Spherically symmetric Einstein-aether perfect fluid models
Coley, Alan A.; Latta, Joey [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5 (Canada); Leon, Genly [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaíso (Chile); Sandin, Patrik, E-mail: aac@mathstat.dal.ca, E-mail: genly.leon@ucv.cl, E-mail: patrik.sandin@aei.mpg.de, E-mail: lattaj@mathstat.dal.ca [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, D-14476 Potsdam (Germany)
2015-12-01
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Spherically symmetric star model in the gravitational gauge theory
Tsou, C [Peking Observatory, China; Ch' en, S; Ho, T; Kuo, H
1976-12-01
It is shown that a star model, which is black hole-free and singularity-free, can be obtained naturally in the gravitational gauge theory, provided the space-time is torsion-free and the matter is spinless. The conclusion in a sense shows that the discussions about the black hole and the singularity based on general relativity may not describe nature correctly.
Spherically symmetric relativistic model for spiral galaxies and dense stars
Hojman, R.; Rodrigues, L.M.C.; Sasse, F.D.
1990-01-01
The behaviour of the pressure and the density as well as the gravitational field of a dense star are studied in some detail. For such a purpose and to take into account relativistic effects, we find a family of exact solutions of the Tolman-Oppenheimer-Volkov equation, which contains as a particular case solutions corresponding to a γ-law equation of state. The mentioned family can also be used to model the (luminous or dark) matter content of spiral galaxies, as it fits the observed data for their orbital velocities profiles. (author)
A new model for spherically symmetric anisotropic compact star
Maurya, S.K.; Dayanandan, Baiju [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)
2016-05-15
In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star. (orig.)
Spherical aberration correction with an in-lens N-fold symmetric line currents model.
Hoque, Shahedul; Ito, Hiroyuki; Nishi, Ryuji
2018-04-01
In our previous works, we have proposed N-SYLC (N-fold symmetric line currents) models for aberration correction. In this paper, we propose "in-lens N-SYLC" model, where N-SYLC overlaps rotationally symmetric lens. Such overlap is possible because N-SYLC is free of magnetic materials. We analytically prove that, if certain parameters of the model are optimized, an in-lens 3-SYLC (N = 3) doublet can correct 3rd order spherical aberration. By computer simulation, we show that the required excitation current for correction is less than 0.25 AT for beam energy 5 keV, and the beam size after correction is smaller than 1 nm at the corrector image plane for initial slope less than 4 mrad. Copyright © 2018 Elsevier B.V. All rights reserved.
A new model for spherically symmetric charged compact stars of embedding class 1
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, U.P. (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Deb, Debabrata [Indian Institute of Engineering Science and Technology, Department of Physics, Howrah, West Bengal (India)
2017-01-15
In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant A = 0, which shows that our solutions represent the so-called 'electromagnetic mass model' [17], and, secondly, the metric function ν(r), for the limit n tending to infinity, converts to ν(r) = Cr{sup 2}+ ln B, which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence. (orig.)
Spherically symmetric charged compact stars
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Jaypee Institute of Information Technology University, Department of Mathematics, Noida, Uttar Pradesh (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Chowdhury, Sourav Roy [Seth Anandaram Jaipuria College, Department of Physics, Kolkata, West Bengal (India)
2015-08-15
In this article we consider the static spherically symmetric metric of embedding class 1. When solving the Einstein-Maxwell field equations we take into account the presence of ordinary baryonic matter together with the electric charge. Specific new charged stellar models are obtained where the solutions are entirely dependent on the electromagnetic field, such that the physical parameters, like density, pressure etc. do vanish for the vanishing charge. We systematically analyze altogether the three sets of Solutions I, II, and III of the stellar models for a suitable functional relation of ν(r). However, it is observed that only the Solution I provides a physically valid and well-behaved situation, whereas the Solutions II and III are not well behaved and hence not included in the study. Thereafter it is exclusively shown that the Solution I can pass through several standard physical tests performed by us. To validate the solution set presented here a comparison has also been made with that of the compact stars, like RX J 1856 - 37, Her X - 1, PSR 1937+21, PSRJ 1614-2230, and PSRJ 0348+0432, and we have shown the feasibility of the models. (orig.)
Mimoso, José Pedro; Mena, Filipe C
2010-01-01
We investigate spherically symmetric perfect fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the ADM mass and to a function of the pressure which we introduce and that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition. We analyse the particular cases of the Lema\\^itre-Tolman-Bondi dust models with a cosmological constant as an example of a $\\Lambda$-CDM model and its generalization to contain a central perfect fluid core. These models provide simple, but physically interesting illustrations of our results.
A Model of Dust-like Spherically Symmetric Gravitational Collapse without Event Horizon Formation
Piñol M.
2015-10-01
Full Text Available Some dynamical aspects of gravitational collapse are explored in this paper. A time- dependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like stress-momentum tensor is considered to obtain analytical solutions of these equations, with the perfect fluid con- sisting of two purely radial fluxes — the inwards flux of collapsing matter and the outwards flux of thermally emitted radiation. Thermal emission is calculated by means of a simplistic but illustrative model of uninteracting collapsing shells. Our results show an asymptotic approach to a maximal space-time deformation without the formation of event horizons. The size of the body is slightly larger than the Schwarzschild radius during most of its lifetime, so that there is no contradiction with either observations or previous theorems on black holes. The relation of the latter with our results is scruti- nized in detail.
Averaging in spherically symmetric cosmology
Coley, A. A.; Pelavas, N.
2007-01-01
The averaging problem in cosmology is of fundamental importance. When applied to study cosmological evolution, the theory of macroscopic gravity (MG) can be regarded as a long-distance modification of general relativity. In the MG approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume-preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a Friedmann-Lemaitre-Robertson-Walker (FLRW) background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We also find that the correlation tensor for a non-FLRW background can be interpreted as the sum of a spatial curvature and an anisotropic fluid. This may lead to interesting effects of averaging on astrophysical scales. We also discuss the results of averaging an inhomogeneous Lemaitre-Tolman-Bondi solution as well as calculations of linear perturbations (that is, the backreaction) in an FLRW background, which support the main conclusions of the analysis
Relativistic fluids in spherically symmetric space
Dipankar, R.
1977-12-01
Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect fluid spheres are generalized. Solutions are spherically symmetric and conformally flat
Beig, Robert; Siddiqui, Azad A.
2007-11-01
It is known that spherically symmetric static spacetimes admit a foliation by flat hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of flat foliations for studying black hole physics. Here, flat spherically symmetric spacelike hypersurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit flat spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the timelike Killing vector. This result guarantees the uniqueness of flat spherically symmetric foliations for such spacetimes.
Spherically symmetric self-similar universe
Dyer, C C [Toronto Univ., Ontario (Canada)
1979-10-01
A spherically symmetric self-similar dust-filled universe is considered as a simple model of a hierarchical universe. Observable differences between the model in parabolic expansion and the corresponding homogeneous Einstein-de Sitter model are considered in detail. It is found that an observer at the centre of the distribution has a maximum observable redshift and can in principle see arbitrarily large blueshifts. It is found to yield an observed density-distance law different from that suggested by the observations of de Vaucouleurs. The use of these solutions as central objects for Swiss-cheese vacuoles is discussed.
Initial value formulation for the spherically symmetric dust solution
Liu, H.
1990-01-01
An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived
Exact solutions of the spherically symmetric multidimensional ...
The complete orthonormalised energy eigenfunctions and the energy eigenvalues of the spherically symmetric isotropic harmonic oscillator in N dimensions, are obtained through the methods of separation of variables. Also, the degeneracy of the energy levels are examined. KEY WORDS: - Schrödinger Equation, Isotropic ...
Araujo, M. E.; Stoeger, W. R.
2009-01-01
A rigorous demonstration that given appropriate data on our past light cone leads to the determination of the metric functions and all their time derivatives on our past light cone is presented, thus showing how to evolve the solution we obtain from data on the light cone off it in a well-defined and straightforward way. It also automatically gives a procedure for constructing the solution for all spherically symmetric, inhomogeneous cosmological Lemaitre-Tolman-Bondi models in observational coordinates as a Taylor series in time of however many terms we need. Our procedure takes into account the essential data giving the maximum of the observer area (angular-diameter) distance, and the redshift z max at which that occurs. This enables the determination of the vacuum-energy density μ Λ , which would otherwise remain undetermined.
Chang Yiren; Hsu Long; Chi Sien
2006-01-01
Since their invention in 1986, optical tweezers have become a popular manipulation and force measurement tool in cellular and molecular biology. However, until recently there has not been a sophisticated model for optical tweezers on trapping cells in the ray-optics regime. We present a model for optical tweezers to calculate the optical force upon a spherically symmetric multilayer sphere representing a common biological cell. A numerical simulation of this model shows that not only is the magnitude of the optical force upon a Chinese hamster ovary cell significantly three times smaller than that upon a polystyrene bead of the same size, but the distribution of the optical force upon a cell is also much different from that upon a uniform particle, and there is a 30% difference in the optical trapping stiffness of these two cases. Furthermore, under a small variant condition for the refractive indices of any adjacent layers of the sphere, this model provides a simple approximation to calculate the optical force and the stiffness of an optical tweezers system
Geometrodynamics of spherically symmetric Lovelock gravity
Kunstatter, Gabor; Taves, Tim; Maeda, Hideki
2012-01-01
We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kuchar (1994 Phys. Rev. D 50 3961) in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner-Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mechanics, Hamiltonian thermodynamics and formation of generic Lovelock black holes. (fast track communication)
Zhuk, Alexander [The International Center of Future Science of the Jilin University, Changchun City (China); Odessa National University, Astronomical Observatory, Odessa (Ukraine); Chopovsky, Alexey; Fakhr, Seyed Hossein [Odessa National University, Astronomical Observatory, Odessa (Ukraine); Shulga, Valerii [The International Center of Future Science of the Jilin University, Changchun City (China); Institut of Radio Astronomy of National Academy of Sciences of Ukraine, Kharkov (Ukraine); Wei, Han [The International Center of Future Science of the Jilin University, Changchun City (China)
2017-11-15
In a multidimensional Kaluza-Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter Ω of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter γ. We define under which conditions γ can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have γ ∼ 1 in the solar system, the mass of scalar field should be μ >or similar 5.05 x 10{sup -49} g ∝ 2.83 x 10{sup -16} eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: Ω = -1/2. (orig.)
Canonical quantization of static spherically symmetric geometries
Christodoulakis, T; Dimakis, N; Terzis, P A; Doulis, G; Grammenos, Th; Melas, E; Spanou, A
2013-01-01
The conditional symmetries of the reduced Einstein–Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''
Stability of transparent spherically symmetric thin shells and wormholes
Ishak, Mustapha; Lake, Kayll
2002-01-01
The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations
All spherically symmetric charged anisotropic solutions for compact stars
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)
2017-06-15
In the present paper we develop an algorithm for all spherically symmetric anisotropic charged fluid distributions. Considering a new source function ν(r) we find a set of solutions which is physically well behaved and represents compact stellar models. A detailed study specifically shows that the models actually correspond to strange stars in terms of their mass and radius. In this connection we investigate several physical properties like energy conditions, stability, mass-radius ratio, electric charge content, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent agreement with the already available evidence in theory as well as observations. (orig.)
Flat synchronizations in spherically symmetric space-times
Herrero, Alicia; Morales-Lladosa, Juan Antonio
2010-01-01
It is well known that the Schwarzschild space-time admits a spacelike slicing by flat instants and that the metric is regular at the horizon in the associated adapted coordinates (Painleve-Gullstrand metric form). We consider this type of flat slicings in an arbitrary spherically symmetric space-time. The condition ensuring its existence is analyzed, and then, we prove that, for any spherically symmetric flat slicing, the densities of the Weinberg momenta vanish. Finally, we deduce the Schwarzschild solution in the extended Painleve-Gullstrand-LemaItre metric form by considering the coordinate decomposition of the vacuum Einstein equations with respect to a flat spacelike slicing.
Spherically symmetric solutions in abelian Kaluza-Klein theories
Angus, I.G.
1986-01-01
We present the most general spherically symmetric solution to the field equations of the truncated five-dimensional Kaluza-Klein theory. We also detail some of the special forms of this solution. With the exception of the Gross-Perry-Sorkin monopole and the Schwarzschild solutions we find that most, and we conjecture all, of the solutions have naked curvature singularities. We then proceed to consider higher-dimensional theories with toroidal compactification and we exhibit a class of nonsingular monopole solutions which are the natural generalization of the Gross-Perry-Sorkin monopole to more than five dimensions. We also present some selected solutions including a solution pertaining to a model with a Ricci-flat, but not curvature-flat, internal manifold. All of these other solutions have naked curvature singularities. (orig.)
Static spherically symmetric wormholes in f(R, T) gravity
Zubair, M.; Ahmad, Yasir [Institute Of Information Technology, Department of Mathematics, COMSATS, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia)
2016-08-15
In this work, we explore wormhole solutions in f(R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f(R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity. (orig.)
Spherically symmetric radiation in gravitational collapse
Bridy, D.J.
1983-01-01
This paper investigates a previously neglected mode by which a star may lose energy in the late stages of gravitational collapse to the black hole state. A model consisting of a Schwarzschild exterior matched to a Friedman interior of collapsing pressureless dust is studied. The matter of the collapsing star is taken as the source of a massive vector boson field and a detailed boundary value problem is carried out. Vector mesons are strongly coupled to all nucleons and will be radiated by ordinary matter during the collapse. The time dependent coupling between interior and exterior modes matched across the moving boundary of the collapsing star and the presence of the gravitational fields and their gradients in the field equations may give rise to a parametric amplification mechanism and permit the gravitational field to pump energy into the boson field, greatly enhancing the amount of boson radiation. The significance of a radiative mechanism driven by collapse is that it can react back upon the collapsing source and deprive it of some of the very mass that drives the collapse via its self gravitation. If the mass loss is great enough, this may provide a mechanism to slow or even halt gravitational collapse in some cases
Implications of the Cosmological Constant for Spherically Symmetric Mass Distributions
Zubairi, Omair; Weber, Fridolin
2013-04-01
In recent years, scientists have made the discovery that the expansion rate of the Universe is increasing rather than decreasing. This acceleration leads to an additional term in Albert Einstein's field equations which describe general relativity and is known as the cosmological constant. This work explores the aftermath of a non-vanishing cosmological constant for relativistic spherically symmetric mass distributions, which are susceptible to change against Einstein's field equations. We introduce a stellar structure equation known as the Tolman-Oppenhiemer-Volkoff (TOV) equation modified for a cosmological constant, which is derived from Einstein's modified field equations. We solve this modified TOV equation for these spherically symmetric mass distributions and obtain stellar properties such as mass and radius and investigate changes that may occur depending on the value of the cosmological constant.
The inverse spatial Laplacian of spherically symmetric spacetimes
Fernandes, Karan; Lahiri, Amitabha
2017-01-01
We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)
Maximal slicing of D-dimensional spherically symmetric vacuum spacetime
Nakao, Ken-ichi; Abe, Hiroyuki; Yoshino, Hirotaka; Shibata, Masaru
2009-01-01
We study the foliation of a D-dimensional spherically symmetric black-hole spacetime with D≥5 by two kinds of one-parameter families of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpetlike shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces avoid the singularity irrespective of the dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. These data will be useful for checking five-dimensional numerical-relativity codes based on the moving puncture approach.
Spherically symmetric solution and a satisfactory energy-momentum complex
Nashed, G.G.L.
2005-01-01
Mikhail et al. obtained two spherically symmetric solution in Moeller tetrad theory of gravitation. They calculated their energy content and obtained a strange value for the second solution, in spite that the associated metric of these solutions is the same (the Schwarzschild metric). We use another method given bu Gibbons and Hawking to calculate the energy content of these solutions. We also obtained a strange value of energy for the second solution. Studying the requirements of the satisfactory energy-momentum complex given by Moeller we find that the second solution which behaves as 1/√r does not transform as a four-vector under Lorentz transformation
Spherically symmetric near-critical accretion onto neutron stars
Miller, G.S.
1990-01-01
Numerical and approximate analytic solutions for time-independent, spherically symmetric, radiation pressure-dominated accretion flows are presented. For flows with luminosities at infinity, L-infinity, sufficiently close to the Eddington limit L-crit, the flow velocity profile is qualitatively different from the modified free-fall profile v(r) = (1 - L-infinity/L-crit)exp 1/2 (2GM/r)exp 1/2. Advective contributions to the comoving radiation flux decelerate the flow within a criical radius, and, in this settling region, the velocity of the flow decreases linearly with decreasing radius. 14 refs
Minimal Length Effects on Tunnelling from Spherically Symmetric Black Holes
Benrong Mu
2015-01-01
Full Text Available We investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole’s mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time.
Integral solution for the spherically symmetric Fokker-Planck equation
Donoso, J.M.; Soler, M.
1993-01-01
We propose an integral method to deal with the spherically symmetric non-linear Fokker-Planck equation appearing in plasma physics. A probability transition expression is obtained, which takes into account the proper domain for the radial velocity component. The analytical and computational results are new, and the time evolution is completely satisfactory. The main achievement of the method is conservation of both the initial norm and energy for unlimited times, which has not been attained in the differential approach to the problem. (orig.)
The theory of spherically symmetric thin shells in conformal gravity
Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury
The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.
Spherically symmetric solutions of general second-order gravity
Whitt, B.
1988-01-01
The general second-order gravity theory, whose Lagrangian includes higher powers of the curvature, is considered in arbitrary dimensions. It is shown that spherically symmetric solutions are static, except in certain, special, unphysical cases. Spherically symmetric solutions are found and classified. Each theory's solutions fall into a number of distinct branches, which may represent finite space with two singular boundaries, or an asymptotically either flat or (anti--)de Sitter space with one singular boundary. A theory may contain at most one branch of solutions in which all singularities are hidden by event horizons. Such horizons generally emit Hawking radiation, though in certain cases the horizon may have zero temperature. Black holes do not necessarily radiate away all their mass: they may terminate in a zero-temperature black hole, a naked singularity, or a hot black hole in equilibrium with a ''cosmological'' event horizon. The thermodynamics of black-hole solutions is discussed; entropy is found to be an increasing function of horizon area, and the first law is shown to hold
Spherical aberration correction with threefold symmetric line currents.
Hoque, Shahedul; Ito, Hiroyuki; Nishi, Ryuji; Takaoka, Akio; Munro, Eric
2016-02-01
It has been shown that N-fold symmetric line current (henceforth denoted as N-SYLC) produces 2N-pole magnetic fields. In this paper, a threefold symmetric line current (N3-SYLC in short) is proposed for correcting 3rd order spherical aberration of round lenses. N3-SYLC can be realized without using magnetic materials, which makes it free of the problems of hysteresis, inhomogeneity and saturation. We investigate theoretically the basic properties of an N3-SYLC configuration which can in principle be realized by simple wires. By optimizing the parameters of a system with beam energy of 5.5keV, the required excitation current for correcting 3rd order spherical aberration coefficient of 400 mm is less than 1AT, and the residual higher order aberrations can be kept sufficiently small to obtain beam size of less than 1 nm for initial slopes up to 5 mrad. Copyright © 2015 Elsevier B.V. All rights reserved.
Information entropy for static spherically symmetric black holes
Jiang Ji-Jian; Li Chuan-An
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.
Notes on entropy force in general spherically symmetric spacetimes
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2010-01-01
In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein's equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.
Timelike geodesics around a charged spherically symmetric dilaton black hole
Blaga C.
2015-01-01
Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
Information entropy for static spherically symmetric black holes
Ji-Jian, Jiang; Chuan-An, Li
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein–Hawking entropy when the suitable cutoff factor is adopted. (general)
Generalized transformations and coordinates for static spherically symmetric general relativity
Hill, James M.; O'Leary, Joseph
2018-04-01
We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.
Absorbed dose from traversing spherically symmetric, Gaussian radioactive clouds
Thompson, J.M.; Poston, J.W.
1999-01-01
If a large radioactive cloud is produced, sampling may require that an airplane traverse the cloud. A method to predict the absorbed dose to the aircrew from penetrating the radioactive cloud is needed. Dose rates throughout spherically symmetric Gaussian clouds of various sizes, and the absorbed doses from traversing the clouds, were calculated. Cloud size is a dominant parameter causing dose to vary by orders of magnitude for a given dose rate measured at some distance. A method to determine cloud size, based on dose rate readings at two or more distances from the cloud center, was developed. This method, however, failed to resolve the smallest cloud sizes from measurements made at 1,000 m to 2,000 m from the cloud center
Observational signatures of spherically-symmetric black hole spacetimes
De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Fromm, Christian; Rezzolla, Luciano; Olivares, Hector
2017-12-01
A binary system composed of a supermassive black hole and a pulsar orbiting around it is studied. The motivation for this study arises from the fact that pulsar timing observations have proven to be a powerful tool in identifying physical features of the orbiting companion. In this study, taking into account a general spherically-symmetric metric, we present analytic calculations of the geodesic motion, and the possible deviations with respect to the standard Schwarzschild case of General Relativity. In particular, the advance at periastron is studied with the aim of identifying corrections to General Relativity. A discussion of the motion of a pulsar very close the supermassive central black hole in our Galaxy (Sgr A*) is reported.
Generalized transformations and coordinates for static spherically symmetric general relativity.
Hill, James M; O'Leary, Joseph
2018-04-01
We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.
Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution
Baradaran, M.; Panahi, H.
2016-01-01
We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.
Gravitational collapse and topology change in spherically symmetric dynamical systems
Csizmadia, Peter; Racz, Istvan, E-mail: cspeter@rmki.kfki.h, E-mail: iracz@rmki.kfki.h [RMKI H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)
2010-01-07
A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.
Generation of spherically symmetric metrics in f(R) gravity
Amirabi, Z.; Halilsoy, M.; Mazharimousavi, S.H. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2016-06-15
In D-dimensional spherically symmetric f(R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, is F(R) = (df(R))/(dR). We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f(R) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples. (orig.)
Rovibrational states of Wigner molecules in spherically symmetric confining potentials
Cioslowski, Jerzy [Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden (Germany)
2016-08-07
The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the “anomalous” weak-confinement behavior of the {sup 1}S{sub +} state of the four-electron species that is absent in its {sup 1}D{sub +} companion of the strong-confinement regime.
A new approach to spherically symmetric junction surfaces and the matching of FLRW regions
Kirchner, U
2004-01-01
We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann-LemaItre-Robertson-Walker (FLRW) models. We discuss 'vacuum bubbles' and closed-open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time
The Spherical Deformation Model
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...
Akbar, M.M., E-mail: akbar@utdallas.edu
2017-06-10
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè–Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè–Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.
The Spherical Deformation Model
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...... a single central section of the object. We use maximum-likelihood-based inference for this purpose and demonstrate the suggested methods on real data....
Axi-symmetric patterns of active polar filaments on spherical and composite surfaces
Srivastava, Pragya; Rao, Madan
2014-03-01
Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.
Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation
Lim, Woei Chet; Regis, Marco; Clarkson, Chris
2013-01-01
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast
Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation
Lim, Woei Chet; Regis, Marco; Clarkson, Chris
2013-10-01
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast.
Dynamics and entanglement in spherically symmetric quantum gravity
Husain, Viqar; Terno, Daniel R.
2010-01-01
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of semiclassical states peaked on constraint-free data. Such states provide explicit examples of physical states. We also show that matter-gravity entanglement is an inherent feature of physical states, whether or not there is a black hole.
Spherically symmetric static spacetimes in vacuum f(T) gravity
Ferraro, Rafael; Fiorini, Franco
2011-01-01
We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Banados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).
Odd-parity pertubations of spherically symmetric star clusters in general relativity
Semenzato, R.; Ipser, J.R.
1981-01-01
The theory of odd-parity nonspherical peturbations of collisionless, isotropic, spherically symmetric star clusters is developed within general relativity for l> or =2. A variational principle is derived for the associated normal modes of oscillation. The variational expression reveals that an unstable normal mode has a pure exponentially growing time dependence--the corresponding complex ''eigenfrequency'' is purely imaginary--and hence that a normal mode can become unstable in a smooth fashion only thorugh zero frequency. Further, it is shown that no instabilities can set in through zero-frequency modes along smooth sequences of models with fewer high-energy stars than low-energy stars. Unless unstable normal modes suddenly appear in a nonsmooth fashion, the implications is that these models possess no unstable normal modes
No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
Shahar Hod
2017-08-01
Full Text Available We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
Matinyan, S.G.; Prokhorenko, E.V.; Savvidy, G.K.
1986-01-01
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. The phase space of this system is shown to have no quasi-periodic motion specific for integrable systems. In particular, the well-known Wu-Yang static solution is unstable, so its vicinity in phase is the stochasticity region
The general class of the vacuum spherically symmetric equations of the general relativity theory
Karbanovski, V. V.; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N.; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-01-01
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g 00 and g 22 is obtained. The properties of the found solutions are analyzed.
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
Matinyan, S G; Prokhorenko, E B; Savvidy, G K
1988-03-07
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.
Brito, Irene; Mena, Filipe C
2017-08-01
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
Maximally Symmetric Composite Higgs Models.
Csáki, Csaba; Ma, Teng; Shu, Jing
2017-09-29
Maximal symmetry is a novel tool for composite pseudo Goldstone boson Higgs models: it is a remnant of an enhanced global symmetry of the composite fermion sector involving a twisting with the Higgs field. Maximal symmetry has far-reaching consequences: it ensures that the Higgs potential is finite and fully calculable, and also minimizes the tuning. We present a detailed analysis of the maximally symmetric SO(5)/SO(4) model and comment on its observational consequences.
Spherically symmetric random walks. II. Dimensionally dependent critical behavior
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1996-01-01
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D approx-gt 0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D approx-gt 0. copyright 1996 The American Physical Society
Invariant identification of naked singularities in spherically symmetric spacetimes
Torres, R
2012-01-01
The study of generic naked singularities and their implications for the cosmic censorship conjecture is still an open issue in the framework of general relativity. One of the obstacles can be traced to the procedures for identifying naked singularities. Usually, the methods applied are not only model and coordinate dependent, but they very often rely in some strong assumptions on the degree of differentiability of the physical magnitudes of the model (such as the mass, density, etc) in the singularity. In this paper, we present a coordinate independent framework for identifying naked singularities based on invariants which is also devoid of strong differentiability requirements. The approach is intended to analyse whole families of models and to provide general results related to the cosmic censorship conjecture. Moreover, since the framework has a strict geometrical nature it can be used with alternative theories of gravitation as long as they assume the existence of a Lorentzian manifold. We exemplify its strength by applying it to the study of the collapse of radiation in radiative coordinates and the collapse of dust in comoving coordinates. (paper)
Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes
Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-01-01
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter. (paper)
All static spherically symmetric perfect-fluid solutions of Einstein's equations
Lake, Kayll
2003-01-01
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by nontrivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions
Undergoing spherically symmetric steady-state accretion stability of white dwarfs
Sienkiewicz, R [Polska Akademia Nauk, Warsaw. N. Copernicus Astronomical Center
1980-01-01
Thermal and vibrational stabilities of accreting white dwarfs with steady-state nuclear burning were considered, assuming spherically symmetric accretion of the hydrogen-rich matter and using linear stability analysis. Almost all models with masses 0.2 M(sun) - 1.39 M(sun) were found to be unstable in some way. The type of instability expected to dominate is given as a function of the accretion rate. For most accretion rates it is the thermal instability. Oscillation periods are given for the models in which the vibrational instability is the most violent one. These periods are of the order of seconds or minutes. We expect that our stability analysis may suggest the cause of the variabilities of the hot components of some symbiotic stars, for a wide range of the accretion rates. In this case our models may serve as the initial conditions for evolutionary computations. The results predict that short-period oscillations should be observed in some hot nuclei of planetary nebulae.
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Wang, Tongjiang; Davila, Joseph M.
2014-01-01
Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.
On the use of the Kodama vector field in spherically symmetric dynamical problems
Racz, Istvan [MTA KFKI, Reszecske- es Magfizikai Kutatointezet, H-1121 Budapest, Konkoly Thege Miklos ut 29-33, (Hungary)
2006-01-07
It is shown that by making use of the Kodama vector field, as a preferred time evolution vector field, in spherically symmetric dynamical systems unexpected simplifications arise. In particular, the evolution equations relevant for the case of a massless scalar field minimally coupled to gravity are investigated. The simplest form of these equations in the 'canonical gauge' is known to possess the character of a mixed first-order elliptic-hyperbolic system. The advantages related to the use of the Kodama vector field are twofold although they show up simultaneously. First, it is found that the true degrees of freedom separate. Second, a subset of the field equations possessing the form of a first-order symmetric hyperbolic system for these preferred degrees of freedom is singled out. It is also demonstrated, in the appendix, that the above results generalize straightforwardly to the case of a generic self-interacting scalar field.
Beyond Extreme Ultra Violet (BEUV) Radiation from Spherically symmetrical High-Z plasmas
Yoshida, Kensuke; Fujioka, Shinsuke; Higashiguchi, Takeshi; Ugomori, Teruyuki; Tanaka, Nozomi; Kawasaki, Masato; Suzuki, Yuhei; Suzuki, Chihiro; Tomita, Kentaro; Hirose, Ryouichi; Eshima, Takeo; Ohashi, Hayato; Nishikino, Masaharu; Scally, Enda; Nshimura, Hiroaki; Azechi, Hiroshi; O'Sullivan, Gerard
2016-03-01
Photo-lithography is a key technology for volume manufacture of high performance and compact semiconductor devices. Smaller and more complex structures can be fabricated by using shorter wavelength light in the photolithography. One of the most critical issues in development of the next generation photo-lithography is to increase energy conversion efficiency (CE) from laser to shorter wavelength light. Experimental database of beyond extreme ultraviolet (BEUV) radiation was obtained by using spherically symmetrical high-Z plasmas generated with spherically allocated laser beams. Absolute energy and spectra of BEUV light emitted from Tb, Gd, and Mo plasmas were measured with a absolutely calibrated BEUV calorimeter and a transmission grating spectrometer. 1.0 x 1012 W/cm2 is the optimal laser intensity to produced efficient BEUV light source plasmas with Tb and Gd targets. Maximum CE is achieved at 0.8% that is two times higher than the published CEs obtained with planar targets.
Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems
Pham, Duc Chinh
2018-02-01
Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (d=2,3). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.
Classic tests of General Relativity described by brane-based spherically symmetric solutions
Cuzinatto, R.R. [Universidade Federal de Alfenas, Instituto de Ciencia e Tecnologia, Pocos de Caldas, MG (Brazil); Pompeia, P.J. [Departamento de Ciencia e Tecnologia Aeroespacial, Instituto de Fomento e Coordenacao Industrial, Sao Jose dos Campos, SP (Brazil); Departamento de Ciencia e Tecnologia Aeroespacial, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, SP (Brazil); De Montigny, M. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); University of Alberta, Campus Saint-Jean, Edmonton, AB (Canada); Khanna, F.C. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); TRIUMF, Vancouver, BC (Canada); University of Victoria, Department of Physics and Astronomy, PO box 1700, Victoria, BC (Canada); Silva, J.M.H. da [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2014-08-15
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter b related to the fifth-coordinate. This constant b can be constrained by comparison with observational data for massive and massless particles. (orig.)
Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory
Janda, A.
2006-01-01
We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)
Spherically Symmetric Geometries in f(T) and f(R) Gravitational Theories
Nashed, Gamal G. L.
2015-01-01
Using the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R=-T-2∇_αT"α, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is, T=T_μ_ν"αS_α"μ"ν=0 or (ii) total derivative term, that is, ∇_αT"α with T"α is the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution for f(T) and f(R) gravitational theories.
On spherically symmetric motions of a viscous compressible barotropic and selfgravitating gas
Ducomet, B.; Nečasová, Šárka; Vasseur, A.
2011-01-01
Roč. 13, č. 2 (2011), s. 191-211 ISSN 1422-6928 R&D Projects: GA ČR GA201/08/0012; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : spherically symmetric motion * selfgravitating gas * non monotone pressure law * density-dependent viscosities Subject RIV: BA - General Mathematics Impact factor: 0.768, year: 2011 http://link.springer.com/article/10.1007%2Fs00021-009-0010-5
Kafka, P; Meszaros, P [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany, F.R.)
1976-11-01
Stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation are constructed. The relevance of these solutions is discussed with respect to the question of whether the limitation of the luminosity (Eddington limit) also implies an upper bound to the possible rate of mass flow. The question remains open until all instabilities have been studied. At the moment a negative answer is favoured.
de Hoop, Maarten V.; Ilmavirta, Joonas
2017-12-01
We study ray transforms on spherically symmetric manifolds with a piecewise C1, 1 metric. Assuming the Herglotz condition, the x-ray transform is injective on the space of L 2 functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C1, 1 metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Clarisse, J.M.
2007-01-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Academic College, Jerusalem (Israel)
2017-12-15
It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass μ and proper frequency ω in the curved background of a spherically symmetric compact reflecting star of mass M and radius R{sub s}. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities 1 - 2M/R{sub s} < (ω/μ){sup 2} < 1. Interestingly, in the regime M/R{sub s} << 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {ω(M,R_s, μ)}{sup n=∞}{sub n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations. (orig.)
Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts
Bičák, Jiří; Hájíček, Petr
2003-11-01
The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components—the ingoing and outgoing dusts—are assumed to interact only through gravitation. Different kinds of singularities, naked or “clothed,” which can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bičák and Kuchař is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).
The Thermal Response of a Pulsar Glitch : The Non-spherical Symmetric Case
Cheng, K. S.; Li, Y.; Suen, W. -M.
1999-01-01
We study the thermal evolution of a pulsar after a glitch in which the energy is released from a relative compact region. A set of relativistic thermal transport and energy balance equations is used to study the thermal evolution, without making the assumption of spherical symmetry. We use an exact cooling model to solve this set of differential equtions. Our results differ significantly from those obtained under the assumption of spherical symmetry. Even for young pulsars with a hot core lik...
Introduction to left-right symmetric models
Grimus, W.
1993-01-01
We motivate left-right symmetric models by the possibility of spontaneous parity breaking. Then we describe the multiplets and the Lagrangian of such models. Finally we discuss lower bounds on the right-handed scale. (author)
Spherically Symmetric Gravitational Collapse of a Dust Cloud in Third-Order Lovelock Gravity
Zhou, Kang; Yang, Zhan-Ying; Zou, De-Cheng; Yue, Rui-Hong
We investigate the spherically symmetric gravitational collapse of an incoherent dust cloud by considering a LTB-type spacetime in third-order Lovelock Gravity without cosmological constant, and give three families of LTB-like solutions which separately corresponding to hyperbolic, parabolic and elliptic. Notice that the contribution of high-order curvature corrections have a profound influence on the nature of the singularity, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the presence of high order Lovelock terms leads to the formation of massive, naked and timelike singularities in the 7D spacetime, which is disallowed in general relativity. Moveover, we point out that the naked singularities in the 7D case may be gravitational weak therefore may not be a serious threat to the cosmic censorship hypothesis, while the naked singularities in the D ≥ 8 inhomogeneous collapse violate the cosmic censorship hypothesis seriously.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-01
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
McDevitt, C. J.; Tang, X.-Z.; Guo, Z. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Berk, H. L. [Department of Physics, University of Texas, Austin, Texas 78712 (United States)
2014-10-15
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Higher spins tunneling from a time dependent and spherically symmetric black hole
Siahaan, Haryanto M.
2016-01-01
The discussions of Hawking radiation via tunneling method have been performed extensively in the case of scalar particles. Moreover, there are also several works in discussing the tunneling method for Hawking radiation by using higher spins, e.g. neutrino, photon, and gravitino, in the background of static black holes. Interestingly, it is found that the Hawking temperature for static black holes using the higher spins particles has no difference compared to the one computed using scalars. In this paper, we study the Hawking radiation for a spherically symmetric and time dependent black holes using the tunneling of Dirac particles, photon, and gravitino. We find that the obtained Hawking temperature is similar to the one derived in the tunneling method by using scalars. (orig.)
Higher spins tunneling from a time dependent and spherically symmetric black hole
Siahaan, Haryanto M. [Parahyangan Catholic University, Physics Department, Bandung (Indonesia)
2016-03-15
The discussions of Hawking radiation via tunneling method have been performed extensively in the case of scalar particles. Moreover, there are also several works in discussing the tunneling method for Hawking radiation by using higher spins, e.g. neutrino, photon, and gravitino, in the background of static black holes. Interestingly, it is found that the Hawking temperature for static black holes using the higher spins particles has no difference compared to the one computed using scalars. In this paper, we study the Hawking radiation for a spherically symmetric and time dependent black holes using the tunneling of Dirac particles, photon, and gravitino. We find that the obtained Hawking temperature is similar to the one derived in the tunneling method by using scalars. (orig.)
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
Starkov, Konstantin E.
2010-01-01
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a 0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a 0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
All the Four-Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory
Cvetic, M.; Youm, D.
1995-01-01
We present the explicit form for all the four-dimensional, static, spherically symmetric solutions in (4+n)-d Abelian Kaluza-Klein theory by performing a subset of SO(2,n) transformations corresponding to four SO(1,1) boosts on the Schwarzschild solution, supplemented by SO(n)/SO(n-2) transformations. The solutions are parametrized by the mass M, Taub-NUT charge a, and n electric rvec Q and n magnetic rvec P charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstroem or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while nonsupersymmetric extreme ones have a global space-time of extreme Reissner-Nordstroem black holes. copyright 1995 The American Physical Society
Finster, Felix; Smoller, Joel; Yau, Shing-Tung
We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.
Araújo, M.E. [Departamento de Física-Matemática, Instituto de Física, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, 21.945-970, Rio de Janeiro, R.J. (Brazil); Stoeger, W.R., E-mail: mearaujo@me.com, E-mail: wstoeger@as.arizona.edu [Vatican Observatory Research Group, Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721 (United States)
2011-07-01
One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions — without, for instance, assuming that the universe is almost Friedmann-Lemaître-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lemaître-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate y is null (light-like) and measured down the past light cone of the observer. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution — i.e. our procedure is not restricted to our past light cone — and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. We also compare the two approaches with regard to determining the cosmological constant Λ. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the
Spherically symmetric conformal gravity and ''gravitational bubbles''
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow, 117312 (Russian Federation)
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Santa Vélez, Camilo; Enea Romano, Antonio
2018-05-01
Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.
Spherical collapse in chameleon models
Brax, Ph.; Rosenfeld, R.; Steer, D.A.
2010-01-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity
Spherical collapse in chameleon models
Brax, Ph. [Institut de Physique Théorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France); Rosenfeld, R. [Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, 01140-070, São Paulo (Brazil); Steer, D.A., E-mail: brax@spht.saclay.cea.fr, E-mail: rosenfel@ift.unesp.br, E-mail: daniele.steer@apc.univ-paris7.fr [APC, UMR 7164, CNRS, Université Paris 7, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13 (France)
2010-08-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity.
Spherical Collapse in Chameleon Models
Brax, Ph; Steer, D A
2010-01-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse depends on the initial comoving size of the inhomogeneity.
Chen, Gui-Qiang G.; Schrecker, Matthew R. I.
2018-04-01
We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).
Herrera, L.
2018-02-01
We put forward a new definition of complexity, for static and spherically symmetric self-gravitating systems, based on a quantity, hereafter referred to as complexity factor, that appears in the orthogonal splitting of the Riemann tensor, in the context of general relativity. We start by assuming that the homogeneous (in the energy density) fluid, with isotropic pressure is endowed with minimal complexity. For this kind of fluid distribution, the value of complexity factor is zero. So, the rationale behind our proposal for the definition of complexity factor stems from the fact that it measures the departure, in the value of the active gravitational mass (Tolman mass), with respect to its value for a zero complexity system. Such departure is produced by a specific combination of energy density inhomogeneity and pressure anisotropy. Thus, zero complexity factor may also be found in self-gravitating systems with inhomogeneous energy density and anisotropic pressure, provided the effects of these two factors, on the complexity factor, cancel each other. Some exact interior solutions to the Einstein equations satisfying the zero complexity criterium are found, and prospective applications of this newly defined concept, to the study of the structure and evolution of compact objects, are discussed.
Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations
Cronstrom, C.
1987-01-01
In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory
Cyclic and heteroclinic flows near general static spherically symmetric black holes
Ahmed, Ayyesha K.; Jamil, Mubasher [National University of Sciences and Technology(NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan); Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey); Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Alberta (Canada); University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada)
2016-05-15
We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the fluid flow. We determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three-velocity vanishes and the pressure diverges on the horizon(s), resulting in a flow-out of the fluid under the effect of its own pressure. This is in favor of the earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like f(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. For de Sitter-like f(R) black holes, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value, allowing for a good estimate of the proper period of the flow. (orig.)
Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory
Moradpour, Hooman; Salako, Ines G.
2016-01-01
The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
Starkov, Konstantin E., E-mail: konst@citedi.m [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)
2010-04-05
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a<0 the location of any compact invariant set is described by some system of linear inequalities. Then we prove that in case s=1; a>0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a<0 and s=-1; a>0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
Single molecule diffusion and the solution of the spherically symmetric residence time equation.
Agmon, Noam
2011-06-16
The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society
Existence and stability of circular orbits in general static and spherically symmetric spacetimes
Jia, Junji; Liu, Jiawei; Liu, Xionghui; Mo, Zhongyou; Pang, Xiankai; Wang, Yaoguang; Yang, Nan
2018-02-01
The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that three SSS spacetimes whose metric function is not completely known will allow the existence of timelike and/or null COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.
Linearized vector radiative transfer model MCC++ for a spherical atmosphere
Postylyakov, O.V.
2004-01-01
Application of radiative transfer models has shown that optical remote sensing requires extra characteristics of radiance field in addition to the radiance intensity itself. Simulation of spectral measurements, analysis of retrieval errors and development of retrieval algorithms are in need of derivatives of radiance with respect to atmospheric constituents under investigation. The presented vector spherical radiative transfer model MCC++ was linearized, which allows the calculation of derivatives of all elements of the Stokes vector with respect to the volume absorption coefficient simultaneously with radiance calculation. The model MCC++ employs Monte Carlo algorithm for radiative transfer simulation and takes into account aerosol and molecular scattering, gas and aerosol absorption, and Lambertian surface albedo. The model treats a spherically symmetrical atmosphere. Relation of the estimated derivatives with other forms of radiance derivatives: the weighting functions used in gas retrieval and the air mass factors used in the DOAS retrieval algorithms, is obtained. Validation of the model against other radiative models is overviewed. The computing time of the intensity for the MCC++ model is about that for radiative models treating sphericity of the atmosphere approximately and is significantly shorter than that for the full spherical models used in the comparisons. The simultaneous calculation of all derivatives (i.e. with respect to absorption in all model atmosphere layers) and the intensity is only 1.2-2 times longer than the calculation of the intensity only
PT symmetric Aubry–Andre model
Yuce, C.
2014-01-01
PT symmetric Aubry–Andre model describes an array of N coupled optical waveguides with position-dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of quasi-periodicity for small number of lattice sites. We obtain the Hofstadter butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserve the total intensity. - Highlights: • We show that PT symmetric Aubry–Andre model may have real spectrum. • We show that the reality of the spectrum depends sensitively on the degree of disorder. • We obtain the Hofstadter butterfly spectrum for PT symmetric Aubry–Andre model. • We discuss that phase transition from extended to localized states exists
PT symmetric Aubry–Andre model
Yuce, C., E-mail: cyuce@anadolu.edu.tr
2014-06-13
PT symmetric Aubry–Andre model describes an array of N coupled optical waveguides with position-dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of quasi-periodicity for small number of lattice sites. We obtain the Hofstadter butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserve the total intensity. - Highlights: • We show that PT symmetric Aubry–Andre model may have real spectrum. • We show that the reality of the spectrum depends sensitively on the degree of disorder. • We obtain the Hofstadter butterfly spectrum for PT symmetric Aubry–Andre model. • We discuss that phase transition from extended to localized states exists.
Maeda, Hideki
2006-01-01
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n(≥5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M≅M 2 xK n-2 with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5 and n≥6. There are two families of solutions, which we call plus-branch and the minus-branch solutions. A plus-branch solution can be attached to the outside vacuum region which is asymptotically anti-de Sitter in spite of the absence of a cosmological constant. Bounce inevitably occurs in the plus-branch solution for n≥6, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of n=5 must be naked. On the other hand, a minus-branch solution can be attached to the outside asymptotically flat vacuum region. We show that naked singularities are massless for n≥6, while massive naked singularities are possible for n=5. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for n≥6, while it is ingoing-null for n=5. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for n≥10 and for n=9 depending on the parameters in the initial data, while a naked singularity is always formed for 5≤n≤8. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated
Modeling mantle convection in the spherical annulus
Hernlund, John W.; Tackley, Paul J.
2008-12-01
Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.
On isotropic cylindrically symmetric stellar models
Nolan, Brien C; Nolan, Louise V
2004-01-01
We attempt to match the most general cylindrically symmetric vacuum spacetime with a Robertson-Walker interior. The matching conditions show that the interior must be dust filled and that the boundary must be comoving. Further, we show that the vacuum region must be polarized. Imposing the condition that there are no trapped cylinders on an initial time slice, we can apply a result of Thorne's and show that trapped cylinders never evolve. This results in a simplified line element which we prove to be incompatible with the dust interior. This result demonstrates the impossibility of the existence of an isotropic cylindrically symmetric star (or even a star which has a cylindrically symmetric portion). We investigate the problem from a different perspective by looking at the expansion scalars of invariant null geodesic congruences and, applying to the cylindrical case, the result that the product of the signs of the expansion scalars must be continuous across the boundary. The result may also be understood in relation to recent results about the impossibility of the static axially symmetric analogue of the Einstein-Straus model
Tang, Xiaping; Churazov, Eugene
2018-04-01
We analyze the impact of thermal conduction on the appearance of a shock-heated gas shell which is produced when a spherically symmetric outburst of a supermassive black hole inflates bubbles of relativistic plasma at the center of a galaxy cluster. The presence of the hot and low-density shell can be used as an ancillary indicator for a high rate of energy release during the outburst, which is required to drive strong shocks into the gas. Here we show that conduction can effectively erase such shell, unless the diffusion of electrons is heavily suppressed. We conclude that a more robust proxy to the energy release rate is the ratio between the shock radius and bubble radius. We also revisited the issue of sound waves dissipation induced by thermal conduction in a scenario, where characteristic wavelength of the sound wave is set by the total energy of the outburst. For a fiducial short outburst model, the dissipation length does not exceed the cooling radius in a typical cluster, provided that the conduction is suppressed by a factor not larger than ˜100. For quasi-continuous energy injection neither the shock-heated shell nor the outgoing sound wave are important and the role of conduction is subdominant.
Mihalas, D.; Kunasz, P.B.; Hummer, D.G.
1976-01-01
A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles
Covariant, chirally symmetric, confining model of mesons
Gross, F.; Milana, J.
1991-01-01
We introduce a new model of mesons as quark-antiquark bound states. The model is covariant, confining, and chirally symmetric. Our equations give an analytic solution for a zero-mass pseudoscalar bound state in the case of exact chiral symmetry, and also reduce to the familiar, highly successful nonrelativistic linear potential models in the limit of heavy-quark mass and lightly bound systems. In this fashion we are constructing a unified description of all the mesons from the π through the Υ. Numerical solutions for other cases are also presented
A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes
O'Connor, Evan; Ott, Christian D
2010-01-01
We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical equations of state and neutrino leakage/heating of a failing core-collapse supernova and black hole formation in a presupernova model of a 40 M o-dot zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.
A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes
O' Connor, Evan; Ott, Christian D, E-mail: evanoc@tapir.caltech.ed, E-mail: cott@tapir.caltech.ed [TAPIR, Mail Code 350-17, California Institute of Technology, Pasadena, CA 91125 (United States)
2010-06-07
We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical equations of state and neutrino leakage/heating of a failing core-collapse supernova and black hole formation in a presupernova model of a 40 M{sub o-dot} zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.
Sphericity in the interacting boson model
Ogata, H.
1977-01-01
The interacting boson model (IBM) of Arima and Iachello is examined. The transition between the rotational and vibrational modes of even-even nuclei is presented as a function of a sphericity parameter, which is determined primarily from yrast band spectra. The backbending feature is reasonably reproduced. (author)
Alexandre, Jean; Pasipoularides, Pavlos
2011-01-01
In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton's Law in the IR limit λ→1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. D 83, 084030 (2011).][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys. 12 (2010) 007.], and we assume, as in [A. M. da Silva, Classical Quantum Gravity 28, 055011 (2011).], that λ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ→1, unless λ does not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby-Thompson approach [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).] in which A is assumed as a part of the space-time metric in the IR.
Spherical Cancer Models in Tumor Biology
Louis-Bastien Weiswald
2015-01-01
Full Text Available Three-dimensional (3D in vitro models have been used in cancer research as an intermediate model between in vitro cancer cell line cultures and in vivo tumor. Spherical cancer models represent major 3D in vitro models that have been described over the past 4 decades. These models have gained popularity in cancer stem cell research using tumorospheres. Thus, it is crucial to define and clarify the different spherical cancer models thus far described. Here, we focus on in vitro multicellular spheres used in cancer research. All these spherelike structures are characterized by their well-rounded shape, the presence of cancer cells, and their capacity to be maintained as free-floating cultures. We propose a rational classification of the four most commonly used spherical cancer models in cancer research based on culture methods for obtaining them and on subsequent differences in sphere biology: the multicellular tumor spheroid model, first described in the early 70s and obtained by culture of cancer cell lines under nonadherent conditions; tumorospheres, a model of cancer stem cell expansion established in a serum-free medium supplemented with growth factors; tissue-derived tumor spheres and organotypic multicellular spheroids, obtained by tumor tissue mechanical dissociation and cutting. In addition, we describe their applications to and interest in cancer research; in particular, we describe their contribution to chemoresistance, radioresistance, tumorigenicity, and invasion and migration studies. Although these models share a common 3D conformation, each displays its own intrinsic properties. Therefore, the most relevant spherical cancer model must be carefully selected, as a function of the study aim and cancer type.
Spherical conformal models for compact stars
Takisa, P.M.; Maharaj, S.D.; Manjonjo, A.M.; Moopanar, S. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2017-10-15
We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints. (orig.)
The generalized spherical model of ferromagnetic films
Costache, G.
1977-12-01
The D→ infinity of the D-vectorial model of a ferromagnetic film with free surfaces is exactly solved. The mathematical mechanism responsible for the onset of a phase transition in the system is a generalized sticking phenomenon. It is shown that the temperature at which the sticking appears, the transition temperature of the model is monotonously increasing with increasing the number of layers of the film, contrary to what happens in the spherical model with overall constraint. Certain correlation inequalities of Griffiths type are shown to hold. (author)
Haisch, B. M.
1976-01-01
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
Hosokawa, Takashi; Omukai, Kazuyuki
2009-01-01
The final mass of a newborn star is set at the epoch when the mass accretion onto the star is terminated. We study the evolution of accreting protostars and the limits of accretion in low-metallicity environments under spherical symmetry. Accretion rates onto protostars are estimated via the temperature evolution of prestellar cores with different metallicities. The derived rates increase with decreasing metallicity, from M-dot≅10 -6 M odot yr -1 at Z = Z sun to 10 -3 M sun yr -1 at Z = 0. With the derived accretion rates, the protostellar evolution is numerically calculated. We find that, at lower metallicity, the protostar has a larger radius and reaches the zero-age main sequence (ZAMS) at higher stellar mass. Using this protostellar evolution, we evaluate the upper stellar mass limit where the mass accretion is hindered by radiative feedback. We consider the effects of radiation pressure exerted on the accreting envelope, and expansion of an H II region. The mass accretion is finally terminated by radiation pressure on dust grains in the envelope for Z ∼> 10 -3 Z sun and by the expanding H II region for lower metallicity. The mass limit from these effects increases with decreasing metallicity from M * ≅ 10 M sun at Z = Z sun to ≅300 M sun at Z = 10 -6 Z sun . The termination of accretion occurs after the central star arrives at the ZAMS at all metallicities, which allows us to neglect protostellar evolution effects in discussing the upper mass limit by stellar feedback. The fragmentation induced by line cooling in low-metallicity clouds yields prestellar cores with masses large enough that the final stellar mass is set by the feedback effects. Although relaxing the assumption of spherical symmetry will alter feedback effects, our results will be a benchmark for more realistic evolution to be explored in future studies.
Simple spherical ablative-implosion model
Mayer, F.J.; Steele, J.T.; Larsen, J.T.
1980-01-01
A simple model of the ablative implosion of a high-aspect-ratio (shell radius to shell thickness ratio) spherical shell is described. The model is similar in spirit to Rosenbluth's snowplow model. The scaling of the implosion time was determined in terms of the ablation pressure and the shell parameters such as diameter, wall thickness, and shell density, and compared these to complete hydrodynamic code calculations. The energy transfer efficiency from ablation pressure to shell implosion kinetic energy was examined and found to be very efficient. It may be possible to attach a simple heat-transport calculation to our implosion model to describe the laser-driven ablation-implosion process. The model may be useful for determining other energy driven (e.g., ion beam) implosion scaling
Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters
Tang, Xiaping; Churazov, Eugene
2017-07-01
We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind active galactic nucleus feedback in the intracluster medium. For a given density and pressure of the medium, the spatial structure and energy partition at a given time tage (since the onset of the outburst) are fully determined by the total injected energy Einj and the duration tb of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of Einj and tb. For an instantaneous outburst with tb → 0, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is ≲12 per cent of Einj. As tb increases, the solution approaches the 'slow piston' limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst (Einj, tb and tage) to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated (Einj, tb and tage) agree with numerical simulations tailored for these objects with 20-30 per cent accuracy.
Spherical collapse and cluster counts in modified gravity models
Martino, Matthew C.; Stabenau, Hans F.; Sheth, Ravi K.
2009-01-01
Modifications to the gravitational potential affect the nonlinear gravitational evolution of large scale structures in the Universe. To illustrate some generic features of such changes, we study the evolution of spherically symmetric perturbations when the modification is of Yukawa type; this is nontrivial, because we should not and do not assume that Birkhoff's theorem applies. We then show how to estimate the abundance of virialized objects in such models. Comparison with numerical simulations shows reasonable agreement: When normalized to have the same fluctuations at early times, weaker large scale gravity produces fewer massive halos. However, the opposite can be true for models that are normalized to have the same linear theory power spectrum today, so the abundance of rich clusters potentially places interesting constraints on such models. Our analysis also indicates that the formation histories and abundances of sufficiently low mass objects are unchanged from standard gravity. This explains why simulations have found that the nonlinear power spectrum at large k is unaffected by such modifications to the gravitational potential. In addition, the most massive objects in models with normalized cosmic microwave background and weaker gravity are expected to be similar to the high-redshift progenitors of the most massive objects in models with stronger gravity. Thus, the difference between the cluster and field galaxy populations is expected to be larger in models with stronger large scale gravity.
Symmetrization of mathematical model of charge transport in semiconductors
Alexander M. Blokhin
2002-11-01
Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.
On the Stability of Spherically Symmetric Self-Gravitating Classical and Quantum Systems
Makedonski, Mathias
on to the description of the corresponding systems in the setting of general relativity, it is shown, that the Tolman-Oppenheimer-Volko equation can be obtained from a suitable variation of the total energy. We prove a previously unnoticed energetic instability of the model. Staying in the general relativistic setting....... As for the perfect fluid, we prove energetic instability and conclude our investigations by constructing a naive quantum version of the free massive scalar eld, that also suers energetic instability. ´...
Sergio C. Ulhoa
2017-01-01
Full Text Available In this paper we investigate scalar perturbations of black holes embedded in a five-dimensional bulk space. The quasinormal frequencies of such black holes are calculated using the third order of Wentzel, Kramers, and Brillouin (WKB approximation for scalar perturbations. The high overtones of quasinormal modes indicate a resonant-like set of black holes suggesting a serious constraint of embedding models in five dimensions.
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong
2017-11-28
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.
Propagation of a shock wave in a radiating spherically symmetric distribution of matter
Herrera, L.; Nunez, L.; Universidad de Los Andes, Merida, Venezuela)
1987-01-01
A method used to study the evolution of radiating spheres reported by Herrera et al. (1980) is extended to the case in which the sphere is divided in two regions by a shock wave front. The equations of state at both sides of the shock are different, and the solutions are matched on it via the Rankine-Hugoniot conditions. The outer-region metric is matched with a Vaidya solution on the boundary surface of the sphere. As an example of the procedure, two known solutions for radiating systems are considered. The matter distribution is free of singularities everywhere within the sphere and a Gaussian-like pulse is assumed to carry out a fraction of the total mass. Exploding models are then obtained. Finally, the results are discussed in the light of recent work on gravitational collapse and supernovae. 29 references
Cosmological observables in the quasi-spherical Szekeres model
Buckley, Robert G.
2014-10-01
The standard model of cosmology presents a homogeneous universe, and we interpret cosmological data through this framework. However, structure growth creates nonlinear inhomogeneities that may affect observations, and even larger structures may be hidden by our limited vantage point and small number of independent observations. As we determine the universe's parameters with increasing precision, the accuracy is contingent on our understanding of the effects of such structures. For instance, giant void models can explain some observations without dark energy. Because perturbation theory cannot adequately describe nonlinear inhomogeneities, exact solutions to the equations of general relativity are important for these questions. The most general known solution capable of describing inhomogeneous matter distributions is the Szekeres class of models. In this work, we study the quasi-spherical subclass of these models, using numerical simulations to calculate the inhomogeneities' effects on observations. We calculate the large-angle CMB in giant void models and compare with simpler, symmetric void models that have previously been found inadequate to matchobservations. We extend this by considering models with early-time inhomogeneities as well. Then, we study distance observations, including selection effects, in models which are homogeneous on scales around 100 Mpc---consistent with standard cosmology---but inhomogeneous on smaller scales. Finally, we consider photon polarizations, and show that they are not directly affected by inhomogeneities. Overall, we find that while Szekeres models have some advantages over simpler models, they are still seriously limited in their ability to alter our parameter estimation while remaining within the bounds of current observations.
Color symmetrical superconductivity in a schematic nuclear quark model
Bohr, Henrik; Providencia, C.; da Providencia, J.
2010-01-01
In this letter, a novel BCS-type formalism is constructed in the framework of a schematic QCD inspired quark model, having in mind the description of color symmetrical superconducting states. In the usual approach to color superconductivity, the pairing correlations affect only the quasi-particle...... states of two colors, the single-particle states of the third color remaining unaffected by the pairing correlations. In the theory of color symmetrical superconductivity here proposed, the pairing correlations affect symmetrically the quasi-particle states of the three colors and vanishing net color...
Nonlinear spherical perturbations in quintessence models of dark energy
Pratap Rajvanshi, Manvendra; Bagla, J. S.
2018-06-01
Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from ‑1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.
Burikham, Piyabut; Cheamsawat, Krai; Harko, Tiberiu; Lake, Matthew J.
2016-01-01
We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a D-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total energy, including the gravitational component, and the stability of objects with minimum mass/radius ratio is also investigated. The minimum energy condition leads to a representation of the mass and radius of the charged objects with minimum mass/radius ratio in terms of the charge and vacuum energy only. As applied to the electron in the four-dimensional case, this procedure allows one to re-obtain the classical electron radius from purely general relativistic considerations. By combining the lower mass bound, in four space-time dimensions, with minimum length uncertainty relations (MLUR) motivated by quantum gravity, we obtain an alternative bound for the maximum charge/mass ratio of a stable, gravitating, charged quantum mechanical object, expressed in terms of fundamental constants. Evaluating this limit numerically, we obtain again the correct order of magnitude value for the charge/mass ratio of the electron, as required by the stability conditions. This suggests that, if the electron were either less massive (with the same charge) or if its charge were any higher (for fixed mass), a combination of electrostatic and dark energy repulsion would destabilize the Compton radius. In other words, the electron would blow itself apart. Our results suggest the existence of a deep connection between gravity, the presence of the cosmological constant, and the stability of fundamental particles. (orig.)
Zielinska, M.; Zawislawski, Z.; Strugalska-Gola, E.; Strugalski, Z.
1991-01-01
It is shown how it is possible to transform known data on radial distribution of the matter layer thickness to unknown radial distribution of the matter density inside spherically symmetric objects. Appropriate formulas and testing of them are presented. An application of the method for the radial distribution of the matter density inside a target nucleus is discussed as an example. 2 refs.; 2 figs
Schneider, M; Hirleman, E D
1994-04-20
A model based on geometric optics for predicting the response of interferometric (phase Doppler) instruments for size measurements of particles with radially symmetric but inhomogeneous internal refractive index profiles is developed. The model and results are important for applications in which heat or mass transfer from the particles or droplets is significant, for example, in liquid-fuel combustion. To quantify the magnitude of potential bias errors introduced by the classical assumption of uniform internal properties on phase Doppler measurements, we compute calibration curves for a sequence of times during the evaporation of a decane droplet immersed in an environment of T = 2000 K and p = 10 bars. The results reveal considerable effects on the relation between phase difference and droplet diameter caused by the refractive index gradients present. The model provides an important tool to assess sizing uncertainties that can be expected when applying conventional (based on uniform properties) phase Doppler calibration curves in spray combustion and similar processes.
A summary view of the symmetric cosmological model
Aldrovandi, R.
1975-01-01
A brief analysis of cosmological models is done, beginning with the standard model and following with the symmetric model of Omnes. Some attempts have been made for the phase transition in thermal radiation at high temperatures, to the annihilation period and to coalescence. One model with equal amounts of matter and antimatter seems to be reasonable [pt
Standing and travelling waves in a spherical brain model: The Nunez model revisited
Visser, S.; Nicks, R.; Faugeras, O.; Coombes, S.
2017-06-01
The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, centre manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions.
Spherical collapse in quintessence models with zero speed of sound
Creminelli, Paolo; D'Amico, Guido; Noreña, Jorge; Senatore, Leonardo; Vernizzi, Filippo
2010-01-01
We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w Q /Ω m . This gives a distinctive modification of the total mass function at low redshift
Higuchi, A.
1987-01-01
The symmetric tensor spherical harmonics (STSH's) on the N-sphere (S/sup N/), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace--Beltrami (LB) operator on S/sup N/, are studied. Specifically, their construction is shown recursively starting from the lower-dimensional ones. The symmetric traceless tensors induced by STSH's are introduced. These play a crucial role in the recursive construction of STSH's. The normalization factors for STSH's are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence-free tensor eigenfunctions of the LB operator in the N-dimensional de Sitter space-time which are obtained by the analytic continuation of the STSH's on S/sup N/ are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group-theoretical explanation of the forbidden mass range observed earlier for the spin-2 field theory in de Sitter space-time
Spherical convolutions and their application in molecular modelling
Boomsma, Wouter; Frellsen, Jes
2017-01-01
Convolutional neural networks are increasingly used outside the domain of image analysis, in particular in various areas of the natural sciences concerned with spatial data. Such networks often work out-of-the box, and in some cases entire model architectures from image analysis can be carried over...... to other problem domains almost unaltered. Unfortunately, this convenience does not trivially extend to data in non-euclidean spaces, such as spherical data. In this paper, we introduce two strategies for conducting convolutions on the sphere, using either a spherical-polar grid or a grid based...... of spherical convolutions in the context of molecular modelling, by considering structural environments within proteins. We show that the models are capable of learning non-trivial functions in these molecular environments, and that our spherical convolutions generally outperform standard 3D convolutions...
Ghosh, Shubhrangshu; Banik, Prabir
2015-07-01
In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central
Effect of Rolling Resistance in Dem Models With Spherical Bodies
Dubina Radek
2016-12-01
Full Text Available The rolling resistance is an artificial moment arising on the contact of two discrete elements which mimics resistance of two grains of complex shape in contact rolling relatively to each other. The paper investigates the influence of rolling resistance on behaviour of an assembly of spherical discrete elements. Besides the resistance to rolling, the contacts between spherical particles obey the Hertzian law in normal straining and Coulomb model of friction in shear.
Models for randomly distributed nanoscopic domains on spherical vesicles
Anghel, Vinicius N. P.; Bolmatov, Dima; Katsaras, John
2018-06-01
The existence of lipid domains in the plasma membrane of biological systems has proven controversial, primarily due to their nanoscopic size—a length scale difficult to interrogate with most commonly used experimental techniques. Scattering techniques have recently proven capable of studying nanoscopic lipid domains populating spherical vesicles. However, the development of analytical methods able of predicting and analyzing domain pair correlations from such experiments has not kept pace. Here, we developed models for the random distribution of monodisperse, circular nanoscopic domains averaged on the surface of a spherical vesicle. Specifically, the models take into account (i) intradomain correlations corresponding to form factors and interdomain correlations corresponding to pair distribution functions, and (ii) the analytical computation of interdomain correlations for cases of two and three domains on a spherical vesicle. In the case of more than three domains, these correlations are treated either by Monte Carlo simulations or by spherical analogs of the Ornstein-Zernike and Percus-Yevick (PY) equations. Importantly, the spherical analog of the PY equation works best in the case of nanoscopic size domains, a length scale that is mostly inaccessible by experimental approaches such as, for example, fluorescent techniques and optical microscopies. The analytical form factors and structure factors of nanoscopic domains populating a spherical vesicle provide a new and important framework for the quantitative analysis of experimental data from commonly studied phase-separated vesicles used in a wide range of biophysical studies.
Multivariate Non-Symmetric Stochastic Models for Spatial Dependence Models
Haslauer, C. P.; Bárdossy, A.
2017-12-01
A copula based multivariate framework allows more flexibility to describe different kind of dependences than what is possible using models relying on the confining assumption of symmetric Gaussian models: different quantiles can be modelled with a different degree of dependence; it will be demonstrated how this can be expected given process understanding. maximum likelihood based multivariate quantitative parameter estimation yields stable and reliable results; not only improved results in cross-validation based measures of uncertainty are obtained but also a more realistic spatial structure of uncertainty compared to second order models of dependence; as much information as is available is included in the parameter estimation: incorporation of censored measurements (e.g., below detection limit, or ones that are above the sensitive range of the measurement device) yield to more realistic spatial models; the proportion of true zeros can be jointly estimated with and distinguished from censored measurements which allow estimates about the age of a contaminant in the system; secondary information (categorical and on the rational scale) has been used to improve the estimation of the primary variable; These copula based multivariate statistical techniques are demonstrated based on hydraulic conductivity observations at the Borden (Canada) site, the MADE site (USA), and a large regional groundwater quality data-set in south-west Germany. Fields of spatially distributed K were simulated with identical marginal simulation, identical second order spatial moments, yet substantially differing solute transport characteristics when numerical tracer tests were performed. A statistical methodology is shown that allows the delineation of a boundary layer separating homogenous parts of a spatial data-set. The effects of this boundary layer (macro structure) and the spatial dependence of K (micro structure) on solute transport behaviour is shown.
Exotic fermions in the left-right symmetric model
Choi, J.; Volkas, R.R.
1992-01-01
A systematic study is made of non-standard fermion multiplets in left-right symmetric models with gauge group SU(3) x SU(2) L x SU(2) R x U(1) BL . Constraints from gauge anomaly cancellation and invariance of Yukawa coupling terms are used to define interesting classes of exotic fermions. The standard quark lepton spectrum of left-right symmetric models was identified as the simplest member of an infinite class. Phenomenological implications of the next simplest member of this class are then studied. Classes of exotic fermions which may couple to the standard fermions through doublet Higgs bosons were also considered, then shown that some of these exotics may be used to induce a generalised universal see-saw mechanism. 12 refs., 1 tab
Superfield Lax formalism of supersymmetric sigma model on symmetric spaces
Saleem, U.; Hassan, M.
2006-01-01
We present a superfield Lax formalism of the superspace sigma model based on the target space G/H and show that a one-parameter family of flat superfield connections exists if the target space G/H is a symmetric space. The formalism has been related to the existence of an infinite family of local and non-local superfield conserved quantities. A few examples have been given to illustrate the results. (orig.)
A time-symmetric Universe model and its observational implication
Futamase, T.; Matsuda, T.
1987-01-01
A time-symmetric closed-universe model is discussed in terms of the radiation arrow of time. The time symmetry requires the occurrence of advanced waves in the recontracting phase of the Universe. The observational consequences of such advanced waves are considered, and it is shown that a test observer in the expanding phase can observe a time-reversed image of a source of radiation in the future recontracting phase
Time-symmetric universe model and its observational implication
Futamase, T.; Matsuda, T.
1987-08-01
A time-symmetric closed-universe model is discussed in terms of the radiation arrow of time. The time symmetry requires the occurrence of advanced waves in the recontracting phase of the Universe. We consider the observational consequences of such advanced waves, and it is shown that a test observer in the expanding phase can observe a time-reversed image of a source of radiation in the future recontracting phase.
Hoshyaripour, A.; Vogel, B.; Vogel, H.
2017-12-01
Mineral dust, emitted from arid and semi-arid regions, is the most dominant atmospheric aerosol by mass. Beside detrimental effect on air quality, airborne dust also influences the atmospheric radiation by absorbing and scattering solar and terrestrial radiation. As a result, while the long-term radiative impacts of dust are important for climate, the short-term effects are significant for the photovoltaic energy production. Therefore, it is a vital requirement to accurately forecast the effects of dust on energy budget of the atmosphere and surface. To this end, a major issue is the fact that dust particles are non-spherical. Thus, the optical properties of such particles cannot be calculated precisely using the conventional methods like Mie theory that are often used in climate and numerical weather forecast models. In this study, T-Matrix method is employed, which is able to treat the non-sphericity of particles. Dust particles are assumed to be prolate spheroids with aspect ratio of 1.5 distributed in three lognormal modes. The wavelength-dependent refractive indices of dust are used in T-Matrix algorithm to calculate the extinction coefficient, single scattering albedo, asymmetry parameter and backscattering ratio at different wavelengths. These parameters are then implemented in ICON-ART model (ICOsahedral Nonhydrostatic model with Aerosols and Reactive Trace gases) to conduct a global simulation with 80 km horizontal resolution and 90 vertical levels. April 2014 is selected as the simulation period during which North African dust plumes reached central Europe and Germany. Results show that treatment of non-sphericity reduces the dust AOD in the range of 10 to 30%/. The impacts on diffuse and direct radiation at global, regional and local scales show strong dependency on the size distribution of the airborne dust. The implications for modeling and remote sensing the dust impacts on solar energy are also discussed.
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G.
2017-01-01
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture
Redshift structure of the big bang in inhomogeneous cosmological models. I. Spherical dust solutions
Hellaby, C.; Lake, K.
1984-01-01
The redshift from the big bang in the standard model is always infinite, but in inhomogeneous cosmological models infinite blueshifts are also possible. To avoid such divergent energy fluxes, we require that all realistic cosmological models must not display infinite blueshifts. We apply this requirement to the Tolman model (spherically symmetric dust), using the geometrical optics approximation, and assuming that the geodesic tangent vectors may be expanded in power series. We conclude that the bang time must be simultaneous. The stronger requirement, that only infinite redshifts from the big bang may occur, does not lead to a stronger condition on the metric. Further consequences of simultaneity are that no decaying mode fluctuations are possible, and that the only acceptable model which is homogeneous at late times is the Robertson-Walker model
Redshift structure of the big bang in inhomogeneous cosmological models. I. Spherical dust solutions
Hellaby, C.; Lake, K.
1984-07-01
The redshift from the big bang in the standard model is always infinite, but in inhomogeneous cosmological models infinite blueshifts are also possible. To avoid such divergent energy fluxes, we require that all realistic cosmological models must not display infinite blueshifts. We apply this requirement to the Tolman model (spherically symmetric dust), using the geometrical optics approximation, and assuming that the geodesic tangent vectors may be expanded in power series. We conclude that the bang time must be simultaneous. The stronger requirement, that only infinite redshifts from the big bang may occur, does not lead to a stronger condition on the metric. Further consequences of simultaneity are that no decaying mode fluctuations are possible, and that the only acceptable model which is homogeneous at late times is the Robertson-Walker model.
Classically integrable boundary conditions for symmetric-space sigma models
MacKay, N.J.; Young, C.A.S.
2004-01-01
We investigate boundary conditions for the non-linear sigma model on the compact symmetric space G/H. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions which correspond to involutions which commute with the involution defining H. Applied to SO(3)/SO(2), the non-linear sigma model on S 2 , these yield the great circles as boundary submanifolds. Applied to GxG/G, they reproduce known results for the principal chiral model
Matrix model calculations beyond the spherical limit
Ambjoern, J.; Chekhov, L.; Kristjansen, C.F.; Makeenko, Yu.
1993-01-01
We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prove that the hermitian and the complex matrix model are equivalent in the double scaling limit and that in this limit they are both equivalent to the Kontsevich model. We discuss how our results away from the double scaling limit are related to the structure of moduli space. (orig.)
El Ghazi, Haddou, E-mail: hadghazi@gmail.com [LPS, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco); Special Mathematics, CPGE, 267 Quartier complémentaire Ennahda 1, Rabat (Morocco); Jorio, Anouar [LPS, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco)
2014-01-01
Within the framework of effective-mass approximation and finite parabolic potential barrier, single particle and ground-state interband recombination energies in Core|well|shell based on GaN|(In,Ga)N|GaN spherical QDQW are investigated as a function of the inner and the outer radii. The temperature dependency of effective-mass, band-gap energy and potential barrier is taken into account. Particle eigenvalue and band-gap energy competing effects are speculated to explain our numerical results which show that the interband recombination energy increases when the temperature increases. The results we obtained are in quite good agreement with the findings.
El Ghazi, Haddou; Jorio, Anouar
2014-01-01
Within the framework of effective-mass approximation and finite parabolic potential barrier, single particle and ground-state interband recombination energies in Core|well|shell based on GaN|(In,Ga)N|GaN spherical QDQW are investigated as a function of the inner and the outer radii. The temperature dependency of effective-mass, band-gap energy and potential barrier is taken into account. Particle eigenvalue and band-gap energy competing effects are speculated to explain our numerical results which show that the interband recombination energy increases when the temperature increases. The results we obtained are in quite good agreement with the findings
Spherical Model Integrating Academic Competence with Social Adjustment and Psychopathology.
Schaefer, Earl S.; And Others
This study replicates and elaborates a three-dimensional, spherical model that integrates research findings concerning social and emotional behavior, psychopathology, and academic competence. Kindergarten teachers completed an extensive set of rating scales on 100 children, including the Classroom Behavior Inventory and the Child Adaptive Behavior…
Vibrational collective model for spheric even-even nuclei
Cruz, M.T.F. da.
1985-01-01
A review is made on the evidences of collective motions in spherical even-even nuclei. The several multipole transitions occuring in such a nuclei are discussed. Some hypothesis which are necessary in order to build-up the model are presented. (L.C.) [pt
Spherical model for superfluidity in a restricted geometry
Fishman, S.; Ziman, T.A.L.
1982-01-01
The spherical model is solved on a hypercubic lattice in d dimensions, each bond of which is decorated with l spins. The thermodynamic functions and the helicity modulus, analogous to a superfluid density, are calculated. We find that at least two spherical fields are required for the model to exhibit low-temperature properties that can approximate reasonably those of O(n) models. The heuristic prediction that the critical temperature behaves as T/sub c/(l)approx.(l+1) -1 is checked for the model and found to hold quite accurately even for small l(> or approx. =2). The helicity modulus and magnetization of the two-constraint spherical model are found to scale approximately with the critical temperature, but the relation between them is more complex than in the undecorated model. This relation is used to check heuristic arguments concerning the helicity modulus at low temperatures. We comment on the relevance to physical systems, in particular, the problem of boson condensation in a restricted geometry
Mixed dark matter in left-right symmetric models
Berlin, Asher [Department of Physics, University of Chicago,Chicago, Illinois 60637 (United States); Fox, Patrick J. [Theoretical Physics Department, Fermilab,Batavia, Illinois 60510 (United States); Hooper, Dan [Center for Particle Astrophysics, Fermi National Accelerator Laboratory,Batavia, Illinois 60510 (United States); Department of Astronomy and Astrophysics, University of Chicago,Chicago, Illinois 60637 (United States); Mohlabeng, Gopolang [Center for Particle Astrophysics, Fermi National Accelerator Laboratory,Batavia, Illinois 60510 (United States); Department of Physics and Astronomy, University of Kansas,Lawrence, Kansas 66045 (United States)
2016-06-08
Motivated by the recently reported diboson and dijet excesses in Run 1 data at ATLAS and CMS, we explore models of mixed dark matter in left-right symmetric theories. In this study, we calculate the relic abundance and the elastic scattering cross section with nuclei for a number of dark matter candidates that appear within the fermionic multiplets of left-right symmetric models. In contrast to the case of pure multiplets, WIMP-nucleon scattering proceeds at tree-level, and hence the projected reach of future direct detection experiments such as LUX-ZEPLIN and XENON1T will cover large regions of parameter space for TeV-scale thermal dark matter. Decays of the heavy charged W{sup ′} boson to particles in the dark sector can potentially shift the right-handed gauge coupling to larger values when fixed to the rate of the Run 1 excesses, moving towards the theoretically attractive scenario, g{sub R}=g{sub L}. This region of parameter space may be probed by future collider searches for new Higgs bosons or electroweak fermions.
Heterotic free fermionic and symmetric toroidal orbifold models
Athanasopoulos, P.; Faraggi, A.E. [Department of Mathematical Sciences, University of Liverpool,Liverpool L69 7ZL (United Kingdom); Nibbelink, S. Groot [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München,80333 München (Germany); Mehta, V.M. [Institute for Theoretical Physics, University of Heidelberg,69120 Heidelberg (Germany)
2016-04-07
Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for ℤ{sub 2}×ℤ{sub 2} orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: we give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all ℤ{sub 2}×ℤ{sub 2} orbifold geometries in six dimensions.
Spherical collapse model in time varying vacuum cosmologies
Basilakos, Spyros; Plionis, Manolis; Sola, Joan
2010-01-01
We investigate the virialization of cosmic structures in the framework of flat Friedmann-Lemaitre-Robertson-Walker cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, 'turn around', and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, Λ=Λ(H). A particularly well-motivated model of this type is the so-called quantum field vacuum, in which Λ(H) is a quadratic function, Λ(H)=n 0 +n 2 H 2 , with n 0 ≠0. This model was previously studied by our team using the latest high quality cosmological data to constrain its free parameters, as well as the predicted cluster formation rate. It turns out that the corresponding Hubble expansion history resembles that of the traditional ΛCDM cosmology. We use this Λ(t)CDM framework to illustrate the fact that the properties of the spherical collapse model (virial density, collapse factor, etc.) depend on the choice of the considered vacuum energy (homogeneous or clustered). In particular, if the distribution of the vacuum energy is clustered, then, under specific conditions, we can produce more concentrated structures with respect to the homogeneous vacuum energy case.
Mihalas, D.; Kunasz, P.B.; Hummer, D.G.
1976-01-01
We investigate the importance of the advection and aberration terms, which are of order V/c, in the comoving-frame transfer equation in spherical geometry. Characteristic trajectories are found which reduce the spatial derivatives to a perfect differential, and a generalization of the numerical procedure developed in the earlier papers of this series that permits the integration of the transfer equation on these characteristics is presented. For cases in which V/cvery-much-less-than1, a perturbation solution is developed which reduces the problem to that solved in the first paper in this series. For velocities of the form V (r) approx.r/subn/(n=0,1,2), it is shown that the magnitude of the effects arising from the advection and aberration terms is about 5V/c relative to the solution with these terms omitted. In stellar winds V/capproximately-less-than0.01; hence we conclude that aberration and advection terms may safely be ignored, and that consideration of the Doppler-shift term alone is adequate in the computation of spectra from such expanding atmospheres
Triplet leptogenesis in left–right symmetric seesaw models
Hällgren, Tomas; Konstandin, Thomas; Ohlsson, Tommy
2008-01-01
We discuss scalar triplet leptogenesis in a specific left–right symmetric seesaw model. We show that the Majorana phases that are present in the model can be effectively used to saturate the existing upper limit on the CP-asymmetry of the triplets. We solve the relevant Boltzmann equations and analyze the viability of triplet leptogenesis. It is known for this kind of scenario that the efficiency of leptogenesis is maximal if there exists a hierarchy between the branching ratios of the triplet decays into leptons and Higgs particles. We show that triplet leptogenesis typically favors branching ratios with not too strong hierarchies, since maximal efficiency can only be obtained at the expense of suppressed CP-asymmetries
Surface multifragmentation investigated with a finite temperature spherical TDHF model
Ngo, H.; Ighezou, F.Z.; Paula, L. De
1992-01-01
A model for multifragmentation caused by heavy ion collision is developed. The initial state is a hot and compressed spherical nucleus in thermal equilibrium. The dynamical evolution of this nucleus is studied. The nuclear density of the system is calculated with mean field approximation. It is shown that, in some cases, the surface of the nucleus breaks up before its volume. (K.A.) 8 refs.; 1 fig
Exact EGB models for spherical static perfect fluids
Hansraj, Sudan; Chilambwe, Brian; Maharaj, Sunil D. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Private Bag 54001, Durban (South Africa)
2015-06-15
We obtain a new exact solution to the field equations for a 5-dimensional spherically symmetric static distribution in the Einstein-Gauss-Bonnet modified theory of gravity. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissibility. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound-speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss-Bonnet and the Einstein case reveal that the pressure is unaffected, while the energy density increases under the influence of the Gauss-Bonnet term. (orig.)
Olson, D. W.; Silk, J.
1979-01-01
This paper studies the density profile that forms around a spherically symmetric bound central core immersed in a homogeneous-background k = 0 or k = -1 Friedmann-Robertson-Walker cosmological model, with zero pressure. Although the density profile in the linearized regime is almost arbitrary, in the nonlinear regime certain universal features of the density profile are obtained that are independent of the details of the initial conditions. The formation of 'halos' ('holes') with densities greater than (less than) the average cosmological density is discussed. It is shown that in most regions 'halos' form, and universal values are obtained for the slope of the ln (density)-ln (radius) profile in those 'halos' at late times, independently of the shape of the initial density profile. Restrictions are derived on where it is possible for 'holes' to exist at late times and on how such 'holes' must have evolved.
Kenkmann, Thomas; Hergarten, Stefan; Kuhn, Thomas; Wilk, Jakob
2016-08-01
Several models of shatter cone formation require a heterogeneity at the cone apex of high impedance mismatch to the surrounding bulk rock. This heterogeneity is the source of spherically expanding waves that interact with the planar shock front or the following release wave. While these models are capable of explaining the overall conical shape of shatter cones, they are not capable of explaining the subcone structure and the diverging and branching striations that characterize the surface of shatter cones and lead to the so-called horse-tailing effect. Here, we use the hierarchical arrangement of subcone ridges of shatter cone surfaces as key for understanding their formation. Tracing a single subcone ridge from its apex downward reveals that each ridge branches after some distance into two symmetrically equivalent subcone ridges. This pattern is repeated to form new branches. We propose that subcone ridges represent convex-curved fracture surfaces and their intersection corresponds to the bifurcation axis. The characteristic diverging striations are interpreted as the intersection lineations delimiting each subcone. Multiple symmetric crack branching is the result of rapid fracture propagation that may approach the Raleigh wave speed. We present a phenomenological model that fully constructs the shatter cone geometry to any order. The overall cone geometry including apex angle of the enveloping cone and the degree of concavity (horse-tailing) is largely governed by the convexity of the subcone ridges. Straight cones of various apical angles, constant slope, and constant bifurcation angles form if the subcone convexity is low (30°). Increasing subcone convexity leads to a stronger horse-tailing effect and the bifurcation angles increase with increasing distance from the enveloping cone apex. The model predicts possible triples of enveloping cone angle, bifurcation angle, and subcone angle. Measurements of these quantities on four shatter cones from different
Two updating methods for dissipative models with non symmetric matrices
Billet, L.; Moine, P.; Aubry, D.
1997-01-01
In this paper the feasibility of the extension of two updating methods to rotating machinery models is considered, the particularity of rotating machinery models is to use non-symmetric stiffness and damping matrices. It is shown that the two methods described here, the inverse Eigen-sensitivity method and the error in constitutive relation method can be adapted to such models given some modification.As far as inverse sensitivity method is concerned, an error function based on the difference between right hand calculated and measured Eigen mode shapes and calculated and measured Eigen values is used. Concerning the error in constitutive relation method, the equation which defines the error has to be modified due to the non definite positiveness of the stiffness matrix. The advantage of this modification is that, in some cases, it is possible to focus the updating process on some specific model parameters. Both methods were validated on a simple test model consisting in a two-bearing and disc rotor system. (author)
Perfect fluid models in noncomoving observational spherical coordinates
Ishak, Mustapha
2004-01-01
We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a noncomoving frame of reference. In this frame, we find that the velocity field has shear, acceleration, and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a noncomoving frame. We use the dust models in a noncomoving frame to outline a fitting procedure
Linet, Bernard; Teyssandier, Pierre
2013-01-01
A new iterative method for calculating the travel time of a photon as a function of the spatial positions of the emitter and the receiver in the field of a static, spherically symmetric body is presented. The components of the metric are assumed to be expressible in power series in m/r, with m being half the Schwarzschild radius of the central body and r a radial coordinate. The procedure exclusively works for a light ray which may be described as a perturbation in powers of G of a Minkowskian null geodesic, with G being the Newtonian gravitational constant. It is shown that the expansion of the travel time of a photon along such a ray only involves elementary integrals whatever the order of approximation. An expansion of the impact parameter in power series of G is also obtained. The method is applied to explicitly calculate the perturbation expansions of the light travel time and the impact parameter up to the third order. The full expression yielding the terms of order G 3 is new. This expression confirms the existence of a third-order enhanced term when the emitter and the receiver are in conjunction relative to the central body. This term is shown to be necessary for determining the post-Newtonian parameter γ at a level of accuracy of 10 −8 with light rays grazing the Sun. (paper)
Modelling the air flow in symmetric and asymmetric street canyons
Santiago, J.L.; Martin, F. [Research Center for Energy, Environment and Technology (CIEMAT), Madrid (Spain). Fossil Fuels Dept., Numerical Simulation and Modelling Program
2004-07-01
In recent years a large amount of research has been conducted on urban scale and street canyon. Control of air quality inside cities is important for human health. To achieve this objective, street canyon modelling plays a significant role. Pollutant dispersion inside canyons are determined by wind flow around this complex geometry. Experimental investigations have been made by means of field measurements such as Vachon, G. et al. or wind tunnel experiences as Meroney, R.N. et al. or Kastner-Klein, P. and E.J. Plate. In many of these researches, they have used CFD models in several configurations, for instance Assimakopoulos, V.D. et al. or Sini, J.-F. et al. These models are based on a numerical resolution of Navier-Stokes equations with a turbulence closure. In this study, the aim is contribute to the understanding of air circulation inside street canyons. In order to achieve this purpose, several configurations of canyons are investigated. Two-dimensional sequences of real-scale street canyons (order to obstacles height is meters) with different features (symmetric canyons and asymmetric canyons forming step-up and step-down notch configurations) are simulated. These general configurations are modified to investigate some parameters such as aspect ratio, W/H, where W is the width of street and H is the height of buildings. Flows with high Reynolds numbers are modelling. FLUENT CFD software is used. (orig.)
The spherical limit of the n-vector model and correlation inequaljties
Angelescu, N.; Bundaru, M.; Costache, G.
1978-08-01
The asymptotics of the state of the n-vector model with a finite number of spins in the spherical limit is studied. Besides rederiving the limit free energy, corresponding to a generalized spherical model (with ''spherical constraint'' at every site), we obtain also the limit of the correlation functions, which allow a precise definition of the state of the latter model. Correlation inequalities are proved for ferromagnetic interactions in the asymptotic regime. In particular, it is shown that the generalized spherical model fulfills the expected Griffiths' type inequalities, differing in this respect from the spherical model with overall constraint. (author)
Characteristic function-based semiparametric inference for skew-symmetric models
Potgieter, Cornelis J.
2012-12-26
Skew-symmetric models offer a very flexible class of distributions for modelling data. These distributions can also be viewed as selection models for the symmetric component of the specified skew-symmetric distribution. The estimation of the location and scale parameters corresponding to the symmetric component is considered here, with the symmetric component known. Emphasis is placed on using the empirical characteristic function to estimate these parameters. This is made possible by an invariance property of the skew-symmetric family of distributions, namely that even transformations of random variables that are skew-symmetric have a distribution only depending on the symmetric density. A distance metric between the real components of the empirical and true characteristic functions is minimized to obtain the estimators. The method is semiparametric, in that the symmetric component is specified, but the skewing function is assumed unknown. Furthermore, the methodology is extended to hypothesis testing. Two tests for a hypothesis of specific parameter values are considered, as well as a test for the hypothesis that the symmetric component has a specific parametric form. A resampling algorithm is described for practical implementation of these tests. The outcomes of various numerical experiments are presented. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.
Behaviour modelling of two aluminas in divergent spherical pyrotechnical experiments
Malaise, F.; Tranchet, J.Y.; Collombet, F.
1997-01-01
Two pure aluminas of different characteristics have been subjected to the propagation of a longitudinal divergent spherical shock wave through pyrotechnical experiments. An approach combining a phenomenological analysis and numerical 1D-calculations is proposed to study the behaviour of these aluminas submitted to that type of wave loading. The modelling, proposed in a previous paper, is refined and gives satisfying experimentation-calculation correlations. An analysis of the influence exerted by the various encountered phenomena (plastic activity, pore closure, microcracking) is performed. The significant consequence of the activation of damage with an extension criterion is also underlined. (orig.)
Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey)
2017-01-15
We present new accretion solutions of a polytropic perfect fluid onto an f(R)-gravity de Sitter-like black hole. We consider two f(R)-gravity models and obtain finite-period cyclic flows oscillating between the event and cosmological horizons as well as semi-cyclic critical flows executing a two-way motion from and back to the same horizon. Besides the generalizations and new solutions presented in this work, a corrigendum to Eur. Phys. J. C (2016) 76:280 is provided. (orig.)
Naturally light Dirac neutrino in Left-Right Symmetric Model
Borah, Debasish [Department of Physics, Indian Institute of Technology Guwahati, Assam-781039 (India); Dasgupta, Arnab, E-mail: dborah@iitg.ernet.in, E-mail: arnab.d@iopb.res.in [Institute of Physics, HBNI, Sachivalaya Marg, Bhubaneshwar-751005 (India)
2017-06-01
We study the possibility of generating tiny Dirac masses of neutrinos in Left-Right Symmetric Model (LRSM) without requiring the existence of any additional symmetries. The charged fermions acquire masses through a universal seesaw mechanism due to the presence of additional vector like fermions. The neutrinos acquire a one-loop Dirac mass from the same additional vector like charged leptons without requiring any additional discrete symmetries. The model can also be extended by an additional Z {sub 2} symmetry in order to have a scotogenic version of this scenario predicting a stable dark matter candidate. We show that the latest Planck upper bound on the effective number of relativistic degrees of freedom N {sub eff}=3.15 ± 0.23 tightly constrains the right sector gauge boson masses to be heavier than 3.548 TeV . This bound on gauge boson mass also affects the allowed values of right scalar doublet dark matter mass from the requirement of satisfying the Planck bound on dark matter relic abundance. We also discuss the possible implications of such a scenario in charged lepton flavour violation and generating observable electric dipole moment of leptons.
Santarius, J. F.
2012-01-01
Converging plasma jets may be able to reach the regime of high energy density plasmas (HEDP). The successful application of plasma jets to magneto-inertial fusion (MIF) would heat the plasma by fusion products and should increase the plasma energy density. This paper reports the results of using the University of Wisconsin’s 1-D Lagrangian, radiation-hydrodynamics, fusion code BUCKY to investigate two MIF converging plasma jet test cases originally analyzed by Samulyak et al.[Physics of Plasmas 17, 092702 (2010)]. In these cases, 15 cm or 5 cm radially thick deuterium-tritium (DT) plasma jets merge at 60 cm from the origin and converge radially onto a DT target magnetized to 2 T and of radius 5 cm. The BUCKY calculations reported here model these cases, starting from the time of initial contact of the jets and target. Compared to the one-temperature Samulyak et al. calculations, the one-temperature BUCKY results show similar behavior, except that the plasma radius remains about twice as long near maximum compression. One-temperature and two-temperature BUCKY results differ, reflecting the sensitivity of the calculations to timing and plasma parameter details, with the two-temperature case giving a more sustained compression.
Fisheye image rectification using spherical and digital distortion models
Li, Xin; Pi, Yingdong; Jia, Yanling; Yang, Yuhui; Chen, Zhiyong; Hou, Wenguang
2018-02-01
Fisheye cameras have been widely used in many applications including close range visual navigation and observation and cyber city reconstruction because its field of view is much larger than that of a common pinhole camera. This means that a fisheye camera can capture more information than a pinhole camera in the same scenario. However, the fisheye image contains serious distortion, which may cause trouble for human observers in recognizing the objects within. Therefore, in most practical applications, the fisheye image should be rectified to a pinhole perspective projection image to conform to human cognitive habits. The traditional mathematical model-based methods cannot effectively remove the distortion, but the digital distortion model can reduce the image resolution to some extent. Considering these defects, this paper proposes a new method that combines the physical spherical model and the digital distortion model. The distortion of fisheye images can be effectively removed according to the proposed approach. Many experiments validate its feasibility and effectiveness.
Ergodic model for the expansion of spherical nanoplasmas.
Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O
2007-06-01
Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.
Brane solutions of a spherical sigma model in six dimensions
Lee, Hyun Min; Papazoglou, Antonios
2005-01-01
We explore solutions of six-dimensional gravity coupled to a non-linear sigma model, in the presence of codimension-two branes. We investigate the compactifications induced by a spherical scalar manifold and analyze the conditions under which they are of finite volume and singularity free. We discuss the issue of single-valuedness of the scalar fields and provide some special embedding of the scalar manifold to the internal space which solves this problem. These brane solutions furnish some self-tuning features, however they do not provide a satisfactory explanation of the vanishing of the effective four-dimensional cosmological constant. We discuss the properties of this model in relation with the self-tuning example based on a hyperbolic sigma model
Spherically symmetric scalar field collapse
2013-03-01
Mar 1, 2013 ... The very recent interest in scalar field collapse stems from a cosmological ... The objective of the present investigation is to explore the collapsing modes of a simple ..... The authors thank the BRNS (DAE) for financial support.
Spherical collapse in quintessence models with zero speed of sound
Creminelli, Paolo; Noreña, Jorge; Senatore, Leonardo; Vernizzi, Filippo
2010-01-01
We study the spherical collapse model in the presence of quintessence with zero speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshif...
Global GPS Ionospheric Modelling Using Spherical Harmonic Expansion Approach
Byung-Kyu Choi
2010-12-01
Full Text Available In this study, we developed a global ionosphere model based on measurements from a worldwide network of global positioning system (GPS. The total number of the international GPS reference stations for development of ionospheric model is about 100 and the spherical harmonic expansion approach as a mathematical method was used. In order to produce the ionospheric total electron content (TEC based on grid form, we defined spatial resolution of 2.0 degree and 5.0 degree in latitude and longitude, respectively. Two-dimensional TEC maps were constructed within the interval of one hour, and have a high temporal resolution compared to global ionosphere maps which are produced by several analysis centers. As a result, we could detect the sudden increase of TEC by processing GPS observables on 29 October, 2003 when the massive solar flare took place.
Venus spherical harmonic gravity model to degree and order 60
Konopliv, Alex S.; Sjogren, William L.
1994-01-01
The Magellan and Pioneer Venus Orbiter radiometric tracking data sets have been combined to produce a 60th degree and order spherical harmonic gravity field. The Magellan data include the high-precision X-band gravity tracking from September 1992 to May 1993 and post-aerobraking data up to January 5, 1994. Gravity models are presented from the application of Kaula's power rule for Venus and an alternative a priori method using surface accelerations. Results are given as vertical gravity acceleration at the reference surface, geoid, vertical Bouguer, and vertical isostatic maps with errors for the vertical gravity and geoid maps included. Correlation of the gravity with topography for the different models is also discussed.
Olafsson, Gestur; Helgason, Sigurdur
1996-01-01
This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
Color-symmetric superconductivity in a phenomenological QCD model
Bohr, Henrik; Providencia, C.; Providencia, J. da
2009-01-01
In this paper, we construct a theory of the NJL type where superconductivity is present, and yet the superconducting state remains, in the average, color symmetric. This shows that the present approach to color superconductivity is consistent with color singletness. Indeed, quarks are free...... in the deconfined phase, but the deconfined phase itself is believed to be a color singlet. The usual description of the color superconducting state violates color singletness. On the other hand, the color superconducting state here proposed is color symmetric in the sense that an arbitrary color rotation leads...
Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks
HUA Da-Yin
2009-01-01
We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion σ(t, L) = (∑i(mi - ρ0)2/L)1/2 is defined to describe the dynamical behaviour where ρ0 is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ(t, L) follows a power-law scaling σ(t, L) ～ tδ1 and σ(t, L) ～ tδ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ(t, L) ～ tδ2 when t＜T and a(t, L) ～ tδ3 when tT. Moreover, it is found numerically that δ2 is near to δ1 for small rewiring probability q, and δ3 hardly changes with varying q and it is almost the same as δ4. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when tT for the small-world networks. We also show that the relaxation time T follows a power-law scaling τ Lz and σ(t, L) in the stationary state follows a power-law σs(L) ～ Lσ for three different structures.
Plane Symmetric Cosmological Model with Quark and Strange ...
Keywords. f(R,T) theory of gravity—plane symmetric space-time—quark and strange quark matter—constant deceleration parameter. 1. Introduction. Modern astrophysical observations point out that present expansion of the Universe is an accelerated epoch. The most fascinating evidence for this is found in measurements ...
AN ANALYTIC MODEL OF DUSTY, STRATIFIED, SPHERICAL H ii REGIONS
Rodríguez-Ramírez, J. C.; Raga, A. C. [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ap. 70-543, 04510 D.F., México (Mexico); Lora, V. [Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität, Mönchhofstr. 12-14, D-69120 Heidelberg (Germany); Cantó, J., E-mail: juan.rodriguez@nucleares.unam.mx [Instituto de Astronomía, Universidad Nacional Autónoma de México, Ap. 70-468, 04510 D. F., México (Mexico)
2016-12-20
We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. We compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.
Fluctuations in the thermal superfluid model for heated spherical nuclei
Nguyen Dinhdang; Nguyen Zuythang
1990-01-01
The effect of the non-vanishing thermal pairing gap due to statistical fluctuations is investigated by calculating fluctuations of selected observables such as the energy and particle number fluctuations, the nuclear level density, the level density parameter and the specific heat within the framework of the thermal nuclear superfluid model. In numerical calculations for heated spherical nuclei 58 Ni, 142 Sm and 208 Pb the realistic single-particle energy spectra defined in the Woods-Saxon potential are used. It is found that the results obtained with the non-vanishing thermal average pairing gap can yield an adequate estimate of the true fluctuations in the finite heating non-rotating nuclear systems. (author)
Plane symmetric cosmological model with thick domain walls in Brans-Dicke theory of gravitation
Pawar, D.; Bayaskar, S.; Patil, V.
2009-01-01
We have investigated plane symmetric cosmological model in presence of thick domain walls in Brans-Dicke theory of gravitation, some geometrical and physical behavior of the model are discussed. (authors)
Modelling of Spherical Gas Bubble Oscillations and Sonoluminescence
Prosperetti, A.; Hao, Y.
1999-01-01
The discovery of single-bubble sonoluminescence has led to a renewed interest in the forced radial oscillations of gas bubbles. Many of the more recent studies devoted to this topic have used several simplifications in the modelling, and in particular in accounting for liquid compressibility and thermal processes in the bubble. In this paper the significance of these simplifications is explored by contrasting the results of Lohse and co-workers with those of a more detailed model. It is found that, even though there may be little apparent difference between the radius-versus time behaviour of the bubble as predicted by the two models, quantities such as the spherical stability boundary and the threshold for rectified diffusion are affected in a quantitatively significant way. These effects are a manifestation of the subtle dependence upon dissipative processes of the phase of radial motion with respect to the driving sound field. The parameter space region, where according to the theory of Lohse and co-workers, sonoluminescence should be observable, is recalculated with the new model and is found to be enlarged with respect to the earlier estimate. The dependence of this parameter region on sound frequency is also illustrated.
Modelling, simulation and experiment of the spherical flexible joint stiffness
S. Li
2018-02-01
Full Text Available The spherical flexible joint is extensively used in engineering. It is designed to provide flexibility in rotation while bearing vertical compression load. The linear rotational stiffness of the flexible joint is formulated. The rotational stiffness of the bonded rubber layer is related to inner radius, thickness and two edge angles. FEM is used to verify the analytical solution and analyze the stiffness. The Mooney–Rivlin, Neo Hooke and Yeoh constitutive models are used in the simulation. The experiment is taken to obtain the material coefficient and validate the analytical and FEM results. The Yeoh model can reflect the deformation trend more accurately, but the error in the nearly linear district is bigger than the Mooney–Rivlin model. The Mooney–Rivlin model can fit the test result very well and the analytical solution can also be used when the rubber deformation in the flexible joint is small. The increase of Poisson's ratio of the rubber layers will enhance the vertical compression stiffness but barely have effect on the rotational stiffness.
Simple and Versatile Dynamic Model of Spherical Roller Bearing
Behnam Ghalamchi
2013-01-01
Full Text Available Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB is one variant witnessing increasing use because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This study introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to the nonlinear Hertzian contact theory. The results reveal how some of the more important parameters, such as diametral clearance, the number of rollers, and osculation number, influence ultimate bearing performance. One pair of calculations looked at bearing displacement with respect to time for two separate arrangements of the caged side-by-side roller arrays, when they are aligned and when they are staggered. As theory suggests, significantly lower displacement variations were predicted for the staggered arrangement. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis.
Childers, W Lee; Kogler, Géza F
2014-01-01
People with amputation move asymmetrically with regard to kinematics (joint angles) and kinetics (joint forces and moments). Clinicians have traditionally sought to minimize kinematic asymmetries, assuming kinetic asymmetries would also be minimized. A cycling model evaluated locomotor asymmetries. Eight individuals with unilateral transtibial amputation pedaled with 172 mm-length crank arms on both sides (control condition) and with the crank arm length shortened to 162 mm on the amputated side (CRANK condition). Pedaling kinetics and limb kinematics were recorded. Joint kinetics, joint angles (mean and range of motion [ROM]), and pedaling asymmetries were calculated from force pedals and with a motion capture system. A one-way analysis of variance with tukey post hoc compared kinetics and kinematics across limbs. Statistical significance was set to p Pedaling asymmetries did not differ and were 23.0% +/= 9.8% and 23.2% +/= 12% for the control and CRANK conditions, respectively. Our results suggest that minimizing kinematic asymmetries does not relate to kinetic asymmetries as clinically assumed. We propose that future research should concentrate on defining acceptable asymmetry.
Modelling of UWB Antenna Perturbed by Human Phantom in Spherical Harmonics Space
Mhedhbi, Meriem; Avrillon, Stephane; Pedersen, Troels
2014-01-01
is attractive for simulation purposes. We propose a simple model for the spherical harmonics coefficients allowing to predict the antenna behavior perturbed by a human phantom. The model is based on knowledge of the spherical harmonic coefficients of antenna in free space and the antenna-phantom distance.......In this paper we study how the antenna radiation pattern is perturbed in the presence of a human phantom in terms of changes in the coefficients of the spherical harmonic antenna representation. The spherical harmonic basis allows for a compact representation of the antenna pattern which...
Lowes, F.J.; Olsen, Nils
2004-01-01
Most modern spherical harmonic geomagnetic models based on satellite data include estimates of the variances of the spherical harmonic coefficients of the model; these estimates are based on the geometry of the data and the fitting functions, and on the magnitude of the residuals. However...
Isomorphism and the #betta#-function of the non-linear sigma model in symmetric spaces
Hikami, S.
1983-01-01
The renormalization group #betta#-function of the non-linear sigma model in symmetric spaces is discussed via the isomorphic relation and the reciprocal relation about a parameter α. The four-loop term is investigated and the symmetric properties of the #betta#-function are studied. The four-loop term in the #betta#-function is shown to be vanishing for the orthogonal Anderson localization problem. (orig.)
Clarisse, J.M
2007-07-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Bhartia, Mini; Chatterjee, Arun Kumar
2015-01-01
A 2D model for the potential distribution in silicon film is derived for a symmetrical double gate MOSFET in weak inversion. This 2D potential distribution model is used to analytically derive an expression for the subthreshold slope and threshold voltage. A drain current model for lightly doped symmetrical DG MOSFETs is then presented by considering weak and strong inversion regions including short channel effects, series source to drain resistance and channel length modulation parameters. These derived models are compared with the simulation results of the SILVACO (Atlas) tool for different channel lengths and silicon film thicknesses. Lastly, the effect of the fixed oxide charge on the drain current model has been studied through simulation. It is observed that the obtained analytical models of symmetrical double gate MOSFETs are in good agreement with the simulated results for a channel length to silicon film thickness ratio greater than or equal to 2. (paper)
Bhartia, Mini; Chatterjee, Arun Kumar
2015-04-01
A 2D model for the potential distribution in silicon film is derived for a symmetrical double gate MOSFET in weak inversion. This 2D potential distribution model is used to analytically derive an expression for the subthreshold slope and threshold voltage. A drain current model for lightly doped symmetrical DG MOSFETs is then presented by considering weak and strong inversion regions including short channel effects, series source to drain resistance and channel length modulation parameters. These derived models are compared with the simulation results of the SILVACO (Atlas) tool for different channel lengths and silicon film thicknesses. Lastly, the effect of the fixed oxide charge on the drain current model has been studied through simulation. It is observed that the obtained analytical models of symmetrical double gate MOSFETs are in good agreement with the simulated results for a channel length to silicon film thickness ratio greater than or equal to 2.
Complex {PT}-symmetric extensions of the nonlinear ultra-short light pulse model
Yan, Zhenya
2012-11-01
The short pulse equation u_{xt}=u+\\frac{1}{2}(u^2u_x)_x is PT symmetric, which arises in nonlinear optics for the ultra-short pulse case. We present a family of new complex PT-symmetric extensions of the short pulse equation, i[(iu_x)^{\\sigma }]_t=au+bu^m+ic[u^n(iu_x)^{\\epsilon }]_x \\,\\, (\\sigma ,\\, \\epsilon ,\\,a,\\,b,\\,c,\\,m,\\,n \\in {R}), based on the complex PT-symmetric extension principle. Some properties of these equations with some chosen parameters are studied including the Hamiltonian structures and exact solutions such as solitary wave solutions, doubly periodic wave solutions and compacton solutions. Our results may be useful to understand complex PT-symmetric nonlinear physical models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Coupled Person Orientation Estimation and Appearance Modeling using Spherical Harmonics
Liem, M.C.; Gavrila, D.M.
2014-01-01
We present a novel approach for the estimation of a person's overall body orientation, 3D shape and texture, from overlapping cameras. A distinguishing aspect of our approach is the use of spherical harmonics for 3D shape- and texture-representation; it offers a compact, low-dimensional
Spherical Detector Device Mathematical Modelling with Taking into Account Detector Module Symmetry
Batyj, V.G.; Fedorchenko, D.V.; Prokopets, S.I.; Prokopets, I.M.; Kazhmuradov, M.A.
2005-01-01
Mathematical Model for spherical detector device accounting to symmetry properties is considered. Exact algorithm for simulation of measurement procedure with multiple radiation sources is developed. Modelling results are shown to have perfect agreement with calibration measurements
Stochastic modeling of cell growth with symmetric or asymmetric division
Marantan, Andrew; Amir, Ariel
2016-07-01
We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.
Emulating Spherical Wave Channel Models in Multi-probe Anechoic Chamber Setups
Fan, Wei; Carreño, Xavier; Nielsen, Jesper Ødum
2015-01-01
to emulate spherical wave channel models in multi-probe anechoic chamber setups. In this paper, a technique based on the field synthesis principle is proposed to approximate spherical waves emitted from arbitrarily located point sources with arbitrary polarizations. Simulation results show that static......Spherical wave channel modeling has attracted huge research attention for massive multiple-input multiple-output (MIMO) and short-distance MIMO systems. Current research work in multi-probe anechoic chamber systems is limited to reproduce radio channels assuming planar wavefronts. There is a need...... spherical waves can be reproduced with a limited number of probes, and the field synthesis accuracy of spherical wave depends on the location of the source point....
EEG-distributed inverse solutions for a spherical head model
Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.
1998-08-01
The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.
The 1/ N Expansion of Tensor Models with Two Symmetric Tensors
Gurau, Razvan
2018-06-01
It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.
Analytical prediction model for non-symmetric fatigue crack growth in Fibre Metal Laminates
Wang, W.; Rans, C.D.; Benedictus, R.
2017-01-01
This paper proposes an analytical model for predicting the non-symmetric crack growth and accompanying delamination growth in FMLs. The general approach of this model applies Linear Elastic Fracture Mechanics, the principle of superposition, and displacement compatibility based on the
Martin Hallnäs
2007-03-01
Full Text Available We review a recent construction of an explicit analytic series representation for symmetric polynomials which up to a groundstate factor are eigenfunctions of Calogero-Sutherland type models. We also indicate a generalisation of this result to polynomials which give the eigenfunctions of so-called 'deformed' Calogero-Sutherland type models.
Mathematical Model of Induction Heating Processes in Axial Symmetric Inductor-Detail Systems
Maik Streblau
2014-05-01
Full Text Available The wide variety of models for analysis of processes in the inductor-detail systems makes it necessary to summarize them. This is a difficult task because of the variety of inductor-detail system configurations. This paper aims to present a multi physics mathematical model for complex analysis of electromagnetic and thermal fields in axial symmetric systems inductor-detail.
Spherical cap modelling of Orsted magnetic field vectors over southern Africa
Kotze, PB
2001-01-01
Full Text Available Vector magnetic field observations by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000, have been employed to derive a spherical cap harmonic model (Haines, 1985) over the southern African region between 10 degrees...
Continuons left-right symmetrical model of electroweak interactions
Boyarkin, O.M.
1993-01-01
The left-right model (LR) is suggested which is characterized by the orientation angle of the SU(2) R generator in the group space. This model reproduces all the known LR models. The production processes of gauge bosons at electron-positron and hardon colliders are investigated
Flat directions in left-right symmetric string derived models
Cleaver, Gerald B.; Clements, David J.; Faraggi, Alon E.
2002-01-01
The only string models known to reproduce the minimal supersymmetric standard model in the low energy effective field theory are those constructed in the free fermionic formulation. We demonstrate the existence of quasirealistic free fermionic heterotic string models in which supersymmetric singlet flat directions do not exist. This raises the possibility that supersymmetry is broken perturbatively in such models by the one-loop Fayet-Iliopoulos term. We show, however, that supersymmetric flat directions that utilize vacuum expectation values of some non-Abelian fields in the massless string spectrum do exist in the model. We argue that hidden sector condensates lift the flat directions and break supersymmetry hierarchically
Cohen, Taco S.; Geiger, Mario; Koehler, Jonas; Welling, Max
2018-01-01
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined t...
The spherical sector of the Calogero model as a reduced matrix model
Hakobyan, Tigran, E-mail: hakob@yerphi.am [Yerevan State University, 1 Alex Manoogian, 0025 Yerevan (Armenia); Yerevan Physics Institute, 2 Alikhanyan Br., 0036 Yerevan (Armenia); Lechtenfeld, Olaf, E-mail: lechtenf@itp.uni-hannover.de [Leibniz Universitaet Hannover, Institut fuer Theoretische Physik, Appelstr. 2, D-30167 Hannover (Germany); Nersessian, Armen, E-mail: arnerses@ysu.am [Yerevan State University, 1 Alex Manoogian, 0025 Yerevan (Armenia)
2012-05-11
We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and calculate their Poisson brackets. In this way we obtain all functionally independent constants of motion to any given order in the momenta. Our technique is related to the valence-bond basis for singlet states.
Cooperative effects in spherical spasers: Ab initio analytical model
Bordo, V. G.
2017-06-01
A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which a shell/core contains an arbitrarily large number of active molecules in the vicinity of a metallic core/shell. An essential aspect of the theory is an ab initio account of the feedback from the core/shell boundaries which significantly modifies the molecular dynamics. The theory provides rigorous, albeit simple and physically transparent, criteria for both plasmonic superradiance and surface plasmon generation.
Quark and gluon propagators in the spherical bag model
Kulish, Yu V [AN Ukrainskoj SSR, Fiziko-Tekhnicheskij Inst., Kharkov
1983-12-01
The quark and gluon propagators in a spherical cavity have been obtained by summation of the quark field modes (J-1/2, J is the total moment) and gluon field modes (J=1). The requirements for the spatial components of the gluon propagator Gsub(ik)(x, x') and the quark propagator S(x, x') to be Green functions of the wave equations result in the coincidence of directions for anti x and anti x' vectors. Relations have been derived which allow verification of the self-consistency of approximations used to calculate dynamic values.
Quark and gluon propagators in the spherical bag model
Kulish, Yu.V.
1983-01-01
The quark and gluon propagators in a spherical cavity have been obtained by summation of the quark field modes (J-1/2, J is the total moment) and gluon field modes (J=1). The requirements for the spatial components of the gluon propagator Gsub(ik)(x, x') and the quark propagator S(x, x') to be Green functions of the wave equations result in the coincidence of directions for anti x and anti x' vectors. Relations have been derived which allow verification of the self-consistency of approximations used to calculate dynamic values
Bartzke, Gerhard; Kuhlmann, Jannis; Huhn, Katrin
2016-04-01
the flow into and within a granular medium composed of spherical and non-spherical shapes under wave forcing. It is concluded that variations in grain shape orientation within a bed appear to control the amount of flow that can be accumulated by the pores, which was illustrated in a conceptual model.
Static solutions with spherical symmetry in f(T) theories
Wang Tower
2011-01-01
The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and then we introduce a particular frame based on the conformally Cartesian coordinates. In this particular frame, the existence conditions of various solutions are presented. Our results imply that only a limited class of f(T) models can be solved in this frame. For more general models, the search for spherically symmetric static solutions is still an open and challenging problem, hopefully solvable in other frames.
Time-invariant PT product and phase locking in PT -symmetric lattice models
Joglekar, Yogesh N.; Onanga, Franck Assogba; Harter, Andrew K.
2018-01-01
Over the past decade, non-Hermitian, PT -symmetric Hamiltonians have been investigated as candidates for both a fundamental, unitary, quantum theory and open systems with a nonunitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the PT (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of PT -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave-function phases at adjacent sites occurs in the PT -symmetry-broken region. Our results pave the way towards understanding the physically observable implications of time invariants in the nonunitary dynamics produced by PT -symmetric Hamiltonians.
On the Decay of Correlations in Non-Analytic SO(n)-Symmetric Models
Naddaf, Ali
We extend the method of complex translations which was originally employed by McBryan-Spencer [2] to obtain a decay rate for the two point function in two-dimensional SO(n)-symmetric models with non-analytic Hamiltonians for $.
Tang, T; Sadleir, R J
2011-01-01
We have developed a robust EEG-based current pattern which shows promise for the detection of intraventricular hemorrhage (IVH) in neonates. Our reconstructions to date are based on a layered spherical head model. In this study, the current pattern was used to gather data from three realistic-shaped neonatal head models and a physical phantom based on one of these models. We found that a sensitivity matrix calculated from a spherical model gave us satisfactory reconstructions in terms of both image quality and quantification. Incorporating correct geometry information into the forward model improved image quality. However, it did not improve quantification accuracy. The results indicate that using a spherical matrix may be a more practical choice for monitoring IVH volumes in neonates for whom patient-specific models are not available
A comparative study of spherical and flat-Earth geopotential modeling at satellite elevations
Parrott, M. H.; Hinze, W. J.; Braile, L. W.; Vonfrese, R. R. B.
1985-01-01
Flat-Earth modeling is a desirable alternative to the complex spherical-Earth modeling process. These methods were compared using 2 1/2 dimensional flat-earth and spherical modeling to compute gravity and scalar magnetic anomalies along profiles perpendicular to the strike of variably dimensioned rectangular prisms at altitudes of 150, 300, and 450 km. Comparison was achieved with percent error computations (spherical-flat/spherical) at critical anomaly points. At the peak gravity anomaly value, errors are less than + or - 5% for all prisms. At 1/2 and 1/10 of the peak, errors are generally less than 10% and 40% respectively, increasing to these values with longer and wider prisms at higher altitudes. For magnetics, the errors at critical anomaly points are less than -10% for all prisms, attaining these magnitudes with longer and wider prisms at higher altitudes. In general, in both gravity and magnetic modeling, errors increase greatly for prisms wider than 500 km, although gravity modeling is more sensitive than magnetic modeling to spherical-Earth effects. Preliminary modeling of both satellite gravity and magnetic anomalies using flat-Earth assumptions is justified considering the errors caused by uncertainties in isolating anomalies.
The Combination of Spherical Photogrammetry and UAV for 3D Modeling
Ihsanudin, T.; Affriani, A. R.
2017-12-01
The complete of 3D models required the object that was recorded from both side and top. If the object recorded from above, then the object from the side can not be covered, and if the objects recorded from the side, it can not be covered from the top. Recording of objects from the side using spherical photogrammetry method and from the top using UAV method. The merge of both models using a conform transformation, by bringing the spherical photogrammetry coordinates system to the UAV model. The object of this research is Ratu Boko temple, Sleman, Yogyakarta. The spherical photogrammetry recording was performed by rotating the camera in 360° angle on the entire area of the temple. The area consists of 12 stations. The UAV method uses a drone with flight attitude of 20 meters. The merge of the both models produced the completeness of the temple model from the top and side.
Equivalence of the spherical and deformed shell-model approach to intruder states
Heyde, K.; Coster, C. de; Ryckebusch, J.; Waroquier, M.
1989-01-01
We point out that the description of intruder states, incorporating particle-hole (p-h) excitation across a closed shell in the spherical shell model or a description starting from the Nilsson model are equivalent. We furthermore indicate that the major part of the nucleon-nucleon interaction, responsible for the low excitation energy of intruder states comes as a two-body proton-neutron quadrupole interaction in the spherical shell model. In the deformed shell model, quadrupole binding energy is gained mainly through the one-body part of the potential. (orig.)
Circuital model for the spherical geodesic waveguide perfect drain
González, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C.
2012-08-01
The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000.
Circuital model for the spherical geodesic waveguide perfect drain
González, Juan C; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C
2012-01-01
The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000. (paper)
On the implementation of the spherical collapse model for dark energy models
Pace, Francesco [Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL (United Kingdom); Meyer, Sven; Bartelmann, Matthias, E-mail: francesco.pace@manchester.ac.uk, E-mail: sven.meyer@uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de [Zentrum für Astronomie der Universität Heidelberg, Institut für theoretische Astrophysik, Philosophenweg 12, D-69120, Heidelberg (Germany)
2017-10-01
In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δ{sub c}, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δ{sub c} for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.
On the implementation of the spherical collapse model for dark energy models
Pace, Francesco; Meyer, Sven; Bartelmann, Matthias
2017-10-01
In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δc, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δc for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.
Resource Symmetric Dispatch Model for Internet of Things on Advanced Logistics
Guofeng Qin; Lisheng Wang; Qiyan Li
2016-01-01
Business applications in advanced logistics service are highly concurrent. In this paper, we propose a resource symmetric dispatch model for the concurrent and cooperative tasks of the Internet of Things. In the model, the terminals receive and deliver commands, data, and information with mobile networks, wireless networks, and sensor networks. The data and information are classified and processed by the clustering servers in the cloud service platform. The cluster service, resource dispatch,...
Kurukuri, Srihari; Worswick, Michael J.
2013-12-01
An alternative approach is proposed to utilize symmetric yield functions for modeling the tension-compression asymmetry commonly observed in hcp materials. In this work, the strength differential (SD) effect is modeled by choosing separate symmetric plane stress yield functions (for example, Barlat Yld 2000-2d) for the tension i.e., in the first quadrant of principal stress space, and compression i.e., third quadrant of principal stress space. In the second and fourth quadrants, the yield locus is constructed by adopting interpolating functions between uniaxial tensile and compressive stress states. In this work, different interpolating functions are chosen and the predictive capability of each approach is discussed. The main advantage of this proposed approach is that the yield locus parameters are deterministic and relatively easy to identify when compared to the Cazacu family of yield functions commonly used for modeling SD effect observed in hcp materials.
Integrating Work and Basic Values into the Spherical Model of Interests
Sodano, Sandro M.
2011-01-01
Two prominent models of values, one in work and the other in life, were examined as they each related to the dimensions underlying the Spherical Model of Interests (Tracey & Rounds, 1996) as measured by the Personal Globe Inventory (PGI; Tracey, 2002). The technique of external property vector fitting was utilized to plot the value constructs onto…
OWL: A code for the two-center shell model with spherical Woods-Saxon potentials
Diaz-Torres, Alexis
2018-03-01
A Fortran-90 code for solving the two-center nuclear shell model problem is presented. The model is based on two spherical Woods-Saxon potentials and the potential separable expansion method. It describes the single-particle motion in low-energy nuclear collisions, and is useful for characterizing a broad range of phenomena from fusion to nuclear molecular structures.
Resource Symmetric Dispatch Model for Internet of Things on Advanced Logistics
Guofeng Qin
2016-04-01
Full Text Available Business applications in advanced logistics service are highly concurrent. In this paper, we propose a resource symmetric dispatch model for the concurrent and cooperative tasks of the Internet of Things. In the model, the terminals receive and deliver commands, data, and information with mobile networks, wireless networks, and sensor networks. The data and information are classified and processed by the clustering servers in the cloud service platform. The cluster service, resource dispatch, and load balance are cooperative for management and monitoring of every application case during the logistics service lifecycle. In order to support the high performance of cloud service, resource symmetric dispatch algorithm among clustering servers and load balancing method among multi-cores in one server, including NIO (Non-blocking Input/Output and RMI (Remote Method Invocation are utilized to dispatch the cooperation of computation and service resources.
Neutrinoless double-beta decay in left-right symmetric models
Picciotto, C.E.; Zahir, M.S.
1982-06-01
Neutrinoless double-beta decay is calculated via doubly charged Higgs, which occur naturally in left-right symmetric models. We find that the comparison with known half-lives yields values of phenomenological parameters which are compatible with earlier analyses of neutral current data. In particular, we obtain a right-handed gauge-boson mass lower bound of the order of 240 GeV. Using this result and expressions for neutrino masses derived in a parity non-conserving left-right symmetric model, we obtain msub(νsub(e)) < 1.5 eV, msub(νsub(μ)) < 0.05 MeV and msub(νsub(tau)) < 18 MeV
Numerical Modeling of a Spherical Array of Monopoles Using FDTD Method
Franek, Ondrej; Pedersen, Gert Frølund; Andersen, Jørgen Bach
2006-01-01
In this paper, the spherical-coordinate finite-difference time-domain method is applied to numerical analysis of phased array of monopoles distributed over a sphere. Outer boundary of the given problem is modeled by accurate spherical-coordinate anisotropic perfectly matched layer. The problem...... of increased cell aspect ratio near the sphere poles causing degradation of results is solved by dispersion optimization through artificial anisotropy. The accuracy of the approach is verified by comparing a model case with an exact solution. Finally, radiation patterns obtained by frequency-domain near-to-far-field...
An SU(2) x SU(2) symmetric Higgs-Fermion model with staggered fermions
Berlin, J.; Heller, U.M.
1991-01-01
We have simulated on SU(2)xSU(2) symmetric Higgs-Fermion model with a four component scalar field coupled with a Yukawa type coupling to two flavours of staggered fermions. The results show two qualitatively different behaviours in the broken phase. One for weak coupling where the fermion masses obey the perturbative tree level relation M F =y , and one for strong coupling where the behaviour agrees with a 1/d expansion. (orig.)
Locally Rotationally Symmetric Bianchi Type-I Model with Time Varying Λ Term
Tiwari, R. K.; Jha, Navin Kumar
2009-01-01
We investigate the locally rotationally symmetric (LRS) Bianchi type-I cosmological model for stiff matter and a vacuum solution with a cosmological term proportional to R −m (R is the scale factor and m is a positive constant). The cosmological term decreases with time. We obtain that for both the cases the present universe is accelerating with a large fraction of cosmological density in the form of a cosmological term
Li, Guohui; Zhang, Songling; Yang, Hong
2017-01-01
Aiming at the irregularity of nonlinear signal and its predicting difficulty, a deep learning prediction model based on extreme-point symmetric mode decomposition (ESMD) and clustering analysis is proposed. Firstly, the original data is decomposed by ESMD to obtain the finite number of intrinsic mode functions (IMFs) and residuals. Secondly, the fuzzy c-means is used to cluster the decomposed components, and then the deep belief network (DBN) is used to predict it. Finally, the reconstructed ...
MODELING OF SYMMETRIC THREE-PHASE ASYNCHRONOUS ELECTRIC MOTOR IN ASYMMETRIC CONNECTION TO NETWORK
V. I. Lukovnikov
2005-01-01
Full Text Available The paper shows how to solve the problem concerning reveal of changes in mathematical models and electric parameters of symmetric three-phase short-circuited asynchronous electric motors in case of their connection to single- or two-phase network in comparison with their connection to three-phase network. The uniform methodological approach permitting to generalize the known data and receive new results is offered in the paper.
Fu Jie; Przhonska, Olga V.; Padilha, Lazaro A.; Hagan, David J.; Van Stryland, Eric W.; Belfield, Kevin D.; Bondar, Mikhail V.; Slominsky, Yuriy L.; Kachkovski, Alexei D.
2006-01-01
One- and two-photon anisotropy spectra of a series of symmetrical and asymmetrical polymethine (PD) and fluorene molecules were measured experimentally and discussed theoretically within the framework of three-state and four-state models. For all the molecules discussed in this paper, the experimental two-photon anisotropy values, r 2PA , lie in the relatively narrow range from 0.47 to 0.57 and remain almost independent of wavelength over at least two electronic transitions. This is in contrast with their one-photon anisotropy, which shows strong wavelength dependence, typically varying from ∼0 to 0.38 over the same transitions. A detailed analysis of the two-photon absorption (2PA) processes allows us to conclude that a three-state model can explain the 2PA anisotropy spectra of most asymmetrical PDs and fluorenes. However, this model is inadequate for all the symmetrical molecules. Experimental values of r 2PA for symmetrical polymethines and fluorenes can be explained by symmetry breaking leading to the deviation of the orientation of the participating transition dipole moments from their 'classical' orientations
Jesus, Danilo A; Iskander, D Robert
2015-12-01
Ray tracing is a powerful technique to understand the light behavior through an intricate optical system such as that of a human eye. The prediction of visual acuity can be achieved through characteristics of an optical system such as the geometrical point spread function. In general, its precision depends on the number of discrete rays and the accurate surface representation of each eye's components. Recently, a method that simplifies calculation of the geometrical point spread function has been proposed for circularly symmetric systems [Appl. Opt.53, 4784 (2014)]. An extension of this method to 2D noncircularly symmetric systems is proposed. In this method, a two-dimensional ray tracing procedure for an arbitrary number of surfaces and arbitrary surface shapes has been developed where surfaces, rays, and refractive indices are all represented in functional forms being approximated by Chebyshev polynomials. The Liou and Brennan anatomically accurate eye model has been adapted and used for evaluating the method. Further, real measurements of the anterior corneal surface of normal, astigmatic, and keratoconic eyes were substituted for the first surface in the model. The results have shown that performing ray tracing, utilizing the two-dimensional Chebyshev function approximation, is possible for noncircularly symmetric models, and that such calculation can be performed with a newly created Chebfun toolbox.
One-degree-of-freedom spherical model for the passive motion of the human ankle joint.
Sancisi, Nicola; Baldisserri, Benedetta; Parenti-Castelli, Vincenzo; Belvedere, Claudio; Leardini, Alberto
2014-04-01
Mathematical modelling of mobility at the human ankle joint is essential for prosthetics and orthotic design. The scope of this study is to show that the ankle joint passive motion can be represented by a one-degree-of-freedom spherical motion. Moreover, this motion is modelled by a one-degree-of-freedom spherical parallel mechanism model, and the optimal pivot-point position is determined. Passive motion and anatomical data were taken from in vitro experiments in nine lower limb specimens. For each of these, a spherical mechanism, including the tibiofibular and talocalcaneal segments connected by a spherical pair and by the calcaneofibular and tibiocalcaneal ligament links, was defined from the corresponding experimental kinematics and geometry. An iterative procedure was used to optimize the geometry of the model, able to predict original experimental motion. The results of the simulations showed a good replication of the original natural motion, despite the numerous model assumptions and simplifications, with mean differences between experiments and predictions smaller than 1.3 mm (average 0.33 mm) for the three joint position components and smaller than 0.7° (average 0.32°) for the two out-of-sagittal plane rotations, once plotted versus the full flexion arc. The relevant pivot-point position after model optimization was found within the tibial mortise, but not exactly in a central location. The present combined experimental and modelling analysis of passive motion at the human ankle joint shows that a one degree-of-freedom spherical mechanism predicts well what is observed in real joints, although its computational complexity is comparable to the standard hinge joint model.
A theoretical-electron-density databank using a model of real and virtual spherical atoms.
Nassour, Ayoub; Domagala, Slawomir; Guillot, Benoit; Leduc, Theo; Lecomte, Claude; Jelsch, Christian
2017-08-01
A database describing the electron density of common chemical groups using combinations of real and virtual spherical atoms is proposed, as an alternative to the multipolar atom modelling of the molecular charge density. Theoretical structure factors were computed from periodic density functional theory calculations on 38 crystal structures of small molecules and the charge density was subsequently refined using a density model based on real spherical atoms and additional dummy charges on the covalent bonds and on electron lone-pair sites. The electron-density parameters of real and dummy atoms present in a similar chemical environment were averaged on all the molecules studied to build a database of transferable spherical atoms. Compared with the now-popular databases of transferable multipolar parameters, the spherical charge modelling needs fewer parameters to describe the molecular electron density and can be more easily incorporated in molecular modelling software for the computation of electrostatic properties. The construction method of the database is described. In order to analyse to what extent this modelling method can be used to derive meaningful molecular properties, it has been applied to the urea molecule and to biotin/streptavidin, a protein/ligand complex.
Xiaochao Jin
Full Text Available The cavity expansion theory is most widely used to predict the depth of penetration of concrete targets. The main purpose of this work is to clarify the differences between the spherical and cylindrical cavity expansion models and their scope of application in predicting the penetration depths of concrete targets. The factors that influence the dynamic cavity expansion process of concrete materials were first examined. Based on numerical results, the relationship between expansion pressure and velocity was established. Then the parameters in the Forrestal's formula were fitted to have a convenient and effective prediction of the penetration depth. Results showed that both the spherical and cylindrical cavity expansion models can accurately predict the depth of penetration when the initial velocity is lower than 800 m/s. However, the prediction accuracy decreases with the increasing of the initial velocity and diameters of the projectiles. Based on our results, it can be concluded that when the initial velocity is higher than the critical velocity, the cylindrical cavity expansion model performs better than the spherical cavity expansion model in predicting the penetration depth, while when the initial velocity is lower than the critical velocity the conclusion is quite the contrary. This work provides a basic principle for selecting the spherical or cylindrical cavity expansion model to predict the penetration depth of concrete targets.
Plane symmetric cosmological micro model in modified theory of Einstein’s general relativity
Panigrahi U.K.
2003-01-01
Full Text Available In this paper, we have investigated an anisotropic homogeneous plane symmetric cosmological micro-model in the presence of massless scalar field in modified theory of Einstein's general relativity. Some interesting physical and geometrical aspects of the model together with singularity in the model are discussed. Further, it is shown that this theory is valid and leads to Einstein's theory as the coupling parameter λ →>• 0 in micro (i.e. quantum level in general.
Maximally Symmetric Two Higgs Doublet Model with Natural Standard Model Alignment
Dev, P S Bhupal
2014-01-01
We study the Higgs mass spectrum as predicted by a Maximally Symmetric Two Higgs Doublet Model (MS-2HDM) potential based on the SO(5) group, softly broken by bilinear Higgs mass terms. We show that the lightest Higgs sector resulting from this MS-2HDM becomes naturally aligned with that of the Standard Model (SM), independently of the charged Higgs boson mass and $\\tan \\beta$. In the context of Type-II 2HDM, SO(5) is the simplest of the three possible symmetry realizations of the scalar potential that can naturally lead to the SM alignment. Nevertheless, renormalization group effects due to the hypercharge gauge coupling $g'$ and third-generation Yukawa couplings may break sizeably this SM alignment, along with the custodial symmetry inherited by the SO(5) group. Using the current Higgs signal strength data from the LHC, which disfavour large deviations from the SM alignment limit, we derive lower mass bounds on the heavy Higgs sector as a function of $\\tan\\beta$, which can be stronger than the existing limit...
Person Appearance Modeling and Orientation Estimation using Spherical Harmonics
Liem, M.C.; Gavrila, D.M.
2013-01-01
We present a novel approach for the joint estimation of a person's overall body orientation, 3D shape and texture, from overlapping cameras. Overall body orientation (i.e. rotation around torso major axis) is estimated by minimizing the difference between a learned texture model in a canonical
Bjelogrlic, Mina; Volery, Maxime; Fuchs, Benjamin
2018-01-01
This work presents the analysis of power transmission of a radiating field inside the human head for microwave imaging applications. For this purpose, a spherical layered model composed of dispersive biological tissues is investigated in the range of (0.5–4) GHz and is confronted to experimental ...
Structure of Vocational Interests in Serbia: Evaluation of the Spherical Model
Hedrih, Vladimir
2008-01-01
To explore the structure of vocational interests in Serbia, 1063 participants of various age, education and gender completed the Serbian version of the Personal Globe Inventory [PGI, Tracey, T. (2002). "Personal Globe Inventory: Measurement of the spherical model of interests and competence beliefs." "Journal of Vocational…
Connection between strong and weak coupling in the mean spherical model in 1 + 1 dimensions
Banks, J.L.
1980-01-01
I extend the strong-coupling expansion obtained by Srednicki, for the β-function of the mean spherical model in 1 + 1 dimensions, in the hamiltonian formulation. I use ordinary and two-point Pade approximants to extrapolate this result to weak coupling. I find a reasonably smooth connection between strong and weak coupling, and good numerical agreement with the exact solution. (orig.)
Calculation of spherical models of lead with a source of 14 MeV-neutrons
Markovskij, D.V.; Borisov, A.A.
1989-01-01
Neutron transport calculations for spherical models of lead have been done with the one-dimensional code BLANK realizing the direct Monte Carlo method in the whole range of neutron energies and they are compared with the experimental results. 6 refs, 10 figs, 3 tabs
Mean spherical model for hard ions and dipoles: Thermodynamics and correlation functions
Vericat, F.; Blum, L.
1980-01-01
The solution of the mean spherical model of a mixture of equal-size hard ions and dipoles is reinvestigated. Simple expressions for the coefficients of the Laplace transform of the pair correlation function and the other thermodynamic properties are given
Towards Relaxing the Spherical Solar Radiation Pressure Model for Accurate Orbit Predictions
Lachut, M.; Bennett, J.
2016-09-01
The well-known cannonball model has been used ubiquitously to capture the effects of atmospheric drag and solar radiation pressure on satellites and/or space debris for decades. While it lends itself naturally to spherical objects, its validity in the case of non-spherical objects has been debated heavily for years throughout the space situational awareness community. One of the leading motivations to improve orbit predictions by relaxing the spherical assumption, is the ongoing demand for more robust and reliable conjunction assessments. In this study, we explore the orbit propagation of a flat plate in a near-GEO orbit under the influence of solar radiation pressure, using a Lambertian BRDF model. Consequently, this approach will account for the spin rate and orientation of the object, which is typically determined in practice using a light curve analysis. Here, simulations will be performed which systematically reduces the spin rate to demonstrate the point at which the spherical model no longer describes the orbital elements of the spinning plate. Further understanding of this threshold would provide insight into when a higher fidelity model should be used, thus resulting in improved orbit propagations. Therefore, the work presented here is of particular interest to organizations and researchers that maintain their own catalog, and/or perform conjunction analyses.
Murata, Isao [Osaka Univ., Suita (Japan); Mori, Takamasa; Nakagawa, Masayuki; Itakura, Hirofumi
1996-03-01
The method to calculate neutronics parameters of a core composed of randomly distributed spherical fuels has been developed based on a statistical geometry model with a continuous energy Monte Carlo method. This method was implemented in a general purpose Monte Carlo code MCNP, and a new code MCNP-CFP had been developed. This paper describes the model and method how to use it and the validation results. In the Monte Carlo calculation, the location of a spherical fuel is sampled probabilistically along the particle flight path from the spatial probability distribution of spherical fuels, called nearest neighbor distribution (NND). This sampling method was validated through the following two comparisons: (1) Calculations of inventory of coated fuel particles (CFPs) in a fuel compact by both track length estimator and direct evaluation method, and (2) Criticality calculations for ordered packed geometries. This method was also confined by applying to an analysis of the critical assembly experiment at VHTRC. The method established in the present study is quite unique so as to a probabilistic model of the geometry with a great number of spherical fuels distributed randomly. Realizing the speed-up by vector or parallel computations in future, it is expected to be widely used in calculation of a nuclear reactor core, especially HTGR cores. (author).
Song, Youngjin; Schwenz, Richard
2013-01-01
This article describes an inquiry-based lesson to deepen preservice teachers' understanding of the spherical Earth model using the Global Positioning System. The lesson was designed with four learning goals: (1) to increase preservice teachers' conceptual knowledge of the spherical Earth model; (2) to develop preservice teachers'…
Mohammad Asif Salam
2017-11-01
Full Text Available The purpose of this study is to analyze different types of supply chain uncertainties and suggest strategies to deal with unexpected contingencies to deliver superior operational performance (OP using symmetrical and asymmetrical modeling approaches. The data were collected through a survey given to 146 supply chain managers within the fast moving consumer goods industry in Thailand. Symmetrical modeling is applied via partial least squares structural equation modeling (PLS-SEM in order to assess the theoretical relationships among the latent variables, while asymmetrical modeling is applied via fuzzy set qualitative comparative analysis (fsQCA to emphasize their combinatory causal relation. The empirical results support the theory by highlighting the mediating effect of supply chain strategy (SCS in the relation between supply chain uncertainty (SCU and firms’ OP and, hence, deliver business sustainability for the firms, demonstrating that the choice of SCS should not be an “either-or” decision. This research contributes by providing an illustration of a PLS-SEM and fsQCA based estimation for the rapidly emerging field of sustainable supply chain management. This study provides empirical support for resource dependence theory (RDT in explaining the relation between SCU and SCS, which leads to sustainable OP. From a methodological standpoint, this study also illustrates predictive validation testing of models using holdout samples and testing for causal asymmetry.
Connecting Dirac and Majorana neutrino mass matrices in the minimal left-right symmetric model.
Nemevšek, Miha; Senjanović, Goran; Tello, Vladimir
2013-04-12
Probing the origin of neutrino mass by disentangling the seesaw mechanism is one of the central issues of particle physics. We address it in the minimal left-right symmetric model and show how the knowledge of light and heavy neutrino masses and mixings suffices to determine their Dirac Yukawa couplings. This in turn allows one to make predictions for a number of high and low energy phenomena, such as decays of heavy neutrinos, neutrinoless double beta decay, electric dipole moments of charged leptons, and neutrino transition moments. We also discuss a way of reconstructing the neutrino Dirac Yukawa couplings at colliders such as the LHC.
Guang-Ming Zhang; Lu Yu
1998-10-01
We consider the symmetric single-impurity Anderson model in the presence of pairing fluctuations. In the isotropic limit, the degrees of freedom of the local impurity are separated into hybridizing and non-hybridizing modes. The self-energy for the hybridizing modes can be obtained exactly, leading to two subbands centered at ±U/2. For the non-hybridizing modes, the second order perturbation yields a singular resonance of the marginal Fermi liquid form. By multiplicative renormalization, the self-energy is derived exactly, showing the resonance is pinned at the Fermi level, while its strength is weakened by renormalization. (author)
Symmetric Anderson impurity model: Magnetic susceptibility, specific heat and Wilson ratio
Zalom, Peter; Pokorný, Vladislav; Janiš, Václav
2018-05-01
We extend the spin-polarized effective-interaction approximation of the parquet renormalization scheme from Refs. [1,2] applied on the symmetric Anderson model by adding the low-temperature asymptotics of the total energy and the specific heat. We calculate numerically the Wilson ratio and determine analytically its asymptotic value in the strong-coupling limit. We demonstrate in this way that the exponentially small Kondo scale from the strong-coupling regime emerges in qualitatively the same way in the spectral function, magnetic susceptibility and the specific heat.
Right-handed quark mixings in minimal left-right symmetric model with general CP violation
Zhang Yue; Ji Xiangdong; An Haipeng; Mohapatra, R. N.
2007-01-01
We solve systematically for the right-handed quark mixings in the minimal left-right symmetric model which generally has both explicit and spontaneous CP violations. The leading-order result has the same hierarchical structure as the left-handed Cabibbo-Kobayashi-Maskawa mixing, but with additional CP phases originating from a spontaneous CP-violating phase in the Higgs vacuum expectation values. We explore the phenomenology entailed by the new right-handed mixing matrix, particularly the bounds on the mass of W R and the CP phase of the Higgs vacuum expectation values
Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts
Rossikhin, Yury A.; Shitikova, Marina V.
2013-06-01
The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.
An analytical drain current model for symmetric double-gate MOSFETs
Fei Yu
2018-04-01
Full Text Available An analytical surface-potential-based drain current model of symmetric double-gate (sDG MOSFETs is described as a SPICE compatible model in this paper. The continuous surface and central potentials from the accumulation to the strong inversion regions are solved from the 1-D Poisson’s equation in sDG MOSFETs. Furthermore, the drain current is derived from the charge sheet model as a function of the surface potential. Over a wide range of terminal voltages, doping concentrations, and device geometries, the surface potential calculation scheme and drain current model are verified by solving the 1-D Poisson’s equation based on the least square method and using the Silvaco Atlas simulation results and experimental data, respectively. Such a model can be adopted as a useful platform to develop the circuit simulator and provide the clear understanding of sDG MOSFET device physics.
An analytical drain current model for symmetric double-gate MOSFETs
Yu, Fei; Huang, Gongyi; Lin, Wei; Xu, Chuanzhong
2018-04-01
An analytical surface-potential-based drain current model of symmetric double-gate (sDG) MOSFETs is described as a SPICE compatible model in this paper. The continuous surface and central potentials from the accumulation to the strong inversion regions are solved from the 1-D Poisson's equation in sDG MOSFETs. Furthermore, the drain current is derived from the charge sheet model as a function of the surface potential. Over a wide range of terminal voltages, doping concentrations, and device geometries, the surface potential calculation scheme and drain current model are verified by solving the 1-D Poisson's equation based on the least square method and using the Silvaco Atlas simulation results and experimental data, respectively. Such a model can be adopted as a useful platform to develop the circuit simulator and provide the clear understanding of sDG MOSFET device physics.
An Angular Leakage Correction for Modeling a Hemisphere, Using One-Dimensional Spherical Coordinates
Schwinkendorf, K.N.; Eberle, C.S.
2003-01-01
A radially dependent, angular leakage correction was applied to a one-dimensional, multigroup neutron diffusion theory computer code to accurately model hemispherical geometry. This method allows the analyst to model hemispherical geometry, important in nuclear criticality safety analyses, with one-dimensional computer codes, which execute very quickly. Rapid turnaround times for scoping studies thus may be realized. This method uses an approach analogous to an axial leakage correction in a one-dimensional cylinder calculation. The two-dimensional Laplace operator was preserved in spherical geometry using a leakage correction proportional to 1/r 2 , which was folded into the one-dimensional spherical calculation on a mesh-by-mesh basis. Hemispherical geometry is of interest to criticality safety because of its similarity to piles of spilled fissile material and accumulations of fissile material in process containers. A hemisphere also provides a more realistic calculational model for spilled fissile material than does a sphere
Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix
Skrypnyk, Taras
2017-05-01
We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3)⊗ so(3)-valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the "separating functions" B( u) and A( u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler's top, Steklov-Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and "spin" generalization of Steklov-Lyapunov model.
SIMPLE MODELS OF THREE COUPLED PT -SYMMETRIC WAVE GUIDES ALLOWING FOR THIRD-ORDER EXCEPTIONAL POINTS
Jan Schnabel
2017-12-01
Full Text Available We study theoretical models of three coupled wave guides with a PT-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3 in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.
Hati, Chandan; Patra, Sudhanwa; Pritimita, Prativa; Sarkar, Utpal
2018-03-01
In this review, we present several variants of left-right symmetric models in the context of neutrino masses and leptogenesis. In particular, we discuss various low scale seesaw mechanisms like linear seesaw, inverse seesaw, extended seesaw and their implications to lepton number violating process like neutrinoless double beta decay. We also visit an alternative framework of left-right models with the inclusion of vector-like fermions to analyze the aspects of universal seesaw. The symmetry breaking of left-right symmetric model around few TeV scale predicts the existence of massive right-handed gauge bosons W_R and Z_R which might be detected at the LHC in near future. If such signals are detected at the LHC that can have severe implications for leptogenesis, a mechanism to explain the observed baryon asymmetry of the Universe. We review the implications of TeV scale left-right symmetry breaking for leptogenesis.
Development of Spherical Near Field Model for Geological Radioactive Waste Repository
Kim, S. Y.; Lee, K. J.; Chang, S. H. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Lee, K. J.; Chang, S. H. [Khalifa Univ. of Science/Technology and Research, Abu Dhabi (United Arab Emirates)
2012-03-15
Modeling for geological radioactive waste repository can be divided into 3 parts. They are near field modeling related to engineered barrier, far field modeling related to natural barrier and biosphere modeling. In order to make the general application for safety assessment of geological waste repository, spherical geometry near field model has been developed. This model can be used quite extensively when users calculate equivalent spherical geometry for specific engineered barrier like equivalent waste radius, equivalent barrier radius and etc. Only diffusion was considered for general purpose but advection part can be updated. Goldsim and Goldsim Radionuclide Transport (RT) module were chosen and used as developing tool for the flexible modeling. Developer can freely make their own model with developer friendly graphic interface by using Goldsim. Furthermore, model with user friendly graphic interface can be developed by using Goldsim Dashboard Authoring module. The model has been validated by comparing the result with that of another model, inserting similar inputs and conditions. The model has been proved to be reasonably operating from the comparison result by validation process. Cylindrical model can be developed as a further work based on the knowledge and experience from this research.
Development of Spherical Near Field Model for Geological Radioactive Waste Repository
Kim, S. Y.; Lee, K. J.; Chang, S. H.; Lee, K. J.; Chang, S. H.
2012-01-01
Modeling for geological radioactive waste repository can be divided into 3 parts. They are near field modeling related to engineered barrier, far field modeling related to natural barrier and biosphere modeling. In order to make the general application for safety assessment of geological waste repository, spherical geometry near field model has been developed. This model can be used quite extensively when users calculate equivalent spherical geometry for specific engineered barrier like equivalent waste radius, equivalent barrier radius and etc. Only diffusion was considered for general purpose but advection part can be updated. Goldsim and Goldsim Radionuclide Transport (RT) module were chosen and used as developing tool for the flexible modeling. Developer can freely make their own model with developer friendly graphic interface by using Goldsim. Furthermore, model with user friendly graphic interface can be developed by using Goldsim Dashboard Authoring module. The model has been validated by comparing the result with that of another model, inserting similar inputs and conditions. The model has been proved to be reasonably operating from the comparison result by validation process. Cylindrical model can be developed as a further work based on the knowledge and experience from this research
The Realistic Versus the Spherical Head Model in EEG Dipole Source Analysis in the Presence of Noise
Vanrumste, Bart
2001-01-01
.... For 27 electrodes, an EEG epoch of one time sample and spatially white Gaussian noise we found that the importance of the realistic head model over the spherical head model reduces by increasing the noise level.
Proton-neutron sdg boson model and spherical-deformed phase transition
Otsuka, Takaharu; Sugita, Michiaki
1988-01-01
The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing + quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects. (orig.)
Proton-neutron sdg boson model and spherical-deformed phase transition
Otsuka, Takaharu; Sugita, Michiaki
1988-12-01
The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.
Proton-neutron sdg boson model and spherical-deformed phase transition
Otsuka, Takaharu; Sugita, Michiaki
1988-12-15
The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing + quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.
Method to determine the optimal constitutive model from spherical indentation tests
Tairui Zhang
2018-03-01
Full Text Available The limitation of current indentation theories was investigated and a method to determine the optimal constitutive model through spherical indentation tests was proposed. Two constitutive models, the Power-law and the Linear-law, were used in Finite Element (FE calculations, and then a set of indentation governing equations was established for each model. The load-depth data from the normal indentation depth was used to fit the best parameters in each constitutive model while the data from the further loading part was compared with those from FE calculations, and the model that better predicted the further deformation was considered the optimal one. Moreover, a Yang’s modulus calculation model which took the previous plastic deformation and the phenomenon of pile-up (or sink-in into consideration was also proposed to revise the original Sneddon-Pharr-Oliver model. The indentation results on six materials, 304, 321, SA508, SA533, 15CrMoR, and Fv520B, were compared with tensile ones, which validated the reliability of the revised E calculation model and the optimal constitutive model determination method in this study. Keywords: Optimal constitutive model, Spherical indentation test, Finite Element calculations, Yang’s modulus
Fujii, Akira; Kluemper, Andreas
1999-01-01
We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation
Hubbard physics in the symmetric half-filled periodic anderson-hubbard model
Hagymási, I.; Itai, K.; Sólyom, J.
2013-05-01
Two very different methods — exact diagonalization on finite chains and a variational method — are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites ( gn d ) as a function of various parameters. In the absence of on-site Coulomb interaction ( U f ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite U f , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ( U {/d c }), which depends on U f and V.
Local lubrication model for spherical particles within incompressible Navier-Stokes flows
Lambert, B.; Weynans, L.; Bergmann, M.
2018-03-01
The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.
Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid
Smit GJF
2010-11-01
Full Text Available the necessity to model the discrete nature of sep- cite this article in press as: G.J.F. Smit et al., Two-phase flow modeling for low concentration spherical particle motion through a ian fluid, Appl. Math. Comput. (2010), doi:10.1016/j.amc.2010.07.055 2... and Ribberin large-scale and long term morphologica Please cite this article in press as: G.J.F. Smit Newtonian fluid, Appl. Math. Comput. (2010), � 2010 Elsevier Inc. All rights reserved. modeling of multiphase flow has increasingly become the subject...
Symmetry-dictated trucation: Solutions of the spherical shell model for heavy nuclei
Guidry, M.W.
1992-01-01
Principles of dynamical symmetry are used to simplify the spherical shell model. The resulting symmetry-dictated truncation leads to dynamical symmetry solutions that are often in quantitative agreement with a variety of observables. Numerical calculations, including terms that break the dynamical symmetries, are shown that correspond to shell model calculations for heavy deformed nuclei. The effective residual interaction is simple, well-behaved, and can be determined from basic observables. With this approach, we intend to apply the shell model in systematic fashion to all nuclei. The implications for nuclear structure far from stability and for nuclear masses and other quantities of interest in astrophysics are discussed
Local lubrication model for spherical particles within incompressible Navier-Stokes flows.
Lambert, B; Weynans, L; Bergmann, M
2018-03-01
The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.
Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case
Hojbota, C I; Toşa, V; Mercea, P V
2013-01-01
We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food
Fundamentals of spherical array processing
Rafaely, Boaz
2015-01-01
This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, includi...
Deflection modeling of permanent magnet spherical chains in the presence of external magnetic fields
O' Donoghue, Kilian, E-mail: kilianod@rennes.ucc.ie; Cantillon-Murphy, Pádraig, E-mail: padraig@alum.mit.edu
2013-10-15
This work examines the interaction of permanently magnetised spheres in the presence of external magnetic fields at the millimetre scale. Static chain formation and deflection models are described for N spheres in the presence of an external magnetic field. Analytical models are presented for the two sphere case by neglecting the effects of magnetocrystalline anisotropy while details of a numerical approach to solve a chain of N spheres are shown. The model is experimentally validated using chain deflections in 4.5 mm diameter spheres in groups of 2, 3 and 4 magnets in the presence of uniform magnetic fields, neglecting gravitational effects, with good agreement between the theoretical model and experimental results. This spherical chain structure could be used as an end effector for catheters as a deflection mechanism for magnetic guidance. The spherical point contacts result in large deflections for navigation around tight corners in endoluminal minimally invasive clinical applications. - Highlights: • We model the interaction of magnetic spheres with uniform external fields. • Analytical models are presented for two spheres interacting with an external field. • Numerical methods are used to model the interaction of N spheres in chain formations. • These models are tested experimentally. • We report good agreement between experiment and theory.
Deflection modeling of permanent magnet spherical chains in the presence of external magnetic fields
O'Donoghue, Kilian; Cantillon-Murphy, Pádraig
2013-01-01
This work examines the interaction of permanently magnetised spheres in the presence of external magnetic fields at the millimetre scale. Static chain formation and deflection models are described for N spheres in the presence of an external magnetic field. Analytical models are presented for the two sphere case by neglecting the effects of magnetocrystalline anisotropy while details of a numerical approach to solve a chain of N spheres are shown. The model is experimentally validated using chain deflections in 4.5 mm diameter spheres in groups of 2, 3 and 4 magnets in the presence of uniform magnetic fields, neglecting gravitational effects, with good agreement between the theoretical model and experimental results. This spherical chain structure could be used as an end effector for catheters as a deflection mechanism for magnetic guidance. The spherical point contacts result in large deflections for navigation around tight corners in endoluminal minimally invasive clinical applications. - Highlights: • We model the interaction of magnetic spheres with uniform external fields. • Analytical models are presented for two spheres interacting with an external field. • Numerical methods are used to model the interaction of N spheres in chain formations. • These models are tested experimentally. • We report good agreement between experiment and theory
Spherical Slepian as a new method for ionospheric modeling in arctic region
Etemadfard, Hossein; Hossainali, Masoud Mashhadi
2016-03-01
From the perspective of the physical, chemical and biological balance in the world, the Arctic has gradually turned into an important region opening ways for new researchers and scientific expeditions. In other words, various researches have been funded in order to study this frozen frontier in details. The current study can be seen in the same milieu where researchers intend to propose a set of new base functions for modeling ionospheric in the Arctic. As such, to optimize the Spherical Harmonic (SH) functions, the spatio-spectral concentration is applied here using the Slepian theory that was developed by Simons. For modeling the ionosphere, six International GNSS Service (IGS) stations located in the northern polar region were taken into account. Two other stations were left out for assessing the accuracy of the proposed model. The adopted GPS data starts at DOY 69 (Day of Year) and ends at DOY 83 (totally 15 successive days) in 2013. Three Spherical Slepian models respectively with the maximal degrees of K=15, 20 & 25 were used. Based on the results, K=15 is the optimum degree for the proposed model. The accuracy and precision of the Slepian model are about 0.1 and 0.05 TECU, respectively (TEC Unit=1016 electron/m2). To understand the advantage of this model, it is compared with polynomial and trigonometric series which are developed using the same set of measurements. The accuracy and precision of trigonometric and polynomial models are at least 4 times worse than the Slepian one.
Waizmann, Jean-Claude
2010-11-24
One of the main objectives of the PLANCK mission is to perform a full-sky cluster survey based on the Sunyaev-Zel'dovich (SZ) effect, which leads to the question of how such a survey would be affected by cosmological models with a different history of structure formation than LCDM. To answer this question, I developed a fast semi-analytic approach for simulating full-sky maps of the Compton-y parameter, ready to be fed into a realistic simulation pipeline. I also implemented a filter and detection pipeline based on spherical multi-frequency matched filters, that was used to study the expected SZ cluster sample of PLANCK. It turned out that realistic samples will comprise 1000 clusters at low rate of contamination, significantly lower than originally anticipated. Driven by wrong estimates of the impact of early dark energy models on structure formation, we studied the spherical collapse model in dark energy model, finding that models with varying equation-of-state have a negligible impact on the structure formation. Yet, the different expansion history for the different models can be detected via volume effects, when counting objects in a known volume. Furthermore, it turned out that the different expansion history strongly affects the angular SZ power spectra for the various models, making them an interesting tool to distinguish and constrain alternative cosmologies. (orig.)
Waizmann, Jean-Claude
2010-01-01
One of the main objectives of the PLANCK mission is to perform a full-sky cluster survey based on the Sunyaev-Zel'dovich (SZ) effect, which leads to the question of how such a survey would be affected by cosmological models with a different history of structure formation than LCDM. To answer this question, I developed a fast semi-analytic approach for simulating full-sky maps of the Compton-y parameter, ready to be fed into a realistic simulation pipeline. I also implemented a filter and detection pipeline based on spherical multi-frequency matched filters, that was used to study the expected SZ cluster sample of PLANCK. It turned out that realistic samples will comprise 1000 clusters at low rate of contamination, significantly lower than originally anticipated. Driven by wrong estimates of the impact of early dark energy models on structure formation, we studied the spherical collapse model in dark energy model, finding that models with varying equation-of-state have a negligible impact on the structure formation. Yet, the different expansion history for the different models can be detected via volume effects, when counting objects in a known volume. Furthermore, it turned out that the different expansion history strongly affects the angular SZ power spectra for the various models, making them an interesting tool to distinguish and constrain alternative cosmologies. (orig.)
Vibration test of spherical shell structure and replacing method into mathematical model
Takayanagi, M.; Suzuki, S.; Okamura, T.; Haas, E.E.; Krutzik, N.J.
1989-01-01
To verify the beam-type and oval-type vibratory characteristics of a spherical shell structure, two test specimens were made and vibration tests were carried out. Results of these tests are compared with results of detailed analyses using 3-D FEM and 2-D axisymmetric FEM models. The analytical results of overall vibratory characteristics are in good agreement with the test results, has been found that the effect of the attached mass should be considered in evaluating local vibration. The replacing method into equivalent beam model is proposed
Modeling and Design of a Nano Scale CMOS Inverter for Symmetric Switching Characteristics
Joyjit Mukhopadhyay
2012-01-01
Full Text Available This paper presents a technique for the modeling and design of a nano scale CMOS inverter circuit using artificial neural network and particle swarm optimization algorithm such that the switching characteristics of the circuit is symmetric, that is, has nearly equal rise and fall time and equal output high-to-low and low-to-high propagation delay. The channel width of the transistors and the load capacitor value are taken as design parameters. The designed circuit has been implemented at the transistor-level and simulated using TSPICE for 45 nm process technology. The PSO-generated results have been compared with SPICE results. A very good accuracy has been achieved. In addition, the advantage of the present approach over an existing approach for the same purpose has been demonstrated through simulation results.
Rational solitons in the parity-time-symmetric nonlocal nonlinear Schrödinger model
Li Min; Xu Tao; Meng Dexin
2016-01-01
In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as |z| → ∞. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions. (author)
Design and Modeling of Symmetric Three Branch Polymer Planar Optical Power Dividers
V. Prajzler
2013-04-01
Full Text Available Two types of polymer-based three-branch symmetric planar optical power dividers (splitters were designed, multimode interference (MMI splitter and triangular shape-spacing splitter. By means of modeling the real structures were simulated as made of Epoxy Novolak Resin on silicon substrate, with silica buffer layer and polymethylmethacrylate as protection cover layer. The design of polymer waveguide structure was done by Beam Propagation Method. After comparing properties of both types of the splitters we have demonstrated that our new polymer based triangular shaped splitter can work simultaneously in broader spectrum, the only condition would be that the waveguides are single-mode guiding. It practically means that, what concerns communication wavelengths, it can on principle simultaneously operate at two mainly used wavelengths, 1310 and 1550 nm.
A see-saw scenario of an $A_4$ flavour symmetric standard model
Dinh, Dinh Nguyen; Văn, Phi Quang; Vân, Nguyen Thi Hông
2016-01-01
A see-saw scenario for an $A_4$ flavour symmetric standard model is presented. As before, the see-saw mechanism can be realized in several models of different types depending on different ways of neutrino mass generation corresponding to the introduction of new fields with different symmetry structures. In the present paper, a general desription of all these see-saw types is made with a more detailed investigation on type-I models. As within the original see-saw mechanism, the symmetry structure of the standard model fields decides the number and the symmetry structure of the new fields. In a model considered here, the scalar sector consists of three standard-model-Higgs-like iso-doublets ($SU_L(2)$-doublets) forming an $A_4$ triplet. The latter is a superposition of three mass-eigen states, one of which could be identified with the recently discovered Higgs boson. A possible relation to the still-deliberated 750 GeV diphoton resonance at the 13 TeV LHC collisions is also discussed. In the lepton sector, the ...
Comparative analysis of Bouc–Wen and Jiles–Atherton models under symmetric excitations
Laudani, Antonino, E-mail: alaudani@uniroma3.it; Fulginei, Francesco Riganti; Salvini, Alessandro
2014-02-15
The aim of the present paper is to validate the Bouc–Wen (BW) hysteresis model when it is applied to predict dynamic ferromagnetic loops. Indeed, although the Bouc–Wen model has had an increasing interest in last few years, it is usually adopted in mechanical and structural systems and very rarely for magnetic applications. Thus, for addressing this goal the Bouc–Wen model is compared with the dynamic Jiles–Atherton model that, instead, was ideated exactly for simulating magnetic hysteresis. The comparative analysis has involved saturated and symmetric hysteresis loops in ferromagnetic materials. In addition in order to identify the Bouc–Wen parameters a very effective recent heuristic, called Metric-Topological and Evolutionary Optimization (MeTEO) has been utilized. It is based on a hybridization of three meta-heuristics: the Flock-of-Starlings Optimization, the Particle Swarm Optimization and the Bacterial Chemotaxis Algorithm. Thanks to the specific properties of these heuristic, MeTEO allow us to achieve effective identification of such kind of models. Several hysteresis loops have been utilized for final validation tests with the aim to investigate if the BW model can follow the different hysteresis behaviors of both static (quasi-static) and dynamic cases.
A.R. Ansari; B. Hossain; B. Koren (Barry); G.I. Shishkin (Gregori)
2007-01-01
textabstractWe investigate the model problem of flow of a viscous incompressible fluid past a symmetric curved surface when the flow is parallel to its axis. This problem is known to exhibit boundary layers. Also the problem does not have solutions in closed form, it is modelled by boundary-layer
Rapid automated superposition of shapes and macromolecular models using spherical harmonics.
Konarev, Petr V; Petoukhov, Maxim V; Svergun, Dmitri I
2016-06-01
A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented ( SUPALM ). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models ( e.g. of protein-nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented in SUPCOMB by Kozin & Svergun [ J. Appl. Cryst. (2001 ▸), 34 , 33-41]. The utility of the new method is demonstrated in a number of test cases and compared with the results of SUPCOMB . The spherical harmonics algorithm is best suited for low-resolution shape models, e.g . those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods.
Numerical modeling of axi-symmetrical cold forging process by ``Pseudo Inverse Approach''
Halouani, A.; Li, Y. M.; Abbes, B.; Guo, Y. Q.
2011-05-01
The incremental approach is widely used for the forging process modeling, it gives good strain and stress estimation, but it is time consuming. A fast Inverse Approach (IA) has been developed for the axi-symmetric cold forging modeling [1-2]. This approach exploits maximum the knowledge of the final part's shape and the assumptions of proportional loading and simplified tool actions make the IA simulation very fast. The IA is proved very useful for the tool design and optimization because of its rapidity and good strain estimation. However, the assumptions mentioned above cannot provide good stress estimation because of neglecting the loading history. A new approach called "Pseudo Inverse Approach" (PIA) was proposed by Batoz, Guo et al.. [3] for the sheet forming modeling, which keeps the IA's advantages but gives good stress estimation by taking into consideration the loading history. Our aim is to adapt the PIA for the cold forging modeling in this paper. The main developments in PIA are resumed as follows: A few intermediate configurations are generated for the given tools' positions to consider the deformation history; the strain increment is calculated by the inverse method between the previous and actual configurations. An incremental algorithm of the plastic integration is used in PIA instead of the total constitutive law used in the IA. An example is used to show the effectiveness and limitations of the PIA for the cold forging process modeling.
ABAREX -- A neutron spherical optical-statistical-model code -- A user`s manual
Smith, A.B. [ed.; Lawson, R.D.
1998-06-01
The contemporary version of the neutron spherical optical-statistical-model code ABAREX is summarized with the objective of providing detailed operational guidance for the user. The physical concepts involved are very briefly outlined. The code is described in some detail and a number of explicit examples are given. With this document one should very quickly become fluent with the use of ABAREX. While the code has operated on a number of computing systems, this version is specifically tailored for the VAX/VMS work station and/or the IBM-compatible personal computer.
Some properties of the statistical models of the spherical Friedman world
Rumyantseva, E.N.
1981-01-01
Considered are some properties of the statistical model of the spherical Friedman world filled with quantum gas of massless particles the spin of which can be equal to 0, 1/2, 1. Obtained are approximate expressions for a number of particles of Fermi- and Bose-gas and for the radius of the world taking into account mainly the dependence on the spin. The dependence of the number of particles on the radius of the world and temperature of the gas is illustrated [ru
Surface critical behavior and scaling functions for the three-dimensional mean spherical model
Amin, Magdy E. [Mathematics Department, Ar' ar Teacher College, Kingdom of Saudi Arabia (Saudi Arabia) and Mathematics Department, Faculty of Science, Minia University (Egypt)]. E-mail: aminmagdy@yahoo.com
2006-10-09
The d-dimensional mean spherical model on a fully finite L{sup d} simple cubic lattice with Neumann-Dirichlet boundary conditions is considered in the presence of a surface external fields acting at the surfaces bounding the system. Exact calculations are evaluated for the fully finite system and in the case of a film geometry Lx{approx}{sup d-1}. Critical finite-size scaling functions both for the specific heat and the mean-square magnetization are derived and investigated close to and below the bulk critical temperature K{sub c}.
Quasiparticle--phonon model of the nucleus. V. Odd spherical nuclei
Vdovin, A.I.; Voronov, V.V.; Solov'ev, V.G.; Stoyanov, C.
1985-01-01
The formalism of the quasiparticle--phonon model of the nucleus for odd spherical nuclei is presented. The exact commutation relations of the quasiparticle and phonon operators together with the anharmonic corrections for the phonon excitations are taken into account in the derivation of equations for the energies and structure coefficients of the wave functions of excited states, which include quasiparticle--phonon and quasiparticle--two-phonon components. The influence of various physical effects and of the dimension of the phonon basis on the fragmentation of the single-quasiparticle and quasiparticle-phonon states is investigated
A calculation model for primary intensity distributions from cylindrically symmetric x-ray lenses
Hristov, Dimitre; Maltz, Jonathan
2008-01-01
A calculation model for the quantitative prediction of primary intensity fluence distributions obtained by the Bragg diffraction focusing of kilovoltage radiation by cylindrical x-ray lenses is presented. The mathematical formalism describes primary intensity distributions from cylindrically-symmetric x-ray lenses, with a planar isotropic radiation source located in a plane perpendicular to the lens axis. The presence of attenuating medium inserted between the lens and the lens focus is accounted for by energy-dependent attenuation. The influence of radiation scattered within the media is ignored. Intensity patterns are modeled under the assumption that photons that are not interacting with the lens are blocked out at any point of interest. The main characteristics of the proposed calculation procedure are that (i) the application of vector formalism allows universal treatment of all cylindrical lenses without the need of explicit geometric constructs; (ii) intensity distributions resulting from x-ray diffraction are described by a 3D generalization of the mosaic spread concept; (iii) the calculation model can be immediately coupled to x-ray diffraction simulation packages such as XOP and Shadow. Numerical simulations based on this model are to facilitate the design of focused orthovoltage treatment (FOT) systems employing cylindrical x-ray lenses, by providing insight about the influence of the x-ray source and lens parameters on quantities of dosimetric interest to radiation therapy
Ramond, P.
1993-01-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures
Universal seesaw and 0νββ in new 3331 left-right symmetric model
Debasish Borah
2017-08-01
Full Text Available We consider a class of left-right symmetric model with enlarged gauge group SU(3c×SU(3L×SU(3R×U(1X without having scalar bitriplet. In the absence of scalar bitriplet, there is no Dirac mass term for fermions including usual quarks and leptons. We introduce new isosinglet vector-like fermions so that all the fermions get their masses through a universal seesaw mechanism. We extend our discussion to neutrino mass and its implications in neutrinoless double beta decay (0νββ. We show that for TeV scale SU(3R gauge bosons, the heavy-light neutrino mixing contributes dominantly to 0νββ that can be observed at ongoing experiments. The new physics contributions arising from purely left-handed currents via exchange of keV scale right-handed neutrinos and the so called mixed helicity λ-diagram can saturate the KamLANDZen bound. We show that the right handed neutrinos in this model can have mass in the sub keV range and can be long lived compared to the age of the Universe. The contributions of these right handed neutrinos to flavour physics observables like μ→eγ and muon g−2 is also discussed. Towards the end we also comment on different possible symmetry breaking patterns of this enlarged gauge symmetry to that of the standard model.
Liu, Xiang; Makeyev, Oleksandr; Besio, Walter
2011-01-01
We have simulated a four-layer concentric spherical head model. We calculated the spline and tripolar Laplacian estimates and compared them to the analytical Laplacian on the spherical surface. In the simulations we used five different dipole groups and two electrode configurations. The comparison shows that the tripolar Laplacian has higher correlation coefficient to the analytical Laplacian in the electrode configurations tested (19, standard 10/20 locations and 64 electrodes).
Modeling of the rough spherical nanoparticles manipulation on a substrate based on the AFM nanorobot
Zakeri, M.; Faraji, J.
2014-12-01
In this paper, dynamic behavior of the rough spherical micro/nanoparticles during pulling/pushing on the flat substrate has been investigated and analyzed. For this purpose, at first, two hexagonal roughness models (George and Cooper) were studied and then evaluations for adhesion force were determined for rough particle manipulation on flat substrate. These two models were then changed by using of the Rabinovich theory. Evaluations were determined for contact adhesion force between rough particle and flat substrate; depth of penetration evaluations were determined by the Johnson-Kendall-Roberts contact mechanic theory and the Schwartz method and according to Cooper and George roughness models. Then, the novel contact theory was used to determine a dynamic model for rough micro/nanoparticle manipulation on flat substrate. Finally, simulation of particle dynamic behavior was implemented during pushing of rough spherical gold particles with radii of 50, 150, 400, 600, and 1,000 nm. Results derived from simulations of particles with several rates of roughness on flat substrate indicated that compared to results for flat particles, inherent roughness on particles might reduce the rate of critical force needed for sliding and rolling given particles. Given a fixed radius for roughness value and increased roughness height, evaluations for sliding and rolling critical forces showed greater reduction. Alternately, the rate of critical force was shown to reduce relative to an increased roughness radius. With respect to both models, based on the George roughness model, the predicted rate of adhesion force was greater than that determined in the Cooper roughness model, and as a result, the predicted rate of critical force based on the George roughness model was closer to the critical force value of flat particle.
What to expect from dynamical modelling of galactic haloes - II. The spherical Jeans equation
Wang, Wenting; Han, Jiaxin; Cole, Shaun; More, Surhud; Frenk, Carlos; Schaller, Matthieu
2018-06-01
The spherical Jeans equation (SJE) is widely used in dynamical modelling of the Milky Way (MW) halo potential. We use haloes and galaxies from the cosmological Millennium-II simulation and hydrodynamical APOSTLE (A Project of Simulations of The Local Environment) simulations to investigate the performance of the SJE in recovering the underlying mass profiles of MW mass haloes. The best-fitting halo mass and concentration parameters scatter by 25 per cent and 40 per cent around their input values, respectively, when dark matter particles are used as tracers. This scatter becomes as large as a factor of 3 when using star particles instead. This is significantly larger than the estimated statistical uncertainty associated with the use of the SJE. The existence of correlated phase-space structures that violate the steady-state assumption of the SJE as well as non-spherical geometries is the principal source of the scatter. Binary haloes show larger scatter because they are more aspherical in shape and have a more perturbed dynamical state. Our results confirm that the number of independent phase-space structures sets an intrinsic limiting precision on dynamical inferences based on the steady-state assumption. Modelling with a radius-independent velocity anisotropy, or using tracers within a limited outer radius, result in significantly larger scatter, but the ensemble-averaged measurement over the whole halo sample is approximately unbiased.
Mathematical Modeling and Kinematics Analysis of Double Spherical Shell Rotary Docking Skirt
Gong Haixia
2017-01-01
Full Text Available In order to solve the problem of large trim and heel angles of the wrecked submarine, the double spherical shell rotating docking skirt is studied. According to the working principle of the rotating docking skirt, and the fixed skirt, the directional skirt, the angle skirt are simplified as the connecting rod. Therefore, the posture equation and kinematics model of the docking skirt are deduced, and according to the kinematics model, the angle of rotation of the directional skirt and the angle skirt is obtained when the wrecked submarine is in different trim and heel angles. Through the directional skirt and angle skirt with the matching rotation can make docking skirt interface in the 0°~2γ range within the rotation, to complete the docking skirt and the wrecked submarine docking. The MATLAB software is used to visualize the rotation angle of fixed skirt and directional skirt, which lays a good foundation for the development of the control of the double spherical shell rotating docking skirt in future.
Aleman, S. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Hamm, L. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Smith, F. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2007-06-27
This report discusses the expected performance of spherical Resorcinol-Formaldehyde (RF) ion exchange resin for the removal of cesium from alkaline Hanford radioactive waste. Predictions of full scale column performance in a carousel mode are made for the Hot Commissioning, Envelope B, and Subsequent Operations waste compositions under nominal operating conditions and for perturbations from the nominal. Only the loading phase of the process cycle is addressed in this report. Pertinent bench-scale column tests, kinetic experiments, and batch equilibrium experiments are used to estimate model parameters and to benchmark the ion-exchange model. The methodology and application presented in this report reflect the expected behavior of spherical RF resin manufactured at the intermediate-scale (i.e., approximately 100 gallon batch size; batch 5E-370/641). It is generally believed that scale-up to production-scale in resin manufacturing will result in similarly behaving resin batches whose chemical selectivity is unaffected while total capacity per gram of resin may vary some. As such, the full-scale facility predictions provided within this report should provide reasonable estimates of production-scale column performance.
Symmetric vectors and algebraic classification
Leibowitz, E.
1980-01-01
The concept of symmetric vector field in Riemannian manifolds, which arises in the study of relativistic cosmological models, is analyzed. Symmetric vectors are tied up with the algebraic properties of the manifold curvature. A procedure for generating a congruence of symmetric fields out of a given pair is outlined. The case of a three-dimensional manifold of constant curvature (''isotropic universe'') is studied in detail, with all its symmetric vector fields being explicitly constructed
Fathallah, F A; Marras, W S; Parnianpour, M
1999-09-01
Most biomechanical assessments of spinal loading during industrial work have focused on estimating peak spinal compressive forces under static and sagittally symmetric conditions. The main objective of this study was to explore the potential of feasibly predicting three-dimensional (3D) spinal loading in industry from various combinations of trunk kinematics, kinetics, and subject-load characteristics. The study used spinal loading, predicted by a validated electromyography-assisted model, from 11 male participants who performed a series of symmetric and asymmetric lifts. Three classes of models were developed: (a) models using workplace, subject, and trunk motion parameters as independent variables (kinematic models); (b) models using workplace, subject, and measured moments variables (kinetic models); and (c) models incorporating workplace, subject, trunk motion, and measured moments variables (combined models). The results showed that peak 3D spinal loading during symmetric and asymmetric lifting were predicted equally well using all three types of regression models. Continuous 3D loading was predicted best using the combined models. When the use of such models is infeasible, the kinematic models can provide adequate predictions. Finally, lateral shear forces (peak and continuous) were consistently underestimated using all three types of models. The study demonstrated the feasibility of predicting 3D loads on the spine under specific symmetric and asymmetric lifting tasks without the need for collecting EMG information. However, further validation and development of the models should be conducted to assess and extend their applicability to lifting conditions other than those presented in this study. Actual or potential applications of this research include exposure assessment in epidemiological studies, ergonomic intervention, and laboratory task assessment.
Perspectives for detecting lepton flavour violation in left-right symmetric models
Bonilla, Cesar [AHEP Group, Instituto de Física Corpuscular - C.S.I.C./Universitat de València,Edificio de Institutos de Paterna, C/Catedratico José Beltrán 2,E-46980 Paterna (València) (Spain); Krauss, Manuel E.; Opferkuch, Toby [Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany); Porod, Werner [Institut für Theoretische Physik und Astronomie, Universität Würzburg,Am Hubland, 97074 Würzburg (Germany)
2017-03-06
We investigate lepton flavour violation in a class of minimal left-right symmetric models where the left-right symmetry is broken by triplet scalars. In this context we present a method to consistently calculate the triplet-Yukawa couplings which takes into account the experimental data while simultaneously respecting the underlying symmetries. Analysing various scenarios, we then calculate the full set of tree-level and one-loop contributions to all radiative and three-body flavour-violating fully leptonic decays as well as μ−e conversion in nuclei. Our method illustrates how these processes depend on the underlying parameters of the theory. To that end we observe that, for many choices of the model parameters, there is a strong complementarity between the different observables. For instance, in a large part of the parameter space, lepton flavour violating τ-decays have a large enough branching ratio to be measured in upcoming experiments. Our results further show that experiments coming online in the immediate future, like Mu3e and BELLE II, or longer-term, such as PRISM/PRIME, will probe significant portions of the currently allowed parameter space.
Perspectives for detecting lepton flavour violation in left-right symmetric models
Bonilla, Cesar; Krauss, Manuel E.; Opferkuch, Toby; Porod, Werner
2017-01-01
We investigate lepton flavour violation in a class of minimal left-right symmetric models where the left-right symmetry is broken by triplet scalars. In this context we present a method to consistently calculate the triplet-Yukawa couplings which takes into account the experimental data while simultaneously respecting the underlying symmetries. Analysing various scenarios, we then calculate the full set of tree-level and one-loop contributions to all radiative and three-body flavour-violating fully leptonic decays as well as μ−e conversion in nuclei. Our method illustrates how these processes depend on the underlying parameters of the theory. To that end we observe that, for many choices of the model parameters, there is a strong complementarity between the different observables. For instance, in a large part of the parameter space, lepton flavour violating τ-decays have a large enough branching ratio to be measured in upcoming experiments. Our results further show that experiments coming online in the immediate future, like Mu3e and BELLE II, or longer-term, such as PRISM/PRIME, will probe significant portions of the currently allowed parameter space.
Non-hermitian symmetric N = 2 coset models, Poincare polynomials, and string compactification
Fuchs, J.; Schweigert, C.
1994-01-01
The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric N = 2 superconformal coset theories. Thereby these models are finally identified as well-defined modular invariant conformal field theories. As an application, the theories are used as subtheories in N = 2 tensor products with c = 9, which in turn are taken as the inner sector of heterotic superstring compactifications. All string theories of this type are classified, and the chiral ring as well as the number of massless generations and anti-generations are computed with the help of the extended Poincare polynomial. Several equivalences between a priori different non-hermitian coset theories show up; in particular there is a level-rank duality for an infinite series of coset theories based on C-type Lie algebras. Further, some general results for generic N = 2 coset theories are proven: a simple formula for the number of identification currents is found, and it is shown that the set of Ramond ground states of any N = 2 coset model is invariant under charge conjugation. (orig.)
Searching for dark matter signals in the left-right symmetric gauge model with CP symmetry
Guo Wanlei; Wu Yueliang; Zhou Yufeng
2010-01-01
We investigate the singlet scalar dark matter (DM) candidate in a left-right symmetric gauge model with two Higgs bidoublets in which the stabilization of the DM particle is induced by the discrete symmetries P and CP. According to the observed DM abundance, we predict the DM direct and indirect detection cross sections for the DM mass range from 10 to 500 GeV. We show that the DM indirect detection cross section is not sensitive to the light Higgs mixing and Yukawa couplings except for the resonance regions. The predicted spin-independent DM-nucleon elastic scattering cross section is found to be significantly dependent on the above two factors. Our results show that the future DM direct search experiments can cover the most parts of the allowed parameter space. The PAMELA antiproton data can only exclude two very narrow regions in the two Higgs bidoublets model. It is very difficult to detect the DM direct or indirect signals in the resonance regions due to the Breit-Wigner resonance effect.
Characteristic function-based semiparametric inference for skew-symmetric models
Potgieter, Cornelis J.; Genton, Marc G.
2012-01-01
testing. Two tests for a hypothesis of specific parameter values are considered, as well as a test for the hypothesis that the symmetric component has a specific parametric form. A resampling algorithm is described for practical implementation
Experimental and modeling studies of small molecule chemistry in expanding spherical flames
Santner, Jeffrey
Accurate models of flame chemistry are required in order to predict emissions and flame properties, such that clean, efficient engines can be designed more easily. There are three primary methods used to improve such combustion chemistry models - theoretical reaction rate calculations, elementary reaction rate experiments, and combustion system experiments. This work contributes to model improvement through the third method - measurements and analysis of the laminar burning velocity at constraining conditions. Modern combustion systems operate at high pressure with strong exhaust gas dilution in order to improve efficiency and reduce emissions. Additionally, flames under these conditions are sensitized to elementary reaction rates such that measurements constrain modeling efforts. Measurement conditions of the present work operate within this intersection between applications and fundamental science. Experiments utilize a new pressure-release, heated spherical combustion chamber with a variety of fuels (high hydrogen content fuels, formaldehyde (via 1,3,5-trioxane), and C2 fuels) at pressures from 0.5--25 atm, often with dilution by water vapor or carbon dioxide to flame temperatures below 2000 K. The constraining ability of these measurements depends on their uncertainty. Thus, the present work includes a novel analytical estimate of the effects of thermal radiative heat loss on burning velocity measurements in spherical flames. For 1,3,5-trioxane experiments, global measurements are sufficiently sensitive to elementary reaction rates that optimization techniques are employed to indirectly measure the reaction rates of HCO consumption. Besides the influence of flame chemistry on propagation, this work also explores the chemistry involved in production of nitric oxide, a harmful pollutant, within flames. We find significant differences among available chemistry models, both in mechanistic structure and quantitative reaction rates. There is a lack of well
Non-symmetric approach to single-screw expander and compressor modeling
Ziviani, Davide; Groll, Eckhard A.; Braun, James E.; Horton, W. Travis; De Paepe, M.; van den Broek, M.
2017-08-01
Single-screw type volumetric machines are employed both as compressors in refrigeration systems and, more recently, as expanders in organic Rankine cycle (ORC) applications. The single-screw machine is characterized by having a central grooved rotor and two mating toothed starwheels that isolate the working chambers. One of the main features of such machine is related to the simultaneous occurrence of the compression or expansion processes on both sides of the main rotor which results in a more balanced loading on the main shaft bearings with respect to twin-screw machines. However, the meshing between starwheels and main rotor is a critical aspect as it heavily affects the volumetric performance of the machine. To allow flow interactions between the two sides of the rotor, a non-symmetric modelling approach has been established to obtain a more comprehensive model of the single-screw machine. The resulting mechanistic model includes in-chamber governing equations, leakage flow models, heat transfer mechanisms, viscous and mechanical losses. Forces and moments balances are used to estimate the loads on the main shaft bearings as well as on the starwheel bearings. An 11 kWe single-screw expander (SSE) adapted from an air compressor operating with R245fa as working fluid is used to validate the model. A total of 60 steady-steady points at four different rotational speeds have been collected to characterize the performance of the machine. The maximum electrical power output and overall isentropic efficiency measured were 7.31 kW and 51.91%, respectively.
A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing
De La Chevrotière, Michèle; Khouider, Boualem
2017-02-01
Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the effect of climate change on the earth system. Climate models are large computer codes based on the discretization of the fluid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly difficult. Here, we develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while
Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations
Hou, Thomas Y.; Liu, Pengfei; Wang, Fei
2018-05-01
We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.
Verfondern, K.; Mueller, D.
1991-01-01
Computer codes for modelling the fission product release behavior of spherical fuel elements for High Temperature Reactors (HTR) have been developed for the purpose of being used in risk analyses for HTRs. An important part of the validation and verification procedure for these calculation models is the theoretical investigation of accident simulation experiments which have been conducted in the KueFA test facility in the Hot Cells at KFA. The paper gives a presentation of the basic modeling and the calculational results of fission product release from modern German HTR fuel elements in the temperature range 1600-1800 deg. C using the TRISO coated particle failure model PANAMA and the diffusion model FRESCO. Measurements of the transient release behavior for cesium and strontium and of their concentration profiles after heating have provided informations about diffusion data in the important retention barriers of the fuel: silicon carbide and matrix graphite. It could be shown that the diffusion coefficients of both cesium and strontium in silicon carbide can significantly be reduced using a factor in the range of 0.02 - 0.15 compared to older HTR fuel. Also in the development of fuel element graphite, a tendency towards lower diffusion coefficients for both nuclides can be derived. Special heating tests focussing on the fission gases and iodine release from the matrix contamination have been evaluated to derive corresponding effective diffusion data for iodine in fuel element graphite which are more realistic than the iodine transport data used so far. Finally, a prediction of krypton and cesium release from spherical fuel elements under heating conditions will be given for fuel elements which at present are irradiated in the FRJ2, Juelich, and which are intended to be heated at 1600/1800 deg. C in the KueFA furnace in near future. (author). 7 refs, 11 figs
Celný David
2016-01-01
Full Text Available Development of methods for accurate modeling of phase interfaces is important for understanding various natural processes and for applications in technology such as power production and carbon dioxide separation and storage. In particular, prediction of the course of the non-equilibrium phase transition processes requires knowledge of the properties of the strongly curved phase interfaces of microscopic droplets. In our work, we focus on the spherical vapor–liquid phase interfaces for binary mixtures. We developed a robust computational method to determine the density and concentration profiles. The fundamentals of our approach lie in the Cahn-Hilliard gradient theory, allowing to transcribe the functional formulation into a system of ordinary Euler-Langrange equations. This system is then split and modified into a shape suitable for iterative computation. For this task, we combine the Newton-Raphson and the shooting methods providing a good convergence speed. For the thermodynamic roperties, the PC–SAFT equation of state is used. We determine the density and concentration profiles for spherical phase interfaces at various saturation factors for the binary mixture of CO2 and C9H20. The computed concentration profiles allow to the determine the work of formation and other characteristics of the microscopic droplets.
Development of the α-decay theory of spherical nuclei by means of the shell model
Holan, S.
1978-01-01
The new results achieved within the α-decay theory of spherical nuclei with a (2)-(5) integral formula, unaffected by arbitrary parameters, taking into account the finite shape of the α particle and using a basis of Woods-Saxon uniparticle functions to describe initial and final nuclei, may be summarized as follows: Through α-width calculations performed for many spherical nuclei it has been proved that experimental classifying of α-transition into favoured and unfavoured transitions as well as the hyperfine structure of the transitions can be theoretically explained if considered the nucleon-nucleon correlations in the description of initial and final nuclei; The absolute values of the theoretical α-widths obtained are about 10 2 times smaller compared to the experimental ones. This might be due to an oversimplified approximation of the α-particle-daughter nucleus interaction potential or either to an inaccuracy of the model functions used in describing nucleus decay in the surface area. (author)
A Spherical Model Based Keypoint Descriptor and Matching Algorithm for Omnidirectional Images
Guofeng Tong
2014-04-01
Full Text Available Omnidirectional images generally have nonlinear distortion in radial direction. Unfortunately, traditional algorithms such as scale-invariant feature transform (SIFT and Descriptor-Nets (D-Nets do not work well in matching omnidirectional images just because they are incapable of dealing with the distortion. In order to solve this problem, a new voting algorithm is proposed based on the spherical model and the D-Nets algorithm. Because the spherical-based keypoint descriptor contains the distortion information of omnidirectional images, the proposed matching algorithm is invariant to distortion. Keypoint matching experiments are performed on three pairs of omnidirectional images, and comparison is made among the proposed algorithm, the SIFT and the D-Nets. The result shows that the proposed algorithm is more robust and more precise than the SIFT, and the D-Nets in matching omnidirectional images. Comparing with the SIFT and the D-Nets, the proposed algorithm has two main advantages: (a there are more real matching keypoints; (b the coverage range of the matching keypoints is wider, including the seriously distorted areas.
On the redistribution of existing inputs using the spherical frontier dea model
José Virgilio Guedes de Avellar
2010-04-01
Full Text Available The Spherical Frontier DEA Model (SFM (Avellar et al., 2007 was developed to be used when one wants to fairly distribute a new and fixed input to a group of Decision Making Units (DMU's. SFM's basic idea is to distribute this new and fixed input in such a way that every DMU will be placed on an efficiency frontier with a spherical shape. We use SFM to analyze the problems that appear when one wants to redistribute an already existing input to a group of DMU's such that the total sum of this input will remain constant. We also analyze the case in which this total sum may vary.O Modelo de Fronteira Esférica (MFE (Avellar et al., 2007 foi desenvolvido para ser usado quando se deseja distribuir de maneira justa um novo insumo a um conjunto de unidades tomadoras de decisão (DMU's, da sigla em inglês, Decision Making Units. A ideia básica do MFE é a de distribuir esse novo insumo de maneira que todas as DMU's sejam colocadas numa fronteira de eficiência com um formato esférico. Neste artigo, usamos MFE para analisar o problema que surge quando se deseja redistribuir um insumo já existente para um grupo de DMU's de tal forma que a soma desse insumo para todas as DMU's se mantenha constante. Também analisamos o caso em que essa soma possa variar.
Model-free and analytical EAP reconstruction via spherical polar Fourier diffusion MRI.
Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid
2010-01-01
How to estimate the diffusion Ensemble Average Propagator (EAP) from the DWI signals in q-space is an open problem in diffusion MRI field. Many methods were proposed to estimate the Orientation Distribution Function (ODF) that is used to describe the fiber direction. However, ODF is just one of the features of the EAP. Compared with ODF, EAP has the full information about the diffusion process which reflects the complex tissue micro-structure. Diffusion Orientation Transform (DOT) and Diffusion Spectrum Imaging (DSI) are two important methods to estimate the EAP from the signal. However, DOT is based on mono-exponential assumption and DSI needs a lot of samplings and very large b values. In this paper, we propose Spherical Polar Fourier Imaging (SPFI), a novel model-free fast robust analytical EAP reconstruction method, which almost does not need any assumption of data and does not need too many samplings. SPFI naturally combines the DWI signals with different b-values. It is an analytical linear transformation from the q-space signal to the EAP profile represented by Spherical Harmonics (SH). We validated the proposed methods in synthetic data, phantom data and real data. It works well in all experiments, especially for the data with low SNR, low anisotropy, and non-exponential decay.
Dowker, J S, E-mail: dowker@man.ac.uk [Theory Group, School of Physics and Astronomy, University of Manchester, Manchester (United Kingdom)
2011-08-07
A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta-function regularization, the vacuum energy of the arrangement is finite for conformal propagation in spacetime. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is repelled or attracted by the nearest wall if d = 3, 7, ... or if d = 1, 5, ... , respectively. For hybrid N-D conditions these requirements are switched. If a mass is added, divergences arise which render the model suspect. The analysis, however, is relatively straightforward and involves the Barnes zeta function. The extension to finite temperatures is made and it is shown that for the 3, 7, ... series of odd spheres, the repulsion by the walls continues but that, above a certain temperature, the free energy acquires two minima symmetrically placed about the midpoint.
Dowker, J S
2011-01-01
A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta-function regularization, the vacuum energy of the arrangement is finite for conformal propagation in spacetime. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is repelled or attracted by the nearest wall if d = 3, 7, ... or if d = 1, 5, ... , respectively. For hybrid N-D conditions these requirements are switched. If a mass is added, divergences arise which render the model suspect. The analysis, however, is relatively straightforward and involves the Barnes zeta function. The extension to finite temperatures is made and it is shown that for the 3, 7, ... series of odd spheres, the repulsion by the walls continues but that, above a certain temperature, the free energy acquires two minima symmetrically placed about the midpoint.
Low energy restrictions for a flipped left-right symmetric model
Eeg, J.O. (Oslo Univ. (Norway). Fysisk Inst.)
1990-05-01
I consider some low energy restrictions for a 'flipped' left-right symmetric model containing exotic fermions of E{sub 6} and a right-handed W-boson, all with odd R-parity. The new interactions due to W{sub R}-exchange have no significant impact on rare kaon decays, because the W{sub R} does not couple to d, s, b quarks. On the other hand, W{sub R} exchanges might induce rare processes like D-anti D mixing, D{sup 0}{yields}{mu}anti {mu}, D{sup 0}{yields}{mu}anti e, {mu}{yields}e{gamma}, {mu}{yields}3e, and {mu}N{yields}eN. It turns out that the strongest bound is obtained from D-anti D mixing. With reasonable extra assumptions, it is found that the exotic right-handed W-boson is likely to be heavier than 500 to 1500 GeV. (orig.).
Detection of heavy neutrinos and right-handed bosons of the left-right symmetric model
Kirsanov, M
2008-01-01
The left-right symmetric model can explain the origin of parity violation in weak interactions and predicts the existence of additional $W_R$ and $Z'$ gauge bosons and heavy right-handed neutrino states $N_l$. $N_l$ can be partners of light neutrino states ($l=e,\\mu,\\tau$), related to their non-zero masses through the see-saw mechanism. This makes the searches of $W_R$, $Z'$ and $N_l$ interesting and important. We studied the potential of the CMS experiment to observe signals from the $N_l$ and $W_R$ production at the LHC. It is shown that their decay signals can be identified over a small background. The mass region up to $M_{W_R} = 2100$ GeV and $M_{N_l} = 1200$ GeV can be explored with an expected Gaussian significance of 5$\\sigma$ with an integrated luminosity $\\mathcal{L}_{int} = 100$ pb$^{-1}$ (at the collision energy $\\sqrt{s}=14$ TeV).
Pressure ionization of dense plasmas in spherical ion-cell model with spin-orbit interactions
Ishikawa, K.; Blenski, T.; Takahashi, H.; Iguchi, T.; Nakazawa, M.
1996-01-01
We study the continuity of pressure of dense plasmas in pressure ionization in case where spin-orbit interactions are taken into account in calculations. Pressure is calculated using a stress-tensor pressure formula in the relativistically-corrected self-consistent field spherical ion-cell model (average-atom model). It appears that calculated pressure and electronic density distribution change continuously in pressure ionization if we take narrow shape resonances into account properly. This observation stresses the need of a coherent description of bound and free electrons. We also compare the results by the stress-tensor pressure formula with those by other pressure formulas. It appears that different pressure formulas give rather discrepant results in some cases. copyright 1996 American Institute of Physics
Theory of a spherical electrostatic probe in a continuum plasma: Analytical models
Brailsford, A.D.
1977-01-01
A simple physical model of the charge distribution surrounding a biased spherical probe in a quiescent plasma, suggested by the theory of Su and Lam, is used to rederive the probe current-voltage characteristic. The result is compared with that of a slightly different version due to Kiel and with the exact numerical results of Baum and Chapkis. It is shown that if the ratio of the probe radius to the Debye length of the plasma is greater than or of the order of unity, the model calculation is in excellent agreement with the exact results when the dimensionless probe voltage phi/sup asterisk//sub p/,=vertical-barephi/sub p//kTvertical-bar in standard notation, is greater than 10, for both thick and thin sheaths. The comparison also provides an assessment of the importance of various additional validity criteria encountered in analytical treatments of the problem
E. Séran
2005-07-01
Full Text Available The segmented Langmuir probe (SLP has been recently proposed by one of the authors (Lebreton, 2002 as an instrument to derive the bulk velocity of terrestrial or planetary plasmas, in addition to the electron density and temperature that are routinely measured by Langmuir probes. It is part of the scientific payload on the DEMETER micro-satellite developed by CNES. The basic concept of this probe is to measure the current distribution over the surface using independent collectors under the form of small spherical caps and to use the angular anisotropy of these currents to obtain the plasma bulk velocity in the probe reference frame. In order to determine the SLP capabilities, we have developed a numerical PIC (Particles In Cell model which provides a tool to compute the distribution of the current collected by a spherical probe. Our model is based on the simultaneous determination of the charge densities in the probe sheath and on the probe surface, from which the potential distribution in the sheath region can be obtained. This method is well adapted to the SLP problem and has some advantages since it provides a natural control of the charge neutrality inside the simulation box, allows independent mesh sizes in the sheath and on the probe surface, and can be applied to complex surfaces. We present in this paper initial results obtained for plasma conditions corresponding to a Debye length equal to the probe radius. These plasma conditions are observed along the Demeter orbit. The model results are found to be in very good agreement with those published by Laframboise (1966 for a spherical probe in a thermal non-flowing plasma. This demonstrates the adequacy of the computation method and of the adjustable numerical parameters (size of the numerical box and mesh, time step, number of macro-particles, etc. for the considered plasma-probe configuration. We also present the results obtained in the case of plasma flowing with mesothermal conditions
E. Séran
2005-07-01
Full Text Available The segmented Langmuir probe (SLP has been recently proposed by one of the authors (Lebreton, 2002 as an instrument to derive the bulk velocity of terrestrial or planetary plasmas, in addition to the electron density and temperature that are routinely measured by Langmuir probes. It is part of the scientific payload on the DEMETER micro-satellite developed by CNES. The basic concept of this probe is to measure the current distribution over the surface using independent collectors under the form of small spherical caps and to use the angular anisotropy of these currents to obtain the plasma bulk velocity in the probe reference frame. In order to determine the SLP capabilities, we have developed a numerical PIC (Particles In Cell model which provides a tool to compute the distribution of the current collected by a spherical probe. Our model is based on the simultaneous determination of the charge densities in the probe sheath and on the probe surface, from which the potential distribution in the sheath region can be obtained. This method is well adapted to the SLP problem and has some advantages since it provides a natural control of the charge neutrality inside the simulation box, allows independent mesh sizes in the sheath and on the probe surface, and can be applied to complex surfaces. We present in this paper initial results obtained for plasma conditions corresponding to a Debye length equal to the probe radius. These plasma conditions are observed along the Demeter orbit. The model results are found to be in very good agreement with those published by Laframboise (1966 for a spherical probe in a thermal non-flowing plasma. This demonstrates the adequacy of the computation method and of the adjustable numerical parameters (size of the numerical box and mesh, time step, number of macro-particles, etc. for the considered plasma-probe configuration. We also present the results obtained in the case of plasma flowing with mesothermal conditions
Method to determine the optimal constitutive model from spherical indentation tests
Zhang, Tairui; Wang, Shang; Wang, Weiqiang
2018-03-01
The limitation of current indentation theories was investigated and a method to determine the optimal constitutive model through spherical indentation tests was proposed. Two constitutive models, the Power-law and the Linear-law, were used in Finite Element (FE) calculations, and then a set of indentation governing equations was established for each model. The load-depth data from the normal indentation depth was used to fit the best parameters in each constitutive model while the data from the further loading part was compared with those from FE calculations, and the model that better predicted the further deformation was considered the optimal one. Moreover, a Yang's modulus calculation model which took the previous plastic deformation and the phenomenon of pile-up (or sink-in) into consideration was also proposed to revise the original Sneddon-Pharr-Oliver model. The indentation results on six materials, 304, 321, SA508, SA533, 15CrMoR, and Fv520B, were compared with tensile ones, which validated the reliability of the revised E calculation model and the optimal constitutive model determination method in this study.
Chiral pion dynamics for spherical nucleon bags
Vento, V.; Rho, M.; Nyman, E.M.; Jun, J.H.; Brown, G.E.; CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette
1980-01-01
A chirally symmetric quark-bag model for the nucleon is obtained by introducing an explicit, classical, pion field exterior to the bag. The coupling at the bag surface is determined by the requirement of a conserved axial-vector current. The pion field satisfies equations of motion corresponding to the non-linear sigma-model. We study on this paper the simplified case where the bag and the pion field are spherically symmetric. Corrections due to gluon exchange between the quarks are ignored along with other interactions which split the N- and Δ-masses. The equations of motion for the pion field are solved and we find a substantial pion pressure at the bag surface, along with an attractive contribution to the nucleon self-energy. The total energy of the system, bag plus meson cloud, turns out to be approximately Msub(n)c 2 for a wide range of bag radii, from 1.5 fm down to about 0.5 fm. Introduction of a form factor for the pion would extend the range of possible radii to even smaller values. We propose that the bag with the smallest allowed radius be identified with the 'little bag' discussed before. One surprising result of the paper is that as long as one restricts to spherically symmetric bags, restoring chiral symmetry to the bag model makes the axial-vector current coupling constant gsub(A) to be always too large compared with the experimental value for any bag radius, suggesting a deviation from spherical symmetry for the intrinsic bag wave functions of the 'ground-state' hadrons. (orig.)
Spherical 2+p spin-glass model: An exactly solvable model for glass to spin-glass transition
Crisanti, A.; Leuzzi, L.
2004-01-01
We present the full phase diagram of the spherical 2+p spin-glass model with p≥4. The main outcome is the presence of a phase with both properties of full replica symmetry breaking phases of discrete models, e.g., the Sherrington-Kirkpatrick model, and those of one replica symmetry breaking. This phase has a finite complexity which leads to different dynamic and static properties. The phase diagram is rich enough to allow the study of different kinds of glass to spin glass and spin glass to spin glass phase transitions
Yu, Hua-Gen
2008-05-21
A spherical electron cloud hopping (SECH) model is proposed to study the product branching ratios of dissociative recombination (DR) of polyatomic systems. In this model, the fast electron-captured process is treated as an instantaneous hopping of a cloud of uniform spherical fractional point charges onto a target M+q ion (or molecule). The sum of point charges (-1) simulates the incident electron. The sphere radius is determined by a critical distance (Rc eM) between the incoming electron (e-) and the target, at which the potential energy of the e(-)-M+q system is equal to that of the electron-captured molecule M+q(-1) in a symmetry-allowed electronic state with the same structure as M(+q). During the hopping procedure, the excess energies of electron association reaction are dispersed in the kinetic energies of M+q(-1) atoms to conserve total energy. The kinetic energies are adjusted by linearly adding atomic momenta in the direction of driving forces induced by the scattering electron. The nuclear dynamics of the resultant M+q(-1) molecule are studied by using a direct ab initio dynamics method on the adiabatic potential energy surface of M+q(-1), or together with extra adiabatic surface(s) of M+q(-1). For the latter case, the "fewest switches" surface hopping algorithm of Tully was adapted to deal with the nonadiabaticity in trajectory propagations. The SECH model has been applied to study the DR of both CH+ and H3O+(H2O)2. The theoretical results are consistent with the experiment. It was found that water molecules play an important role in determining the product branching ratios of the molecular cluster ion.
Towards Spherical Mesh Gravity and Magnetic Modelling in an HPC Environment
Lane, R. J.; Brodie, R. C.; de Hoog, M.; Navin, J.; Chen, C.; Du, J.; Liang, Q.; Wang, H.; Li, Y.
2013-12-01
Staff at Geoscience Australia (GA), Australia's Commonwealth Government geoscientific agency, have routinely performed 3D gravity and magnetic modelling as part of geoscience investigations. For this work, we have used software programs that have been based on a Cartesian mesh spatial framework. These programs have come as executable files that were compiled to operate in a Windows environment on single core personal computers (PCs). To cope with models with higher resolution and larger extents, we developed an approach whereby a large problem could be broken down into a number of overlapping smaller models (';tiles') that could be modelled separately, with the results combined back into a single output model. To speed up the processing, we established a Condor distributed network from existing desktop PCs. A number of factors have caused us to consider a new approach to this modelling work. The drivers for change include; 1) models with very large lateral extents where the effects of Earth curvature are a consideration, 2) a desire to ensure that the modelling of separate regions is carried out in a consistent and managed fashion, 3) migration of scientific computing to off-site High Performance Computing (HPC) facilities, and 4) development of virtual globe environments for integration and visualization of 3D spatial objects. Some of the more surprising realizations to emerge have been that; 1) there aren't any readily available commercial software packages for modelling gravity and magnetic data in a spherical mesh spatial framework, 2) there are many different types of HPC environments, 3) no two HPC environments are the same, and 4) the most common virtual globe environment (i.e., Google Earth) doesn't allow spatial objects to be displayed below the topographic/bathymetric surface. Our response has been to do the following; 1) form a collaborative partnership with researchers at the Colorado School of Mines (CSM) and the China University of Geosciences (CUG
Scalar dark matter explanation of the DAMPE data in the minimal left-right symmetric model
Cao, Junjie; Guo, Xiaofei; Shang, Liangliang; Wang, Fei; Wu, Peiwen; Zu, Lei
2018-03-01
The left-right symmetric model (LRSM) is an attractive extension of the Standard Model (SM) that can address the origin of parity violation in the SM electroweak interactions, generate tiny neutrino masses, accommodate dark matter (DM) candidates, and provide a natural framework for baryogenesis through leptogenesis. In this work, we utilize the minimal LRSM to study the recently reported DAMPE results of the cosmic e+e- spectrum, which exhibits a tentative peak around 1.4 TeV, while satisfying the current neutrino data. We propose to explain the DAMPE peak with a complex scalar DM χ in two scenarios: (1) χ χ*→H1++H1-→ℓi+ℓi+ℓj-ℓj- , and (2) χ χ*→Hk++Hk-→ℓi+ℓi+ℓj-ℓj- accompanied by χ χ*→H1+H1-→ℓi+νℓiℓj-νℓj , with ℓi,j=e , μ , τ and k =1 , 2. We fit the theoretical prediction of the e+e- spectrum to relevant experimental data to determine the scalar mass spectrum favored by the DAMPE excess. We also consider various constraints from theoretical principles and collider experiments, as well as DM relic density and direct search experiments. We find that there is ample parameter space to interpret the DAMPE data while also passing the constraints. On the other hand, our explanations usually imply the existence of other new physics at an energy scale ranging from 107 to 1011 GeV . Collider tests of our explanations are also discussed.
Trapped surfaces in spherical stars
Bizon, P.; Malec, E.; O'Murchadha, N.
1988-01-01
We give necessary and sufficient conditions for the existence of trapped surfaces in spherically symmetric spacetimes. These conditions show that the formation of trapped surfaces depends on both the degree of concentration and the average flow of the matter. The result can be considered as a partial validation of the cosmic-censorship hypothesis
Integrated predictive modeling simulations of the Mega-Amp Spherical Tokamak
Nguyen, Canh N.; Bateman, Glenn; Kritz, Arnold H.; Akers, Robert; Byrom, Calum; Sykes, Alan
2002-01-01
Integrated predictive modeling simulations are carried out using the BALDUR transport code [Singer et al., Comput. Phys. Commun. 49, 275 (1982)] for high confinement mode (H-mode) and low confinement mode (L-mode) discharges in the Mega-Amp Spherical Tokamak (MAST) [Sykes et al., Phys. Plasmas 8, 2101 (2001)]. Simulation results, obtained using either the Multi-Mode transport model (MMM95) or, alternatively, the mixed-Bohm/gyro-Bohm transport model, are compared with experimental data. In addition to the anomalous transport, neoclassical transport is included in the simulations and the ion thermal diffusivity in the inner third of the plasma is found to be predominantly neoclassical. The sawtooth oscillations in the simulations radially spread the neutral beam injection heating profiles across a broad sawtooth mixing region. The broad sawtooth oscillations also flatten the central temperature and electron density profiles. Simulation results for the electron temperature and density profiles are compared with experimental data to test the applicability of these models and the BALDUR integrated modeling code in the limit of low aspect ratio toroidal plasmas
Qian, Ma; Ma, Jie
2009-06-07
Fletcher's spherical substrate model [J. Chem. Phys. 29, 572 (1958)] is a basic model for understanding the heterogeneous nucleation phenomena in nature. However, a rigorous thermodynamic formulation of the model has been missing due to the significant complexities involved. This has not only left the classical model deficient but also likely obscured its other important features, which would otherwise have helped to better understand and control heterogeneous nucleation on spherical substrates. This work presents a rigorous thermodynamic formulation of Fletcher's model using a novel analytical approach and discusses the new perspectives derived. In particular, it is shown that the use of an intermediate variable, a selected geometrical angle or pseudocontact angle between the embryo and spherical substrate, revealed extraordinary similarities between the first derivatives of the free energy change with respect to embryo radius for nucleation on spherical and flat substrates. Enlightened by the discovery, it was found that there exists a local maximum in the difference between the equivalent contact angles for nucleation on spherical and flat substrates due to the existence of a local maximum in the difference between the shape factors for nucleation on spherical and flat substrate surfaces. This helps to understand the complexity of the heterogeneous nucleation phenomena in a practical system. Also, it was found that the unfavorable size effect occurs primarily when R<5r( *) (R: radius of substrate and r( *): critical embryo radius) and diminishes rapidly with increasing value of R/r( *) beyond R/r( *)=5. This finding provides a baseline for controlling the size effects in heterogeneous nucleation.
Kim, Song Hyun; Kim, Do Hyun; Kim, Jong Kyung [Hanyang Univ., Seoul (Korea, Republic of); Noh, Jea Man [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-10-15
To the high computational efficiency and user convenience, the implicit method had received attention; however, it is noted that the implicit method in the previous studies has low accuracy at high packing fraction. In this study, a new implicit method, which can be used at any packing fraction with high accuracy, is proposed. In this study, the implicit modeling method in the spherical particle distributed medium for using the MC simulation is proposed. A new concept in the spherical particle sampling was developed to solve the problems in the previous implicit methods. The sampling method was verified by simulating the sampling method in the infinite and finite medium. The results show that the particle implicit modeling with the proposed method was accurately performed in all packing fraction boundaries. It is expected that the proposed method can be efficiently utilized for the spherical particle distributed mediums, which are the fusion reactor blanket, VHTR reactors, and shielding analysis.
How Spherical Is a Cube (Gravitationally)?
Sanny, Jeff; Smith, David
2015-01-01
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…
Phenomenology of a left-right-symmetric model inspired by the trinification model
Hetzel, Jamil
2015-02-04
The trinification model is an interesting extension of the Standard Model based on the gauge group SU(3){sub C} x SU(3){sub L} x SU(3){sub R}. It naturally explains parity violation as a result of spontaneous symmetry breaking, and the observed fermion masses and mixings can be reproduced using only a few parameters. We study the low-energy phenomenology of the trinification model in order to compare its predictions to experiment. To this end, we construct a low-energy effective field theory, thereby reducing the number of particles and free parameters that need to be studied. We constrain the model parameters using limits from new-particle searches as well as precision measurements. The scalar sector of the model allows for various phenomenological scenarios, such as the presence of a light fermiophobic scalar in addition to a Standard-Model-like Higgs, or a degenerate (twin) Higgs state at 126 GeV. We show how a measurement of the Higgs couplings can be used to distinguish such scenarios from the Standard Model. We find that the trinification model predicts that several new scalar particles have masses in the O(100 GeV) range. Moreover, large regions of the parameter space lead to measurable deviations from Standard-Model predictions of the Higgs couplings. Hence the trinification model awaits crucial tests at the Large Hadron Collider in the coming years.
Effects of snow grain non-sphericity on climate simulations: Sensitivity tests with the NorESM model
Räisänen, Petri; Makkonen, Risto; Kirkevåg, Alf
2017-04-01
Snow grains are non-spherical and generally irregular in shape. Still, in radiative transfer calculations, they are often treated as spheres. This also applies to the computation of snow albedo in the Snow, Ice, and Aerosol Radiation (SNICAR) model and in the Los Alamos sea ice model, version 4 (CICE4), both of which are employed in the Community Earth System Model and in the Norwegian Earth System Model (NorESM). In this work, we evaluate the effect of snow grain shape on climate simulated by NorESM in a slab ocean configuration of the model. An experiment with spherical snow grains (SPH) is compared with another (NONSPH) in which the snow shortwave single-scattering properties are based on a combination of non-spherical snow grain shapes optimized using measurements of angular scattering by blowing snow. The key difference between these treatments is that the asymmetry parameter is smaller in the non-spherical case (≈ 0.78 in the visible region) than in the spherical case (≈ 0.89). Therefore, for a given snow grain size, the use of non-spherical snow grains yields a higher snow broadband albedo, typically by ≈0.03. Consequently, considering the spherical case as the baseline, the use of non-spherical snow grains results in a negative radiative forcing (RF), with a global-mean top-of-the-model value of ≈ -0.22 W m-2. Although this global-mean RF is modest, it has a rather substantial impact on the climate simulated by NoRESM. In particular, the global annual-mean 2-m air temperature in NONSPH is 1.17 K lower than in SPH, with substantially larger differences at high latitudes. The climatic response is amplified by strong snow and sea ice feedbacks. It is further found that the difference between NONSPH and SPH could be largely "tuned away" by adjusting the snow grain size in the NONSPH experiment by ≈ 70%. The impact of snow grain shape on the radiative effect (RE) of absorbing aerosols in snow (black carbon and mineral dust) is also discussed. For an
Padrino, Juan C.; Sprittles, James; Lockerby, Duncan
2017-11-01
Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).
Penner, Joyce E.; Andronova, Natalia; Oehmke, Robert C.; Brown, Jonathan; Stout, Quentin F.; Jablonowski, Christiane; van Leer, Bram; Powell, Kenneth G.; Herzog, Michael
2007-07-01
One of the most important advances needed in global climate models is the development of atmospheric General Circulation Models (GCMs) that can reliably treat convection. Such GCMs require high resolution in local convectively active regions, both in the horizontal and vertical directions. During previous research we have developed an Adaptive Mesh Refinement (AMR) dynamical core that can adapt its grid resolution horizontally. Our approach utilizes a finite volume numerical representation of the partial differential equations with floating Lagrangian vertical coordinates and requires resolving dynamical processes on small spatial scales. For the latter it uses a newly developed general-purpose library, which facilitates 3D block-structured AMR on spherical grids. The library manages neighbor information as the blocks adapt, and handles the parallel communication and load balancing, freeing the user to concentrate on the scientific modeling aspects of their code. In particular, this library defines and manages adaptive blocks on the sphere, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. We have successfully tested the library in a 2-D (longitude-latitude) implementation. During the past year, we have extended the library to treat adaptive mesh refinement in the vertical direction. Preliminary results are discussed. This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NOAA GFDL.
Application of the spherical harmonic gravity model in high precision inertial navigation systems
Wang, Jing; Yang, Gongliu; Zhou, Xiao; Li, Xiangyun
2016-01-01
The spherical harmonic gravity model (SHM) may, in general, be considered as a suitable alternative to the normal gravity model (NGM), because it represents the Earth’s gravitational field more accurately. However, the high-resolution SHM has never been used in current inertial navigation systems (INSs) due to its extremely complex expression. In this paper, the feasibility and accuracy of a truncated SHM are discussed for application in a real-time free-INS with a precision demand better than 0.8 nm h −1 . In particular, the time and space complexity are analyzed mathematically to verify the feasibility of the SHM. Also, a test on a typical navigation computer shows a storable range of cut-off degrees. To further evaluate the appropriate degree and accuracy of the truncated SHM, analyses of covariance and truncation error are proposed. Finally, a SHM of degree 12 is demonstrated to be the appropriate model for routine INSs in the precision range of 0.4–0.75 nm h −1 . Flight simulations and road tests show its outstanding performance over the traditional NGM. (paper)
The influence of primordial magnetic fields on the spherical collapse model in cosmology
Shibusawa, Y.; Ichiki, K.; Kadota, K.
2014-01-01
Despite the ever growing observational evidence for the existence of the large scale magnetic fields, their origin and the evolution are not fully understood. If the magnetic fields are of primordial origin, they result in the generation of the secondary matter density perturbations and the previous studies show that such density perturbations enhance the number of dark matter halos. We extend the conventional spherical collapse model by including the Lorentz force which has not been implemented in the previous analysis to study the evolution of density perturbations produced by primordial magnetic fields. The critical over-density δ c characterizing the halo mass function turns out to be a bigger value, δ c ≅ 1.78, than the conventional one δ c ≅ 1.69 for the perturbations evolved only by the gravitational force. The difference in δ c between our model and the fully matter dominated cosmological model is small at a low redshift and, hence, only the high mass tail of the mass function is affected by the magnetic fields. At a high redshift, on the other hand, the difference in δ c becomes large enough to suppress the halo abundance over a wide range of mass scales. The halo abundance is reduced for instance by as large a factor as ∼10 5 at z=9
Penner, Joyce E; Andronova, Natalia; Oehmke, Robert C; Brown, Jonathan; Stout, Quentin F; Jablonowski, Christiane; Leer, Bram van; Powell, Kenneth G; Herzog, Michael
2007-01-01
One of the most important advances needed in global climate models is the development of atmospheric General Circulation Models (GCMs) that can reliably treat convection. Such GCMs require high resolution in local convectively active regions, both in the horizontal and vertical directions. During previous research we have developed an Adaptive Mesh Refinement (AMR) dynamical core that can adapt its grid resolution horizontally. Our approach utilizes a finite volume numerical representation of the partial differential equations with floating Lagrangian vertical coordinates and requires resolving dynamical processes on small spatial scales. For the latter it uses a newly developed general-purpose library, which facilitates 3D block-structured AMR on spherical grids. The library manages neighbor information as the blocks adapt, and handles the parallel communication and load balancing, freeing the user to concentrate on the scientific modeling aspects of their code. In particular, this library defines and manages adaptive blocks on the sphere, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. We have successfully tested the library in a 2-D (longitude-latitude) implementation. During the past year, we have extended the library to treat adaptive mesh refinement in the vertical direction. Preliminary results are discussed. This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NOAA GFDL
Yin, Chungen; Rosendahl, Lasse Aistrup; Kær, Søren Knudsen
2004-01-01
-area-to-volume ratio and thus experiences a totally different motion and reaction as a non-spherical particle. Therefore, an advanced non-spherical particle-tracking model is developed to calculate the motion and reaction of nonspherical biomass particles. The biomass particles are assumed as solid or hollow cylinders......-gradient force. Since the drag and lift forces are both shape factor- and orientation-dependent, coupled particle rotation equations are resolved to update particle orientation. In the reaction of biomass particles, the actual particle surface area available and the average oxygen mass flux at particle surface...
Phenomenological study of the minimal R-symmetric supersymmetric standard model
Diessner, Philip
2016-01-01
The Standard Model (SM) of particle physics gives a comprehensive description of numerous phenomena concerning the fundamental components of nature. Still, open questions and a clouded understanding of the underlying structure remain. Supersymmetry is a well motivated extension that may account for the observed density of dark matter in the universe and solve the hierarchy problem of the SM. The minimal supersymmetric extension of the SM (MSSM) provides solutions to these challenges. Furthermore, it predicts new particles in reach of current experiments. However, the model has its own theoretical challenges and is under fire from measurements provided by the Large Hadron Collider (LHC). Nevertheless, the concept of supersymmetry has an elegance which not only shines in the MSSM. Hence, it is also of interest to examine non-minimal supersymmetric models. They have benefits similar to the MSSM and may solve its shortcomings. R-symmetry is the only global symmetry allowed that does not commutate with supersymmetry and Lorentz symmetry. Thus, extending a supersymmetric model with R-symmetry is a theoretically well motivated endeavor to achieve the complete symmetry content of a field theory. Such a model provides a natural explanation for non-discovery in the early runs of the LHC and leads to further predictions distinct from those of the MSSM. The work described in this thesis contributes to the effort by studying the minimal R-symmetric supersymmetric extension of the SM (MRSSM). Important aspects of its physics and the dependence of observables on the parameter space of the MRSSM are investigated. The discovery of a scalar particle compatible with the Higgs boson of the SM at the LHC was announced in 2012. It is the first and crucial task of this thesis to understand the underlying mechanisms leading to the correct Higgs boson mass prediction in the MRSSM. Then, the relevant regions of parameter space are investigated and it is shown that they are also in agreement
Phenomenological study of the minimal R-symmetric supersymmetric standard model
Diessner, Philip
2016-10-20
The Standard Model (SM) of particle physics gives a comprehensive description of numerous phenomena concerning the fundamental components of nature. Still, open questions and a clouded understanding of the underlying structure remain. Supersymmetry is a well motivated extension that may account for the observed density of dark matter in the universe and solve the hierarchy problem of the SM. The minimal supersymmetric extension of the SM (MSSM) provides solutions to these challenges. Furthermore, it predicts new particles in reach of current experiments. However, the model has its own theoretical challenges and is under fire from measurements provided by the Large Hadron Collider (LHC). Nevertheless, the concept of supersymmetry has an elegance which not only shines in the MSSM. Hence, it is also of interest to examine non-minimal supersymmetric models. They have benefits similar to the MSSM and may solve its shortcomings. R-symmetry is the only global symmetry allowed that does not commutate with supersymmetry and Lorentz symmetry. Thus, extending a supersymmetric model with R-symmetry is a theoretically well motivated endeavor to achieve the complete symmetry content of a field theory. Such a model provides a natural explanation for non-discovery in the early runs of the LHC and leads to further predictions distinct from those of the MSSM. The work described in this thesis contributes to the effort by studying the minimal R-symmetric supersymmetric extension of the SM (MRSSM). Important aspects of its physics and the dependence of observables on the parameter space of the MRSSM are investigated. The discovery of a scalar particle compatible with the Higgs boson of the SM at the LHC was announced in 2012. It is the first and crucial task of this thesis to understand the underlying mechanisms leading to the correct Higgs boson mass prediction in the MRSSM. Then, the relevant regions of parameter space are investigated and it is shown that they are also in agreement
Freeden, Willi; Schreiner, Michael
2018-01-01
This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.
Modeling of phonon heat transfer in spherical segment of silica aerogel grains
Han, Ya-Fen; Xia, Xin-Lin, E-mail: xiaxl@hit.edu.cn; Tan, He-Ping, E-mail: tanheping@hit.edu.cn; Liu, Hai-Dong
2013-07-01
Phonon heat transfer in spherical segment of nano silica aerogel grains is investigated by the lattice Boltzmann method (LBM). For various sizes of grains, the temperature distribution and the thermal conductivity are obtained by the numerical simulation, in which the size effects of the gap surface are also considered. The results indicate that the temperature distribution in the silica aerogel grain depends strongly on the size. Both the decreases in the diameter of spherical segment and the ratio of the diameter of gap surface to the diameter of spherical segment reduce its effective thermal conductivity obviously. In addition, the phonon scattering at the boundary surfaces becomes more prominent when grain size decreases.
Modeling of phonon heat transfer in spherical segment of silica aerogel grains
Han, Ya-Fen; Xia, Xin-Lin; Tan, He-Ping; Liu, Hai-Dong
2013-01-01
Phonon heat transfer in spherical segment of nano silica aerogel grains is investigated by the lattice Boltzmann method (LBM). For various sizes of grains, the temperature distribution and the thermal conductivity are obtained by the numerical simulation, in which the size effects of the gap surface are also considered. The results indicate that the temperature distribution in the silica aerogel grain depends strongly on the size. Both the decreases in the diameter of spherical segment and the ratio of the diameter of gap surface to the diameter of spherical segment reduce its effective thermal conductivity obviously. In addition, the phonon scattering at the boundary surfaces becomes more prominent when grain size decreases
Coding Model and Mapping Method of Spherical Diamond Discrete Grids Based on Icosahedron
LIN Bingxian
2016-12-01
Full Text Available Discrete Global Grid(DGG provides a fundamental environment for global-scale spatial data's organization and management. DGG's encoding scheme, which blocks coordinate transformation between different coordination reference frames and reduces the complexity of spatial analysis, contributes a lot to the multi-scale expression and unified modeling of spatial data. Compared with other kinds of DGGs, Diamond Discrete Global Grid(DDGG based on icosahedron is beneficial to the spherical spatial data's integration and expression for much better geometric properties. However, its structure seems more complicated than DDGG on octahedron due to its initial diamond's edges cannot fit meridian and parallel. New challenges are posed when it comes to the construction of hierarchical encoding system and mapping relationship with geographic coordinates. On this issue, this paper presents a DDGG's coding system based on the Hilbert curve and designs conversion methods between codes and geographical coordinates. The study results indicate that this encoding system based on the Hilbert curve can express space scale and location information implicitly with the similarity between DDG and planar grid put into practice, and balances efficiency and accuracy of conversion between codes and geographical coordinates in order to support global massive spatial data's modeling, integrated management and all kinds of spatial analysis.
Resistor mesh model of a spherical head: part 1: applications to scalp potential interpolation.
Chauveau, N; Morucci, J P; Franceries, X; Celsis, P; Rigaud, B
2005-11-01
A resistor mesh model (RMM) has been implemented to describe the electrical properties of the head and the configuration of the intracerebral current sources by simulation of forward and inverse problems in electroencephalogram/event related potential (EEG/ERP) studies. For this study, the RMM representing the three basic tissues of the human head (brain, skull and scalp) was superimposed on a spherical volume mimicking the head volume: it included 43 102 resistances and 14 123 nodes. The validation was performed with reference to the analytical model by consideration of a set of four dipoles close to the cortex. Using the RMM and the chosen dipoles, four distinct families of interpolation technique (nearest neighbour, polynomial, splines and lead fields) were tested and compared so that the scalp potentials could be recovered from the electrode potentials. The 3D spline interpolation and the inverse forward technique (IFT) gave the best results. The IFT is very easy to use when the lead-field matrix between scalp electrodes and cortex nodes has been calculated. By simple application of the Moore-Penrose pseudo inverse matrix to the electrode cap potentials, a set of current sources on the cortex is obtained. Then, the forward problem using these cortex sources renders all the scalp potentials.
Liu, Hua; Wu, Wen
2017-06-13
For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF) is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM) filter and the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF). The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with the interacting multiple model unscented Kalman filter (IMMUKF), the interacting multiple model cubature Kalman filter (IMMCKF) and the interacting multiple model fifth-degree cubature Kalman filter (IMM5thCKF).
Hua Liu
2017-06-01
Full Text Available For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM filter and the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF. The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with the interacting multiple model unscented Kalman filter (IMMUKF, the interacting multiple model cubature Kalman filter (IMMCKF and the interacting multiple model fifth-degree cubature Kalman filter (IMM5thCKF.
Compressible convection in a rotating spherical shell. II. A linear anelastic model
Glatzmaier, G.A.; Gilman, P.A.
1981-01-01
We study the onset of convection for a compressible fluid in a rotating spherical shell via linear anelastic fluid equations for a depth of 40% of the radius, constant kinematic viscosity and thermometric diffusivity, Taylor numbers up to 10 5 , and density stratifications up to seven e-folds across the zone. The perturbations are expanded in spherical harmonics, and the radially dependent equations are solved with a Newton-Raphson relaxation method
Effects of rotation on crystal settling in a terrestrial magma ocean: Spherical shell model
Maas, C.; Hansen, U.
2015-12-01
Like Moon or Mars, Earth experienced one or several deep magma ocean periods of globalextent in a later stage of its accretion. The crystallization of these magma oceans is of keyimportance for the chemical structure of Earth, the mantle evolution and the onset of platetectonics. Due to the fast rotation of early Earth and the small magma viscosity, rotationprobably had a profound effect on differentiation processes. For example, Matyska et al.[1994] propose that the distribution of heterogeneities like the two large low shear velocityprovinces (LLSVP) at the core mantle boundary is influenced by rotational dynamicsof early Earth. Further Garnero and McNamara [2008] suggest that the LLSVPs arevery long-living anomalies, probably reaching back to the time of differentiation andsolidification of Earth. However, nearly all previous studies neglect the effects of rotation.In our previous work using a Cartesian model, a strong influence of rotation as well asof latitude on the differentiation processes in an early magma ocean was revealed. Weshowed that crystal settling in an early stage of magma ocean crystallization cruciallydepends on latitude as well as on rotational strength and crystal density.In order to overcome the restrictions as to the geometry of the Cartesian model, we arecurrently developing a spherical model to simulate crystal settling in a rotating sphericalshell. This model will allow us not only to investigate crystal settling at the poles andthe equator, but also at latitudes in-between these regions, as well as the migration ofcrystals between poles and equator. ReferencesE. J. Garnero and A. K. McNamara. Structure and dynamics of earth's lower mantle.Science, 320(5876):626-628, 2008.C. Matyska, J. Moser, and D. A. Yuen. The potential influence of radiative heat transferon the formation of megaplumes in the lower mantle. Earth and Planetary ScienceLetters, 125(1):255-266, 1994.
A model experiment to study swallowing of spherical and elongated particles
Marconati Marco
2017-01-01
Full Text Available Swallowing disorders are not uncommon among elderly and people affected by neurological diseases. For these patients the ingestion of solid grains, such as pharmaceutical oral solid formulations, could result in choking. This generally results in a low compliance in taking solid medications. The effect of the solid medication size on the real or perceived ease of swallowing is still to be understood from the mechanistic viewpoint. The interplay of the inclusion shape and the rheology of the liquid being swallowed together with the medication is also not fully understood. In this study, a model experiment was developed to study the oropharyngeal phase of swallowing, replicating the dynamics of the bolus flow induced by the tongue (by means of a roller driven by an applied force. Experiments were performed using a wide set of solid inclusions, dispersed in a thick Newtonian liquid. Predictions for a simple theory are compared with experiments. Results show that an increase in the grain size results in a slower dynamics of the swallowing. Furthermore, the experiments demonstrated the paramount role of shape, as flatter and more streamlined inclusions flow faster than spherical. This approach can support the design of new oral solid formulations that can be ingested more easily and effectively also by people with mild swallowing disorders.
Teiji, KUNIHIRO; Tatsuyuki, TAKATSUKA; Ryozo, TAMAGAKI; Department of National Sciences, Ryukoku University; College of Humanities and Social Sciences, Iwate University; Department of Physics, Kyoto University
1985-01-01
Pion condensation in the symmetric nuclear matter is investigated on the basis of the ALS (alternating-layer-spin) model which provides a good description for the π^0 condensation. We perform energy calculations in a realistic way where the isobar (Δ)-mixing, the short range effects and the exchange energy of the interaction are taken into account. The Δ-mixing effect is built in the model state as previously done in the neutron matter. We preferentially employ G-0 force of Sprung and Banerje...
Matsui Toshinori
2018-01-01
Full Text Available Among various scenarios of baryon asymmetry of the Universe, electroweak baryogenesis is directly connected with physics of the Higgs sector. We discuss spectra of gravitational waves which are originated by the strongly first order phase transition at the electroweak symmetry breaking, which is required for a successful scenario of electroweak baryogenesis. In the Z3 symmetric singlet scalar model, the significant gravitational waves are caused by the multi-step phase transition. We show that the model can be tested by measuring the characteristic spectra of the gravitational waves at future interferometers such as LISA and DECIGO.
Chang, D.; Mohapatra, R.N.; Parida, M.K.
1984-01-01
A new approach to left-right symmetric models is proposed, where the left-right discrete-symmetry- and SU(2)/sub R/-breaking scales are decoupled from each other. This changes the spectrum of physical Higgs bosons which leads to different patterns for gauge hierarchies in SU(2)/sub L/xSU(2)/sub R/xSU(4)/sub C/ and SO(10) models. Most interesting are two SO(10) symmetry-breaking chains with an intermediate U(1)/sub R/ symmetry. These are such as to provide new motivation to search for ΔB = 2 and right-handed current effects at low energies
Lee, Jae Yong; Kim, Song Hyun; Shin, Chang Ho; Kim, Jong Kyung [Hanyang Univ., Seoul (Korea, Republic of)
2014-05-15
In this study, as a preliminary study to develop an implicit method having high accuracy, the distribution characteristics of spherical particles were evaluated by using explicit modeling techniques in various volume packing fractions. This study was performed to evaluate implicitly simulated distribution of randomly packed spheres in a medium. At first, an explicit modeling method to simulate random packed spheres in a hexahedron medium was proposed. The distributed characteristics of l{sub p} and r{sub p}, which are used in the particle position sampling, was estimated. It is analyzed that the use of the direct exponential distribution, which is generally used in the implicit modeling, can cause the distribution bias of the spheres. It is expected that the findings in this study can be utilized for improving the accuracy in using the implicit method. Spherical particles, which are randomly distributed in medium, are utilized for the radiation shields, fusion reactor blanket, fuels of VHTR reactors. Due to the difficulty on the simulation of the stochastic distribution, Monte Carlo (MC) method has been mainly considered as the tool for the analysis of the particle transport. For the MC modeling of the spherical particles, three methods are known; repeated structure, explicit modeling, and implicit modeling. Implicit method (called as the track length sampling method) is a modeling method that is the sampling based modeling technique of each spherical geometry (or track length of the sphere) during the MC simulation. Implicit modeling method has advantages in high computational efficiency and user convenience. However, it is noted that the implicit method has lower modeling accuracy in various finite mediums.
3-D Spherical Convection Modeling Applied to Mercury: Dislocation Versus Diffusion Rheology
Robertson, S. D.; King, S. D.
2016-12-01
Mercury is the smallest among the terrestrial planets and, prior to NASA's MESSENGER mission was thought to be the least tectonically and volcanically active body. Gravity and moment of inertia from MESSENGER constrain Mercury to have a thin silicate mantle shell of approximately 400 km over a massive iron core. This mantle is thinner than previously thought and the smallest end-member in comparison with the other terrestrial planets. Although Mercury currently has a stagnant lid and the present day mantle is likely not convecting, a significant proportion of Mercury's surface features could have been derived from convection in the viscous mantle. Given Mercury's small size, the amount of volcanism and tectonic activity was a surprise. We investigate the effect of dislocation creep rheology in olivine on the dynamics of Mercury. At the pressures and temperatures of Mercury's mantle, laboratory creep studies indicate that olivine deforms by dislocation creep. Previous studies using diffusion creep rheology find that the thin mantle shell of Mercury quickly becomes diffusive and, this is difficult to reconcile with the surface observations. We use the three-dimensional spherical code, CitcomS, to compare numerical models with both dislocation and diffusion creep. We compare gravity, topography, and mantle temperature as a function of time from the models with constraints on the timing of volcanic and tectonic activity on Mercury. The results show that with the dislocation creep mechanism, there is potential for convective flow in the mantle over billions of years. In contrast, models with the diffusion creep mechanism start with a convecting mantle that transitions to global diffusive cooling within 500 Myrs. Diffusion creep rheology does not adequately produce a dynamic interior that is consistent with the historical volcanic and tectonic evolution of the planet. This research is the result of participation in GLADE, a nine-week summer REU program directed by Dave
A modulation model for mode splitting of magnetic perturbations in the Mega Ampere Spherical Tokamak
Hole, M J; Appel, L C
2009-01-01
Recent observations of magnetic fluctuation activity in the Mega Ampere Spherical Tokamak (MAST) reveal the presence of plasmas with bands of both low and high frequency magnetic fluctuations. Such plasmas exhibit a spectrum of low frequency modes with adjacent toroidal mode numbers, for which the measured frequency is near the Doppler shifted rotation frequency of the plasma. These are thought to be tearing modes. Also present are a spectrum of high frequency modes (e.g. Alfven, fishbone and/or ICE). The frequency and mode number of the tearing mode and its harmonics is identical to the frequency and mode number splitting of the high frequency MHD activity, strongly suggesting that the high frequency splitting is produced by modulation of the high and low frequency modes. We describe a strong modulation model, in which the nonlinear terms are fitted to produce the amplitude envelope profile of the tearing mode. A bispectral analysis proves that the low frequency modes are indeed in phase with the fundamental, while Fourier-SVD mode analysis confirms the mode numbers are toroidal harmonics. Employing this model, the sideband amplitude profile of the high frequency modes is predicted, and found to be in good agreement with experimental observations. Also, toroidal mode number splitting of the high frequency activity matches the mode number of the tearing mode. Weak evidence is found to indicate the Alfvenic sidebands are in phase with the Alfven eigenmode fundamental. The findings support predictions of a strong modulation model, and suggest a need to further develop nonlinear MHD theory to predict the amplitude of coupled sidebands, and so corroborate the observed nonlinear plasma response.
Symmetric and asymmetric nuclear matter in the Thomas-Fermi model at finite temperatures
Strobel, K.; Weber, F.; Weigel, M.K.
1999-01-01
The properties of warm symmetric and asymmetric nuclear matter are investigated in the frame of the Thomas-Fermi approximation using a recent modern parameterization of the effective nucleon-nucleon interaction of Myers and Swiatecki. Special attention is paid to the liquid-gas phase transition, which is of special interest in modern nuclear physics. We have determined the critical temperature, critical density and the so-called flash temperature. Furthermore, the equation of state for cold neutron star matter is calculated. (orig.)
Dominguez, L.; Camargo, C.T.M.
1984-09-01
The first step of the project for implementation of two non-symmetric cooling loops modeled by the ALMOD3 computer code is presented. This step consists of the introduction of a simplified model for simulating the steam generator. This model is the GEVAP computer code, integrant part of LOOP code, which simulates the primary coolant circuit of PWR nuclear power plants during transients. The ALMOD3 computer code has a model for the steam generator, called UTSG, which is very detailed. This model has spatial dependence, correlations for 2-phase flow, distinguished correlations for different heat transfer process. The GEVAP model has thermal equilibrium between phases (gaseous and liquid homogeneous mixture), no spatial dependence and uses only one generalized correlation to treat several heat transfer processes. (Author) [pt
An Analysis of $B_{s}$ Decays in the Left-Right-Symmetric Model with Spontaneous CP Violation
Ball, Patricia; Ball, Patricia; Fleischer, Robert
2000-01-01
Non-leptonic B_s decays into CP eigenstates that are caused by \\bar b -> \\bar cc\\bar s quark-level transitions, such as B_s -> D_s^+D^-_s, J/psi eta^(') or J/psi phi, provide a powerful tool to search for ``new physics'', as the CP-violating effects in these modes are tiny in the Standard Model. We explore these effects for a particular scenario of new physics, the left-right-symmetric model with spontaneous CP violation. In our analysis, we take into account all presently available experimental constraints on the parameters of this model, i.e. those implied by K- and B-decay observables; we find that CP asymmetries as large as O(40%) may arise in the B_s channels, whereas the left-right-symmetric model favours a small CP asymmetry in the ``gold-plated'' mode B_d -> J/psi K_S. Such a pattern would be in favour of B-physics experiments at hadron machines, where the B_s modes are very accessible.
A wide low-mass binary model for the origin of axially symmetric non-thermal radio sources
Kool, M. de; Heuvel, E.P.J. van den
1985-01-01
An accreting binary model has been proposed by recent workers to account for the origin of the axially symmetric non-thermal radio sources. The authors show that the only type of binary system that can produce the observed structural properties, is a relatively wide neutron star binary, in which the companion of the neutron star is a low-mass giant. Binaries of this type are expected to resemble closely the eight brightest galactic bulge X-ray sources as well as the progenitors of the two wide radio pulsar binaries. (U.K.)
Silva, Alice Cunha da; Su, Jian
2013-01-01
The High Temperature Gas cooled Reactor (HTGR) is a fourth generation thermal nuclear reactor, graphite-moderated and helium cooled. The HTGRs have important characteristics making essential the study of these reactors, as well as its fuel element. Examples of these are: high thermal efficiency,low operating costs and construction, passive safety attributes that allow implication of the respective plants. The Pebble Bed Modular Reactor (PBMR) is a HTGR with spherical fuel elements that named the reactor. This fuel element is composed by a particulate region with spherical inclusions, the fuel UO2 particles, dispersed in a graphite matrix and a convective heat transfer by Helium happens on the outer surface of the fuel element. In this work, the transient heat conduction in a spherical fuel element of a pebble-bed high temperature reactor was studied in a transient situation of combined convective and radiative cooling. Improved lumped parameter model was developed for the transient heat conduction in the two-layer composite sphere subjected to combined convective and radiative cooling. The improved lumped model was obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of the two-layer spherical fuel element was analyzed to illustrate the applicability of the proposed lumped model, with respect to die rent values of the Biot number, the radiation-conduction parameter, the dimensionless thermal contact resistance, the dimensionless inner diameter and coating thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the improved lumped model, with H2,1/H1,1/H0,0 approximation yielded significant improvement of average temperature prediction over the classical lumped model. (author)
Krakoviack, V.
2007-01-01
Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the spherical s+p mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that the phase behavior of these systems is not yet fully understood when s and p are well separated. First, there seems to be a possibility of glass-glass transition scenarios in these systems. Second, we find clear indications that the 1RSB solution cannot be correct in the full glassy phase. Therefore, while the proposed analysis is clearly naive and probably inexact, it definitely calls for a reassessment of the physics of these systems, with the promise of potentially interesting developments in the theory of disordered and complex systems
Hedrih Vladimir
2016-01-01
Full Text Available The aim of this study was to validate Holland’s hexagonal and Tracey’s spherical model of vocational interests in young adults in Serbia and Bulgaria. To this end, 1250 participants, 560 from Serbia and 690 from Bulgaria, filled in Serbian and Bulgarian versions of the Personal Globe Inventory (PGI, Tracey, 2002. Hubert and Arabie’s randomization test of hypothetical orders, multidimensional scaling with fixed coordinates, Myors test and exploratory factor analysis were used. The results showed that the hexagonal and spherical models well explained the structure of vocational interests in both samples. The level of fit of the hexagonal model to the data obtained by using the PGI was generally higher than those established in the studies that used other Holland-based instruments. Furthermore, the levels of fit of both hexagonal and spherical model were in the same range like those obtained in previous studies in other countries. The results also pointed out a remarkable similarity in the structure of vocational interests in the Bulgarian and Serbian samples. [Projekat Ministarstva nauke Republike Srbije, br. 179002
Nesterenko, V.O.; Kleinig, W.
1995-01-01
The self-consistent vibrating potential model (VPM) is extended for description of Eλ collective excitations in atomic nuclei and metal clusters with practically any kind of static deformation. The model is convenient for a qualitative analysis and provides the RPA accuracy of numerical calculations. The VPM is applied to study Eλ giant resonances in spherical metal clusters and deformed and superdeformed nuclei. It is shown that the deformation splitting of superdeformed nuclei results in a very complicated (''jungle-like'') structure of the resonances, which makes the experimental observation of E2 and E3 giant resonances in superdeformed nuclei quite problematic. Calculations of E1 giant resonance in spherical sodium clusters Na 8 , Na 20 and Na 40 are presented, as a test of the VPM in this field. The results are in qualitative agreement with the experimental data. (orig.)
Electron and hole states in quantum dot quantum wells within a spherical eight-band model
Pokatilov, E.P.; Fonoberov, V.A.; Fomin, V.; Devreese, J.T.
2001-01-01
In order to study heterostructures composed both of materials with strongly different parameters and of materials with narrow band gaps, we have developed an approach [E. P. Pokatilov [etal], Phys. Rev. B 64, 245328 (2001), (preceding paper)], which combines the spherical eight-band effective-mass
March, N.H.; Ludena, Eduardo V.
2004-01-01
For three model problems concerning two-electron spin-compensated ground states with spherical density, the third-order linear homogeneous differential equation constructed for the determination of ρ(r) is used here in conjunction with the von Weizsacker functional to characterize the one-body potential of density functional theory (DFT). Correlated von Weizsacker-type terms are compared to the exact DFT functional
Doblas, Ana; Dutta, Ananya; Saavedra, Genaro; Preza, Chrysanthe
2018-02-01
Previously, a wavefront encoded (WFE) imaging system implemented using a squared cubic (SQUBIC) phase mask has been verified to reduce the sensitivity of the imaging system to spherical aberration (SA). The strength of the SQUBIC phase mask and, as consequence, the performance of the WFE system are controlled by a design parameter, A. Although the higher the A-value, the more tolerant the WFE system is to SA, this is accomplished at the expense of the effective imaging resolution. In this contribution, we investigate this tradeoff in order to find an optimal A-value to balance the effect of SA and loss of resolution.
Hu, Shuai; Gao, Taichang; Li, Hao; Yang, Bo; Jiang, Zidong; Liu, Lei; Chen, Ming
2017-10-01
The performance of absorbing boundary condition (ABC) is an important factor influencing the simulation accuracy of MRTD (Multi-Resolution Time-Domain) scattering model for non-spherical aerosol particles. To this end, the Convolution Perfectly Matched Layer (CPML), an excellent ABC in FDTD scheme, is generalized and applied to the MRTD scattering model developed by our team. In this model, the time domain is discretized by exponential differential scheme, and the discretization of space domain is implemented by Galerkin principle. To evaluate the performance of CPML, its simulation results are compared with those of BPML (Berenger's Perfectly Matched Layer) and ADE-PML (Perfectly Matched Layer with Auxiliary Differential Equation) for spherical and non-spherical particles, and their simulation errors are analyzed as well. The simulation results show that, for scattering phase matrices, the performance of CPML is better than that of BPML; the computational accuracy of CPML is comparable to that of ADE-PML on the whole, but at scattering angles where phase matrix elements fluctuate sharply, the performance of CPML is slightly better than that of ADE-PML. After orientation averaging process, the differences among the results of different ABCs are reduced to some extent. It also can be found that ABCs have a much weaker influence on integral scattering parameters (such as extinction and absorption efficiencies) than scattering phase matrices, this phenomenon can be explained by the error averaging process in the numerical volume integration.
Legendre Duality of Spherical and Gaussian Spin Glasses
Genovese, Giuseppe; Tantari, Daniele
2015-01-01
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model
Legendre Duality of Spherical and Gaussian Spin Glasses
Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)
2015-12-15
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John
2017-10-01
The structure/amplitude of the Jovian equatorially symmetric gravitational field is affected by both rotational distortion and the fast equatorially symmetric zonal flow. We construct a fully self-consistent, four-layer, non-spheroidal (i.e, the shape is irregular) model of Jupiter that comprises an inner core, a metallic region, an outer molecular envelope and a thin transition layer between the metallic and molecular regions. While the core is assumed to have a uniform density, three different equations of state are adopted for the metallic, molecular and transition regions. We solve the governing equations via a perturbation approach. The leading-order problem accounts for the full effect of rotational distortion, and determines the density, size and shape of the core, the location and thickness of the transition layer, and the shape of the 1-bar pressure level; it also produces the mass, the equatorial and polar radii of Jupiter, and the even zonal gravitational coefficients caused by the rotational distortion. The next-order problem determines the corrections caused by the zonal flow which is assumed to be confined within the molecular envelope and on cylinders parallel to the rotation axis. Our model provides the total even gravitational coefficients that can be compared with those acquired by the Juno spacecraft.
Data Assimilation and Adjusted Spherical Harmonic Model of VTEC Map over Thailand
Klinngam, Somjai; Maruyama, Takashi; Tsugawa, Takuya; Ishii, Mamoru; Supnithi, Pornchai; Chiablaem, Athiwat
2016-07-01
The global navigation satellite system (GNSS) and high frequency (HF) communication are vulnerable to the ionospheric irregularities, especially when the signal travels through the low-latitude region and around the magnetic equator known as equatorial ionization anomaly (EIA) region. In order to study the ionospheric effects to the communications performance in this region, the regional map of the observed total electron content (TEC) can show the characteristic and irregularities of the ionosphere. In this work, we develop the two-dimensional (2D) map of vertical TEC (VTEC) over Thailand using the adjusted spherical harmonic model (ASHM) and the data assimilation technique. We calculate the VTEC from the receiver independent exchange (RINEX) files recorded by the dual-frequency global positioning system (GPS) receivers on July 8th, 2012 (quiet day) at 12 stations around Thailand: 0° to 25°E and 95°N to 110°N. These stations are managed by Department of Public Works and Town & Country Planning (DPT), Thailand, and the South East Asia Low-latitude ionospheric Network (SEALION) project operated by National Institute of Information and Communications Technology (NICT), Japan, and King Mongkut's Institute of Technology Ladkrabang (KMITL). We compute the median observed VTEC (OBS-VTEC) in the grids with the spatial resolution of 2.5°x5° in latitude and longitude and time resolution of 2 hours. We assimilate the OBS-VTEC with the estimated VTEC from the International Reference Ionosphere model (IRI-VTEC) as well as the ionosphere map exchange (IONEX) files provided by the International GNSS Service (IGS-VTEC). The results show that the estimation of the 15-degree ASHM can be improved when both of IRI-VTEC and IGS-VTEC are weighted by the latitude-dependent factors before assimilating with the OBS-VTEC. However, the IRI-VTEC assimilation can improve the ASHM estimation more than the IGS-VTEC assimilation. Acknowledgment: This work is partially funded by the
Wang, Rongjiang; Heimann, Sebastian; Zhang, Yong; Wang, Hansheng; Dahm, Torsten
2017-09-01
A hybrid method is proposed to calculate complete synthetic seismograms based on a spherically symmetric and self-gravitating Earth with a multilayered structure of atmosphere, ocean, mantle, liquid core and solid core. For large wavelengths, a numerical scheme is used to solve the geodynamic boundary-value problem without any approximation on the deformation and gravity coupling. With decreasing wavelength, the gravity effect on the deformation becomes negligible and the analytical propagator scheme can be used. Many useful approaches are used to overcome the numerical problems that may arise in both analytical and numerical schemes. Some of these approaches have been established in the seismological community and the others are developed for the first time. Based on the stable and efficient hybrid algorithm, an all-in-one code QSSP is implemented to cover the complete spectrum of seismological interests. The performance of the code is demonstrated by various tests including the curvature effect on teleseismic body and surface waves, the appearance of multiple reflected, teleseismic core phases, the gravity effect on long period surface waves and free oscillations, the simulation of near-field displacement seismograms with the static offset, the coupling of tsunami and infrasound waves, and free oscillations of the solid Earth, the atmosphere and the ocean. QSSP is open source software that can be used as a stand-alone FORTRAN code or may be applied in combination with a Python toolbox to calculate and handle Green's function databases for efficient coding of source inversion problems.
Interference between light and heavy neutrinos for 0νββ decay in the left–right symmetric model
Ahmed, Fahim, E-mail: ahmed1f@cmich.edu; Neacsu, Andrei, E-mail: neacs1a@cmich.edu; Horoi, Mihai, E-mail: mihai.horoi@cmich.edu
2017-06-10
Neutrinoless double-beta decay is proposed as an important low energy phenomenon that could test beyond the Standard Model physics. There are several potentially competing beyond the Standard Model mechanisms that can induce the process. It thus becomes important to disentangle the different processes. In the present study we consider the interference effect between the light left-handed and heavy right-handed Majorana neutrino exchange mechanisms. The decay rate, and consequently, the phase-space factors for the interference term are derived, based on the left–right symmetric model. The numerical values for the interference phase-space factors for several nuclides are calculated, taking into consideration the relativistic Coulomb distortion of the electron wave function and finite-size of the nucleus. The variation of the interference effect with the Q-value of the process is studied.
Schmitt, J. C.; Talmadge, J. N.; Anderson, D. T. [Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Hanson, J. D. [Department of Physics, Auburn University, Auburn, Alabama 36849 (United States)
2014-09-15
The bootstrap current for three electron cyclotron resonance heated plasma scenarios in a quasihelically symmetric stellarator (the Helically Symmetric Experiment) are analyzed and compared to a neoclassical transport code PENTA. The three conditions correspond to 50 kW input power with a resonance that is off-axis, 50 kW on-axis heating and 100 kW on-axis heating. When the heating location was moved from off-axis to on-axis with 50 kW heating power, the stored energy and the extrapolated steady-state current were both observed to increase. When the on-axis heating power was increased from 50 kW to 100 kW, the stored energy continued to increase while the bootstrap current slightly decreased. This trend is qualitatively in agreement with the calculations which indicate that a large positive electric field for the 100 kW case was driving the current negative in a small region close to the magnetic axis and accounting for the decrease in the total integrated current. This trend in the calculations is only observed to occur when momentum conservation between particle species is included. Without momentum conservation, the calculated bootstrap current increases monotonically. We show that the magnitude of the bootstrap current as calculated by PENTA agrees better with the experiment when momentum conservation between plasma species is included in the calculation. The total current was observed in all cases to flow in a direction to unwind the transform, unlike in a tokamak in which the bootstrap current adds to the transform. The 3-D inductive response of the plasma is simulated to predict the evolution of the current profile during the discharge. The 3-D equilibrium reconstruction code V3FIT is used to reconstruct profiles of the plasma pressure and current constrained by measurements with a set of magnetic diagnostics. The reconstructed profiles are consistent with the measured plasma pressure profile and the simulated current profile when the
On the spherical symmetry of static perfect fluids in general relativity
Beig, R.; Simon, W.
1990-01-01
We present a theorem which establishes uniqueness, in particular spherical symmetry, of a wide class of general relativistic, static perfect-fluid models provided there exists a spherically symmetric model with the same equation of state and surface potential. The method of proof, which is inspired by recent work of Masood-ul-Alam, is illustrated by demonstrating uniqueness of a class of solutions due to Buchdahl which correspond to an extreme case of the inequality on the equation of state required by our theorem. 16 refs. (Authors)
Studies on radiation symmetrization in heavy-ion driven hohlraum targets
Temporal, M.; Atzeni, S.
1993-01-01
Radiation symmetrization within spherical, ellipsoidal and cylindral hohlraum targets for heavy ion inertial confinement fusion (ICF) is studied by means of a 3-D numerical, static model, in which realistic assumptions are made concerning the geometry of the system and, particularly, of the radiation converters. Among the systems so far studied, only spherical hohlraums with six converters achieve the illumination symmetry of the fusion capsule considered necessary for ICF applications. A parametric study of cylindrical hohlraums enlightens the effect of several parameter changes, and suggests directions for further studies, aiming at the design of two-converter targets
On the spherical harmonic expansion of the neutron angular distribution function
Depken, Sven
1959-03-15
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.
On the spherical harmonic expansion of the neutron angular distribution function
Depken, Sven
1959-03-01
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases
3D dynamic modeling of spherical wheeled self-balancing mobile robot
İnal, Ali Nail
2012-01-01
Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2012. Thesis (Master's) -- Bilkent University, 2012. Includes bibliographical references. In recent years, dynamically stable platforms that move on spherical wheels, also known as BallBots, gained popularity in the robotics literature as an alternative locomotion method to statically stable wheeled mobile robots. In contrast to wheeled ...
Plane Symmetric Dark Energy Models in the Form of Wet Dark Fluid in f ( R, T) Gravity
Chirde, V. R.; Shekh, S. H.
2016-06-01
In this paper, we have investigated the plane symmetric space-time with wet dark fluid (WDF), which is a candidate for dark energy, in the framework of f ( R, T) gravity Harko et al. 2011, Phys. Rev. D, 84, 024020), where R and T denote the Ricci scalar and the trace of the energy-momentum tensor respectively. We have used the equation of state in the form of WDF for the dark energy component of the Universe. It is modeled on the equation of state p = ω( ρ - ρ ∗). The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied. Also, we have discussed the well-known astrophysical phenomena, namely the look-back time, proper distance, the luminosity distance and angular diameter distance with red shift.
Cuspidal discrete series for semisimple symmetric spaces
Andersen, Nils Byrial; Flensted-Jensen, Mogens; Schlichtkrull, Henrik
2012-01-01
We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical discrete series are non-cuspidal. (C) 2012 Elsevier Inc. All...
Klevers, Denis [Theoretical Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); Taylor, Washington [Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue Cambridge, MA 02139 (United States)
2016-06-29
We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimension two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g=3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by “unHiggsing” a model with a U(1) gauge factor under which there is matter with charge q=3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G{sub 2}×SU(2) models with more conventional matter content or SU(2){sup 3} models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass realization in the general form found by Morrison-Park, suggesting that a generalization of that form may be needed to incorporate models with arbitrary matter representations and gauge groups localized on singular divisors.
Klevers, Denis
2016-01-01
We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimension two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g=3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by "unHiggsing" a model with a U(1) gauge factor under which there is matter with charge q=3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G_2xSU(2) models with more conventional matter content or SU(2)^3 models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass real...
Testing quark mixing in minimal left–right symmetric models with b-tags at the LHC
Fowlie, Andrew; Marzola, Luca
2014-01-01
Motivated by a hint in a CMS search for right-handed W-bosons in eejj final states, we propose an experimental test of quark-mixing matrices in a general left–right symmetric model, based on counting the numbers of b-tags from right-handed W-boson hadronic decays. We find that, with our test, differences between left- and right-handed quark-mixing matrices could be detected at the LHC with √(s)=14 TeV. With an integrated luminosity of about 20/fb, our test is sensitive to right-handed quark-mixing angles as small as about 30° and with 3000/fb, our test's sensitivity improves to right-handed mixing angles as small as about 7.5°. Our test's sensitivity might be further enhanced by tuning b-tagging efficiency against purity
Bertolami, Orfeu; Paramos, Jorge
2011-01-01
The purpose of this study is to describe a perfect fluid matter distribution that leads to a constant curvature region, thanks to the effect of a nonminimal coupling. This distribution exhibits a density profile within the range found in the interstellar medium and an adequate matching of the metric components at its boundary. By identifying this constant curvature with the value of the cosmological constant and superimposing the spherical distributions arising from different matter sources throughout the universe, one is able to mimic a large-scale homogeneous cosmological constant solution.
Arvieu, Robert
1963-01-01
This research thesis deals with nuclear physics theory, and more particularly with the issues of collective states and matching properties. In a first part, the author presents the formalism and approximations used to obtain individual states and collective states of spherical nuclei, notably by studying the Bogoliubov-Valatin transformation and how it is possible to report matching phenomena, and then by introducing collective modes by means of an approximate diagonalization and of the 'quasi bosons' method. The phenomenon mechanism is described on a simple example, and, in a second part, the theory is applied to the detailed description of tin isotopes by means of finite range interaction
Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.; Wiegelmann, T.
2012-01-01
We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, 20° × 20°. Additionally, we apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free, and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.
Gray S. Chang
2005-01-01
The currently being developed advanced High Temperature gas-cooled Reactors (HTR) is able to achieve a simplification of safety through reliance on innovative features and passive systems. One of the innovative features in these HTRs is reliance on ceramic-coated fuel particles to retain the fission products even under extreme accident conditions. Traditionally, the effect of the random fuel kernel distribution in the fuel pebble/block is addressed through the use of the Dancoff correction factor in the resonance treatment. However, the Dancoff correction factor is a function of burnup and fuel kernel packing factor, which requires that the Dancoff correction factor be updated during Equilibrium Fuel Cycle (EqFC) analysis. An advanced KbK-sph model and whole pebble super lattice model (PSLM), which can address and update the burnup dependent Dancoff effect during the EqFC analysis. The pebble homogeneous lattice model (HLM) is verified by the burnup characteristics with the double-heterogeneous KbK-sph lattice model results. This study summarizes and compares the KbK-sph lattice model and HLM burnup analyzed results. Finally, we discuss the Monte-Carlo coupling with a fuel depletion and buildup code--ORIGEN-2 as a fuel burnup analysis tool and its PSLM calculated results for the HTR EqFC burnup analysis
Electron Optics for Biologists: Physical Origins of Spherical Aberrations
Geissler, Peter; Zadunaisky, Jose
1974-01-01
Reports on the physical origins of spherical aberrations in axially symmetric electrostatic lenses to convey the essentials of electon optics to those who must think critically about the resolution of the electron microscope. (GS)
Corver, M.P.; Doust, H.; van Wees, J.D.A.M.; Cloetingh, S.A.P.L.
2011-01-01
We present the results of an integrated analogue and numerical modeling study with a focus on structural, stratigraphic and thermal differences between symmetric and asymmetric grabens. These models enable fault interpretation and subsidence analyses in studies of active rifting and graben
Kim, Song Hyun; Lee, Jae Yong; KIm, Do Hyun; Kim, Jong Kyung [Dept. of Nuclear Engineering, Hanyang University, Seoul (Korea, Republic of); Noh, Jae Man [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-08-15
Chord length sampling method in Monte Carlo simulations is a method used to model spherical particles with random sampling technique in a stochastic media. It has received attention due to the high calculation efficiency as well as user convenience; however, a technical issue regarding boundary effect has been noted. In this study, after analyzing the distribution characteristics of spherical particles using an explicit method, an alternative chord length sampling method is proposed. In addition, for modeling in finite media, a correction method of the boundary effect is proposed. Using the proposed method, sample probability distributions and relative errors were estimated and compared with those calculated by the explicit method. The results show that the reconstruction ability and modeling accuracy of the particle probability distribution with the proposed method were considerably high. Also, from the local packing fraction results, the proposed method can successfully solve the boundary effect problem. It is expected that the proposed method can contribute to the increasing of the modeling accuracy in stochastic media.
Eck, Simon; Wörz, Stefan; Müller-Ott, Katharina; Hahn, Matthias; Biesdorf, Andreas; Schotta, Gunnar; Rippe, Karsten; Rohr, Karl
2016-08-01
The genome is partitioned into regions of euchromatin and heterochromatin. The organization of heterochromatin is important for the regulation of cellular processes such as chromosome segregation and gene silencing, and their misregulation is linked to cancer and other diseases. We present a model-based approach for automatic 3D segmentation and 3D shape analysis of heterochromatin foci from 3D confocal light microscopy images. Our approach employs a novel 3D intensity model based on spherical harmonics, which analytically describes the shape and intensities of the foci. The model parameters are determined by fitting the model to the image intensities using least-squares minimization. To characterize the 3D shape of the foci, we exploit the computed spherical harmonics coefficients and determine a shape descriptor. We applied our approach to 3D synthetic image data as well as real 3D static and real 3D time-lapse microscopy images, and compared the performance with that of previous approaches. It turned out that our approach yields accurate 3D segmentation results and performs better than previous approaches. We also show that our approach can be used for quantifying 3D shape differences of heterochromatin foci. Copyright © 2016 Elsevier B.V. All rights reserved.
Kim, Song Hyun; Lee, Jae Yong; KIm, Do Hyun; Kim, Jong Kyung; Noh, Jae Man
2015-01-01
Chord length sampling method in Monte Carlo simulations is a method used to model spherical particles with random sampling technique in a stochastic media. It has received attention due to the high calculation efficiency as well as user convenience; however, a technical issue regarding boundary effect has been noted. In this study, after analyzing the distribution characteristics of spherical particles using an explicit method, an alternative chord length sampling method is proposed. In addition, for modeling in finite media, a correction method of the boundary effect is proposed. Using the proposed method, sample probability distributions and relative errors were estimated and compared with those calculated by the explicit method. The results show that the reconstruction ability and modeling accuracy of the particle probability distribution with the proposed method were considerably high. Also, from the local packing fraction results, the proposed method can successfully solve the boundary effect problem. It is expected that the proposed method can contribute to the increasing of the modeling accuracy in stochastic media
Chudnovsky, D.V.; Chudnovsky, G.V.
1981-01-01
We consider general expressions of factorized S-matrices with Abelian symmetry expressed in terms of theta-functions. These expressions arise from representations of the Heisenberg group. New examples of factorized S-matrices lead to a large class of completely integrable models of statistical mechanics which generalize the XYZ-model of the eight-vertex model. (orig.)
Hobiny, Aatef D.; Abbas, Ibrahim A.
2018-01-01
The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace's transform, the physical variable solutions are obtained analytically. The numerical computations for the silicon-like semiconductor material are obtained. The comparison among the theories, i.e., dual phase lag (DPL), Lord and Shulman's (LS) and the classically coupled thermoelastic (CT) theory is presented graphically. The results further show that the analytical scheme can overcome mathematical problems by analyzing these problems.
Conformally symmetric traversable wormholes
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
2007-01-01
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced
A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID
Feng, Xueshang; Zhang, Man; Zhou, Yufen, E-mail: fengx@spaceweather.ac.cn [SIGMA Weather Group, State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China)
2014-09-01
In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.
Modelling of parameters for asymmetric halo and symmetric DHDMG n-MOSFETs
De, Swapnadip; Sarkar, Angsuman; Sarkar, Chandan Kumar
2011-10-01
This article presents an analytical surface potential, threshold voltage and drain current model for asymmetric pocket-implanted, single-halo dual material gate and double-halo dual material gate (DHDMG) n-MOSFET (MOSFET, metal-oxide-semiconductor field-effect transistor) operating up to 40 nm regime. The model is derived by applying Gauss's law to a rectangular box, covering the entire depletion region. The asymmetric pocket-implanted model takes into account the effective doping concentration of the two linear pocket profiles at the source and the drain ends along with the inner fringing capacitances at both the source and the drain ends and the subthreshold drain and the substrate bias effect. Using the surface potential model, the threshold voltage and drain currents are estimated. The same model is used to find the characteristic parameters for dual-material gate (DMG) with halo implantations and double gate. The characteristic improvement is investigated. It is concluded that the DHDMG device structure exhibits better suppression of the short-channel effect (SCE) and the threshold voltage roll-off than DMG and double-gate MOSFET. The adequacy of the model is verified by comparing with two-dimensional device simulator DESSIS. A very good agreement of our model with DESSIS is obtained proving the validity of our model used in suppressing the SCEs.
Telles, J. E.; de Souza, R. E.; Penereiro, J. C.
1990-11-01
RESUMEN. Presentamos fotometria fotografica de 8 objetos y espectrosco- pla para 3 galaxias, las cuales son buenos candidatos para galaxias esfericas. Los resultados fotometricos se presentan en la forma de iso- fotas y de perfiles radiales promedlo, de los cuales se derivan para- metros estructurales. Estas observaciones combinadas con parametros di- namicos obtenidos de observaciones espectrosc6picas, son consistentes con el plano fundamental derivado por Djorgovski y Davis (1987). ABSTRACT. We present photographic surface photometry for 8 objects and spectroscopy for 3 galaxies which are good candidates for spherical galaxies. Photometric results are presented in the form of isophotes and mean radial profiles from which we derived structural parameters. These observations combined with dynamical parameters obtained from spectroscopic observations are consistent with the fundamental plane derived by Djorgovski and Davis (1987). Keq wo : CALAXIES-ELLIPTICAL
A spherical model for the transient x-ray source A0620-00
Dilworth, C.; Maraschi, L.; Perola, G.C.
1977-01-01
The continuum spectrum of the transient X-ray source A0620-00, from infrared to X-ray frequencies, is interpreted as emission from a uniform spherical cloud of hot gas in which the free-free spectrum is modified by Thomson scattering. On this basis, the radius and the density of the cloud, and the distance of the source, are derived. The change of the spectrum with the time indicates a decrease of both radius and density with decreasing luminosity. Considering the production of X-rays to be due to impulsive accretion in a low-mass binary system, these results open the question as to whether the accreting object is a white dwarf rather than a neutron star. (author)
Deconvolving the wedge: maximum-likelihood power spectra via spherical-wave visibility modelling
Ghosh, A.; Mertens, F. G.; Koopmans, L. V. E.
2018-03-01
Direct detection of the Epoch of Reionization (EoR) via the red-shifted 21-cm line will have unprecedented implications on the study of structure formation in the infant Universe. To fulfil this promise, current and future 21-cm experiments need to detect this weak EoR signal in the presence of foregrounds that are several orders of magnitude larger. This requires extreme noise control and improved wide-field high dynamic-range imaging techniques. We propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere, or equivalently in the uvw-domain. The method uses the one-to-one relation between spherical waves and spherical harmonics (SpH). It consistently handles signals from the entire sky, and does not require a w-term correction. The SpH coefficients represent the sky-brightness distribution and the visibilities in the uvw-domain, and provide a direct estimate of the spatial power spectrum. Using these spectrally smooth SpH coefficients, bright foregrounds can be removed from the signal, including their side-lobe noise, which is one of the limiting factors in high dynamics-range wide-field imaging. Chromatic effects causing the so-called `wedge' are effectively eliminated (i.e. deconvolved) in the cylindrical (k⊥, k∥) power spectrum, compared to a power spectrum computed directly from the images of the foreground visibilities where the wedge is clearly present. We illustrate our method using simulated Low-Frequency Array observations, finding an excellent reconstruction of the input EoR signal with minimal bias.
Neutrino masses in the SU(5) x (lower case x) SU(5)' mirror symmetric model
Collie, M.; Foot, R.
1998-02-01
Motivated by the atmospheric and solar neutrino anomalies, we study neutrino masses in a parity invariant SU(5) x SU(5)' grand unified model. Two distinct ways of incorporating neutrino masses into this model are envisaged. One way involves adding a gauge singlet fermion to each generation. The other way, is to extend the scalar sector. This possibility suggests that photon - mirror photon kinetic mixing is non-zero since is generated radiatively. It is argued that the kinetic mixing is such models may well be close to the experimental limit
Non-minimal flavored S{sub 3} x Z{sub 2} left-right symmetric model
Gomez-Izquierdo, Juan Carlos [Tecnologico de Monterrey, Campus Estado de Mexico, Estado de Mexico, Estado de Mexico (Mexico); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico); Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico)
2017-08-15
We propose a non-minimal left-right symmetric model with parity symmetry where the fermion mixings arise as a result of imposing an S{sub 3} x Z{sub 2} flavor symmetry, and an extra Z{sup e}{sub 2} symmetry is considered in the lepton sector. Then the neutrino mass matrix possesses approximately the μ-τ symmetry. The breaking of the μ-τ symmetry induces sizable non-zero θ{sub 13}, and the deviation of θ{sub 23} from 45 {sup circle} is strongly controlled by an ε free parameter and the neutrino masses. So, an analytic study of the CP parities in the neutrino masses is carried out to constrain the ε parameter and the lightest neutrino mass that accommodate the mixing angles. The results are: (a) the normal hierarchy is ruled out for any values of the Majorana phases; (b) for the inverted hierarchy the values of the reactor and atmospheric angles are compatible up to 2, 3 σ C.L.; (c) the degenerate ordering is the most favorable such that the reactor and atmospheric angle are compatible with the experimental data for a large set of values of the free parameters. The model predicts defined regions for the effective neutrino mass, the neutrino mass scale and the sum of the neutrino masses for the favored cases. Therefore, this model may be testable by the future experiments. (orig.)
SP(6) X SU(2) and SO(8) X SU(2) - symmetric fermion-dynamic model of multinucleon systems
Baktybaev, K.
2007-01-01
In last years a new approach describing collective states of multinucleon system on the base of their fermion dynamic symmetry was developed. Such fermion model is broad and logical one in comparison with the phenomenological model of interacting bosons. In cut fermion S- and D- pair spaces complicated nucleons interactions are approximating in that way so multinucleon system Hamiltonian becomes a simple function of fermion generators forming corresponding Lie algebra. Correlation fermion pairs are structured in such form so its operators of birth and destruction together with a set multiband operators are formed Sp(6) and SO(8) algebra of these pairs and SU(2)-algebra for so named anomalous pairs. For convenience at the model practical application to concrete systems the dynamical-symmetric Hamiltonian is writing by means of independent Casimir operators of subgroup are reductions of a large group. It is revealed, that observed Hamiltonians besides the known SU 3 , and SO 6 asymptotic borders have also more complicated 'vibration-like' borders SO 7 , SO 5 XSU 2 and SU 2 XSO 3 . In the paper both advantages and disadvantages of these borders and some its applications to specific nuclear systems are discussing
Boonlamp, M.
2005-03-01
Full Text Available A spherical double shell model (SDM for a single cell has been developed, using Laplace’s equation in spherical coordinates and boundary conditions. Electric field intensities and dielectric constants of each region inside and outside of the cell have been estimated. The dielectrophoretic spectrum of the real part of a complex function (Re[f ( ω] were computed using Visual Foxpro Version 6, which gave calculated values pertaining to electrical properties of the cell model as compared with experimental values. The process was repeated until the error percentile was in an acceptable range. The calculated parameters were the dielectric constants and the conductivities of the inner cytoplasm ( εic, σic, the outer cytoplasm ( εoc, σoc, the inner membrane ( εim, σim, the outer membrane ( εom, σom, the suspending solution( εs, σs and the thickness of each layer (dom, doc, dim, respectively. This computer program provides estimated values of cell electrical properties with high accuracy and required minimal computational time.
Wang, Kun; Schoonover, Robert W; Su, Richard; Oraevsky, Alexander; Anastasio, Mark A
2014-05-01
Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.
Global properties of symmetric competition models with riddling and blowout phenomena
Giant-italo Bischi
2000-01-01
Full Text Available In this paper the problem of chaos synchronization, and the related phenomena of riddling, blowout and on–off intermittency, are considered for discrete time competition models with identical competitors. The global properties which determine the different effects of riddling and blowout bifurcations are studied by the method of critical curves, a tool for the study of the global dynamical properties of two-dimensional noninvertible maps. These techniques are applied to the study of a dynamic market-share competition model.
2017-01-01
top rotor superimposes an effective correlation time, τe, onto a symmetric top rotor to account for internal motion. 2. THEORY The purpose...specifically describe how simple 13C relaxation theory is used to describe quantitatively simple molecular 3 motions. More-detailed accounts ...of nuclear magnetic relaxation can be found in a number of basic textbooks (i.e., Farrar and Becker, 1971; Fukushima and Roeder, 1981; Harris, 1986
Marcus Völp
2012-11-01
Full Text Available Reliability in terms of functional properties from the safety-liveness spectrum is an indispensable requirement of low-level operating-system (OS code. However, with evermore complex and thus less predictable hardware, quantitative and probabilistic guarantees become more and more important. Probabilistic model checking is one technique to automatically obtain these guarantees. First experiences with the automated quantitative analysis of low-level operating-system code confirm the expectation that the naive probabilistic model checking approach rapidly reaches its limits when increasing the numbers of processes. This paper reports on our work-in-progress to tackle the state explosion problem for low-level OS-code caused by the exponential blow-up of the model size when the number of processes grows. We studied the symmetry reduction approach and carried out our experiments with a simple test-and-test-and-set lock case study as a representative example for a wide range of protocols with natural inter-process dependencies and long-run properties. We quickly see a state-space explosion for scenarios where inter-process dependencies are insignificant. However, once inter-process dependencies dominate the picture models with hundred and more processes can be constructed and analysed.
Hilbert Space Inner Products for PJ-symmetric Su-Schrieffer-Heeger Models
Růžička, František
2015-01-01
Roč. 54, č. 11 (2015), s. 4154-4163 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : Su-Schrieffer-Heeger model * physical inner products * complete set of pseudometrics * exceptional points Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
On large N fixed points of a U(N) symmetric (phisup(*)xphi)3sub(D=3) model coupled to fermions
Nissimov, E.R.; Pacheva, S.J.
1984-01-01
The three-dimensional U(N) symmetric eta(phisup(*) x phi) 3 model coupled to N component fermions is considered within the 1/N expansion. In contrast to the purely bosonic case, here we find in the large N limit only a (nonperturbative) ultraviolet fixed point at eta=etasup(*) approx.= 179, whereas infrared fixed points are absent. (orig.)
Ringenberg, Hunter; Rogers, Dylan; Wei, Nathaniel; Krane, Michael; Wei, Timothy
2017-11-01
The objective of this study is to apply experimental data to theoretical framework of Krane (2013) in which the principal aeroacoustic source is expressed in terms of vocal fold drag, glottal jet dynamic head, and glottal exit volume flow, reconciling formal theoretical aeroacoustic descriptions of phonation with more traditional lumped-element descriptions. These quantities appear in the integral equations of motion for phonatory flow. In this way time resolved velocity field measurements can be used to compute time-resolved estimates of the relevant terms in the integral equations of motion, including phonation aeroacoustic source strength. A simplified 10x scale vocal fold model from Krane, et al. (2007) was used to examine symmetric, i.e. `healthy', oscillatory motion of the vocal folds. By using water as the working fluid, very high spatial and temporal resolution was achieved. Temporal variation of transglottal pressure was simultaneously measured with flow on the vocal fold model mid-height. Experiments were dynamically scaled to examine a range of frequencies corresponding to male and female voice. The simultaneity of the pressure and flow provides new insights into the aeroacoustics associated with vocal fold oscillations. Supported by NIH Grant No. 2R01 DC005642-11.
Forecasting the variance and return of Mexican financial series with symmetric GARCH models
Fátima Irina VILLALBA PADILLA
2013-03-01
Full Text Available The present research shows the application of the generalized autoregresive conditional heteroskedasticity models (GARCH in order to forecast the variance and return of the IPC, the EMBI, the weighted-average government funding rate, the fix exchange rate and the Mexican oil reference, as important tools for investment decisions. Forecasts in-sample and out-of-sample are performed. The covered period involves from 2005 to 2011.
Mancusi, D; Charity, R J; Cugnon, J
2013-01-01
The de-excitation of compound nuclei has been successfully described for several decades by means of statistical models. However, accurate predictions require some fine-tuning of the model parameters. This task can be simplified by studying several entrance channels, which populate different regions of the parameter space of the compound nucleus. Fusion reactions play an important role in this strategy because they minimise the uncertainty on the entrance channel by fixing mass, charge and excitation energy of the compound nucleus. If incomplete fusion is negligible, the only uncertainty on the compound nucleus comes from the spin distribution. However, some de-excitation channels, such as fission, are quite sensitive to spin. Other entrance channels can then be used to discriminate between equivalent parameter sets. The focus of this work is on fission and intermediate-mass-fragment emission cross sections of compound nuclei with 70 70 ≲ A ≲ 240. 240. The statistical de-excitation model is GEMINI++. The choice of the observables is natural in the framework of GEMINI++, which describes fragment emission using a fissionlike formalism. Equivalent parameter sets for fusion reactions can be resolved using the spallation entrance channel. This promising strategy can lead to the identification of a minimal set of physical ingredients necessary for a unified quantitative description of nuclear de-excitation.
Andrew Phiri
2017-09-01
Full Text Available In this study, we examine linear and nonlinear cointegration and causal relations between unemployment and stock market returns in South Africa using quarterly data collected between 1994:Q1 and 2016:Q1. Our empirical results reveal significant cointegration effects between the time series in both linear and nonlinear models, even though both frameworks ultimately reject the notion of any causal relations between the variables. Collectively, our study rejects the notion of unemployment being a good predictor for stock market returns and neither do developments in the stock market have any effect on the unemployment rate. Such evidence advocates for weak-form efficiency in the JSE equity prices whereby unemployment data cannot help investors to predict the movement of future share prices and further suggests that policymakers cannot rely on stock market development as an avenue towards lowering the prevailingly high levels of unemployment as set in current macroeconomic policy objectives.
Symmetric splitting of very light systems in the coalescence and reseparation model
Blocki, J.; Grotowski, K.; Planeta, R.; Swiatecki, W.J.
1985-01-01
This is theoretical study stimulated by recent experiments at the 88-Inch Cyclotron on the binary decay of the light composite systems 46 V, 49 Cr and 52 Fe produced in collisions of 6 Li, 9 Be, and 12 C with 40 C. The dynamics of the collision is followed using the chaotic regime idealization (Liquid-Drop potential energy, wall-and-window dissipation and Werner-Wheeler inertia). Parametrization of the nuclear shapes and angular momentum are included. According to the model calculations, the decay of these systems is predicted to be the result of the fission of a rotating super-deformed configuration. The calculations suggest an angular momentum window for this type of reaction between about 30 Planck's Constant and 43 Planck's Constant. The relevant saddle-point configurations are close to scission and there is relatively little damping before fission
Simplified models of the symmetric single-pass parallel-plate counterflow heat exchanger: a tutorial
Pickard, William F.; Abraham-Shrauner, Barbara
2018-03-01
The heat exchanger is important in practical thermal processes, especially those of (i) the molten-salt storage schemes, (ii) compressed air energy storage schemes and (iii) other load-shifting thermal storage presumed to undergird a Smart Grid. Such devices, although central to the utilization of energy from sustainable (but intermittent) renewable sources, will be unfamiliar to many scientists, who nevertheless need a working knowledge of them. This tutorial paper provides a largely self-contained conceptual introduction for such persons. It begins by modelling a novel quantized exchanger,1 impractical as a device, but useful for comprehending the underlying thermophysics. It then reviews the one-dimensional steady-state idealization which demonstrates that effectiveness of heat transfer increases monotonically with (device length)/(device throughput). Next, it presents a two-dimensional steady-state idealization for plug flow and from it derives a novel formula for effectiveness of transfer; this formula is then shown to agree well with a finite-difference time-domain solution of the two-dimensional idealization under Hagen-Poiseuille flow. These results are consistent with a conclusion that effectiveness of heat exchange can approach unity, but may involve unwelcome trade-offs among device cost, size and throughput.
Jiang, Haiyong
2016-04-11
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong; Yan, Dong-Ming; Dong, Weiming; Wu, Fuzhang; Nan, Liangliang; Zhang, Xiaopeng
2016-01-01
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Jiang, Haiyong; Dong, Weiming; Yan, Dongming; Zhang, Xiaopeng
2016-01-01
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong
2016-02-26
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Khodjaev, L.Sh.
2004-01-01
Full text: We review the conceptual foundation of Yang-Mills gauge field theories. On these gauge theories the Standard Model (SM) are constructed. The fundamental postulates and their immediate consequence of the SM are formulated. The SM is a Yang-Mills type gauge field theory basically dictated by the Generalized Gauge Principle (GGP). According to this principle all fundamental forces of nature such as strong, electroweak, gravitational are mediated by an exchange of the Yang-Mills gauge fields corresponding gauge group. The SM is constructed by extension of the global non-Abelian SU(3)xSU(2)xU(1) symmetry to the local SU(3)xSU(2)xU(1) symmetry under which the Lagrangian of the SM invariant. This full symmetry has to be broken by Higgs mechanism down to the Electroweak gauge symmetry. The concept of fundamental particles does not exist. To Look for not Fundamental Particles but Fundamental symmetries. By searching of more general theory it is natural to search first of all Global symmetries and then to learn consequences connected with the localization of the global symmetries like wise of SM. The SM is renormalizable and therefor potentially consist at all energy scales. The SM in principle can describe the properties of the Universe beginning at 10 -43 sec. after BIG BANG. A SM of the BIG BANG Particle physics provides one of the few windows of the high energy world beyond SM which is consistent with SM and Cosmology. All the fundamental particles of the SM such as quarks, leptons and weak intermediate vector-gauge Bosons except one Higgs boson H 0 have been discovered and there masses and spins have been determined. The SM is stunning. Until now, no cracks have been found. There is no experiment that contradicts the SM. Moreover there is nothing observed beyond the SM. The SM works better and better. We proposed to construct colour singular nuclear forces theory based on Quantum Chromodynamics (QCD). As well Theological aspects of the BIG BANG
Wei Li
2012-01-01
Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.
Mohammad Kamaei
2016-06-01
Full Text Available Introduction: Although human industrial activities are as a part of efforts to achieve greater prosperity, the risks related to these activities are also expanding. Hazard identification and risk assessment in the oil and gas industries are essential to reduce the frequency and severity of accidents and minimize damage to people and property before their occurrence. The aim of this study was to evaluate the liquefied and pressurized petroleum gas spherical tanks in a refinery and assessing the risks of Boiling Liquid Expanding Vapor Explosion (BLEVE phenomenon. Material and Method: In this study, the risks of BLEVE phenomenon were assessed, using the Bowtie method. The consequences of explosion wave phenomenon and the resulting wave quantity and its impacts on the neighboring machineries and equipment were analyzed. PHAST software version 6.54 has been used for modeling the BLEVE phenomenon. Result: In this evaluation, generally five causes and two consequences were identified for BLEVE phenomenon. In order to reduce its consequences, forty-three controlling measures were introduced to prevent the BLEVE phenomenon and the impacts of 31 control measures were identified. According to the conducted analysis, it was found that the spherical tank blast wave caused by LPG can lead to explosion of close located tanks which can create a chain of explosions. Conclusion: The results of modeling and risk assessment can be used to identify the BLEVE phenomenon causes and its effects on nearby people and equipment. Based on these results, preventive controlling measures can be implemented and also be determined by adopting proper design and layout, margin of safety for personnel, equipment and accessories.
Zhao, G.; Liu, J.; Chen, B.; Guo, R.; Chen, L.
2017-12-01
Forward modeling of gravitational fields at large-scale requires to consider the curvature of the Earth and to evaluate the Newton's volume integral in spherical coordinates. To acquire fast and accurate gravitational effects for subsurface structures, subsurface mass distribution is usually discretized into small spherical prisms (called tesseroids). The gravity fields of tesseroids are generally calculated numerically. One of the commonly used numerical methods is the 3D Gauss-Legendre quadrature (GLQ). However, the traditional GLQ integration suffers from low computational efficiency and relatively poor accuracy when the observation surface is close to the source region. We developed a fast and high accuracy 3D GLQ integration based on the equivalence of kernel matrix, adaptive discretization and parallelization using OpenMP. The equivalence of kernel matrix strategy increases efficiency and reduces memory consumption by calculating and storing the same matrix elements in each kernel matrix just one time. In this method, the adaptive discretization strategy is used to improve the accuracy. The numerical investigations show that the executing time of the proposed method is reduced by two orders of magnitude compared with the traditional method that without these optimized strategies. High accuracy results can also be guaranteed no matter how close the computation points to the source region. In addition, the algorithm dramatically reduces the memory requirement by N times compared with the traditional method, where N is the number of discretization of the source region in the longitudinal direction. It makes the large-scale gravity forward modeling and inversion with a fine discretization possible.
Kunasz, P.B.; Hummer, D.G.; Mihalas, D.
1975-01-01
Spherical static non-LTE model atmospheres are presented for stars with M/M/sub sun/=30 and 60 at various points on their evolutionary tracks, and for some nuclei of planetary nebulae at two points of a modified Harman-Seaton sequence. The method of Mihalas and Hummer was employed, which uses a parametrized radiation force multiplier to simulate the force of radiation arising from the entire line spectrum. However, in the present work the density structure computed in the LTE models was held fixed in the calculation of the corresponding non-LTE models; in addition, the opacity of an ''average light ion'' was taken into account. The temperatures for the non-LTE models are generally lower, at a given depth, than for the corresponding LTE models when T/sub eff/<45,000 K, while the situation is reversed at higher temperatures. The continuous energy distributions are generally flattened by extension. The Lyman jump is in emission for extended models of massive stars, but never for the models of nuclei of planetary nebulae (this is primarily a temperature effect). The Balmer jumps are always in absorption. The Lyman lines are in emission, and the Balmer lines in absorption; He ii lambda4686 comes into emission in the most extended models without hydrogen line pumping, showing that it is an indicator of atmospheric extension. Very severe limb darkening is found for extended models, which have apparent angular sized significantly smaller than expected from the geometrical size of the star. Extensive tables are given of monochromatic magnitudes, continuum jumps and gradients, Stomgren-system colors, monochromatic extensions, and the profiles and equivalent widths of the hydrogen lines for all models, and of the He ii lines for some of the 60 M/sub X/ models
Effective pair potentials for spherical nanoparticles
Van Zon, Ramses
2009-01-01
An effective description for rigid spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, as can occur for some forms of the pair potentials, the effective potential generally has non-analytic points. It is shown that for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Even when only non-overlapping situations are possible, the auxiliary potentials facilitate the formulation of the effective potentials. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered and shown to be related to those for solid nanoparticles. For hollow nanoparticles overlap is more physical, since this covers the case of a smaller particle embedded in a larger, hollow nanoparticle. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London–van der Waals, Morse, Buckingham, and Lennard-Jones potentials. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure
A model study of aggregates composed of spherical soot monomers with an acentric carbon shell
Luo, Jie; Zhang, Yongming; Zhang, Qixing
2018-01-01
Influences of morphology on the optical properties of soot particles have gained increasing attentions. However, studies on the effect of the way primary particles are coated on the optical properties is few. Aimed to understand how the primary particles are coated affect the optical properties of soot particles, the coated soot particle was simulated using the acentric core-shell monomers model (ACM), which was generated by randomly moving the cores of concentric core-shell monomers (CCM) model. Single scattering properties of the CCM model with identical fractal parameters were calculated 50 times at first to evaluate the optical diversities of different realizations of fractal aggregates with identical parameters. The results show that optical diversities of different realizations for fractal aggregates with identical parameters cannot be eliminated by averaging over ten random realizations. To preserve the fractal characteristics, 10 realizations of each model were generated based on the identical 10 parent fractal aggregates, and then the results were averaged over each 10 realizations, respectively. The single scattering properties of all models were calculated using the numerically exact multiple-sphere T-matrix (MSTM) method. It is found that the single scattering properties of randomly coated soot particles calculated using the ACM model are extremely close to those using CCM model and homogeneous aggregate (HA) model using Maxwell-Garnett effective medium theory. Our results are different from previous studies. The reason may be that the differences in previous studies were caused by fractal characteristics but not models. Our findings indicate that how the individual primary particles are coated has little effect on the single scattering properties of soot particles with acentric core-shell monomers. This work provides a suggestion for scattering model simplification and model selection.
Kent mixture model for classification of remote sensing data on spherical manifolds
Lunga, D
2011-10-01
Full Text Available Modern remote sensing imaging sensor technology provides detailed spectral and spatial information that enables precise analysis of land cover usage. From a research point of view, traditional widely used statistical models are often limited...
Huang, Guo-Jiao; Bai, Chao-Ying; Greenhalgh, Stewart
2013-09-01
The traditional grid/cell-based wavefront expansion algorithms, such as the shortest path algorithm, can only find the first arrivals or multiply reflected (or mode converted) waves transmitted from subsurface interfaces, but cannot calculate the other later reflections/conversions having a minimax time path. In order to overcome the above limitations, we introduce the concept of a stationary minimax time path of Fermat's Principle into the multistage irregular shortest path method. Here we extend it from Cartesian coordinates for a flat earth model to global ray tracing of multiple phases in a 3-D complex spherical earth model. The ray tracing results for 49 different kinds of crustal, mantle and core phases show that the maximum absolute traveltime error is less than 0.12 s and the average absolute traveltime error is within 0.09 s when compared with the AK135 theoretical traveltime tables for a 1-D reference model. Numerical tests in terms of computational accuracy and CPU time consumption indicate that the new scheme is an accurate, efficient and a practical way to perform 3-D multiphase arrival tracking in regional or global traveltime tomography.
Spherically symmetric inhomogeneous bianisotropic media: Wave propagation and light scattering
Novitsky, Andrey; Shalin, Alexander S.; Lavrinenko, Andrei
2017-01-01
We develop a technique for finding closed-form expressions for electromagnetic fields in radially inhomogeneous bianisotropic media, both the solutions of the Maxwell equations and material tensors being defined by the set of auxiliary two-dimensional matrices. The approach is applied to determine...
Optics of relativistic sources in a spherically symmetric gravitational field
Campbell, G.A.
1975-01-01
The effects of spectral shifts and gravitational focussing on radiation from sources moving geodesically in the Schwarzschild gravitational field is analyzed using the general-relativistic equations for geodesic motion and for the propagation of radiation along null geodesics in the geometrical optics approximation. The exact solutions of the Schwarzschild geodesic equations are briefly discussed for the null and time-like cases, and the method of classifying the orbital types of motion based on the effective radial potential is presented. A method of finding the stability of these orbits using this technique is discussed. The geometrical optics approximation for the propagation of radiation is discussed, and the area-intensity law for the Schwarzschild field is derived. The particularly interesting region near R = 3m is investigated by means of expansions of the exact equations. Numerical techniques for calculating radiation patterns from the propagation equations are discussed, including techniques for obtaining the time variation along geodesics and differences in propagation time along different null geodesics. Finally, the implications of these calculations for the apparent contradiction in energy requirements set by Joseph Weber's observations of galactic gravitational radiation and by astronomical observation are discussed. (Diss. Abstr. Int., B)
Boundary stress tensors for spherically-symmetric conformal Rindler observers
Culetu, Hristu [Ovidius University, Constanta (Romania)
2010-06-15
The boundary energy-momentum tensors for a static observer in the conformally flat Rindler geometry are considered. We find that the surface energy density is positive far from the Planck world, but that the transversal pressures are negative. The kinematical parameters associated with the nongeodesic congruence of static observers are computed. The entropy S corresponding to the degrees of freedom on the 2-surface of constant {rho} and t equals the horizon entropy of a black hole with a time-dependent mass, and the Padmanabhan expression E = 2ST is obeyed. The 2-surface shear tensor is vanishing, and the coefficient of the bulk viscosity {zeta} is 1/16 {pi}, so the negative pressure due to it acts as a surface tension.
Kim, Hyun Keol; Montejo, Ludguier D; Jia, Jingfei; Hielscher, Andreas H
2017-06-01
We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n -th order absorption coefficients (FD-SP N ) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SP N based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SP N model with 3 rd order absorption coefficient (i.e., FD-SP 3 ) is used as a forward model to solve the inverse problem. The FD-SP 3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals. The forward results show that the FD-SP 3 model approximates the FD-ERT (S 12 ) solution within relatively high accuracy; the average error in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP 3 model than those with the SP 1 model. Therefore, this work shows that the FD-SP 3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S 12 ) and also it is more accurate than the FD-SP 1 .
Rockstroh, J.M.
1977-01-01
Cosmic-ray electrons generate the observed radio-frequency background. Previous attempts in the literature to reconcile quantitatively the measured radio-frequency intensity with the intensity deduced from the electron spectrum measured at earth have culminated in the problem that to get the respective emissivities to agree, an unacceptably high interstellar B field must be chosen. In the light of new experimental data on the emissivity as deduced from H II region studies and on the functional dependence of the diffusion coefficient with solar radius and particle rigidity, the assumptions under which the electron emissivity comparison has been made have been reexamined closely. The paradox between predicted and measured emissivity was resolved by ascribing to the magnetic fields of the galaxy a distribution of magnetic field strengths. From modified synchrotron formulas, the interstellar electron spectrum has been constructed from the radio frequency emission data with greatly improved precision. The interstellar electron spectrum has been determined independently of the solar modulation and provides, therefore, an estimate of the absolute depth of the electron modulation. Then the measured electron, proton, and helium-nuclei fluxes were systematically compared to the predictions of the spherically symmetric Fokker-Planck equation using the electron modulation as a base. A previously unnoticed non-tracking of the modulation parameters was observed during the recent recovery that did not occur during the 1965 to 1969 period. Although the argument could be presented just as well by attributing the anomaly to the nuclei, the discussion here arbitrarily tailored it to the electrons, and this new phenomenon was named, the modulation reluctance of the cosmic-ray electrons
Resistor mesh model of a spherical head: part 2: a review of applications to cortical mapping.
Chauveau, N; Morucci, J P; Franceries, X; Celsis, P; Rigaud, B
2005-11-01
A resistor mesh model (RMM) has been validated with reference to the analytical model by consideration of a set of four dipoles close to the cortex. The application of the RMM to scalp potential interpolation was detailed in Part 1. Using the RMM and the same four dipoles, the different methods of cortical mapping were compared and have shown the potentiality of this RMM for obtaining current and potential cortical distributions. The lead-field matrices are well-adapted tools, but the use of a square matrix of high dimension does not permit the inverse solution to be improved in the presence of noise, as a regularisation technique is necessary with noisy data. With the RMM, the transfer matrix and the cortical imaging technique proved to be easy to implement. Further development of the RMM will include application to more realistic head models with more accurate conductivities.
A polytropic model of a critical two-phase flow in a bed of spherical particles
Tairov Emir
2017-01-01
Full Text Available The paper is concerned with a model of isenthalpic flow of vapor-water mixture in a fixed bed of solid particles. The mixture expansion process is considered to be polytropic. Similarly to the known problem of gas dynamics of a granular bed we obtained the relationships for calculation of a critical mass velocity. The results of the calculation based on a theoretical model are compared with the experimental data obtained in the packed beds of steel balls, 2 mm and 4 mm in diameter.
Relating the Spherical representation of vocational interests to the HEXACO personality model
Holtrop, D.J.; Born, M.Ph.; de Vries, R.E.
2015-01-01
The present study extends previous research on interests-personality relations by comparing recent models of vocational interests (using the Personal Globe Inventory; PGI, Tracey, 2002) and personality (using the HEXACO-PI-R; Ashton, Lee, & de Vries, 2014) with each other. First, the structure of
Models of direct reactions and quantum pre-equilibrium for nucleon scattering on spherical nuclei
Dupuis, M.
2006-01-01
When a nucleon collides with a target nucleus, several reactions may occur: elastic and inelastic scatterings, charge exchange... In order to describe these reactions, different models are involved: the direct reactions, pre-equilibrium and compound nucleus models. Our goal is to study, within a quantum framework and without any adjustable parameter, the direct and pre-equilibrium reactions for nucleons scatterings off double closed-shell nuclei. We first consider direct reactions: we are studying nucleon scattering with the Melbourne G-matrix, which represents the interaction between the projectile and one target nucleon, and with random phase approximation (RPA) wave functions which describe all target states. This is a fully microscopic approach since no adjustable parameters are involved. A second part is dedicated to the study of nucleon inelastic scattering for large energy transfer which necessarily involves the pre-equilibrium mechanism. Several models have been developed in the past to deal with pre-equilibrium. They start from the Born expansion of the transition amplitude which is associated to the inelastic process and they use several approximations which have not yet been tested. We have achieved some comparisons between second order cross sections which have been calculated with and without these approximations. Our results allow us to criticize some of these approximations and give several directions to improve the quantum pre-equilibrium models. (author)
Golden, Ryan; Cho, Ilwoo
2015-01-01
In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...
Shahab, S.; Gray, M.; Erturk, A., E-mail: alper.erturk@me.gatech.edu [G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-03-14
Contactless powering of small electronic components has lately received growing attention for wireless applications in which battery replacement or tethered charging is undesired or simply impossible, and ambient energy harvesting is not a viable solution. As an alternative to well-studied methods of contactless energy transfer, such as the inductive coupling method, the use of ultrasonic waves transmitted and received by piezoelectric devices enables larger power transmission distances, which is critical especially for deep-implanted electronic devices. Moreover, energy transfer by means of acoustic waves is well suited in situations where no electromagnetic fields are allowed. The limited literature of ultrasonic acoustic energy transfer is mainly centered on proof-of-concept experiments demonstrating the feasibility of this method, lacking experimentally validated modeling efforts for the resulting multiphysics problem that couples the source and receiver dynamics with domain acoustics. In this work, we present fully coupled analytical, numerical, and experimental multiphysics investigations for ultrasonic acoustic energy transfer from a spherical wave source to a piezoelectric receiver bar that operates in the 33-mode of piezoelectricity. The fluid-loaded piezoelectric receiver under free-free mechanical boundary conditions is shunted to an electrical load for quantifying the electrical power output for a given acoustic source strength of the transmitter. The analytical acoustic-piezoelectric structure interaction modeling framework is validated experimentally, and the effects of system parameters are reported along with optimal electrical loading and frequency conditions of the receiver.
Shahab, S.; Gray, M.; Erturk, A.
2015-01-01
Contactless powering of small electronic components has lately received growing attention for wireless applications in which battery replacement or tethered charging is undesired or simply impossible, and ambient energy harvesting is not a viable solution. As an alternative to well-studied methods of contactless energy transfer, such as the inductive coupling method, the use of ultrasonic waves transmitted and received by piezoelectric devices enables larger power transmission distances, which is critical especially for deep-implanted electronic devices. Moreover, energy transfer by means of acoustic waves is well suited in situations where no electromagnetic fields are allowed. The limited literature of ultrasonic acoustic energy transfer is mainly centered on proof-of-concept experiments demonstrating the feasibility of this method, lacking experimentally validated modeling efforts for the resulting multiphysics problem that couples the source and receiver dynamics with domain acoustics. In this work, we present fully coupled analytical, numerical, and experimental multiphysics investigations for ultrasonic acoustic energy transfer from a spherical wave source to a piezoelectric receiver bar that operates in the 33-mode of piezoelectricity. The fluid-loaded piezoelectric receiver under free-free mechanical boundary conditions is shunted to an electrical load for quantifying the electrical power output for a given acoustic source strength of the transmitter. The analytical acoustic-piezoelectric structure interaction modeling framework is validated experimentally, and the effects of system parameters are reported along with optimal electrical loading and frequency conditions of the receiver
Analytic sensing for multi-layer spherical models with application to EEG source imaging
Kandaswamy, Djano; Blu, Thierry; Van De Ville, Dimitri
2013-01-01
Source imaging maps back boundary measurements to underlying generators within the domain; e. g., retrieving the parameters of the generating dipoles from electrical potential measurements on the scalp such as in electroencephalography (EEG). Fitting such a parametric source model is non-linear in the positions of the sources and renewed interest in mathematical imaging has led to several promising approaches. One important step in these methods is the application of a sensing principle that ...
Numerical Field Model Simulation of Full Scale Fire Tests in a Closed Spherical/Cylindrical Vessel.
1987-12-01
the behavior of an actual fire on board a ship. The computer model will be verified by the experimental data obtained in Fire-l. It is important to... behavior in simulations where convection is important. The upwind differencing scheme takes into account the unsymmetrical phenomenon of convection by using...TANK CELL ON THE NORTH SIDE) FOR A * * PARTICULAR FIRE CELL * * COSUMS (I,J) = THE ARRAY TO STORE THE SIMILIAR VALUE FOR THE FIRE * * CELL TO THE SOUTH
Modeling of the Indentation of Fiber Reinforced Materials Using Spherical Indenters
Gountsidou, V.; Polatoglou, H. M.
2010-01-01
Following the enormous development of the technology there is a great need for complex engineering materials to be studied in multilayered films at the nano-level. Careful modeling of the structure of engineering materials, using finite element analysis may reveal specific behavior of the component materials and the filling materials, such as mortars, which are the important boundaries of all the engineering materials. The instruments used for experiments are expensive and their utilization is hindered by many unexpected factors. With the help of computer programs it is possible to achieve virtual nanoindentation, a widely known non-destructive method. It is easy to model structures in whatever shape or dimensions we wish, with one or more layers and with linear or nonlinear materials in order to obtain stress, strain, displacement curves, study microhardness, etc. The purpose of this paper is to model the nanoindentation process for fiber-reinforced concrete and to study the mechanical properties as a function of the distance of a particular fibre.
Haghshenas, R.; Sheng, D. N.
2018-05-01
We develop an improved variant of U (1 ) -symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground-state phase diagram of the spin-1 /2 square J1-J2 Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the U (1 ) -symmetric iPEPS ansatz (for a fixed bond dimension D ) set a better upper bound, improving previous tensor-network-based results. By studying the finite-D scaling of the magnetically order parameter, we find a Néel phase for J2/J1place at J2c2/J1=0.610 (2 ) to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.
Aleman, S.; Hamm, L.; Smith, F.
2011-01-01
The current strategy for removal of cesium from the Hanford waste stream is ion-exchange using spherical Resorcinol-Formaldehyde (sRF) resin. The original resin of choice was granular SuperLig 644 resin and during testing of this resin several operational issues were identified. For example, the granular material had a high angle of internal friction resulting in fragmentation of resin particles along its edges during cycling and adverse hydraulic performance. Efforts to replace SuperLig 644 were undertaken and one candidate was the granular Resorcinol-Formaldehyde (RF) resin where experience with this cation exchanger dates back to the late 1940's. To minimize hydraulic concerns a spherical version of RF was developed and several different chemically produced batches were created. The 5E-370/641 batch of sRF was selected and for the last decade numerous studies have been performed (e.g., batch contact tests, column loading and elution tests). The Waste Treatment Plant (WTP) flowsheet shows that the aqueous phase waste stream will have a wide range of ionic concentrations (e.g., during the loading step 0-3 M free OH, 5+ M Na, 0-1 M K, 0-3 M NO 3 ). Several steps are required in the ion-exchange process to achieve the required Cs separation factors: loading, displacement, washing, elution, and regeneration. The sRF resin will be operated over a wide range in pH (i.e., pH of 12-14 during the loading step and pH of 0.01-1 during the elution step). During some of these steps very high levels of counter-ions and co-ions will be present within the aqueous phase. Alternative process feeds are under consideration as well (e.g., sodium levels as high as 8 M and column operation up to 45 C during loading, reduced and recycled HNO 3 during elution). In order to model the performance of sRF resin through an entire ion-exchange cycle, a more robust isotherm model is required. To achieve this more robust isotherm model requires knowledge of the numbers and kinds of fixed
Aleman, S.; Hamm, L.; Smith, F.
2011-10-03
The current strategy for removal of cesium from the Hanford waste stream is ion-exchange using spherical Resorcinol-Formaldehyde (sRF) resin. The original resin of choice was granular SuperLig 644 resin and during testing of this resin several operational issues were identified. For example, the granular material had a high angle of internal friction resulting in fragmentation of resin particles along its edges during cycling and adverse hydraulic performance. Efforts to replace SuperLig 644 were undertaken and one candidate was the granular Resorcinol-Formaldehyde (RF) resin where experience with this cation exchanger dates back to the late 1940's. To minimize hydraulic concerns a spherical version of RF was developed and several different chemically produced batches were created. The 5E-370/641 batch of sRF was selected and for the last decade numerous studies have been performed (e.g., batch contact tests, column loading and elution tests). The Waste Treatment Plant (WTP) flowsheet shows that the aqueous phase waste stream will have a wide range of ionic concentrations (e.g., during the loading step 0-3 M free OH, 5+ M Na, 0-1 M K, 0-3 M NO{sub 3}). Several steps are required in the ion-exchange process to achieve the required Cs separation factors: loading, displacement, washing, elution, and regeneration. The sRF resin will be operated over a wide range in pH (i.e., pH of 12-14 during the loading step and pH of 0.01-1 during the elution step). During some of these steps very high levels of counter-ions and co-ions will be present within the aqueous phase. Alternative process feeds are under consideration as well (e.g., sodium levels as high as 8 M and column operation up to 45 C during loading, reduced and recycled HNO{sub 3} during elution). In order to model the performance of sRF resin through an entire ion-exchange cycle, a more robust isotherm model is required. To achieve this more robust isotherm model requires knowledge of the numbers and kinds of
Neutrino jets from high-mass WR gauge bosons in TeV-scale left-right symmetric models
Mitra, Manimala; Ruiz, Richard; Scott, Darren J.; Spannowsky, Michael
2016-11-01
We reexamine the discovery potential at hadron colliders of high-mass right-handed (RH) gauge bosons WR—an inherent ingredient of left-right symmetric models (LRSM). We focus on the regime where the WR is very heavy compared to the heavy Majorana neutrino N , and we investigate an alternative signature for WR→N decays. The produced neutrinos are highly boosted in this mass regime. Subsequently, their decays via off-shell WR bosons to jets, i.e., N →ℓ±jj, are highly collimated, forming a single neutrino jet (jN). The final-state collider signature is then ℓ±jN, instead of the widely studied ℓ±ℓ±j j . Present search strategies are not sensitive to this hierarchical mass regime due to the breakdown of the collider signature definition. We take into account QCD corrections beyond next-to-leading order (NLO) that are important for high-mass Drell-Yan processes at the 13 TeV Large Hadron Collider (LHC). For the first time, we evaluate WR production at NLO with threshold resummation at next-to-next-to-leading logarithm (NNLL) matched to the threshold-improved parton distributions. With these improvements, we find that a WR of mass MWR=3 (4 )[5 ] TeV and mass ratio of (mN/MWR)discovered with a 5 - 6 σ statistical significance at 13 TeV after 10 (100 )[2000 ] fb-1 of data. Extending the analysis to the hypothetical 100 TeV Very Large Hadron Collider (VLHC), 5 σ can be obtained for WR masses up to MW R=15 (30 ) with approximately 100 fb-1 (10 ab-1 ). Conversely, with 0.9 (10 )[150 ] fb-1 of 13 TeV data, MWR<3 (4 )[5 ] TeV and (mN/MWR)<0.1 can be excluded at 95% C.L.; with 100 fb-1 (2.5 ab-1 ) of 100 TeV data, MW R<22 (33 ) TeV can be excluded.
Crisanti, Andrea; Leuzzi, Luca
2013-01-01
We report some results on the quenched disordered Spherical multi-p-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the mean-field approximation, the behavior of most known transitions in glassy materials, including dynamic arrest in super-cooled liquids, amorphous–amorphous transitions and spin–glass transitions. A simplified notation is introduced in order to compute systems properties in terms of an effective, self-induced, field encoding the whole ferromagnetic information
Mueller, J. M.; Shane, R.; Waldecker, S. J.; Dickhoff, W. H.; Charity, R. J.; Sobotka, L. G.; Crowell, A. S.; Esterline, J. H.; Fallin, B.; Howell, C. R.; Westerfeldt, C.; Youngs, M.; Crowe, B. J. III; Pedroni, R. S.
2011-01-01
Neutron elastic-scattering angular distributions were measured at beam energies of 11.9 and 16.9 MeV on 40,48 Ca targets. These data plus other elastic-scattering measurements, total and reaction cross-sections measurements, (e,e ' p) data, and single-particle energies for magic and doubly magic nuclei have been analyzed in the dispersive optical-model (DOM), generating nucleon self-energies (optical-model potentials) that can be related, via the many-body Dyson equation, to spectroscopic factors and occupation probabilities. It is found that, for stable nuclei with N≥Z, the imaginary surface potential for protons exhibits a strong dependence on the neutron-proton asymmetry. This result leads to a more modest dependence of the spectroscopic factors on asymmetry. The measured data and the DOM analysis of all considered nuclei clearly demonstrate that the neutron imaginary surface potential displays very little dependence on the neutron-proton asymmetry for nuclei near stability (N≥Z).
Sahni, D.C.; Sharma, A.
2000-01-01
The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson
Study of a phase change energy storage using spherical capsules. Part II: Numerical modelling
Bedecarrats, J.P.; Castaing-Lasvignottes, J.; Strub, F.; Dumas, J.P.
2009-01-01
The objective of this work is the numerical study of an industrial process of energy storage which consists in the use of a cylindrical tank filled with encapsulated phase change materials (PCM). A particularity is present in this kind of processes; it concerns the delay of the crystallization of the PCM, called supercooling phenomenon. The development of the model for cold storage with heat transfer fluid flowing enables a detailed analysis of this process. The effects of different parameters on the behaviour of the tank, such as the inlet temperature, the flow rate, are examined when the tank is in vertical position. There is substantial agreement between the prediction and the experimental values already presented in part I.
A spherical model with directional interactions: II. Dynamics and landscape properties
Mayer, Christian; Sciortino, Francesco; Tartaglia, Piero; Zaccarelli, Emanuela
2010-01-01
We study a binary non-additive hard-sphere mixture with square well interactions only between dissimilar particles. An appropriate choice of the inter-particle potential parameters favors the formation of equilibrium structures with tetrahedral ordering (Zaccarelli et al 2007 J. Chem. Phys. 127 174501). By performing extensive event-driven molecular dynamics simulations, we monitor the dynamics of the system, locating the iso-diffusivity lines in the phase diagram, and discuss their location with respect to the gas-liquid phase separation. We observe the formation of an ideal gel which continuously crosses towards an attractive glass upon increasing the density. Moreover, we evaluate the statistical properties of the potential energy landscape for this model. We find that the configurational entropy, for densities within the optimal network-forming region, is finite even in the ground state and obeys a logarithmic dependence on the energy.
Comprehensive asynchronous symmetric rendezvous algorithm in ...
Meenu Chawla
2017-11-10
Nov 10, 2017 ... Simulation results affirm that CASR algorithm performs better in terms of average time-to-rendezvous as compared ... process; neighbour discovery; symmetric rendezvous algorithm. 1. .... dezvous in finite time under the symmetric model. The CH ..... CASR algorithm in Matlab 7.11 and performed several.
Rui Xu
2013-01-01
Full Text Available Minimum description length (MDL based group-wise registration was a state-of-the-art method to determine the corresponding points of 3D shapes for the construction of statistical shape models (SSMs. However, it suffered from the problem that determined corresponding points did not uniformly spread on original shapes, since corresponding points were obtained by uniformly sampling the aligned shape on the parameterized space of unit sphere. We proposed a particle-system based method to obtain adaptive sampling positions on the unit sphere to resolve this problem. Here, a set of particles was placed on the unit sphere to construct a particle system whose energy was related to the distortions of parameterized meshes. By minimizing this energy, each particle was moved on the unit sphere. When the system became steady, particles were treated as vertices to build a spherical mesh, which was then relaxed to slightly adjust vertices to obtain optimal sampling-positions. We used 47 cases of (left and right lungs and 50 cases of livers, (left and right kidneys, and spleens for evaluations. Experiments showed that the proposed method was able to resolve the problem of the original MDL method, and the proposed method performed better in the generalization and specificity tests.
Wiegel, B.; Alevra, A.V.; Siebert, B.R.L.
1994-11-01
A realistic geometry model of a Bonner sphere system with a spherical 3 He-filled proportional counter and 12 polyethylene moderating spheres with diameters ranging from 7,62 cm (3'') to 45,72 cm (18'') is introduced. The MCNP Monte Carlo computer code is used to calculate the responses of this Bonner sphere system to monoenergetic neutrons in the energy range between 1 meV to 20 MeV. The relative uncertainties of the responses due to the Monte Carlo calculations are less than 1% for spheres up to 30,48 cm (12'') in diameter and less than 2% for the 15'' and 18'' spheres. Resonances in the carbon cross section are seen as significant structures in the response functions. Additional calculations were made to study the influence of the 3 He number density and the polyethylene mass density on the response as well as the angular dependence of the Bonner sphere system. The calculated responses can be adjusted to a large set of calibration measurements with only a single fit factor common to all sphere diameters and energies. (orig.) [de
Lopes, Oscar; Reyes, Miguel; Escalera, Sergio; Gonzàlez, Jordi
2014-12-01
The use of depth maps is of increasing interest after the advent of cheap multisensor devices based on structured light, such as Kinect. In this context, there is a strong need of powerful 3-D shape descriptors able to generate rich object representations. Although several 3-D descriptors have been already proposed in the literature, the research of discriminative and computationally efficient descriptors is still an open issue. In this paper, we propose a novel point cloud descriptor called spherical blurred shape model (SBSM) that successfully encodes the structure density and local variabilities of an object based on shape voxel distances and a neighborhood propagation strategy. The proposed SBSM is proven to be rotation and scale invariant, robust to noise and occlusions, highly discriminative for multiple categories of complex objects like the human hand, and computationally efficient since the SBSM complexity is linear to the number of object voxels. Experimental evaluation in public depth multiclass object data, 3-D facial expressions data, and a novel hand poses data sets show significant performance improvements in relation to state-of-the-art approaches. Moreover, the effectiveness of the proposal is also proved for object spotting in 3-D scenes and for real-time automatic hand pose recognition in human computer interaction scenarios.
Matsui, H.; Buffett, B. A.
2017-12-01
The flow in the Earth's outer core is expected to have vast length scale from the geometry of the outer core to the thickness of the boundary layer. Because of the limitation of the spatial resolution in the numerical simulations, sub-grid scale (SGS) modeling is required to model the effects of the unresolved field on the large-scale fields. We model the effects of sub-grid scale flow and magnetic field using a dynamic scale similarity model. Four terms are introduced for the momentum flux, heat flux, Lorentz force and magnetic induction. The model was previously used in the convection-driven dynamo in a rotating plane layer and spherical shell using the Finite Element Methods. In the present study, we perform large eddy simulations (LES) using the dynamic scale similarity model. The scale similarity model is implement in Calypso, which is a numerical dynamo model using spherical harmonics expansion. To obtain the SGS terms, the spatial filtering in the horizontal directions is done by taking the convolution of a Gaussian filter expressed in terms of a spherical harmonic expansion, following Jekeli (1981). A Gaussian field is also applied in the radial direction. To verify the present model, we perform a fully resolved direct numerical simulation (DNS) with the truncation of the spherical harmonics L = 255 as a reference. And, we perform unresolved DNS and LES with SGS model on coarser resolution (L= 127, 84, and 63) using the same control parameter as the resolved DNS. We will discuss the verification results by comparison among these simulations and role of small scale fields to large scale fields through the role of the SGS terms in LES.
New mathematical framework for spherical gravitational collapse
Giambo, Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo
2003-01-01
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)
Symmetric cryptographic protocols
Ramkumar, Mahalingam
2014-01-01
This book focuses on protocols and constructions that make good use of symmetric pseudo random functions (PRF) like block ciphers and hash functions - the building blocks for symmetric cryptography. Readers will benefit from detailed discussion of several strategies for utilizing symmetric PRFs. Coverage includes various key distribution strategies for unicast, broadcast and multicast security, and strategies for constructing efficient digests of dynamic databases using binary hash trees. • Provides detailed coverage of symmetric key protocols • Describes various applications of symmetric building blocks • Includes strategies for constructing compact and efficient digests of dynamic databases
Yoshida, M.
2010-12-01
A new numerical simulation model of mantle convection with a compositionally and rheologically heterogeneous, deformable, mobile continental lithosphere is presented for the first time by using three-dimensional regional spherical-shell geometry (Yoshida, 2010, Earth Planet. Sci. Lett.). The numerical results revealed that one of major factor that realizes the supercontinental breakup and subsequent continental drift is a pre-existing, weak (low-viscosity) continental margin (WCM) in the supercontinent. Characteristic tectonic structures such as young orogenic belts and suture zones in a continent are expected to be mechanically weaker than the stable part of the continental lithosphere with the cratonic root (or cratonic lithosphere) and yield lateral viscosity variations in the continental lithosphere. In the present-day Earth's lithosphere, the pre-existing, mechanically weak zones emerge as a diffuse plate boundary. However, the dynamic role of the WCM in the stability of continental lithosphere has not been understood in terms of geophysics. In my numerical model, a compositionally buoyant and highly viscous continental assemblage with pre-existing WCMs, analogous to the past supercontinent, is modeled and imposed on well-developed mantle convection whose vigor of convection, internal heating rate, and rheological parameters are appropriate for the Earth's mantle. The visco-plastic oceanic lithosphere and the associated subduction of oceanic plates are incorporated. The time integration of the advection of continental materials with zero chemical diffusion is performed by a tracer particle method. The time evolution of mantle convection after setting the model supercontinent is followed over 800 Myr. Earth-like continental drift is successfully reproduced, and the characteristic thermal interaction between the mantle and the continent/supercontinent is observed in my new numerical model. Results reveal that the WCM protects the cratonic lithosphere from being
Rotationally symmetric breather-like solutions to the sine-Gordon equation
Olsen, O.H.; Samuelsen, M.R.
1980-01-01
Breather-like solutions to the spherically symmetric sine-Gordon equation are examined numerically. Depending on the initial conditions they either exhibit a return effect or expand towards infinity. (orig.)
In Vivo Evaluation of a New Embolic Spherical Particle (HepaSphere) in a Kidney Animal Model
Luis, Esther de; Bilbao, Jose I.; Ciercoles, Jose A. Garcia Jalon de; Martinez-Cuesta, Antonio; Martino Rodriguez, Alba de; Lozano, Maria D.
2008-01-01
HepaSphere is a new spherical embolic material developed in a dry state that absorbs fluids and adapts to the vessel wall, leaving no space between the particle and the arterial wall. The aim of this study was to elucidate the final in vivo size, deformation, final location, and main properties of the particles when reconstituted with two different contrast media (Iodixanol and Ioxaglate) in an animal model. Two sizes of 'dry-state' particles (50-100 and 150-200 μm) were reconstituted using both ionic and nonionic contrast media. The mixture was used to partly embolize both kidneys in an animal model (14 pigs). The animals were sacrificed 4 weeks after the procedure and the samples processed. The final size of the particles was 230.2 ± 62.5 μm for the 50- to 100-μm dry-state particles and 314.4 ± 71 μm for the 150- to 200-μm dry-state particles. When the contrast medium (ionic versus nonionic) used for the reconstitution was studied to compare (Student's t-test) the final size of the particles, no differences were found (p > 0.05). The mean in vivo deformation for HepaSphere was 17.1% ± 12.3%. No differences (p > 0.05) were found in the deformation of the particle regarding the dry-state size or the contrast medium (Mann-Whitney test). We conclude that HepaSphere is stable, occludes perfectly, and morphologically adapts to the vessel lumen of the arteries embolized. There is no recanalization of the arteries 4 weeks after embolization. Its final in vivo size is predictable and the particle has the same properties in terms of size and deformation with the two different contrast media (Iodixanol and Ioxaglate)
Kaye, S. M., E-mail: skaye@pppl.gov; Guttenfelder, W.; Bell, R. E.; Gerhardt, S. P.; LeBlanc, B. P.; Maingi, R. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
2014-08-15
A representative H-mode discharge from the National Spherical Torus eXperiment is studied in detail to utilize it as a basis for a time-evolving prediction of the electron temperature profile using an appropriate reduced transport model. The time evolution of characteristic plasma variables such as β{sub e}, ν{sub e}{sup ∗}, the MHD α parameter, and the gradient scale lengths of T{sub e}, T{sub i}, and n{sub e} were examined as a prelude to performing linear gyrokinetic calculations to determine the fastest growing micro instability at various times and locations throughout the discharge. The inferences from the parameter evolutions and the linear stability calculations were consistent. Early in the discharge, when β{sub e} and ν{sub e}{sup ∗} were relatively low, ballooning parity modes were dominant. As time progressed and both β{sub e} and ν{sub e}{sup ∗} increased, microtearing became the dominant low-k{sub θ} mode, especially in the outer half of the plasma. There are instances in time and radius, however, where other modes, at higher-k{sub θ}, may, in addition to microtearing, be important for driving electron transport. Given these results, the Rebut-Lallia-Watkins (RLW) electron thermal diffusivity model, which is based on microtearing-induced transport, was used to predict the time-evolving electron temperature across most of the profile. The results indicate that RLW does a good job of predicting T{sub e} for times and locations where microtearing was determined to be important, but not as well when microtearing was predicted to be stable or subdominant.
Spherical cows in dark matter indirect detection
Bernal, Nicolás [Centro de Investigaciones, Universidad Antonio Nariño, Cra 3 Este # 47A-15, Bogotá (Colombia); Necib, Lina; Slatyer, Tracy R., E-mail: nicolas.bernal@uan.edu.co, E-mail: lnecib@mit.edu, E-mail: tslatyer@mit.edu [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2016-12-01
Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.
Equilibrium location for spherical DNA and toroidal cyclodextrin
Sarapat, Pakhapoom; Baowan, Duangkamon; Hill, James M.
2018-05-01
Cyclodextrin comprises a ring structure composed of glucose molecules with an ability to form complexes of certain substances within its central cavity. The compound can be utilised for various applications including food, textiles, cosmetics, pharmaceutics, and gene delivery. In gene transfer, the possibility of forming complexes depends upon the interaction energy between cyclodextrin and DNA molecules which here are modelled as a torus and a sphere, respectively. Our proposed model is derived using the continuum approximation together with the Lennard-Jones potential, and the total interaction energy is obtained by integrating over both the spherical and toroidal surfaces. The results suggest that the DNA prefers to be symmetrically situated about 1.2 Å above the centre of the cyclodextrin to minimise its energy. Furthermore, an optimal configuration can be determined for any given size of torus and sphere.
Spherical cows in the sky with fab four
Kaloper, Nemanja; Sandora, McCullen, E-mail: kaloper@physics.ucdavis.edu, E-mail: mesandora@ucdavis.edu [Department of Physics, University of California, Davis, CA 95616 (United States)
2014-05-01
We explore spherically symmetric static solutions in a subclass of unitary scalar-tensor theories of gravity, called the 'Fab Four' models. The weak field large distance solutions may be phenomenologically viable, but only if the Gauss-Bonnet term is negligible. Only in this limit will the Vainshtein mechanism work consistently. Further, classical constraints and unitarity bounds constrain the models quite tightly. Nevertheless, in the limits where the range of individual terms at large scales is respectively Kinetic Braiding, Horndeski, and Gauss-Bonnet, the horizon scale effects may occur while the theory satisfies Solar system constraints and, marginally, unitarity bounds. On the other hand, to bring the cutoff down to below a millimeter constrains all the couplings scales such that 'Fab Fours' can't be heard outside of the Solar system.
Münch, Ingo; Neff, Patrizio; Madeo, Angela; Ghiba, Ionel-Dumitrel
2015-01-01
We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress tensor is traceless and may be symmetric anyway. To this aim, the origin of couple stress is discussed on the basis of certain properties of the total stress itself. In contrast to classical continuum mechanics, the balance of linear momentum and the balance of...
Deformation and orientation effects in the binary symmetric decay of 20,21,22Ne*
Singh, BirBikram; Kaur, Manpreet; Gupta, Raj K.
2014-01-01
We have extended the study of binary symmetric decay (BSD) of extremely light mass compound systems 20,21,22 Ne* formed in 10,11 B+ 10,11 B reactions at E lab = 48 MeV, to explore the role of deformations and orientations, using the Dynamical Cluster decay Model (DCM). In the present work, we find that with inclusion of quadruple deformations and 'hot compact' orientations of nuclei σ ff increases in comparison to the case of spherical considerations of nuclei
Rotationally symmetric numerical solutions to the sine-Gordon equation
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...
Centrioles in Symmetric Spaces
Quast, Peter
2011-01-01
We describe all centrioles in irreducible simply connected pointed symmetric spaces of compact type in terms of the root system of the ambient space, and we study some geometric properties of centrioles.
A symmetrical rail accelerator
Igenbergs, E.
1991-01-01
This paper reports on the symmetrical rail accelerator that has four rails, which are arranged symmetrically around the bore. The opposite rails have the same polarity and the adjacent rails the opposite polarity. In this configuration the radial force acting upon the individual rails is significantly smaller than in a conventional 2-rail configuration and a plasma armature is focussed towards the axis of the barrel. Experimental results indicate a higher efficiency compared to a conventional rail accelerator
Matsuki, Takayuki
1976-01-01
Symmetric eikonal expansion for the scattering amplitude is formulated for nonrelativistic and relativistic potential scatterings and also for the quantum field theory. The first approximations coincide with those of Levy and Sucher. The obtained scattering amplitudes are time reversal invariant for all cases and are crossing symmetric for the quantum field theory in each order of approximation. The improved eikonal phase introduced by Levy and Sucher is also derived from the different approximation scheme from the above. (auth.)
A cosmological problem for maximally symmetric supergravity
German, G.; Ross, G.G.
1986-01-01
Under very general considerations it is shown that inflationary models of the universe based on maximally symmetric supergravity with flat potentials are unable to resolve the cosmological energy density (Polonyi) problem. (orig.)
Xujian Shu
2018-03-01
Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.