications, Paris, March 191J Contract N00014-82-K.0703...Gene Golub. Private comunication . given inputs x and n 2 , compute 2 2 2 2 /6/ G. H. Golub and F. T. Luk : "Singular Value I + X1 Decomposition
Sporadic simple groups and quotient singularities
International Nuclear Information System (INIS)
Cheltsov, I A; Shramov, C A
2013-01-01
We show that if a faithful irreducible representation of a central extension of a sporadic simple group with centre contained in the commutator subgroup gives rise to an exceptional (resp. weakly exceptional but not exceptional) quotient singularity, then that simple group is the Hall-Janko group (resp. the Suzuki group)
Singularity is the Future of ICT Research
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
2014-06-01
Jun 1, 2014 ... innovation if the black race are not to be left one hundred years ... aspects of innovation in mechatronics design philosophy which illustrate the benefits obtainable by an a priori ..... An overview of models of technological singularity ... the Singularity—representing a profound and disruptive transformation in.
Buhrman, Robert; Daughton, James; Molnár, Stephan; Roukes, Michael
2004-01-01
This report is a comparative review of spin electronics ("spintronics") research and development activities in the United States, Japan, and Western Europe conducted by a panel of leading U.S. experts in the field. It covers materials, fabrication and characterization of magnetic nanostructures, magnetism and spin control in magnetic nanostructures, magneto-optical properties of semiconductors, and magnetoelectronics and devices. The panel's conclusions are based on a literature review and a series of site visits to leading spin electronics research centers in Japan and Western Europe. The panel found that Japan is clearly the world leader in new material synthesis and characterization; it is also a leader in magneto-optical properties of semiconductor devices. Europe is strong in theory pertaining to spin electronics, including injection device structures such as tunneling devices, and band structure predictions of materials properties, and in development of magnetic semiconductors and semiconductor heterost...
Generalized Parton Distributions and their Singularities
Energy Technology Data Exchange (ETDEWEB)
Anatoly Radyushkin
2011-04-01
A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function $f(\\beta)/\\beta$ rather than with the usual parton density $f(\\beta)$. This results in a non-integrable singularity at $\\beta=0$ exaggerated by the fact that $f(\\beta)$'s, on their own, have a singular $\\beta^{-a}$ Regge behavior for small $\\beta$. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs $H(x,\\xi)$ that are finite and continuous at the "border point'' $x=\\xi$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $\\beta=0$ singularities is proposed that is based on the separation of the initial single DD $f(\\beta, \\alpha)$ into the "plus'' part $[f(\\beta,\\alpha)]_{+}$ and the $D$-term. It is demonstrated that the "DD+D'' separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution $f(x)=H(x,0)$ and the border function $H(x,x)$ with the $D$-term function $D(\\alpha)$.
International Nuclear Information System (INIS)
Anon.
1983-01-01
The 5th International Symposium on High Energy Spin Physics met in September at Brookhaven. The symposium has evolved to include a number of diverse specialities: theory, including parity violations and proposed quantum chromodynamics (QCD) tests with polarized beams; experiment, including the large spin effects discovered in high transverse momentum elastic scattering and hyperon production, dibaryons, and magnetic moments; acceleration and storage of polarized protons and electrons; and development of polarized sources and targets
São Carlos Workshop on Real and Complex Singularities
Ruas, Maria
2007-01-01
The São Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains papers presented at the eighth workshop, held at the IML, Marseille, July 19–23, 2004. The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities. This is reflected by the contributions in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.
On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications
Directory of Open Access Journals (Sweden)
Kelong Cheng
2014-01-01
Full Text Available Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.
THE EXT RACORPOREAL FERTILIZATION TECHNOLOGIES AND THE SINGULARITY PROBLEMS
Directory of Open Access Journals (Sweden)
S. V. Denysenko
2013-05-01
Full Text Available The peculiarities of modern medicine development connected with the technological and informative singularity are analyzed. The risks of realization of extracorporeal fertilization are examined from positions of development of informative singularity. The warning problems of origin of singularity are discussed on t h e base of t h e newest technologies development.
On the nature of naked singularities in Vaidya spacetimes
Energy Technology Data Exchange (ETDEWEB)
Dwivedi, I.H. (Aligarh Muslim Univ. (India). Dept. of Physics); Joshi, P.S. (Tata Inst. of Fundamental Research, Bombay (India))
1989-11-01
The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author).
On the nature of naked singularities in Vaidya spacetimes
International Nuclear Information System (INIS)
Dwivedi, I.H.
1989-01-01
The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author)
7 CFR 1200.50 - Words in the singular form.
2010-01-01
... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to import...
7 CFR 900.1 - Words in the singular form.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...
7 CFR 900.20 - Words in the singular form.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed to...
7 CFR 900.36 - Words in the singular form.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall be...
7 CFR 900.100 - Words in the singular form.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...
7 CFR 46.1 - Words in singular form.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the plural...
7 CFR 900.50 - Words in the singular form.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...
7 CFR 61.1 - Words in singular form.
2010-01-01
... 7 Agriculture 3 2010-01-01 2010-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall be...
Singularities and the geometry of spacetime
Hawking, Stephen
2014-11-01
The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove
Kalmar, Boldizsar
2006-01-01
We give a Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps, and obtain results about cobordism and bordism groups of -1 codimensional stable maps with prescribed singular fibers.
Okuma, Nobuyuki
2017-09-01
We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120° structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the z -axis spin rotational symmetry, which can be explained in the context of a singular band point or a U (1 ) symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number Q =-2 , while the typical one observed in topological insulator surface states is characterized by Q =+1 . A magnonic analogue of the surface states, the Dirac magnon with Q =+1 , is found in another kagome lattice antiferromagnet. We also derive the sum rule for Q by using the Poincaré-Hopf index theorem.
Okuma, Nobuyuki
2017-09-08
We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120° structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the z-axis spin rotational symmetry, which can be explained in the context of a singular band point or a U(1) symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number Q=-2, while the typical one observed in topological insulator surface states is characterized by Q=+1. A magnonic analogue of the surface states, the Dirac magnon with Q=+1, is found in another kagome lattice antiferromagnet. We also derive the sum rule for Q by using the Poincaré-Hopf index theorem.
Singularities in the general theory of relativity
International Nuclear Information System (INIS)
Treder, H.J.
1980-01-01
'Regular solutions of Einstein's equations' mean very different things. In the case of the empty-space equations, Rsub(ik) = o, such solutions must be metrics gsub(ik)(xsup(l)) without additionaly singular 'field sources' (Einstein's 'Particle problem'). However the 'phenomenological matter' is defined by the Einstein equations Rsub(ik) - 1/2gsub(ik)R = -kappaTsub(ik) itselves. Therefore if 10 regular functions gsub(ik)(xsup(l)) are given (which the inequalities of Lorentz-signature fulfil) then these gsub(ik) define 10 functions Tsub(ik)(xsup(l)) without singularities. But, the matter-tensor Tsub(ik) must fulfil the two inequalities T >= o, T 0 0 >= 1/2 T only and therefore the Einstein-equations with 'phenomenological matter' mean the two inequalities R >= o, R 0 0 <= o which are incompatible with a permanently regular metric with Lorentz-signature, generally. (author)
Singularity theory and equivariant symplectic maps
Bridges, Thomas J
1993-01-01
The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate student...
Dirac operator on spaces with conical singularities
International Nuclear Information System (INIS)
Chou, A.W.
1982-01-01
The Dirac operator on compact spaces with conical singularities is studied via the separation of variables formula and the functional calculus of the Dirac Laplacian on the cone. A Bochner type vanishing theorem which gives topological obstructions to the existence of non-negative scalar curvature k greater than or equal to 0 in the singular case is proved. An index formula relating the index of the Dirac operator to the A-genus and Eta-invariant similar to that of Atiyah-Patodi-Singer is obtained. In an appendix, manifolds with boundary with non-negative scalar curvature k greater than or equal to 0 are studied, and several new results on constructing complete metrics with k greater than or equal to on them are obtained
Further holographic investigations of big bang singularities
Energy Technology Data Exchange (ETDEWEB)
Engelhardt, Netta [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States); Hertog, Thomas [Institute for Theoretical Physics, KU Leuven,3001 Leuven (Belgium); Horowitz, Gary T. [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States)
2015-07-09
We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves N=4 super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.
Further holographic investigations of big bang singularities
Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T.
2015-07-01
We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.
Singular tachyon kinks from regular profiles
International Nuclear Information System (INIS)
Copeland, E.J.; Saffin, P.M.; Steer, D.A.
2003-01-01
We demonstrate how Sen's singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important role in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action, we are able circumvent the results of a recent paper which derived two conditions on the asymptotic tachyon potential such that the singular kink could be recovered in the large amplitude limit of periodic solutions. We show that this is explained by the non-commuting nature of two limits, and that Sen's solution is recovered if the order of the limits is chosen appropriately
The technological singularity and exponential medicine
Iraj Nabipour; Majid Assadi
2016-01-01
The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested th...
Non-singular spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Guardiola, R.
1990-01-01
A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
Constraint theory, singular lagrangians and multitemporal dynamics
International Nuclear Information System (INIS)
Lusanna, L.
1988-01-01
Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory
An Exact Solution of the Binary Singular Problem
Directory of Open Access Journals (Sweden)
Baiqing Sun
2014-01-01
Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.
International Nuclear Information System (INIS)
Gaarde, C.
1985-01-01
An analysis of spectra of (p,n) reactions showed that they were very selective in exciting spin modes. Charge exchange reactions at intermediate energies give important new understanding of the M1-type of excitations and of the spin structure of continuum p spectra in general. In this paper, the author discusses three charge exchange reactions: (p,n); ( 3 H,t); and (d,2p) at several targets. Low-lying states and the Δ region are discussed separately. Finally, the charge exchange reaction with heavy ion beams is briefly discussed. (G.J.P./Auth.)
Schwarz, H.
2017-01-01
The thesis "Spinning Worlds" is about the characterisation of two types of gas-giant exoplanets: Hot Jupiters, with orbital periods of fewer than five days, and young, wide-orbit gas giants, with orbital periods as long as thousands of years. The thesis is based on near-infrared observations of 1
Singular Spectrum Near a Singular Point of Friedrichs Model Operators of Absolute Type
International Nuclear Information System (INIS)
Iakovlev, Serguei I.
2006-01-01
In L 2 (R) we consider a family of self adjoint operators of the Friedrichs model: A m =|t| m +V. Here |t| m is the operator of multiplication by the corresponding function of the independent variable t element of R, and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel ν(t,x) satisfying some smoothness condition. These absolute type operators have one singular point of order m>0. Conditions on the kernel ν(t,x) are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity. The sharpness of these conditions is confirmed by counterexamples
On the equivalence of N=1 brane worlds and geometric singularities with flux
International Nuclear Information System (INIS)
Kaste, Peter; Partouche, Herve
2004-01-01
We consider Kaluza Klein reductions of M-theory on the Z N orbifold of the spin bundle over S 3 along two different U(1) isometries. The first one gives rise to the familiar 'large-N duality' of the N=1 SU(N) gauge theory in which the UV is realized as the world-volume theory of N D6-branes wrapped on S 3 , whereas the IR involves N units of RR flux through an S 2 . The second reduction gives an equivalent version of this duality in which the UV is realized geometrically in terms of a P 1 of A N-1 singularities, with one unit of RR flux through the P 1 . The IR is reached via a geometric transition and involves a single D6 brane on a lens space S 3 /Z N or, alternatively, a singular background (S 2 xR 4 )/Z N , with one unit of RR flux through S 2 and, localized at the singularities, an action of their stabilizer group in the U(1) RR gauge bundle, so that no massless twisted states occur. We also consider linear s-model descriptions of these backgrounds. (author)
Energy Technology Data Exchange (ETDEWEB)
Bratek, Lukasz, E-mail: lukasz.bratek@ifj.edu.pl [Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskego 152, PL-31342 Krakow (Poland)
2011-05-13
There are two relativistic rotators with Casimir invariants of the Poincare group being fixed parameters. The particular models of spinning particles were studied in the past both at the classical and quantum level. Recently, a minimal interaction with electromagnetic field has been considered. We show that the dynamical systems can be uniquely singled out from among other relativistic rotators by the unphysical requirement that the Hessian referring to the physical degrees of freedom should be singular. Closely related is the fact that the equations of free motion are not independent, making the evolution indeterminate. We show that the Hessian singularity cannot be removed by the minimal interaction with the electromagnetic field. By making use of a nontrivial Hessian null space, we show that a single constraint appears in the external field for consistency of the equations of motion with the Hessian singularity. The constraint imposes unphysical limitation on the initial conditions and admissible motions. We discuss the mechanism of appearance of unique solutions in external fields on an example of motion in the uniform magnetic field. We give a simple model to illustrate that similarly constrained evolution cannot be determinate in arbitrary fields.
Spectral asymptotics for nonsmooth singular Green operators
DEFF Research Database (Denmark)
Grubb, Gerd
2014-01-01
is a singular Green operator. It is well-known in smooth cases that when G is of negative order −t on a bounded domain, its eigenvalues ors-numbers have the behavior (*)s j (G) ∼ cj −t/(n−1) for j → ∞, governed by the boundary dimension n − 1. In some nonsmooth cases, upper estimates (**)s j (G) ≤ Cj −t/(n−1...
Singularity spectrum of self-organized criticality
International Nuclear Information System (INIS)
Canessa, E.
1992-10-01
I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality. Numerical support is given by a comparison with reported simulation data. Within the theory the origin of self-organized critical phenomena is analysed in terms of a nonlinear singularity spectrum different form the typical convex shape due to multifractal measures. (author). 29 refs, 5 figs
Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
DEFF Research Database (Denmark)
Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy
2014-01-01
We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic ...... singularities and is free of any poles at infinity—properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA)....
The Singularity May Never Be Near
Walsh, Toby
2017-01-01
There is both much optimisim and pessimism around artificial intelligence (AI) today. The optimists are investing millions of dollars, and even in some cases billions of dollars into AI. The pessimists, on the other hand, predict that AI will end many things: jobs, warfare, and even the human race. Both the optimists and the pessimists often appeal to the idea of a technological singularity, a point in time where machine intelligence starts to run away, and a new, more in- telligent “species”...
Compacted dimensions and singular plasmonic surfaces
Pendry, J. B.; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele
2017-11-01
In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.
Ensemble singular vectors and their use as additive inflation in EnKF
Directory of Open Access Journals (Sweden)
Shu-Chih Yang
2015-07-01
Full Text Available Given an ensemble of forecasts, it is possible to determine the leading ensemble singular vector (ESV, that is, the linear combination of the forecasts that, given the choice of the perturbation norm and forecast interval, will maximise the growth of the perturbations. Because the ESV indicates the directions of the fastest growing forecast errors, we explore the potential of applying the leading ESVs in ensemble Kalman filter (EnKF for correcting fast-growing errors. The ESVs are derived based on a quasi-geostrophic multi-level channel model, and data assimilation experiments are carried out under framework of the local ensemble transform Kalman filter. We confirm that even during the early spin-up starting with random initial conditions, the final ESVs of the first analysis with a 12-h window are strongly related to the background errors. Since initial ensemble singular vectors (IESVs grow much faster than Lyapunov Vectors (LVs, and the final ensemble singular vectors (FESVs are close to convergence to leading LVs, perturbations based on leading IESVs grow faster than those based on FESVs, and are therefore preferable as additive inflation. The IESVs are applied in the EnKF framework for constructing flow-dependent additive perturbations to inflate the analysis ensemble. Compared with using random perturbations as additive inflation, a positive impact from using ESVs is found especially in areas with large growing errors. When an EnKF is ‘cold-started’ from random perturbations and poor initial condition, results indicate that using the ESVs as additive inflation has the advantage of correcting large errors so that the spin-up of the EnKF can be accelerated.
Beyond the singularity of the 2-D charged black hole
International Nuclear Information System (INIS)
Giveon, Amit; Rabinovici, Eliezer; Sever, Amit
2003-01-01
Two dimensional charged black holes in string theory can be obtained as exact SL(2,R) x U(1)/U(1) quotient CFTs. The geometry of the quotient is induced from that of the group, and in particular includes regions beyond the black hole singularities. Moreover, wavefunctions in such black holes are obtained from gauge invariant vertex operators in the SL(2,R) CFT, hence their behavior beyond the singularity is determined. When the black hole is charged we find that the wavefunctions are smooth at the singularities. Unlike the uncharged case, scattering waves prepared beyond the singularity are not fully reflected; part of the wave is transmitted through the singularity. Hence, the physics outside the horizon of a charged black hole is sensitive to conditions set behind the past singularity. (author)
Logarithmic of mass singularities theorem in non massive quantum electrodynamics
International Nuclear Information System (INIS)
Mares G, R.; Luna, H.
1997-01-01
We give an explicit example of the use of dimensional regularization to calculate in a unified approach, all the ultraviolet, infrared and mass singularities, by considering the LMS (logarithms of mass singularities) theorem in the frame of massless QED (Quantum electrodynamics). In the calculation of the divergent part of the cross section, all singularities are found to cancel provided soft and hard photon emission are both taken into account. (Author)
Singular vectors of Malikov-Fagin-Fux in topological theories
International Nuclear Information System (INIS)
Semikhatov, A.M.
1993-01-01
Coincidence of singular vectors in relation to the sl(2) Katza-Mudi algebra and the algebra of the N=2 (twisted) supersymmetry is established. On the base of the Kazama-Suzuki simplest model is obtained a representation for the sl(2) currents in terms of an interacting with mater gravitation. From the Malikov-Fagin-Fux formulae for the sl(2) singular currents is obtained the general expression for singular vectors in topological theories
Observer-dependent sign inversions of polarization singularities.
Freund, Isaac
2014-10-15
We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.
Transmutation of planar media singularities in a conformal cloak.
Liu, Yichao; Mukhtar, Musawwadah; Ma, Yungui; Ong, C K
2013-11-01
Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes.
Deficiency indices and singular boundary conditions in quantum mechanics
International Nuclear Information System (INIS)
Bulla, W.
1984-01-01
We consider Schroedinger operators H in L 2 (Rsup(n)), n from IN, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions
Naked singularities in self-similar spherical gravitational collapse
International Nuclear Information System (INIS)
Ori, A.; Piran, T.
1987-01-01
We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (Γ-1<<1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold
7 CFR 900.80 - Words in the singular form.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice versa...
Spin Coherence in Semiconductor Nanostructures
National Research Council Canada - National Science Library
Flatte, Michael E
2006-01-01
... dots, tuning of spin coherence times for electron spin, tuning of dipolar magnetic fields for nuclear spin, spontaneous spin polarization generation and new designs for spin-based teleportation and spin transistors...
Quantum singularities in the FRW universe revisited
International Nuclear Information System (INIS)
Letelier, Patricio S.; Pitelli, Joao Paulo M.
2010-01-01
The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state p=(1/3)ρ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied, and it is shown that the energy conditions are violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the nonsingular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of nonnormalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.
Finite-time singularity signature of hyperinflation
Sornette, D.; Takayasu, H.; Zhou, W.-X.
2003-07-01
We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.
Consideration on Singularities in Learning Theory and the Learning Coefficient
Directory of Open Access Journals (Sweden)
Miki Aoyagi
2013-09-01
Full Text Available We consider the learning coefficients in learning theory and give two new methods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves to measure the learning efficiency in singular learning models. Mathematically, the learning coefficient corresponds to a real log canonical threshold of singularities for the Kullback functions (relative entropy in learning theory.
Identification of discrete chaotic maps with singular points
Directory of Open Access Journals (Sweden)
P. G. Akishin
2001-01-01
Full Text Available We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.
Numerical investigation of stress singularities in cracked bimaterial body
Czech Academy of Sciences Publication Activity Database
Náhlík, Luboš; Šestáková, Lucie; Hutař, Pavel
2008-01-01
Roč. 385-387, - (2008), s. 125-128 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics /7./. Seoul, 09.09.2008-11.09.2008] R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GP106/06/P239; GA ČR GA106/08/1409 Institutional research plan: CEZ:AV0Z20410507 Keywords : bimaterial interface * stress singularity exponent * corner singularity * vertex singularity * general singular stress concentrator Subject RIV: JL - Materials Fatigue, Friction Mechanics
The road to singularities, and the roses on the way
International Nuclear Information System (INIS)
Collins, C.B.
1978-01-01
A survey of current investigations of space-time singularities is given. The different approaches adopted by various research schools is discussed, and an analogy is drawn between this study and the mounting of an expedition that sets out on a long trail of discovery. A heuristic discussion is given of the latest classification of singularities and some brief comments are made on how physically relevant each type of singularity is. Roughly speaking, it seems that the milder types (at which quantities remain well behaved) are pathological cases, whereas the crude 'big-bang' type of singularity is more generic. (author)
Can non-commutativity resolve the big-bang singularity?
Energy Technology Data Exchange (ETDEWEB)
Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)
2004-08-01
A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)
Directory of Open Access Journals (Sweden)
Rachel Bullough
2013-09-01
Full Text Available Al fotógrafo británico, Charles Clifford (1819-1863 se le conoce como uno de los pioneros de la fotografía comercial en España. Sin embargo, hasta ahora, poco se sabe sobre el papel que jugó su libro A Photographic Scramble through Spain como complemento a sus fotografías. Este trabajo analiza el uso del libro, no sólo como herramienta comercial, sino en su papel de proyectar la imagen de España que Clifford deseaba mostrar a sus clientes y lectores en el Reino Unido.The British photographer, Charles Clifford (1819-1863 is best known as one of the pioneers of commercial photography in Spain. However, until now, little has been said about the role of his book, A Photographic Scramble through Spain as a complement to his photographs. This study will show how Clifford not only used the book as a commercial instrument but also as a means to convey the image of Spain that he wished to show to his potential buyers and readers in the United Kingdom
Entanglement in the XY spin chain
International Nuclear Information System (INIS)
Its, A R; Jin, B-Q; Korepin, V E
2005-01-01
We consider the entanglement in the ground state of the XY model of an infinite chain. Following Bennett, Bernstein, Popescu and Schumacher, we use the entropy of a sub-system as a measure of entanglement. Vidal, Latorre, Rico and Kitaev have conjectured that the von Neumann entropy of a large block of neighbouring spins approaches a constant as the size of the block increases. We evaluate this limiting entropy as a function of anisotropy and transverse magnetic field. We use the methods based on the integrable Fredholm operators and the Riemann-Hilbert approach. It is shown how the entropy becomes singular at the phase transition points
Amirjanyan, A. A.; Sahakyan, A. V.
2017-08-01
A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.
Metric dimensional reduction at singularities with implications to Quantum Gravity
International Nuclear Information System (INIS)
Stoica, Ovidiu Cristinel
2014-01-01
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained
A vida singular de um jovem militante
Directory of Open Access Journals (Sweden)
Áurea Maria Guimarães
2012-01-01
Full Text Available Esse artigo é fruto de uma pesquisa realizada no período de 2007 a 2010, junto a jovens militantes da cidade de Campinas, com o objetivo de compreender as diferentes maneiras que conduziam esses jovens tanto a reproduzir um modelo de vida quanto a criar outras possibilidades de militância na relação com esse modelo. Entre as histórias orais de vida narradas por jovens que militavam em diferentes grupos ou instituições, escolhi a vida de Biula, representante do movimento estudantil secundarista, procurando evidenciar que a singularidade desta vida, como também e a de outros jovens, estava conectada à problematização que faziam no interior de certas práticas, histórica e culturalmente constituídas, possibilitando a criação de novas formas de subjetivação nas quais se modificava a experiência que tinham deles mesmos na relação com os seus heróis ou modelos de referência. Palavras-chave: história oral – transcriação – heróis – resistência - processos de singularização. THE SINGULAR LIFE OF A YOUNG MILITANT ABSTRACT This article is the result of a research carried out from 2007 to 2010 with young militants in the city of Campinas, aiming to understand the different ways which conducted these youngsters to both reproduce a life model and create other possibilities of militancy in the relationship with this model. Among oral stories narrated by young militants from different groups or institutions, I have chosen the life of Biula, a representative of the secondary students’ movement, trying to show that the singularity of this life and other youngsters’ lives was connected to the problematization they promoted within certain practices, historically and culturally built, thus enabling the creation of new subjectification modes in which the experience they had of themselves in the relationship with their heroes or reference models has changed. Key words: oral history - transcreation – heroes
International Nuclear Information System (INIS)
Mookerjee, Abhijit
1976-01-01
''Spin glasses'', are entire class of magnetic alloys of moderate dilution, in which the magnetic atoms are far enough apart to be unlike the pure metal, but close enough so that the indirect exchange energy between them (mediated by the s-d interaction between local moments and conduction electrons) dominates all other energies. Characteristic critical phenomena displayed such as freezing of spin orientation at 'Tsub(c)' and spreading of magnetic ordering, are pointed out. Anomalous behaviour, associated with these critical phenomena, as reflected in : (i) Moessbauer spectroscopy giving hyperfine splitting at Tsub(c), (ii) maxima in susceptibility and remanent magnetism, (iii) thermopower maxima and change in slope, (iv) Characteristic cusp in susceptibility and its removal by very small magnetic fields, and (v) conductivity-resistivity measurements, are discussed. Theoretical developments aimed at explaining these phenomena, in particular, the ideas from percolation and localisation theories, and the approach based on the gellations of polymers, are discussed. Finally, a new approach based on renormalisation group in disordered systems is also briefly mentioned. (K.B.)
The technological singularity and exponential medicine
Directory of Open Access Journals (Sweden)
Iraj Nabipour
2016-01-01
Full Text Available The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested that three revolutions in science and technology consisting genetic and molecular science, nanotechnology, and robotic (artificial intelligence provided an exponential growth rate for medicine. The "exponential medicine" is going to create more disruptive technologies in healthcare industry. The exponential medicine shifts the paradigm of medical philosophy and produces significant impacts on the healthcare system and patient-physician relationship.
String wave function across a Kasner singularity
International Nuclear Information System (INIS)
Copeland, Edmund J.; Niz, Gustavo; Turok, Neil
2010-01-01
A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a 1+1-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.
Directory of Open Access Journals (Sweden)
Gilles Ferréol
2012-06-01
Full Text Available Cet ouvrage, structuré en onze chapitres eux-mêmes regroupés en trois grandes parties, entend présenter au lecteur français les principales facettes de l’œuvre de Clifford Geertz (1926-2006, l’une des figures les plus marquantes de l’anthropologie nord-américaine du XXe siècle.Dans un premier temps, sont exposés un certain nombre de positionnements d’ordres conceptuel et méthodologique. Lahouari Addi, tout d’abord, met en exergue le bien-fondé de la critique du positivisme et du structuro-fo...
Branes at Singularities in Type 0 String Theory
Alishahiha, M; Brandhuber, A; Oz, Y
1999-01-01
We consider Type 0B D3-branes placed at conical singularities and analyze in detail the conifold singularity. We study the non supersymmetric gauge theories on their worldvolume and their conjectured dual gravity descriptions. In the ultraviolet the solutions exhibit a logarithmic running of the gauge coupling. In the infrared we find confining solutions and IR fixed points.
Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues
García Planas, María Isabel; Tarragona Romero, Sonia
2014-01-01
The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family
Singularities of elastic scattering amplitude by long-range potentials
International Nuclear Information System (INIS)
Kvitsinsky, A.A.; Komarov, I.V.; Merkuriev, S.P.
1982-01-01
The angular peculiarities and the zero energy singularities of the elastic scattering amplitude by a long-range potential are described. The singularities of the elastic (2 → 2) scattering amplitude for a system of three Coulomb particles are considered [ru
Singularly perturbed volterra integro-differential equations | Bijura ...
African Journals Online (AJOL)
Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject
Non-uniqueness of the source for singular gauge fields
International Nuclear Information System (INIS)
Lanyi, G.; Pappas, R.
1977-01-01
It is shown that the singular Wu-Yang solution for SU(2) gauge fields may be interpreted as due to a point source at the origin. However, the electric or magnetic nature of the source depends on whether one approaches the singularity by means of a 'smeared' potential or a 'smeared' field strength. (Auth.)
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...
K3-fibered Calabi-Yau threefolds II, singular fibers
Hunt, Bruce
1999-01-01
In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur. This differs from previous work since the fibrations we discuss have constant modulus, and the singular fibers have torsion monodromy.
Some BMO estimates for vector-valued multilinear singular integral ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
the multilinear operator related to some singular integral operators is obtained. The main purpose of this paper is to establish the BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators. First, let us introduce some notations [10,16]. Throughout this paper, Q = Q(x,r).
Infinite derivative gravity : non-singular cosmology & blackhole solutions
Mazumdar, Anupam
2017-01-01
Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and
A Note on Inclusion Intervals of Matrix Singular Values
Directory of Open Access Journals (Sweden)
Shu-Yu Cui
2012-01-01
Full Text Available We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.
Simpson's neutrino and the singular see-saw
International Nuclear Information System (INIS)
Allen, T.J.; Johnson, R.; Ranfone, S.; Schechter, J.; Walle, J.W.F.
1991-01-01
The authors of this paper derive explicit forms for the neutrino and lepton mixing-matrices which describe the generic singular see-saw model. The dependence on the hierarchy parameter is contrasted with the non-singular case. Application is made to Simpson's 17 keV neutrino
On reliability of singular-value decomposition in attractor reconstruction
International Nuclear Information System (INIS)
Palus, M.; Dvorak, I.
1990-12-01
Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, is only of a limited power when nonlinear structures are studied. (author). 29 refs, 9 figs
One Critical Case in Singularly Perturbed Control Problems
Sobolev, Vladimir
2017-02-01
The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.
7 CFR 1200.1 - Words in the singular form.
2010-01-01
... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in this...
Periodic solutions to second-order indefinite singular equations
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Zamora, M.
2017-01-01
Roč. 263, č. 1 (2017), s. 451-469 ISSN 0022-0396 Institutional support: RVO:67985840 Keywords : degree theory * indefinite singularity * periodic solution * singular differential equation Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039617301134
Non-singular cosmologies in the conformally invariant gravitation theory
International Nuclear Information System (INIS)
Kembhavi, A.K.
1976-01-01
It is shown that in the framework of a conformally invariant gravitation theory, the singularity which is present in some anisotropic universes in general relativity is due to a wrong choice of conformal frame. Frames exist in which these models can be made singularity free. (author)
A numerical method for solving singular De`s
Energy Technology Data Exchange (ETDEWEB)
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS
International Nuclear Information System (INIS)
Chu Zhe; Lin, W. P.; Yang Xiaofeng
2013-01-01
Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.
Singular Null Hypersurfaces in General Relativity
International Nuclear Information System (INIS)
Dray, T
2006-01-01
Null hypersurfaces are a mathematical consequence of the Lorentzian signature of general relativity; singularities in mathematical models usually indicate where the interesting physics takes place. This book discusses what happens when you combine these ideas. Right from the preface, this is a no-nonsense book. There are two principal approaches to singular shells, one distributional and the other 'cut and paste'; both are treated in detail. A working knowledge of GR is assumed, including familiarity with null tetrads, differential forms, and 3 + 1 decompositions. Despite my own reasonably extensive, closely related knowledge, there was material unfamiliar to me already in chapter 3, although I was reunited with some old friends in later chapters. The exposition is crisp, with a minimum of transition from chapter to chapter. In fact, my main criticism is that there is no clear statement of the organization of the book, nor is there an index. Everything is here, and the story is compelling if you know what to look for, although it is less easy to follow the story if you are not already familiar with it. But this is really a book for experts, and the authors certainly qualify, having played a significant role in developing and extending the results they describe. It is also entirely appropriate that the book is dedicated to Werner Israel, who pioneered the thin-shell approach to (non-null) singular surfaces and later championed the use of similar methods for analysing null shells. After an introductory chapter on impulsive signals, the authors show how the Bianchi identities can be used to classify spacetimes with singular null hypersurfaces. This approach, due to the authors, generalizes the framework originally proposed by Penrose. While astrophysical applications are discussed only briefly, the authors point out that detailed physical characteristics of signals from isolated sources can be determined in this manner. In particular, they describe the behaviour of
Schertzer, D. J. M.; Tchiguirinskaia, I.
2016-12-01
Multifractal fields, whose definition is rather independent of their domain dimension, have opened a new approach of geophysics enabling to explore its spatial extension that is of prime importance as underlined by the expression "spatial chaos". However multifractals have been until recently restricted to be scalar valued, i.e. to one-dimensional codomains. This has prevented to deal with the key question of complex component interactions and their non trivial symmetries. We first emphasize that the Lie algebra of stochastic generators of cascade processes enables us to generalize multifractals to arbitrarily large codomains, e.g. flows of vector fields on large dimensional manifolds. In particular, we have recently investigated the neat example of stable Levy generators on Clifford algebra that have a number of seductive properties, e.g. universal statistical and robust algebra properties, both defining the basic symmetries of the corresponding fields (Schertzer and Tchiguirinskaia, 2015). These properties provide a convenient multifractal framework to study both the symmetries of the fields and how they stochastically break the symmetries of the underlying equations due to boundary conditions, large scale rotations and forcings. These developments should help us to answer to challenging questions such as the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013), to fully address the question of the limitations of quasi- geostrophic turbulence (Schertzer et al., 2012) and to explore the peculiar phenomenology of turbulent dynamics of the atmosphere or oceans that is neither two- or three-dimensional. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.8183. Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra
International Nuclear Information System (INIS)
Ohnuma, Yuichi; Matsuo, Mamoru; Maekawa, Sadamichi; Saitoh, Eeiji
2017-01-01
Spin Seebeck and spin Peltier effects, which are mutual conversion phenomena of heat and spin, are discussed on the basis of the microscopic theory. First, the spin Seebeck effect, which is the spin-current generation due to heat current, is discussed. The recent progress in research on the spin Seebeck effect are introduced. We explain the origin of the observed sign changes of the spin Seebeck effect in compensated ferromagnets. Next, the spin Peltier effect, which is the heat-current generation due to spin current, is discussed. Finally, we show that the spin Seebeck and spin Peltier effects are summarized by Onsager's reciprocal relation and derive Kelvin's relation for the spin and heat transports. (author)
Entangled spins and ghost-spins
Directory of Open Access Journals (Sweden)
Dileep P. Jatkar
2017-09-01
Full Text Available We study patterns of quantum entanglement in systems of spins and ghost-spins regarding them as simple quantum mechanical toy models for theories containing negative norm states. We define a single ghost-spin as in [20] as a 2-state spin variable with an indefinite inner product in the state space. We find that whenever the spin sector is disentangled from the ghost-spin sector (both of which could be entangled within themselves, the reduced density matrix obtained by tracing over all the ghost-spins gives rise to positive entanglement entropy for positive norm states, while negative norm states have an entanglement entropy with a negative real part and a constant imaginary part. However when the spins are entangled with the ghost-spins, there are new entanglement patterns in general. For systems where the number of ghost-spins is even, it is possible to find subsectors of the Hilbert space where positive norm states always lead to positive entanglement entropy after tracing over the ghost-spins. With an odd number of ghost-spins however, we find that there always exist positive norm states with negative real part for entanglement entropy after tracing over the ghost-spins.
Complexity, Analysis and Control of Singular Biological Systems
Zhang, Qingling; Zhang, Xue
2012-01-01
Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the ...
Managing focal fields of vector beams with multiple polarization singularities.
Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin
2016-11-10
We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.
Workshop on Singularities in Geometry, Topology, Foliations and Dynamics
Lê, Dung; Oka, Mutsuo; Snoussi, Jawad
2017-01-01
This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.
Cusp singularities in f(R) gravity: pros and cons
International Nuclear Information System (INIS)
Chen, Pisin; Yeom, Dong-han
2015-01-01
We investigate cusp singularities in f(R) gravity, especially for Starobinsky and Hu-Sawicki dark energy models. We illustrate that, by using double-null numerical simulations, a cusp singularity can be triggered by gravitational collapses. This singularity can be cured by adding a quadratic term, but this causes a Ricci scalar bump that can be observed by an observer outside the event horizon. Comparing with cosmological parameters, it seems that it would be difficult to see super-Planckian effects by astrophysical experiments. On the other hand, at once there exists a cusp singularity, it can be a mechanism to realize a horizon scale curvature singularity that can be interpreted by a firewall
Fold points and singularity induced bifurcation in inviscid transonic flow
International Nuclear Information System (INIS)
Marszalek, Wieslaw
2012-01-01
Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.
Czech Academy of Sciences Publication Activity Database
Knésl, Zdeněk; Klusák, Jan; Náhlík, Luboš
2007-01-01
Roč. 14, č. 6 (2007), s. 399-408 ISSN 1802-1484 R&D Projects: GA ČR(CZ) GA101/05/0320; GA ČR GA101/05/0227 Institutional research plan: CEZ:AV0Z20410507 Keywords : fracture mechanics * stability criteria * singular stress concentrations * crack initiation * critical stress Subject RIV: JL - Materials Fatigue, Friction Mechanics
A nonperturbative treatment of spin-dependent interactions of light and heavy quarkonia
International Nuclear Information System (INIS)
Schoeberl, F.
1986-01-01
We propose a nonrelativistic potential model with a regularized Coulomb potential at short range which leads to spin-dependent interactions which are at most as singular as 1/r. The Schroedinger equation is solved numerically including all spin-dependent interactions nonperturbatively. The predicted spectrum of light and heavy quarkonia is in remarkable agreement with experiment. Even the leptonic decay widths as well as the M1 transitions are in agreement with experiment. (Author)
Pramanik, S.; bandyopadhyay, S.; Cahay, M.
2003-01-01
We study high-field spin transport of electrons in a quasi one-dimensional channel of a $GaAs$ gate controlled spin interferometer (SPINFET) using a semiclassical formalism (spin density matrix evolution coupled with Boltzmann transport equation). Spin dephasing (or depolarization) is predominantly caused by D'yakonov-Perel' relaxation associated with momentum dependent spin orbit coupling effects that arise due to bulk inversion asymmetry (Dresselhaus spin orbit coupling) and structural inve...
3rd Singularity Theory Meeting of Northeast region & the Brazil-Mexico 2nd Meeting on Singularities
Neto, Aurélio; Mond, David; Saia, Marcelo; Snoussi, Jawad; BMMS 2/NBMS 3; ENSINO; Singularities and foliations geometry, topology and applications
2018-01-01
This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.
Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept
Directory of Open Access Journals (Sweden)
M. Y. Barabanenkov
2012-07-01
Full Text Available If a scatterer and an observation point (receive both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering.
Solutions of dissimilar material singularity and contact problems
International Nuclear Information System (INIS)
Yang, Y.
2003-09-01
Due to the mismatch of the material properties of joined components, after a homogeneous temperature change or under a mechanical loading, very high stresses occur near the intersection of the interface and the outer surface, or near the intersection of two interfaces. For most material combinations and joint geometries, there exists even a stress singularity. These high stresses may cause fracture of the joint. The investigation of the stress situation near the singular point, therefore, is of great interest. Especially, the relationship between the singular stress exponent, the material data and joint geometry is important for choosing a suitable material combination and joint geometry. In this work, the singular stress field is described analytically in case of the joint having a real and a complex eigenvalue. Solutions of different singularity problems are given, which are two dissimilar materials joint with free edges; dissimilar materials joint with edge tractions; joint with interface corner; joint with a given displacement at one edge; cracks in dissimilar materials joint; contact problem in dissimilar materials and logarithmic stress singularity. For an arbitrary joint geometry and material combination, the stress singular exponent, the angular function and the regular stress term can be calculated analytically. The stress intensity factors for a finite joint can be determined applying numerical methods, e.g. the finite element method (FEM). The method to determine more than one stress intensity factor is presented. The characteristics of the eigenvalues and the stress intensity factors are shown for different joint conditions. (orig.)
Boundary singularities produced by the motion of soap films.
Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I
2014-06-10
Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.
Quantum healing of classical singularities in power-law spacetimes
Energy Technology Data Exchange (ETDEWEB)
Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)
2007-07-07
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.
Magnetic Nanostructures Spin Dynamics and Spin Transport
Farle, Michael
2013-01-01
Nanomagnetism and spintronics is a rapidly expanding and increasingly important field of research with many applications already on the market and many more to be expected in the near future. This field started in the mid-1980s with the discovery of the GMR effect, recently awarded with the Nobel prize to Albert Fert and Peter Grünberg. The present volume covers the most important and most timely aspects of magnetic heterostructures, including spin torque effects, spin injection, spin transport, spin fluctuations, proximity effects, and electrical control of spin valves. The chapters are written by internationally recognized experts in their respective fields and provide an overview of the latest status.
Tangled nonlinear driven chain reactions of all optical singularities
Vasil'ev, V. I.; Soskin, M. S.
2012-03-01
Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.
Fermi-edge singularity in one-dimensional electron systems with long-range Coulomb interactions
International Nuclear Information System (INIS)
Otani, H.; Ogawa, T.
1996-01-01
Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the x -1 type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, λ e and λ h , of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (λ e h max[λ e ,λ h ]/v F . Corresponding optical spectrum near the Fermi edge (within an energy range of ℎv F /max[λ e ,λ h ]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the x -1 type (i.e., λ e →∞ and/or λ h →∞), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity
Biswas, Sounak; Damle, Kedar
2018-02-01
A transverse magnetic field Γ is known to induce antiferromagnetic three-sublattice order of the Ising spins σz in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q : ˜cos(Q .R ⃗) /|R⃗| η (T ) with the temperature-dependent power-law exponent η (T )∈(1 /9 ,1 /4 ) . Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility χu(L ) of an L ×L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence χu(L ) ˜L2 -9 η when η (T ) is in the range (1 /9 ,2 /9 ) . This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility χu(B ) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, χu(B ) ˜|B| -4/-18 η 4 -9 η for η (T )∈(1 /9 ,2 /9 ) , although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility χQ) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
Repulsive and attractive timelike singularities in vacuum cosmologies
International Nuclear Information System (INIS)
Miller, B.D.
1979-01-01
Spherically symmetric cosmologies whose big bang is partially spacelike and partially timelike are constrained to occur only in the presence of certain types of matter, and in such cosmologies the timelike part of the big bang is a negative-mass singularity. In this paper examples are given of cylindrically symmetric cosmologies whose big bang is partially spacelike and partially timelike. These cosmologies are vacuum. In some of them, the timelike part of the big bang is clearly a (generalized) negative-mass singularity, while in others it is a (generalized) positive-mass singularity
On the singular perturbations for fractional differential equation.
Atangana, Abdon
2014-01-01
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
An investigation of singular Lagrangians as field systems
International Nuclear Information System (INIS)
Rabei, E.M.
1995-07-01
The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs
Singularity, initial conditions and quantum tunneling in modern cosmology
International Nuclear Information System (INIS)
Khalatnikov, I M; Kamenshchik, A Yu
1998-01-01
The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and L D Landau's old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties. (special issue)
On the Singular Perturbations for Fractional Differential Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
Finger image quality based on singular point localization
DEFF Research Database (Denmark)
Wang, Jinghua; Olsen, Martin A.; Busch, Christoph
2014-01-01
Singular points are important global features of fingerprints and singular point localization is a crucial step in biometric recognition. Moreover the presence and position of the core point in a captured fingerprint sample can reflect whether the finger is placed properly on the sensor. Therefore...... and analyze the importance of singular points on biometric accuracy. The experiment is based on large scale databases and conducted by relating the measured quality of a fingerprint sample, given by the positions of core points, to the biometric performance. The experimental results show the positions of core...
Naked singularities in higher dimensional Vaidya space-times
International Nuclear Information System (INIS)
Ghosh, S. G.; Dadhich, Naresh
2001-01-01
We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension
Singular Value Decomposition and Ligand Binding Analysis
Directory of Open Access Journals (Sweden)
André Luiz Galo
2013-01-01
Full Text Available Singular values decomposition (SVD is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound, which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.
Singular limits in thermodynamics of viscous fluids
Feireisl, Eduard
2017-01-01
This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids. "The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits." Milan Pokorný (zbMATH) "This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament al importance. It is self-contained, thanks to Chapt...
Singularity fitting in hydrodynamical calculations II
International Nuclear Information System (INIS)
Richtmyer, R.D.; Lazarus, R.B.
1975-09-01
This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self-similar solutions for γ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary-value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of γ; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows
Singular perturbation in the physical sciences
Neu, John C
2015-01-01
This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and p...
Singular solutions for the rigid plastic double slip and rotation model under plane strain
Alexandrov, S.; Lyamina, E.
2018-02-01
In the mechanics of granular and other materials the system of equations comprising the rigid plastic double slip and rotation model together with the stress equilibrium equations under plane strain conditions forms a hyperbolic system. Boundary value problems for this system of equations can involve a frictional interface. An envelope of characteristics may coincide with this interface. In this case, the solution is singular. In particular, some components of the strain rate tensor approach infinity in the vicinity of the frictional interface. Such behavior of solutions is in qualitative agreement with experimental data that show that a narrow layer of localized plastic deformation is often generated near frictional interfaces. The present paper deals with asymptotic analysis of the aforementioned system of equations in the vicinity of an envelope of characteristics. It is shown that the shear strain rate and the spin component in a local coordinate system connected to the envelope follow an inverse square root rule in its vicinity.
Singularity of the London penetration depth at quantum critical points in superconductors.
Chowdhury, Debanjan; Swingle, Brian; Berg, Erez; Sachdev, Subir
2013-10-11
We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with Z2 fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe2(As(1-x)P(x))2 [K. Hashimoto et al., Science 336, 1554 (2012)].
International Nuclear Information System (INIS)
Bamba, Kazuharu; Odintsov, Sergei D.; Sebastiani, Lorenzo; Zerbini, Sergio
2010-01-01
We study all four types of finite-time future singularities emerging in the late-time accelerating (effective quintessence/phantom) era from F(R,G)-gravity, where R and G are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of F(R,G)-gravity, we also investigate modified Gauss-Bonnet gravity, so-called F(G)-gravity. In particular, we reconstruct the F(G)-gravity and F(R,G)-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in F(G)-gravity and F(R,G)-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory a non-singular one as well. (orig.)
Spin-polarized spin excitation spectroscopy
International Nuclear Information System (INIS)
Loth, Sebastian; Lutz, Christopher P; Heinrich, Andreas J
2010-01-01
We report on the spin dependence of elastic and inelastic electron tunneling through transition metal atoms. Mn, Fe and Cu atoms were deposited onto a monolayer of Cu 2 N on Cu(100) and individually addressed with the probe tip of a scanning tunneling microscope. Electrons tunneling between the tip and the substrate exchange energy and spin angular momentum with the surface-bound magnetic atoms. The conservation of energy during the tunneling process results in a distinct onset threshold voltage above which the tunneling electrons create spin excitations in the Mn and Fe atoms. Here we show that the additional conservation of spin angular momentum leads to different cross-sections for spin excitations depending on the relative alignment of the surface spin and the spin of the tunneling electron. For this purpose, we developed a technique for measuring the same local spin with a spin-polarized and a non-spin-polarized tip by exchanging the last apex atom of the probe tip between different transition metal atoms. We derive a quantitative model describing the observed excitation cross-sections on the basis of an exchange scattering process.
Energy Technology Data Exchange (ETDEWEB)
Lorenzen, R.
2007-03-15
Starting from the assumption of modular P{sub 1}CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P{sub 1}CT symmetry constitutes no loss of generality because it is a
International Nuclear Information System (INIS)
Lorenzen, R.
2007-03-01
Starting from the assumption of modular P 1 CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P 1 CT symmetry constitutes no loss of generality because it is a consequence of
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor ... It is to observe the layer behavior of the solution for smaller values of ε leading to singular ...... Burger equation, momentum gas equation and heat equation.
Coulomb singularity effects in tunnelling spectroscopy of individual impurities
Arseyev, P. I.; Maslova, N. S.; Panov, V. I.; Savinov, S. V.
2002-01-01
Non-equilibrium Coulomb effects in resonant tunnelling processes through deep impurity states are analyzed. It is shown that Coulomb vertex corrections to the tunnelling transfer amplitude lead to a power-law singularity in current- voltage characteristics
Singularities of robot mechanisms numerical computation and avoidance path planning
Bohigas, Oriol; Ros, Lluís
2017-01-01
This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves...
Dark energy and dark matter perturbations in singular universes
International Nuclear Information System (INIS)
Denkiewicz, Tomasz
2015-01-01
We discuss the evolution of density perturbations of dark matter and dark energy in cosmological models which admit future singularities in a finite time. Up to now geometrical tests of the evolution of the universe do not differentiate between singular universes and ΛCDM scenario. We solve perturbation equations using the gauge invariant formalism. The analysis shows that the detailed reconstruction of the evolution of perturbations within singular cosmologies, in the dark sector, can exhibit important differences between the singular universes models and the ΛCDM cosmology. This is encouraging for further examination and gives hope for discriminating between those models with future galaxy weak lensing experiments like the Dark Energy Survey (DES) and Euclid or CMB observations like PRISM and CoRE
Quantum gravitational collapse: non-singularity and non-locality
International Nuclear Information System (INIS)
Greenwood, Eric; Stojkovic, Dejan
2008-01-01
We investigate gravitational collapse in the context of quantum mechanics. We take primary interest in the behavior of the collapse near the horizon and near the origin (classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning the horizon is not an obstacle for him. However, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Also, near the classical singularity, some non-local effects become important. In the Schrodinger equation describing behavior near the origin, derivatives of the wave function at one point are related to the value of the wave function at some other distant point.
Phase Singularities and Termination of Spiral Wave Reentry
National Research Council Canada - National Science Library
Eason, James
2001-01-01
In order to elucidate the mechanisms by which a strong shock terminates reentrant wavefronts, we employed phase analysis techniques to study phase singularity dynamics in a finite element model of cardiac tissue...
A singular value sensitivity approach to robust eigenstructure assignment
DEFF Research Database (Denmark)
Søgaard-Andersen, Per; Trostmann, Erik; Conrad, Finn
1986-01-01
A design technique for improving the feedback properties of multivariable state feedback systems designed using eigenstructure assignment is presented. Based on a singular value analysis of the feedback properties a design parameter adjustment procedure is outlined. This procedure allows...
Normal families and isolated singularities of meromorphic functions
International Nuclear Information System (INIS)
Chee, P.S.; Subramaniam, A.
1985-06-01
Based on the criterion of Zalcman for normal families, a generalization of a well-known result relating normal families and isolated essential singularities of meromorphic functions is proved, using a theorem of Lehto and Virtanen on normal functions. (author)
Singularity confinement for maps with the Laurent property
International Nuclear Information System (INIS)
Hone, A.N.W.
2007-01-01
The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: The iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities
On the collinear singularity problem of hot QCD
International Nuclear Information System (INIS)
Candelpergher, B.; Grandou, T.
2002-01-01
The collinear singularity problem of hot QCD is revisited within a perturbative resummation scheme (PR) of the leading thermal fluctuations. On the basis of actual calculations, new aspects are discovered concerning the origin of the singularity plaguing the soft real photon emission rate out of a quark-gluon plasma at thermal equilibrium, when the latter is calculated by means of the Resummation Program (RP)
Classical resolution of black hole singularities via wormholes
Energy Technology Data Exchange (ETDEWEB)
Olmo, Gonzalo J. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Rubiera-Garcia, D. [Universidade de Lisboa, Faculdade de Ciencias, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Sanchez-Puente, A. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain)
2016-03-15
In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)
Dimension counts for singular rational curves via semigroups
Cotterill, Ethan; Feital, Lia; Martins, Renato Vidal
2015-01-01
We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $\\sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $\\mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $\\mb{P}^n$, holds whenever $g$ is small.
Modified Differential Transform Method for Two Singular Boundary Values Problems
Directory of Open Access Journals (Sweden)
Yinwei Lin
2014-01-01
Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.
Propagation of singularities for linearised hybrid data impedance tomography
DEFF Research Database (Denmark)
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2017-01-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic con......For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non...
Singular f-sum rule for superfluid 4He
International Nuclear Information System (INIS)
Wong, V.K.
1979-01-01
The validity and applicability to inelastic neutron scattering of a singular f-sum rule for superfluid helium, proposed by Griffin to explain the rhosub(s) dependence in S(k, ω) as observed by Woods and Svensson, are examined in the light of similar sum rules rigorously derived for anharmonic crystals and Bose liquids. It is concluded that the singular f-sum rules are only of microscopic interest. (Auth,)
The Notion of 'Singularity' in the Work of Gilles Deleuze
DEFF Research Database (Denmark)
Borum, Peter
2017-01-01
In Deleuze, singularity replaces generality in the economy of thought. A Deleuzian singularity is an event, but the notion comprises the effectuation of the event into form. The triptych émission–distribution–répartition itself distributes the dimensions of the passage from form-giving event to t......-drama-different/ciation’. The essay concludes that it is art that may let us consciously contemplate our pre-individual differences....
On singular interaction potentials in classical statistical mechanics
International Nuclear Information System (INIS)
Zagrebnov, V.A.; Pastur, L.A.
1978-01-01
A classical system of particles with stable two-body interaction potential is considered. It is shown that for a certain class of highly singular stable two-body potentials a cut-off procedure preserves the stability of the potential. The thermodynamical potentials (pressure and free energy density) and correlation functions are proved to have the property of asymptotic independence with respect to the continuation of the interaction potentials near singularity
Multifractal signal reconstruction based on singularity power spectrum
International Nuclear Information System (INIS)
Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning
2016-01-01
Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.
Removal of apparent singularity in grid computations
International Nuclear Information System (INIS)
Jakubovics, J.P.
1993-01-01
A self-consistency test for magnetic domain wall models was suggested by Aharoni. The test consists of evaluating the ratio S = var-epsilon wall /var-epsilon wall , where var-epsilon wall is the wall energy, and var-epsilon wall is the integral of a certain function of the direction cosines of the magnetization, α, β, γ over the volume occupied by the domain wall. If the computed configuration is a good approximation to one corresponding to an energy minimum, the ratio is close to 1. The integrand of var-epsilon wall contains terms that are inversely proportional to γ. Since γ passes through zero at the centre of the domain wall, these terms have a singularity at these points. The integral is finite and its evaluation does not usually present any problems when the direction cosines are known in terms of continuous functions. In many cases, significantly better results for magnetization configurations of domain walls can be obtained by computations using finite element methods. The direction cosines are then only known at a set of discrete points, and integration over the domain wall is replaced by summation over these points. Evaluation of var-epsilon wall becomes inaccurate if the terms in the summation are taken to be the values of the integrand at the grid points, because of the large contribution of points close to where γ changes sign. The self-consistency test has recently been generalised to a larger number of cases. The purpose of this paper is to suggest a method of improving the accuracy of the evaluation of integrals in such cases. Since the self-consistency test has so far only been applied to two-dimensional magnetization configurations, the problem and its solution will be presented for that specific case. Generalisation to three or more dimensions is straight forward
Singular vectors, predictability and ensemble forecasting for weather and climate
International Nuclear Information System (INIS)
Palmer, T N; Zanna, Laure
2013-01-01
The local instabilities of a nonlinear dynamical system can be characterized by the leading singular vectors of its linearized operator. The leading singular vectors are perturbations with the greatest linear growth and are therefore key in assessing the system’s predictability. In this paper, the analysis of singular vectors for the predictability of weather and climate and ensemble forecasting is discussed. An overview of the role of singular vectors in informing about the error growth rate in numerical models of the atmosphere is given. This is followed by their use in the initialization of ensemble weather forecasts. Singular vectors for the ocean and coupled ocean–atmosphere system in order to understand the predictability of climate phenomena such as ENSO and meridional overturning circulation are reviewed and their potential use to initialize seasonal and decadal forecasts is considered. As stochastic parameterizations are being implemented, some speculations are made about the future of singular vectors for the predictability of weather and climate for theoretical applications and at the operational level. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (review)
Singular spectrum analysis of sleep EEG in insomnia.
Aydın, Serap; Saraoǧlu, Hamdi Melih; Kara, Sadık
2011-08-01
In the present study, the Singular Spectrum Analysis (SSA) is applied to sleep EEG segments collected from healthy volunteers and patients diagnosed by either psycho physiological insomnia or paradoxical insomnia. Then, the resulting singular spectra computed for both C3 and C4 recordings are assigned as the features to the Artificial Neural Network (ANN) architectures for EEG classification in diagnose. In tests, singular spectrum of particular sleep stages such as awake, REM, stage1 and stage2, are considered. Three clinical groups are successfully classified by using one hidden layer ANN architecture with respect to their singular spectra. The results show that the SSA can be applied to sleep EEG series to support the clinical findings in insomnia if ten trials are available for the specific sleep stages. In conclusion, the SSA can detect the oscillatory variations on sleep EEG. Therefore, different sleep stages meet different singular spectra. In addition, different healthy conditions generate different singular spectra for each sleep stage. In summary, the SSA can be proposed for EEG discrimination to support the clinical findings for psycho-psychological disorders.
Curing Black Hole Singularities with Local Scale Invariance
Directory of Open Access Journals (Sweden)
Predrag Dominis Prester
2016-01-01
Full Text Available We show that Weyl-invariant dilaton gravity provides a description of black holes without classical space-time singularities. Singularities appear due to the ill behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are as follows: (1 singularities signal a phase transition from broken to unbroken phase of Weyl symmetry; (2 instead of a singularity, there is a “baby universe” or a white hole inside a black hole; (3 in the baby universe scenario, there is a critical mass after which reducing mass makes the black hole larger as viewed by outside observers; (4 if a black hole could be connected with white hole through the “singularity,” this would require breakdown of (classical geometric description; (5 the singularity of Schwarzschild BH solution is nongeneric and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information loss puzzle. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point.
Spin nematics next to spin singlets
Yokoyama, Yuto; Hotta, Chisa
2018-05-01
We provide a route to generate nematic order in a spin-1/2 system. Unlike the well-known magnon-binding mechanism, our spin nematics requires neither the frustration effect nor spin polarization in a high field or in the vicinity of a ferromagnet, but instead appears next to the spin singlet phase. We start from a state consisting of a quantum spin-1/2 singlet dimer placed on each site of a triangular lattice, and show that interdimer ring exchange interactions efficiently dope the SU(2) triplets that itinerate and interact, easily driving a stable singlet state to either Bose-Einstein condensates or a triplet crystal, some hosting a spin nematic order. A variety of roles the ring exchange serves includes the generation of a bilinear-biquadratic interaction between nearby triplets, which is responsible for the emergent nematic order separated from the singlet phase by a first-order transition.
Resonant spin Hall effect in two dimensional electron gas
Shen, Shun-Qing
2005-03-01
Remarkable phenomena have been observed in 2DEG over last two decades, most notably, the discovery of integer and fractional quantum Hall effect. The study of spin transport provides a good opportunity to explore spin physics in two-dimensional electron gas (2DEG) with spin-orbit coupling and other interaction. It is already known that the spin-orbit coupling leads to a zero-field spin splitting, and competes with the Zeeman spin splitting if the system is subjected to a magnetic field perpendicular to the plane of 2DEG. The result can be detected as beating of the Shubnikov-de Haas oscillation. Very recently the speaker and his collaborators studied transport properties of a two-dimensional electron system with Rashba spin-orbit coupling in a perpendicular magnetic field. The spin-orbit coupling competes with the Zeeman splitting to generate additional degeneracies between different Landau levels at certain magnetic fields. It is predicted theoretically that this degeneracy, if occurring at the Fermi level, gives rise to a resonant spin Hall conductance, whose height is divergent as 1/T and whose weight is divergent as -lnT at low temperatures. The charge Hall conductance changes by 2e^2/h instead of e^2/h as the magnetic field changes through the resonant point. The speaker will address the resonance condition, symmetries in the spin-orbit coupling, the singularity of magnetic susceptibility, nonlinear electric field effect, the edge effect and the disorder effect due to impurities. This work was supported by the Research Grants Council of Hong Kong under Grant No.: HKU 7088/01P. *S. Q. Shen, M. Ma, X. C. Xie, and F. C. Zhang, Phys. Rev. Lett. 92, 256603 (2004) *S. Q. Shen, Y. J. Bao, M. Ma, X. C. Xie, and F. C. Zhang, cond-mat/0410169
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xiyuan [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Fan, Jiyu, E-mail: jiyufan@nuaa.edu.cn [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Xu, Lisa [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Tong, Wei [High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031 (China); Hu, Dazhi [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); He, Xun [College of Environmental Science and Engineering, Hunan University, Changsha 410082 (China); Zhang, Lei; Pi, Li; Zhang, Yuheng [High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031 (China)
2016-06-01
We present an investigation of Griffiths singularity in La{sub 0.5} Sr{sub 0.5} MnO{sub 3} nanocrystalline by means of magnetic susceptibility and electron paramagnetic resonance (EPR). An unusual platform was found in paramagnetic region. Based on the analysis of EPR spectrum and magnetization variation across the whole temperature range of phase transition, we confirm it is due to the presence of Griffiths singularity rather than a superparamagnetic state in the nanocrystalline system. Such a singularity phase is constituted with some correlated ferromagnetic clusters which embed in paramagnetic matrix. Although they form ferromagnetic spin correlation, the system do not yield any spontaneous magnetization. According to core–shell model, the emergence of Griffiths singularity can be considered due to the presence of local ferromagnetic fluctuations originated from surface spin disorder as the sample size is confined to nanoscale. - Highlights: • Griffiths singularity rather than superparamagnetism occurs in La{sub 0.5}Sr{sub 0.5}MnO{sub 3} nanoparticals. • The sample’s size reduced to nanoscale results in the short-range ferromagnetic interaction. • The core-shell model is used to understand the formation of Griffiths phase in nanometer La{sub 0.5}Sr{sub 0.5}MnO{sub 3}.
Segmentation of singularity maps in the context of soil porosity
Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.
2016-04-01
Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in
International Nuclear Information System (INIS)
Cao, Yi; Zhou, Hui; Li, Baokun; Shen, Long
2011-01-01
This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulators for special orientations. Based on the kinematic relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed and some typical singular configurations of the 6-3 Stewart-Gough parallel manipulators are also addressed in detail. With the above-mentioned condition, a symbolic analytical polynomial expression of degree three in the moving platform position parameters, representing the position-singularity locus of the 6-3 Stewart-Gough manipulators for special orientations, is derived: and the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulator for these special orientations is investigated at length. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and a hyperbolic paraboloid, even three intersecting planes
Matsuo, Mamoru; Saitoh, Eiji; Maekawa, Sadamichi
2017-01-01
We investigate the interconversion phenomena between spin and mechanical angular momentum in moving objects. In particular, the recent results on spin manipulation and spin-current generation by mechanical motion are examined. In accelerating systems, spin-dependent gauge fields emerge, which enable the conversion from mechanical angular momentum into spins. Such a spin-mechanical effect is predicted by quantum theory in a non-inertial frame. Experiments which confirm the effect, i.e., the resonance frequency shift in nuclear magnetic resonance, the stray field measurement of rotating metals, and electric voltage generation in liquid metals, are discussed.
Stretchable Persistent Spin Helices in GaAs Quantum Wells
Dettwiler, Florian; Fu, Jiyong; Mack, Shawn; Weigele, Pirmin J.; Egues, J. Carlos; Awschalom, David D.; Zumbühl, Dominik M.
2017-07-01
The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba α and renormalized Dresselhaus β couplings to equal fixed strengths α =β , the total SO field becomes unidirectional, thus rendering the electron spins immune to decay due to momentum scattering. A robust persistent spin helix (PSH), i.e., a helical spin-density wave excitation with constant pitch P =2 π /Q , Q =4 m α /ℏ2, has already been experimentally realized at this singular point α =β , enhancing the spin lifetime by up to 2 orders of magnitude. Here, we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with independent electrical control over the SO couplings via top gate voltage VT and back gate voltage VB to extract all SO couplings when combined with detailed numerical simulations. We demonstrate for the first time the gate control of the renormalized β and the continuous locking of the SO fields at α =β ; i.e., we are able to vary both α and β controllably and continuously with VT and VB, while keeping them locked at equal strengths. This makes possible a new concept: "stretchable PSHs," i.e., helical spin patterns with continuously variable pitches P over a wide parameter range. Stretching the PSH, i.e., gate controlling P while staying locked in the PSH regime, provides protection from spin decay at the symmetry point α =β , thus offering an important advantage over other methods. This protection is limited mainly by the cubic Dresselhaus term, which breaks the unidirectionality of the total SO field and causes spin decay at higher electron densities. We quantify the cubic term, and find it to be sufficiently weak so that
Stretchable Persistent Spin Helices in GaAs Quantum Wells
Directory of Open Access Journals (Sweden)
Florian Dettwiler
2017-07-01
Full Text Available The Rashba and Dresselhaus spin-orbit (SO interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba α and renormalized Dresselhaus β couplings to equal fixed strengths α=β, the total SO field becomes unidirectional, thus rendering the electron spins immune to decay due to momentum scattering. A robust persistent spin helix (PSH, i.e., a helical spin-density wave excitation with constant pitch P=2π/Q, Q=4mα/ℏ^{2}, has already been experimentally realized at this singular point α=β, enhancing the spin lifetime by up to 2 orders of magnitude. Here, we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with independent electrical control over the SO couplings via top gate voltage V_{T} and back gate voltage V_{B} to extract all SO couplings when combined with detailed numerical simulations. We demonstrate for the first time the gate control of the renormalized β and the continuous locking of the SO fields at α=β; i.e., we are able to vary both α and β controllably and continuously with V_{T} and V_{B}, while keeping them locked at equal strengths. This makes possible a new concept: “stretchable PSHs,” i.e., helical spin patterns with continuously variable pitches P over a wide parameter range. Stretching the PSH, i.e., gate controlling P while staying locked in the PSH regime, provides protection from spin decay at the symmetry point α=β, thus offering an important advantage over other methods. This protection is limited mainly by the cubic Dresselhaus term, which breaks the unidirectionality of the total SO field and causes spin decay at higher electron densities. We quantify the cubic term, and find it to be
Fermionic bound states in Minkowski space. Light-cone singularities and structure
Energy Technology Data Exchange (ETDEWEB)
Paula, Wayne de; Frederico, Tobias; Pimentel, Rafael [Instituto Tecnologico de Aeronautica, DCTA, Dept. de Fisica, Sao Jose dos Campos, Sao Paulo (Brazil); Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Viviani, Michele [Istituto Nazionale di Fisica Nucleare, Pisa (Italy)
2017-11-15
The Bethe-Salpeter equation for two-body bound system with spin 1/2 constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one (i) to deal with end-point singularities one meets and (ii) to find stable results, up to strongly relativistic regimes, which settle in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion 0{sup +} state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector-boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in 0{sup -} state, taking both constituent-fermion and exchanged-boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom. (orig.)
Energy Technology Data Exchange (ETDEWEB)
NONE
2006-07-01
The following topics were ealt with: Hadron physics with proton and deuteron probes, physics projects with Georgian participation, spin physics with antiprotons and leptons, spin filtering experiments, ISTC projects, technical issues for FAIR. (HSI)
Dynamic nuclear spin polarization
Energy Technology Data Exchange (ETDEWEB)
Stuhrmann, H B [GKSS-Forschungszentrum Geesthacht GmbH (Germany)
1996-11-01
Polarized neutron scattering from dynamic polarized targets has been applied to various hydrogenous materials at different laboratories. In situ structures of macromolecular components have been determined by nuclear spin contrast variation with an unprecedented precision. The experiments of selective nuclear spin depolarisation not only opened a new dimension to structural studies but also revealed phenomena related to propagation of nuclear spin polarization and the interplay of nuclear polarisation with the electronic spin system. The observation of electron spin label dependent nuclear spin polarisation domains by NMR and polarized neutron scattering opens a way to generalize the method of nuclear spin contrast variation and most importantly it avoids precontrasting by specific deuteration. It also likely might tell us more about the mechanism of dynamic nuclear spin polarisation. (author) 4 figs., refs.
International Nuclear Information System (INIS)
Ji Xiangdong
2003-01-01
Spin is a beautiful concept that plays an ever important role in modern physics. In this talk, I start with a discussion of the origin of spin, and then turn to three themes in which spin has been crucial in subatomic physics: a lab to explore physics beyond the standard model, a tool to measure physical observables that are hard to obtain otherwise, a probe to unravel nonperturbative QCD. I conclude with some remarks on a world without spin
Buterakos, Donovan; Throckmorton, Robert E.; Das Sarma, S.
2018-01-01
In addition to magnetic field and electric charge noise adversely affecting spin-qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge: crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We then provide an estimate of the error as a function of the noise and capacitive coupling to compare the fidelity of our corrected gates to their uncorrected versions. Dynamical error correction protocols presented in this work are important for the next generation of singlet-triplet qubit devices where coupling among many qubits will become relevant.
Singular value correlation functions for products of Wishart random matrices
International Nuclear Information System (INIS)
Akemann, Gernot; Kieburg, Mario; Wei, Lu
2013-01-01
We consider the product of M quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalizes the classical Wishart–Laguerre Gaussian unitary ensemble with M = 1. In this paper, we first compute the joint probability distribution for the singular values of the product matrix when the matrix size N and the number M are fixed but arbitrary. This leads to a determinantal point process which can be realized in two different ways. First, it can be written as a one-matrix singular value model with a non-standard Jacobian, or second, for M ⩾ 2, as a two-matrix singular value model with a set of auxiliary singular values and a weight proportional to the Meijer G-function. For both formulations, we determine all singular value correlation functions in terms of the kernels of biorthogonal polynomials which we explicitly construct. They are given in terms of the hypergeometric and Meijer G-functions, generalizing the Laguerre polynomials for M = 1. Our investigation was motivated from applications in telecommunication of multi-layered scattering multiple-input and multiple-output channels. We present the ergodic mutual information for finite-N for such a channel model with M − 1 layers of scatterers as an example. (paper)
Singularity detection by wavelet approach: application to electrocardiogram signal
Jalil, Bushra; Beya, Ouadi; Fauvet, Eric; Laligant, Olivier
2010-01-01
In signal processing, the region of abrupt changes contains the most of the useful information about the nature of the signal. The region or the points where these changes occurred are often termed as singular point or singular region. The singularity is considered to be an important character of the signal, as it refers to the discontinuity and interruption present in the signal and the main purpose of the detection of such singular point is to identify the existence, location and size of those singularities. Electrocardiogram (ECG) signal is used to analyze the cardiovascular activity in the human body. However the presence of noise due to several reasons limits the doctor's decision and prevents accurate identification of different pathologies. In this work we attempt to analyze the ECG signal with energy based approach and some heuristic methods to segment and identify different signatures inside the signal. ECG signal has been initially denoised by empirical wavelet shrinkage approach based on Steins Unbiased Risk Estimate (SURE). At the second stage, the ECG signal has been analyzed by Mallat approach based on modulus maximas and Lipschitz exponent computation. The results from both approaches has been discussed and important aspects has been highlighted. In order to evaluate the algorithm, the analysis has been done on MIT-BIH Arrhythmia database; a set of ECG data records sampled at a rate of 360 Hz with 11 bit resolution over a 10mv range. The results have been examined and approved by medical doctors.
International Nuclear Information System (INIS)
Anon.
1980-01-01
From 25 September to 1 October, some 150 spin enthusiasts gathered in Lausanne for the 1980 International Symposium on High Energy Physics with Polarized Beams and Polarized Targets. The programme was densely packed, covering physics interests with spin as well as the accelerator and target techniques which make spin physics possible
DEFF Research Database (Denmark)
Yu, Xiao-Qin; Zhu, Zhen-Gang; Su, Gang
2017-01-01
The thermoelectric performance of a topological energy converter is analyzed. The H-shaped device is based on a combination of transverse topological effects involving the spin: the inverse spin Hall effect and the spin Nernst effect. The device can convert a temperature drop in one arm into an e...
Cross, Rod
2013-01-01
Measurements are presented on the rise of a spinning egg. It was found that the spin, the angular momentum and the kinetic energy all decrease as the egg rises, unlike the case of a ballerina who can increase her spin and kinetic energy by reducing her moment of inertia. The observed effects can be explained, in part, in terms of rolling friction…
Skyrmion formation and optical spin-Hall effect in an expanding coherent cloud of indirect excitons.
Vishnevsky, D V; Flayac, H; Nalitov, A V; Solnyshkov, D D; Gippius, N A; Malpuech, G
2013-06-14
We provide a theoretical description of the polarization pattern and phase singularities experimentally evidenced recently in a condensate of indirect excitons [H. High et al., Nature 483, 584 (2012)]. We show that the averaging of the electron and hole orbital motion leads to a comparable spin-orbit interaction for both types of carriers. We demonstrate that the interplay between a radial coherent flux of bright indirect excitons and the Dresselhaus spin-orbit interaction results in the formation of spin domains and of topological defects similar to Skyrmions. We reproduce qualitatively all the features of the experimental data and obtain a polarization pattern as in the optical spin-Hall effect despite the different symmetry of the spin-orbit interactions.
Geometric singular perturbation analysis of systems with friction
DEFF Research Database (Denmark)
Bossolini, Elena
This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter......, two mechanical problems with two diﬀerent formulations of the friction force are introduced and analysed. The ﬁrst mechanical problem is a one-dimensional spring-block model describing earthquake faulting. The dynamics of earthquakes is naturally a multiple timescale problem: the timescale...... scales. The action of friction is generally explained as the loss and restoration of linkages between the surface asperities at the molecular scale. However, the consequences of friction are noticeable at much larger scales, like hundreds of kilometers. By using geometric singular perturbation theory...
Body frames and frame singularities for three-atom systems
International Nuclear Information System (INIS)
Littlejohn, R.G.; Mitchell, K.A.; Aquilanti, V.; Cavalli, S.
1998-01-01
The subject of body frames and their singularities for three-particle systems is important not only for large-amplitude rovibrational coupling in molecular spectroscopy, but also for reactive scattering calculations. This paper presents a geometrical analysis of the meaning of body frame conventions and their singularities in three-particle systems. Special attention is devoted to the principal axis frame, a certain version of the Eckart frame, and the topological inevitability of frame singularities. The emphasis is on a geometrical picture, which is intended as a preliminary study for the more difficult case of four-particle systems, where one must work in higher-dimensional spaces. The analysis makes extensive use of kinematic rotations. copyright 1998 The American Physical Society
Identity and singularity: Metastability and morphogenesis in light of Deleuze
Directory of Open Access Journals (Sweden)
Barison Marcello
2015-01-01
Full Text Available The question of life is inextricably connected with the problem of identification and with the fact that each identification process includes the acquisition of a form. Nevertheless, it appears that at the biological level, that is, for what concerns a morphogenetic description of the status of the living being, the term singularity comes into play right there where you would expect to get into the notion of identity. According to Christian De Duve, the organic form has no identity, but it expresses - and is an expression of - a singularity. Given these observations, this is the object of the paper: to explain in a clear and consistent way how these terms - namely identity and singularity - differ and whether it is possible to ground their distinction in a coherent theoretical manner.
Analytic Evolution of Singular Distribution Amplitudes in QCD
Energy Technology Data Exchange (ETDEWEB)
Radyushkin, Anatoly V. [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Tandogan Kunkel, Asli [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
2014-03-01
We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, anti-symmetric at DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.
Quantum no-singularity theorem from geometric flows
Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag
2018-04-01
In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.
Hidden singularities in non-abelian gauge fields
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.
1978-01-01
It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the cause, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain A sub(μ) (associated with the given regularization) represents the vacuum when F sub(μν) is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A vetor = i (sigma vetor Λ r vetor / r 2 ). For this example it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point [pt
Singular ways to search for the Higgs boson
De Rújula, A
2012-01-01
The discovery or exclusion of the fundamental standard scalar is a hot topic, given the data of LEP, the Tevatron and the LHC, as well as the advanced status of the pertinent theoretical calculations. With the current statistics at the hadron colliders, the workhorse decay channel, at all relevant H masses, is H to WW, followed by W to light leptons. Using phase-space singularity techniques, we construct and study a plethora of "singularity variables" meant to facilitate the difficult tasks of separating signal and backgrounds and of measuring the mass of a putative signal. The simplest singularity variables are not invariant under boosts along the collider's axes and the simulation of their distributions requires a good understanding of parton distribution functions, perhaps not a serious shortcoming during the boson hunting season. The derivation of longitudinally boost-invariant variables, which are functions of the four charged-lepton observables that share this invariance, is quite elaborate. But their u...
TRUST MODEL FOR SOCIAL NETWORK USING SINGULAR VALUE DECOMPOSITION
Directory of Open Access Journals (Sweden)
Davis Bundi Ntwiga
2016-06-01
Full Text Available For effective interactions to take place in a social network, trust is important. We model trust of agents using the peer to peer reputation ratings in the network that forms a real valued matrix. Singular value decomposition discounts the reputation ratings to estimate the trust levels as trust is the subjective probability of future expectations based on current reputation ratings. Reputation and trust are closely related and singular value decomposition can estimate trust using the real valued matrix of the reputation ratings of the agents in the network. Singular value decomposition is an ideal technique in error elimination when estimating trust from reputation ratings. Reputation estimation of trust is optimal at the discounting of 20 %.
Two-scale approach to oscillatory singularly perturbed transport equations
Frénod, Emmanuel
2017-01-01
This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.
Singularities in x-ray spectra of metals
International Nuclear Information System (INIS)
Mahan, G.D.
1987-08-01
The x-ray spectroscopies discussed are absorption, emission, and photoemission. The singularities show up in each of them in a different manner. In absorption and emission they show up as power law singularities at the thresholds frequencies. This review will emphasize two themes. First a simple model is proposed to describe this phenomena, which is now called the MND model after MAHAN-NOZIERES-DeDOMINICIS. Exact analytical solutions are now available for this model for the three spectroscopies discussed above. These analytical models can be evaluated numerically in a simple way. The second theme of this review is that great care must be used when comparing the theory to experiment. A number of factors influence the edge shapes in x-ray spectroscopy. The edge singularities play an important role, and are observed in many matals. Quantitative fits of the theory to experiment require the consideration of other factors. 51 refs
Symposium on Singularities, Representation of Algebras, and Vector Bundles
Trautmann, Günther
1987-01-01
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.
Polarization singularities of the object field of skin surface
International Nuclear Information System (INIS)
Angelsky, O V; Ushenko, A G; Ushenko, Yu A; Ushenko, Ye G
2006-01-01
The paper deals with the investigation of formation mechanisms of laser radiation polarization structure scattered by an optically thin surface layer of human skin in two registration zones: a boundary field and a far zone of Fraunhofer diffraction. The conditions of forming polarization singularities by such an object in the scattered radiation field have been defined. Statistical and fractal polarization structure of object fields of physiologically normal and pathologically changed skin has been studied. It has been shown that polarization singularities of radiation scattered by physiologically normal skin samples have a fractal coordinate structure. It is characteristic for fields of pathologically changed skin to have a statistical coordinate structure of polarization singularities in all diffraction zones
Singular perturbations introduction to system order reduction methods with applications
Shchepakina, Elena; Mortell, Michael P
2014-01-01
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...
Breakdown of predictability: an investigation on the nature of singularities
International Nuclear Information System (INIS)
Tahir Shah, K.
1980-12-01
When relations are extrapolated beyond their premises of discovery, the operation sometimes results in an undefined object, i.e., one which cannot be identified within the given structure. The thesis is put forth that the occurrence of singularities is due to ''incompleteness'' in knowledge. An intuitive answer on how to deal with singularities (in, for instance, the real number system, space-time, quantum field theory) is presented first. Then a quasi-formalistic approach, e.g. non-standard models in higher-order languages and Lawvere's axiomatic formulation of categories, is set out. The independence of singularity with respect to other primitive notions of the Universe of knowledge is noted
Fermi-edge singularity and the functional renormalization group
Kugler, Fabian B.; von Delft, Jan
2018-05-01
We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.
Pan, Supriya
2018-01-01
Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.
Spin physics in semiconductors
2017-01-01
This book offers an extensive introduction to the extremely rich and intriguing field of spin-related phenomena in semiconductors. In this second edition, all chapters have been updated to include the latest experimental and theoretical research. Furthermore, it covers the entire field: bulk semiconductors, two-dimensional semiconductor structures, quantum dots, optical and electric effects, spin-related effects, electron-nuclei spin interactions, Spin Hall effect, spin torques, etc. Thanks to its self-contained style, the book is ideally suited for graduate students and researchers new to the field.
Inverse spin Hall effect by spin injection
Liu, S. Y.; Horing, Norman J. M.; Lei, X. L.
2007-09-01
Motivated by a recent experiment [S. O. Valenzuela and M. Tinkham, Nature (London) 442, 176 (2006)], the authors present a quantitative microscopic theory to investigate the inverse spin-Hall effect with spin injection into aluminum considering both intrinsic and extrinsic spin-orbit couplings using the orthogonalized-plane-wave method. Their theoretical results are in good agreement with the experimental data. It is also clear that the magnitude of the anomalous Hall resistivity is mainly due to contributions from extrinsic skew scattering.
Hilbert schemes of points on some classes surface singularities
Gyenge, Ádám
2016-01-01
We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...
Three dimensional nilpotent singularity and Sil'nikov bifurcation
International Nuclear Information System (INIS)
Li Xindan; Liu Haifei
2007-01-01
In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∼ -equivalent toy-bar -bar x+z-bar -bar y+ax 3 y-bar -bar z,with a 0, and analytically prove the existence of Sil'nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions
Singularities and n-dimensional black holes in torsion theories
Energy Technology Data Exchange (ETDEWEB)
Cembranos, J.A.R.; Valcarcel, J. Gigante; Torralba, F.J. Maldonado, E-mail: cembra@fis.ucm.es, E-mail: jorgegigante@ucm.es, E-mail: fmaldo01@ucm.es [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)
2017-04-01
In this work we have studied the singular behaviour of gravitational theories with non symmetric connections. For this purpose we introduce a new criteria for the appearance of singularities based on the existence of black/white hole regions of arbitrary codimension defined inside a spacetime of arbitrary dimension. We discuss this prescription by increasing the complexity of the particular torsion theory under study. In this sense, we start with Teleparallel Gravity, then we analyse Einstein-Cartan theory, and finally dynamical torsion models.
Surface singularities in Eddington-inspired Born-Infeld gravity.
Pani, Paolo; Sotiriou, Thomas P
2012-12-21
Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubt on its viability.
Harnack's Inequality for Degenerate and Singular Parabolic Equations
DiBenedetto, Emmanuele; Vespri, Vincenzo
2012-01-01
Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive
Kalman Filtering for Delayed Singular Systems with Multiplicative Noise
Institute of Scientific and Technical Information of China (English)
Xiao Lu; Linglong Wang; Haixia Wang; Xianghua Wang
2016-01-01
Kalman filtering problem for singular systems is dealt with, where the measurements consist of instantaneous measurements and delayed ones, and the plant includes multiplicative noise. By utilizing standard singular value decomposition, the restricted equivalent delayed system is presented, and the Kalman filters for the restricted equivalent system are given by using the well-known re-organization of innovation analysis lemma. The optimal Kalman filter for the original system is given based on the above Kalman filter by recursive Riccati equations, and a numerical example is presented to show the validity and efficiency of the proposed approach, where the comparison between the filter and predictor is also given.
Special relativity with a discrete spectrum of singular velocities
International Nuclear Information System (INIS)
Gonzales Gascon, F.
1977-01-01
The introduction of real transformation formulae containing a whole discrete spectrum of singularities is suggested. Some phenomenological hypotheses are introduced and the group property is substituted by weaker conditions. The first singular speed (c 1 =c) is invariant with respect to the measures of it from subluminal frames, but the remaining speeds are not invariant. The proposed transformations do not form a closed set (for the superluminal speeds) and, therefore, the problem of having (within this framework) a principle of relativity valid for any velocity remains open
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Einstein equation solutions with axial symmetry, conical and essential singularities
International Nuclear Information System (INIS)
Oliveira, S.R. de.
1986-01-01
New classes of exact solutions to the Einstein equations of a static axisymetric space-time associated with rings and disks are found. Also, the solutions associated to a axisymetric superposition of punctual bodies, bars, rings and disks are obtained. These solutions have a strut singularities to keep the bodies apart. When one of the bodies of the superposition is a ring, the ring interior is covered with a membrane that serve as a support for the strut that hold the other body. Furthermore, the curvature singularities for different solutions ae analised. (author) [pt
Propagation of singularities for linearised hybrid data impedance tomography
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2018-02-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.
Tensor renormalization group with randomized singular value decomposition
Morita, Satoshi; Igarashi, Ryo; Zhao, Hui-Hai; Kawashima, Naoki
2018-03-01
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.
Microlocal study of S-matrix singularity structure
International Nuclear Information System (INIS)
Kawai, Takahiro; Kyoto Univ.; Stapp, H.P.
1975-01-01
Support is adduced for two related conjectures of simplicity of the analytic structure of the S-matrix and related function; namely, Sato's conjecture that the S-matrix is a solution of a maximally over-determined system of pseudo-differential equations, and our conjecture that the singularity spectrum of any bubble diagram function has the conormal structure with respect to a canonical decomposition of the solutions of the relevant Landau equations. This latter conjecture eliminates the open sets of allowed singularities that existing procedures permit. (orig.) [de
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
The eigenvalue problem for a singular quasilinear elliptic equation
Directory of Open Access Journals (Sweden)
Benjin Xuan
2004-02-01
Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
Singular charge density at the center of the pion?
International Nuclear Information System (INIS)
Miller, Gerald A.
2009-01-01
We relate the three-dimensional infinite momentum frame spatial charge density of the pion to its electromagnetic form factor F π (Q 2 ). Diverse treatments of the measured form factor data including phenomenological fits, nonrelativistic quark models, the application of perturbative quantum chromodynamics (QCD), QCD sum rules, holographic QCD, and the Nambu-Jona-Lasinio (NJL) model all lead to the result that the charge density at the center of the pion has a logarithmic divergence. Relativistic constituent quark models do not display this singularity. Future measurements planned for larger values of Q 2 may determine whether or not a singularity actually occurs.
Can noncommutativity resolve the Big-Bang singularity?
Maceda, M; Manousselis, P; Zoupanos, George
2004-01-01
A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a noncommutative version of the Kasner metric is constructed which is nonsingular at all scales and becomes commutative at large length scales.
Energy Technology Data Exchange (ETDEWEB)
Eisenbart, Constanze (ed.) [Forschungsstaette der Evangelischen Studiengemeinschaft (FEST), Heidelberg (Germany)
2012-07-01
The book contains the following contributions: Why do we talk about the atomic age? The language of the atomic myth - comments to a protestant debate. Nuclear singularity between fiction and reality. Only one can get through: military singularity of nuclear weapons. Physical singularity of nuclear weapons. Nuclear weapons test and fall-out. Quantitative disarmament and qualitative rearmament. Do mini nukes neutralize the singularity? The vulnerability of the industrial society by the nuclear electromagnetic momentum. Nuclear weapons as national status symbol - the example of India. The general regulations of international laws and the singularity of nuclear weapons. The construction of normative singularity - development and change of the nuclear taboo.
Bulk electron spin polarization generated by the spin Hall current
Korenev, V. L.
2005-01-01
It is shown that the spin Hall current generates a non-equilibrium spin polarization in the interior of crystals with reduced symmetry in a way that is drastically different from the previously well-known equilibrium polarization during the spin relaxation process. The steady state spin polarization value does not depend on the strength of spin-orbit interaction offering possibility to generate relatively high spin polarization even in the case of weak spin-orbit coupling.
Bulk electron spin polarization generated by the spin Hall current
Korenev, V. L.
2006-07-01
It is shown that the spin Hall current generates a nonequilibrium spin polarization in the interior of crystals with reduced symmetry in a way that is drastically different from the previously well-known “equilibrium” polarization during the spin relaxation process. The steady state spin polarization value does not depend on the strength of spin-orbit interaction offering possibility to generate relatively high spin polarization even in the case of weak spin-orbit coupling.
Muon spin relaxation in random spin systems
International Nuclear Information System (INIS)
Toshimitsu Yamazaki
1981-01-01
The longitudinal relaxation function Gsub(z)(t) of the positive muon can reflect dynamical characters of local field in a unique way even when the correlation time is longer than the Larmor period of local field. This method has been applied to studies of spin dynamics in spin glass systems, revealing sharp but continuous temperature dependence of the correlation time. Its principle and applications are reviewed. (author)
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
particular case of radial pressure pr(r) has been illustrated in details to get a ... In §2, we briefly summarize the analysis given in [3] and state the conditions on ...... taken for other shells to reach the singularity can be determined from the Taylor.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...
Non-perturbative string theories and singular surfaces
International Nuclear Information System (INIS)
Bochicchio, M.
1990-01-01
Singular surfaces are shown to be dense in the Teichmueller space of all Riemann surfaces and in the grasmannian. This happens because a regular surface of genus h, obtained identifying 2h disks in pairs, can be approximated by a very large genus singular surface with punctures dense in the 2h disks. A scale ε is introduced and the approximate genus is defined as half the number of connected regions covered by punctures of radius ε. The non-perturbative partition function is proposed to be a scaling limit of the partition function on such infinite genus singular surfaces with a weight which is the coupling constant g raised to the approximate genus. For a gaussian model in any space-time dimension the regularized partition function on singular surfaces of infinite genus is the partition function of a two-dimensional lattice gas of charges and monopoles. It is shown that modular invariance of the partition function implies a version of the Dirac quantization condition for the values of the e/m charges. Before the scaling limit the phases of the lattice gas may be classified according to the 't Hooft criteria for the condensation of e/m operators. (orig.)
On p dependent boundedness of singular integral operators
Czech Academy of Sciences Publication Activity Database
Honzík, Petr
2011-01-01
Roč. 267, 3-4 (2011), s. 931-937 ISSN 0025-5874 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular integral operators Subject RIV: BA - General Mathematics Impact factor: 0.749, year: 2011 http://www.springerlink.com/content/k507g30163351250/
Discrete singular convolution for the generalized variable-coefficient ...
African Journals Online (AJOL)
Numerical solutions of the generalized variable-coefficient Korteweg-de Vries equation are obtained using a discrete singular convolution and a fourth order singly diagonally implicit Runge-Kutta method for space and time discretisation, respectively. The theoretical convergence of the proposed method is rigorously ...
Classical Liouville action on the sphere with three hyperbolic singularities
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl
2004-08-30
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
Hadasz, Leszek; Jaskólski, Zbigniew
2004-08-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
International Nuclear Information System (INIS)
Hadasz, Leszek; Jaskolski, Zbigniew
2004-01-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory
SINGULAR SPECTRUM ANALYSIS: METHODOLOGY AND APPLICATION TO ECONOMICS DATA
Institute of Scientific and Technical Information of China (English)
Hossein HASSANI; Anatoly ZHIGLJAVSKY
2009-01-01
This paper describes the methodology of singular spectrum analysis (SSA) and demonstrate that it is a powerful method of time series analysis and forecasting, particulary for economic time series. The authors consider the application of SSA to the analysis and forecasting of the Iranian national accounts data as provided by the Central Bank of the Islamic Republic of lran.
Singular limit analysis of a model for earthquake faulting
DEFF Research Database (Denmark)
Bossolini, Elena; Brøns, Morten; Kristiansen, Kristian Uldall
2017-01-01
In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake episodes. In particular, the limit cycles arise from...
Singularity free non-rotating cosmological solutions for perfect fluids ...
Indian Academy of Sciences (India)
Singularity free cosmological solutions of the type stated in the title known so far are of a very special class and have the following characteristics: (a) The space time is cylindrically symmetric. (b) In case the metric is diagonal, the μ's are of the form μ = a function of time multiplied by a function of the radial coordinate.
Singular problems in shell theory. Computing and asymptotics
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM
2010-07-01
It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)