Hui, Ping; Fang, Xi-Yan; Shi, Ting-Yun
2004-01-01
Using the coupled cluster expansion with the random phase approximation, we calculate the long wavelength vacuum wave function and the vacuum energy of 2+1 dimensional Hamiltonian SU(2) lattice gauge theory (LGT) up to the seventh order. The coefficients $\\mu_0$, $\\mu_2$ of the vacuum wave function show good scaling behavior and convergence in high order calculations.
Dark soliton solutions of (N+1)-dimensional nonlinear evolution equations
Demiray, Seyma Tuluce; Bulut, Hasan
2016-06-01
In this study, we investigate exact solutions of (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation by using generalized Kudryashov method. (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation can be returned to nonlinear ordinary differential equation by suitable transformation. Then, generalized Kudryashov method has been used to seek exact solutions of the (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation. Also, we obtain dark soliton solutions for these (N+1)-dimensional nonlinear evolution equations. Finally, we denote that this method can be applied to solve other nonlinear evolution equations.
Entropy spectrum of (1+1) dimensional stringy black holes
We explore the entropy spectrum of (1+1) dimensional dilatonic stringy black holes via the adiabatic invariant integral method known as Jiang and Han's method (Phys Lett B 718:584, 2012) and the Bohr-Sommerfeld quantization rule. It is found that the corresponding spectrum depends on black hole parameters like charge, ADM mass, and, more interestingly, on the dilatonic field. We calculate the entropy of the present black hole system via the Euclidean treatment of quantum gravity and study the thermodynamics of the black hole and find that the system does not undergo any phase transition. (orig.)
(2+1)-dimensional quantum gravity
The (2+1)-dimensional pure Einstein gravity is studied in the canonical ADM formalism, assuming that the space-time topology is Σ2 (a closed and compact 2-surface) x R1. The dynamical variables are reduced to the moduli parameters of the 2-surface. Upon quantization, the system becomes a quantum mechanics of moduli parameters in a curved space endowed with the Weil-Petersson metric. In the case of torus in particular, the superspace, on which the wave function of universe is defined, turns out to be the fundamental region in the moduli space. The solution of the Wheeler-DeWitt equation is explicitly given as the Maass form which is perfectly regular in the superspace. (author)
(2+1)-dimensional quantum gravity
The (2+1)-dimensional pure Einstein gravity is studied in the canonical ADM formalism, assuming that the spatial surface is closed and compact. Owing to the constraints, the dynamical variables are reduced to the moduli parameters of the 2-surface. Upon quantization, the system becomes a quantum mechanics of moduli parameters in a curved space endowed with the Weil-Petersson metric. In the case of torus in particular, the superspace, on which the wave function of universe is defined, turns out to be the fundamental region is the moduli space. The solution of the Wheeler-DeWitt equation is explicitly given as the Maass form which is perfectly regular in the superspace. (author)
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Exploration of similarity renormalization group generators in 1-dimensional potentials
Heinz, Matthias
2015-10-01
The Similarity Renormalization Group (SRG) is used in nuclear theory to decouple high- and low-momentum components of potentials to improve convergence and thus reduce the computational requirements of many-body calculations. The SRG is a series of unitary transformations defined by a differential equation for the Hamiltonian. It includes a matrix called the generator that defines how the transformation will change the Hamiltonian. The commonly used SRG generators evolve the Hamiltonian into a band-diagonal shape. Evolving potentials using SRG induces many-body forces. If these forces are truncated at the N-body level, this systematically introduces errors from omitted (N+1)-body forces when modeling many-body systems. While established generators are fairly successful, alternative generators may converge faster, be faster to calculate, or lead to smaller many-body forces. In particular, recent findings suggest that a block diagonal generator may induce smaller many-body forces. We use 1-dimensional systems of two, three, and four bosons as a theoretical laboratory for studying how these alternative generators perform, and to observe how they induce many-body forces.
Nonpropagating Solitary Waves in (2+1)-Dimensional Nonlinear Systems
MENG Jian-Ping; ZHANG Jie-Fang
2005-01-01
By means of extended homogeneous balance method and variable separation approach, quite a general variable separation solution of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation is derived. From the variable separation solution and by selecting appropriate functions, a new class of (2+1)-dimensional nonpropagating solitary waves are found. The novel features exhibited by these new structures are first revealed.
Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations
The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space—time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space—time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system. (general)
DAI Chao-Qing; YAN Cai-Jie; ZHANG Jie-Fang
2006-01-01
In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1+1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3+1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2+ 1 )-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.
Lessons from (2+1)-dimensional quantum gravity
Schroers, B. J.
2007-01-01
Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincare symmetry are examined in the context of (2+1)-dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck's constant and the cosmological constant enter the non-commutative and non-cocommutative structures arising in (2+1)-dimensional quantum gravity. It is emphasised that the much studied bicrossproduct kappa-Poincare ...
Critical behavior of 2+1 dimensional CPN-1 model with a Chern-Simons term
I investigate the critical behaviour of 2+1 dimensional CPN-1 model with a Chern-Simons term. I derive the 1/N expansion in this model and show that the theory is renormalizable in this framework. The critical exponents η and υ are calculated to the O(1/N). They exhibit θ (coefficient of the Chern-Simons term) dependence. (author). 14 refs, 6 figs
Hypocycloidal throat for 2 + 1-dimensional thin-shell wormholes
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2015-11-15
Recently we have shown that for 2 + 1-dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider an angular dependent throat geometry embedded in a 2 + 1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided by a hypocycloid. That is, two flat 2 + 1 dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one. (orig.)
Thermodynamics of event horizons in (2+1)-dimensional gravity
Although gravity in 2+1 dimensions is very different in nature from gravity in 3+1 dimensions, it is shown that the laws of thermodynamics for event horizons can be manifested also for (2+1)-dimensional gravity. The validity of the classical laws of horizon mechanics is verified in general and exemplified for the (2+1)-dimensional analogues of Reissner-Nordstroem and Schwarzschild--de Sitter spacetimes. We find that the entropy is given by 1/4L, where L is the length of the horizon. A consequence of having consistent thermodynamics is that the second law fixes the sign of Newton's constant to be positive
ZHANG Huan; TIAN Bo; ZHANG Hai-Qiang; GENG Tao; MENG Xiang-Hua; LIU Wen-Jun; CAI Ke-Jie
2008-01-01
For describing various complex nonlinear phenomena in the realistic world, the higher-dimensional nonlinear evolution equations appear more attractive in many fields of physical and engineering sciences. In this paper, by virtue of the Hirota bilinear method and Riemann theta functions, the periodic wave solutions for the (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation are obtained. Furthermore, it is shown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.
Geodesic bi-scalars in (n+1)-dimensional spacetimes
This is a sequel to the previous papers RRK 85 - 12 and 85 - 18 (1985), which dealt with the geodesic bi-scalars in a Robertson-Walker universe with flat 3-space and in an anisotropic homogeneous universe, respectively. In the present article, the results obtained before are extended to the case of a (n+1)-dimensional spacetime. (author)
Upon Generating (2+1)-dimensional Dynamical Systems
Zhang, Yufeng; Bai, Yang; Wu, Lixin
2016-06-01
Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.
Md Nur Alam; M Ali Akbar; M Fazlul Hoque
2014-09-01
In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown that the new approach of generalized (′/)-expansion method is a straightforward and effective mathematical tool for solving nonlinear evolution equations in applied mathematics, mathematical physics and engineering. Moreover, this procedure reduces the large volume of calculations.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R.; Nicolini, Piero
2011-01-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\\sqrt{\\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scal...
(N+1)-dimensional Lorentzian evolving wormholes supported by polytropic matter
Cataldo, Mauricio [Universidad del Bio-Bio, Departamento de Fisica, Facultad de Ciencias, Concepcion (Chile); Arostica, Fernanda; Bahamonde, Sebastian [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile)
2013-08-15
In this paper we study (N+1)-dimensional evolving wormholes supported by energy satisfying a polytropic equation of state. The considered evolving wormhole models are described by a constant redshift function and generalizes the standard flat Friedmann-Robertson-Walker spacetime. The polytropic equation of state allows us to consider in (3+1)-dimensions generalizations of the phantom energy and the generalized Chaplygin gas sources. (orig.)
Causality in 1+1-dimensional Yukawa model-II
Asrarul Haque; Satish D Joglekar
2013-10-01
The limits → large, $M →$ large with ($g^{3}/M$) = const. of the 1+1-dimensional Yukawa model are discussed. The conclusion of the results on bound states of the Yukawa model in this limit (obtained in arXiv:0908.4510v3 [hep-th]) is taken into account. It is found that model reduces to an effective non-local 3 theory in this limit. Causality violation also is observed in this limit.
Horizons in (1 + 1)-dimensional dilaton gravity coupled to matter
We study static solutions of a general (1 + 1)-dimensional dilaton gravity coupled to scalar fields and Abelian gauge fields near horizons. This includes, in particular, reductions of higher-dimensional theories invariant under a sufficiently large isometry group. The solution near the horizon can be obtained by solving a system of integral equations or alternatively in the form of a convergent series in the dilaton field
Non-trivial 2+1-Dimensional Gravity
Grigore, D. R.; Scharf, G.
2010-01-01
We analyze 2+1-dimensional gravity in the framework of quantum gauge theory. We find that Einstein gravity has a trivial physical subspace which reflects the fact that the classical solution in empty space is flat. Therefore we study massive gravity which is not trivial. In the limit of vanishing graviton mass we obtain a non-trivial massless theory different from Einstein gravity. We derive the interaction from descent equations and obtain the cosmological topologically massive gravity. Howe...
A pseudoCoulombian potential in D=1 dimensional space
In the D=1 dimensional space, we study the bound state solutions of the potential V(x)=-c/x+b/x2 (e, b>0). They occur on the right half-plane xin[0, ∞[. In the limit b→0, we recover the spectrum of the D=1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant.
Exact solutions of (3 + 1)-dimensional stochastic Burgers equation
A generalized tan h function method is used for constructing exact travelling wave solutions of nonlinear stochastic partial differential equations. The main idea of this method is to take full advantage of the Riccati equation, which has more exact solutions. More Wick-type stochastic multiple soliton-like solutions and triangular periodic solutions are obtained for the (3 + 1)-dimensional Wick-type stochastic Burgers equation via Hermite transformation
Exact interior solutions in 2 + 1-dimensional spacetime
We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)
X-ray spontaneous emission control by 1-dimensional photonic bandgap structure
André, Jean-Michel; Jonnard, Philippe
2010-01-01
Paper available at http://epjd.edpsciences.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/epjd/abs/2010/06/d09549/d09549.html International audience The possibility of controlling the X-ray spontaneous emission of atoms embedded in a 1-dimensional photonic bandgap structure by the so-called Purcell effect, is studied. Calculations of the spontaneously emitted power are presented from Fermi's golden rule in the framework of the Wigner-time approach extended to ...
GUP Corrected Fermion Tunnelling from 2 + 1 Dimensional Black String
Tang, Jian; Feng, Zhongwen; Ren, Wei; Chen, Bingbing
2016-01-01
In this paper, using the generalized Dirac equation which is modified by GUP, we study the fermion tunneling from 2 + 1 dimensional black string. Our results show that the Hawking temperature is not only depended on the event horizon of black string but also related to the quantum number of emitted fermion (energy and mass). Meanwhile, we find the GUP can slow down the Hawking temperature increase and lead to the remnants. It implies that the GUP can avoid the evaporation of black holes.
Nucleosynthetic Signatures of Asymmetric Supernovae - Lessons from 1-dimensional Explosions
We review the evidence for asymmetries in explosions, and in particular, the nucleosynthetic signatures from these asymmetries. To guide our intuition for these yields, we have modeled a series of spherically symmetric explosions with a range of explosion energies. Here we present the results from these 1-dimensional simulations, focusing on the yields of the radioactive elements 44Ti and 56Ni. We find that, although the abundance yields of 44Ti do depend sensitively on the explosion energy, the trend (whether it increases or decreases with explosion energy) depends very sensitively on the model
Nucleosynthetic Signatures of Asymmetric Supernovae - Lessons from 1-dimensional Explosions
Hungerford, A. L.; Fryer, C. L.; Timmes, F. X.; McGhee, K.
2005-07-01
We review the evidence for asymmetries in explosions, and in particular, the nucleosynthetic signatures from these asymmetries. To guide our intuition for these yields, we have modeled a series of spherically symmetric explosions with a range of explosion energies. Here we present the results from these 1-dimensional simulations, focusing on the yields of the radioactive elements 44Ti and 56Ni. We find that, although the abundance yields of 44Ti do depend sensitively on the explosion energy, the trend (whether it increases or decreases with explosion energy) depends very sensitively on the model.
Quantum Interest in (3+1) dimensional Minkowski space
Abreu, Gabriel
2008-01-01
The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially preventing the existence of exotic phenomena such as "Alcubierre warp-drives" or "traversable wormholes". Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.
A pseudoCoulombian potential in D=1 dimensional space
Lombard, R J [Groupe de Physique theorique, Institut de Physique Nucleaire, 91406 Orsay Cedex (France); Mezhoud, R [Faculty of Sciences, Boumerdes University, 35000 Boumerdes (Algeria); Yekken, R [Institut de Physique, USTHB Bab Ezzouar, Alger (Algeria)], E-mail: lombard@ipno.in2p3.fr, E-mail: mezhoudreda@yahoo.fr, E-mail: rabia_yek@yahoo.fr
2009-12-15
In the D=1 dimensional space, we study the bound state solutions of the potential V(x)=-c/x+b/x{sup 2} (e, b>0). They occur on the right half-plane xin[0, {infinity}[. In the limit b{yields}0, we recover the spectrum of the D=1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant.
Perturbational blowup solutions to the compressible 1-dimensional Euler equations
Yuen, Manwai, E-mail: nevetsyuen@hotmail.com [Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon (Hong Kong)
2011-10-24
We construct non-radially symmetry solutions for the compressible 1-dimensional adiabatic Euler equations in this Letter. In detail, we perturb the linear velocity with a drifting term: (1)u=c(t)x+b(t), to seek new solutions. Then, we transform the problem into the analysis of ordinary differential equations. By investigating the corresponding ordinary differential equations, a new class of blowup or global solutions can be given. Here, our constructed solutions can provide the mathematical explanations for the drifting phenomena of some propagation wave like Tsunamis. And when we adopt the Galilean-like transformation to a drifting frame, the constructed solutions are self-similar. -- Highlights: → We construct non-radially symmetry solutions for the 1-dimensional Euler equations. → We perturb the linear velocity with a drifting term to seek new solutions. → We transform the Euler system into the ordinary differential equations analysis. → The solutions model the drifting phenomena of some propagation wave like Tsunamis. → Under the Galilean-like transformation, the constructed solutions are self-similar.
Generalized (2+1) dimensional black hole by Noether symmetry
Darabi, F. [Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM), Maragha (Iran, Islamic Republic of); Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Atazadeh, K.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of)
2013-12-15
We use the Noether symmetry approach to find f(R) theory of (2+1) dimensional gravity and (2+1) dimensional black hole solution consistent with this f(R) gravity and the associated symmetry. We obtain f(R)=D{sub 1} R(n/n+1)(R/K){sup 1/n} + D{sub 2}R + D{sub 3}, where the constant term D{sub 3} plays no dynamical role. Then, we find general spherically symmetric solution for this f(R) gravity which is potentially capable of being as a black hole. Moreover, in the special case D{sub 1} = 0, D{sub 2} = 1, namely f(R) = R + D{sub 3}, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D{sub 3} and represents symmetry of the action under the transformation R {yields}R' = R + D{sub 3} along the killing vector {partial_derivative}{sub R}. The ordinary BTZ black hole is obtained as the special case where D{sub 3} is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q=0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy-Verlinde formula. (orig.)
Quantum Holonomies in (2+1)-Dimensional Gravity
Nelson, J E
2004-01-01
We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and upper--triangular form are constructed, which in the latter case exhibit additional, non--trivial internal relations for each holonomy matrix. This leads to the notion of quantum matrix pairs. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of powers of the matrices obey the same pattern of internal relations as the original pair. This has implications for the classical moduli space, described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices.
Quench dynamics in confined 1 + 1-dimensional systems
We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT. (letter)
Quench dynamics in confined 1 + 1-dimensional systems
Engelhardt, Dalit
2016-03-01
We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT.
Aspects of noncommutative (1+1)-dimensional black holes
We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length √(θ) cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R.; Nicolini, Piero
2011-08-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length θ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R
2011-01-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\\sqrt{\\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass $M$, cosmological constant $\\Lambda$, etc...), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Entanglement and majorization in (1+1)-dimensional quantum systems
Orus, R
2005-01-01
Motivated by the idea of entanglement loss along Renormalization Group flows, analytical majorization relations are proven for the ground state of (1+1)-dimensional conformal field theories. For any of these theories, majorization is proven to hold in the spectrum of the reduced density matrices in a bipartite system when changing the size L of one of the subsystems. Continuous majorization along uniparametric flows is also proven as long as part of the conformal structure is preserved under the deformation and some monotonicity conditions hold as well. As particular examples of our derivations, we study the cases of the XX, Heisenberg and XY quantum spin chains. Our results provide in a rigorous way explicit proves for all the majorization conjectures raised by Latorre, Lutken, Rico, Vidal and Kitaev in previous papers on quantum spin chains.
3+1-dimensional multi-Hamiltonian integrable systems
In this work we will present multi-Hamiltonian systems in 3+1 dimensions. In literature there are many examples for non-linear second order differential equations in 1+1 dimensions which are completely integrable by Magri's theorem. But not too much in 2+1 and almost no examples in 3+1 dimensions. Therefore it becomes very important to get multi-Hamiltonian integrable systems in four dimensions. Very recently Nutku Y, Sheftel M B and collaborates discovered multi-Hamiltonian structure for Plebanski's second heavenly equation and for complex Monge-Ampere (CMA) equation. Both of these equations possess partner symmetries which plays very imported role in constructing the recursion operator for the systems. We will give the method how to obtain multi-Hamiltonian structure for 3+1 dimensional evolutionary systems and the latest development in this subject
Minimal Wormholes in an (n + 1)-Dimensional Cosmological Background
Zangeneh, M Kord
2011-01-01
In this article, we discuss a class of expanding traversable wormholes in an (n+1)-dimensional Robertson-Walker (RW) background with Ricci scalar independent of the r-coordinate. With this condition, we obtain a wormhole metric which in general depends on the curvature constant k. For the flat (k = 0) case, we obtain the scale factor R(t) by using the Friedmann equations in the large r limit and use this to obtain the diagonal energy-momentum tensor. Applying the weak energy condition (WEC) we obtain a critical radius and a critical time that are limits of the violation of WEC. Although it is proved that the throat is a null hypersurface but it is shown that wormhole has no horizon and is traversable from both sides of this hypersurface.
On (2+1)-Dimensional Non-isospectral Toda Lattice Hierarchy and Integrable Coupling System
By considering (2+1)-dimensional non-isospectral discrete zero curvature equation, the (2+1)-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the (2+1)-dimensional Toda lattice hierarchy are given. Finally, the (2+1)-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.
Li-Li, Huang; Yong, Chen
2016-06-01
In this paper, the truncated Painlevé analysis, nonlocal symmetry, Bäcklund transformation of the (2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented. Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system. In addition, the (2+1)-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton–cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to find by other traditional methods. Moreover figures are given out to show the properties of the explicit analytic interaction solutions. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213).
Boundary dynamics and the statistical mechanics of the 2 + 1-dimensional black hole
We calculate the density of states of the 2 + 1-dimensional BTZ black hole in the micro-and grand-canonical ensembles. Our starting point is the relation between 2 + 1-dimensional quantum gravity and quantised Chern-Simons theory. In the micro-canonical ensemble, we find the Bekenstein-Hawking entropy by relating a Kac-Moody algebra of global gauge charges to a Virasoro algebra with a classical central charge via a twisted Sugawara construction. This construction is valid at all values of the black hole radius. At infinity it gives the asymptotic isometries of the black hole, and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same Virasoro algebra. In the grand-canonical ensemble we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole. We then compute the partition function directly in a boundary Wess-Zumino-Witten theory, and find that we obtain the correct result only after we include a source term at the horizon that induces a non-trivial spin-structure on the WZW partition function
Quantum cosmology in (1 +1 )-dimensional Hořava-Lifshitz theory of gravity
Pitelli, J. P. M.
2016-05-01
In a recent paper [Phys. Rev. D 92, 084012 (2015)], the author studied the classical (1 +1 )-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in the Hořava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will take one step further in the understanding of (1 +1 )-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with the equation of state (EoS) p =w ρ . The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schrödinger equation for the wave function of the universe has the following properties: for w =1 (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for w ≠1 , a characteristic inverse square potential appears in addition to a regular polynomial that depends on the EoS. Explicit solutions for a few cases of interest will be found and the expectation value of the scale factor will be calculated. As in usual quantum cosmology, it will be shown that the quantum theory smooths out the big-bang singularity, but the classical behavior of the universe is recovered in the low-energy limit.
Boundary dynamics and the statistical mechanics of the 2 + 1-dimensional black hole
Baniados, M; Ortiz, M E
1999-01-01
We calculate the density of states of the 2 + 1-dimensional BTZ black hole in the micro-and grand-canonical ensembles. Our starting point is the relation between 2 + 1-dimensional quantum gravity and quantised Chern-Simons theory. In the micro-canonical ensemble, we find the Bekenstein-Hawking entropy by relating a Kac-Moody algebra of global gauge charges to a Virasoro algebra with a classical central charge via a twisted Sugawara construction. This construction is valid at all values of the black hole radius. At infinity it gives the asymptotic isometries of the black hole, and at the horizon it gives an explicit form for a set of deformations of the horizon whose algebra is the same Virasoro algebra. In the grand-canonical ensemble we define the partition function by using a surface term at infinity that is compatible with fixing the temperature and angular velocity of the black hole. We then compute the partition function directly in a boundary Wess-Zumino-Witten theory, and find that we obtain the correc...
We apply Pauli--Villars regularization and discrete light-cone quantization to the nonperturbative solution of a (3+1)-dimensional model field theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of the complex symmetric Lanczos algorithm. This permits the calculation of each Fock-sector wave function, and from these we obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form factor slope
(2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves
2015-01-01
By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. Furthermore, the (2+1)-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1)-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1)-dimensional mKdV eq...
2 + 1-dimensional traversable wormholes supported by positive energy
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2015-02-01
We revisit the shapes of the throats of wormholes, including thin-shell wormholes (TSWs) in 2 + 1 dimensions. In particular, in the case of TSWs this is done in a flat 2 + 1-dimensional bulk spacetime by using the standard method of cut-and-paste. Upon departing from a pure time-dependent circular shape i.e., r = a(t) for the throat, we employ a θ-dependent closed loop of the form r = R(t, θ), and in terms of R(t, θ) we find the surface energy density σ on the throat. For the specific convex shapes we find that the total energy which supports the wormhole is positive and finite. In addition, we analyze the general wormhole's throat. By considering the specific equation of r = R(θ) instead of r = r{sub 0} = const., and upon certain choices of functions for R(θ), we find the total energy of the wormhole to be positive. (orig.)
2 + 1-dimensional traversable wormholes supported by positive energy
We revisit the shapes of the throats of wormholes, including thin-shell wormholes (TSWs) in 2 + 1 dimensions. In particular, in the case of TSWs this is done in a flat 2 + 1-dimensional bulk spacetime by using the standard method of cut-and-paste. Upon departing from a pure time-dependent circular shape i.e., r = a(t) for the throat, we employ a θ-dependent closed loop of the form r = R(t, θ), and in terms of R(t, θ) we find the surface energy density σ on the throat. For the specific convex shapes we find that the total energy which supports the wormhole is positive and finite. In addition, we analyze the general wormhole's throat. By considering the specific equation of r = R(θ) instead of r = r0 = const., and upon certain choices of functions for R(θ), we find the total energy of the wormhole to be positive. (orig.)
3+1 dimensional viscous hydrodynamics at high baryon densities
Karpenko, Iu; Bleicher, M.; Huovinen, P.; Petersen, H.
2015-05-01
A 3+1 dimensional event-by-event viscous hydrodynamic + cascade model is applied for the simulation of heavy ion collision reactions at \\sqrt{sNN} = 6.3... 200 GeV. UrQMD cascade is used for the pre-thermal (pre-hydro) and final (post-hydro) stages of the reaction. The baryon, as well as electric charge densities are consistently taken into account in the model. For this aim the equation of state based on a Chiral model coupled to the Polyakov loop is used in hydrodynamic phase of evolution. As a result of the model adjustment to the experimental data, the effective values of the shear viscosity over entropy density η/s are obtained for different collision energies in the BES region. A decrease of the effective values of η/s from 0.2 to 0.08 is observed as collision energy increases from \\sqrt{s} ≈ 7 to 39 GeV.
The Casimir energy of skyrmions in the 2+1-dimensional O(3)-model
Walliser, H
1999-01-01
One-loop quantum corrections to the classical vortices in 2+1 dimensional O(3)-models are evaluated. Skyrme and Zeeman potential terms are used to stabilize the size of topological solitons. Contributions from zero modes, bound-states and scattering phase-shifts are calculated for vortices with winding index n=1 and n=2. For both cases the S-matrix shows a pronounced series of resonances for magnon-vortex scattering in analogy to the well-established baryon resonances in hadron physics, while vortices with n>2 are already classically unstable against decay. The quantum corrections destabilize the classically bound n=2 configuration. Approximate independence of the results with respect to changes in the renormalization scale is demonstrated.
张解放; 吴锋民
2002-01-01
We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.
3+1 -dimensional Schwinger terms and non-commutative geometry
Langmann, E; Edwin Langmann; Jouko Mickelsson
1994-01-01
Abstract: We discuss 2-cocycles of the Lie algebra \\Map(M^3;\\g) of smooth, compactly supported maps on 3-dimensional manifolds M^3 with values in a compact, semi-simple Lie algebra \\g. We show by explicit calculation that the Mickelsson-Faddeev-Shatashvili cocycle \\f{\\ii}{24\\pi^2}\\int\\trac{A\\ccr{\\dd X}{\\dd Y}} is cohomologous to the one obtained from the cocycle given by Mickelsson and Rajeev for an abstract Lie algebra \\gz of Hilbert space operators modeled on a Schatten class in which \\Map(M^3;\\g) can be naturally embedded. This completes a rigorous field theory derivation of the former cocycle as Schwinger term in the anomalous Gauss' law commutators in chiral QCD(3+1) in an operator framework. The calculation also makes explicit a direct relation of Connes' non-commutative geometry to (3+1)-dimensional gauge theory and motivates a novel calculus generalizing integration of \\g-valued forms on 3-dimensional manifolds to the non-commutative case.
(3+1)-dimensional light-front model with spontaneous breaking of chiral symmetry
We investigate a (3+1)-dimensional toy model that exhibits spontaneous breakdown of chiral symmetry, both in a light-front (LF) Hamiltonian and in a Euclidean Schwinger-Dyson (SD) formulation. We show that both formulations are completely equivalent, provided the renormalization is properly done. The counterterm can be constructed explicitly by eliminating zero-mode degrees of freedom, giving rise to to an effective interaction: i.e., zero-mode dynamics, in the sense of an effective action, leads to a very simple set of modifications for the nonzero modes. We find that it is sufficient to renormalize terms that exist already in the canonical LF Hamiltonian independently. Chiral symmetry breaking is manifested via a open-quotes kinetic massclose quotes counterterm, which is eventually responsible for the mass generation of the physical fermion of the model. The vertex mass in the LF calculation must be taken to be the same as the current quark mass in the SD calculation. copyright 1997 The American Physical Society
Variable separation solutions and new solitary wave structures to the (1+1)-dimensional Ito system
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2006-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physics system.The variable separation solution of (1+1)-dimensional Ito system is obtained.Some special types of solutions such as non-propagating solitary wave solution,propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.
Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations
Guo, Xiu-Rong
2016-06-01
We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58
Electrostatic self-force in (2+1)-dimensional cosmological gravity
Furtado, C; Furtado, Claudio; Moraes, Fernando
1996-01-01
Point sources in (2+1)-dimensional gravity are conical singularities that modify the global curvature of the space giving rise to self-interaction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge in the presence of point masses in (2+1)-dimensional gravity with a cosmological constant.
Horizons in 2+1-dimensional collapse of particles
Dieter Brill; Puneet Khetarpal; Vijay Kaul
2007-07-01
A simple, geometrical construction is given for three-dimensional spacetimes with negative cosmological constant that contain two particles colliding head-on. Depending on parameters like particle masses and distance, the combined geometry will be that of a particle, or of a black hole. In the black hole case the horizon is calculated. It is found that the horizon typically starts at a point and spreads into a closed curve with corners, which propagate along spacelike caustics and disappear as the horizon passes the particles.
3+1 dimensional viscous hydrodynamics at high baryon densities
Karpenko, Iu; Huovinen, P; Petersen, H
2013-01-01
We apply a 3+1D viscous hydrodynamic + cascade model to the heavy ion collision reactions with $\\sqrt{s_{NN}}=6.3\\dots39$ GeV. To accommodate the model for a given collision energy range, the initial conditions for hydrodynamic phase are taken from UrQMD, and the equation of state at finite baryon density is based on Chiral model coupled to the Polyakov loop. We study the collision energy dependence of pion and kaon rapidity distributions and $m_T$-spectra, as well as charged hadron elliptic flow and how shear viscosity affects them. The model calculations are compared to the data for Pb-Pb collisions at CERN SPS, as well as for Au-Au collisions in the Beam Energy Scan (BES) program energies at BNL RHIC. The data favours the value of shear viscosity $\\eta/s\\gtrsim0.2$ for this collision energy range.
Zhou, Tianci; Faulkner, Thomas; Fradkin, Eduardo
2016-01-01
We investigate the entanglement entropy (EE) of circular entangling cuts in the 2+1-dimensional quantum Lifshitz model, whose ground state wave function is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose weight is the Gibbs weight of 2D Euclidean free boson. We show that the finite subleading corrections of EE to the area-law term as well as the mutual information are conformal invariants and calculate them for cylinder, disk-like and spherical manifolds with various spatial cuts. The subtlety due to the boson compactification in the replica trick is carefully addressed. We find that in the geometry of a punctured plane with many small holes, the constant piece of EE is proportional to the number of holes, indicating the ability of entanglement to detect topological information of the configuration. Finally, we compare the mutual information of two small distant disks with Cardy's relativistic CFT scaling proposal. We find that in the quantum Lifshitz model, the mutual information al...
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
Pérez, Margarita García; González-Arroyo, Antonio; Okawa, Masanori
2013-09-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the Z N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λ N L and an angle defined in terms of the magnetic flux (λ is `t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence ( N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
Pérez, Margarita García; Okawa, Masanori
2013-01-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=\\lambda NL and an angle defined in terms of the magnetic flux (\\lambda\\ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable sc...
Logarithmic corrections in (4+1) -dimensional directed percolation.
Grassberger, Peter
2009-05-01
We simulate directed site percolation on two lattices with four spatial and one timelike dimensions (simple and body-centered hypercubic in space) with the standard single cluster spreading scheme. For efficiency, the code uses the same ingredients (hashing, histogram reweighing, and improved estimators) as described by Grassberger [Phys. Rev. E 67, 036101 (2003)]. Apart from providing the most precise estimates for p_{c} on these lattices, we provide a detailed comparison with the logarithmic corrections calculated by [Janssen and Stenull [Phys. Rev. E 69, 016125 (2004)]. Fits with the leading logarithmic terms alone would give estimates of the powers of these logarithms which are too big by typically 50%. When the next-to-leading terms are included, each of the measured quantities (the average number of sites wetted at time t , their average distance from the seed, and the probability of cluster survival) can be fitted nearly perfectly. But these fits would not be mutually consistent. With a consistent set of fit parameters, one obtains still much improvement over the leading log approximation. In particular we show that there is one combination of these three observables which seems completely free of logarithmic terms. PMID:19518501
Ruiyu Hao; Guosheng Zhou
2008-01-01
The(2+1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2+1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2+1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations
Two Darboux transformations of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka (CDGKS) equation and (2+1)-dimensional modified Korteweg-de Vries (mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the (2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the (2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
ZHANG Jie-Fang
2001-01-01
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
New Soliton-like Solutions for (2+1)-Dimensional Breaking Soliton Equation
XIE Zheng; ZHANG Hong-Qing
2005-01-01
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kinds of new special exact soltion-like solutions of (2+1)-dimensional breaking soliton equation are obtained by using some general transformations and the further generalized projective Riccati equation method.
Bosonic and Fermionic Entropy of (2+1)-Dimensional Charged Black Hole
CHEN Ju-Hua; WANG Yong-Jiu; JING Ji-Liang
2001-01-01
From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2+1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.
Lei Ya; Yang Duo
2013-01-01
In this paper,the finite symmetry transformation group of the (2+ 1)-dimensional coupled Burgers equation is studied by the modified direct method,and with the help of the truncated Painlevé expansion approach,some special localized structures for the (2+ 1)-dimensional coupled Burgers equation are obtained,in particular,the dromion-like and solitoff-like structures.
New Explicit Exact Solutions to (2+1)-Dimensional Generalized Broer-Kaup System
HUANG Ding-Jiang; ZHANG Hong-Qing
2005-01-01
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.
Lie symmetry group of (2+1-dimensional Jaulent-Miodek equation
Ma Hong-Cai
2014-01-01
Full Text Available In this paper, we consider a system of (2+1-dimensional non-linear model by using auxiliary equation method and Clarkson-Kruskal direct method which is very important in fluid and physics. We construct some new exact solutions of (2+1-dimensional non-linear models with the aid of symbolic computation which can illustrate some actions in fluid in the future.
In this paper, the multiple Riccati equations rational expansion method is further extended to construct non-travelling wave solutions of the (2 + 1)-dimensional Painleve integrable Burgers equation and the (2 + 1)-dimensional Breaking soliton equation, as a result, some double solitary-like wave solutions and complexiton solutions of the two equations are obtained. The extended method can also be applied to solve some other nonlinear evolution equations
Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity
Ariwahjoedi, Seramika; Rovelli, Carlo; Zen, Freddy P
2015-01-01
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2+1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.
Anomaly-Induced Magnetic Screening in 2+1 dimensional QED at Finite Density
Stefano ForteINFN Torino, Italy
1993-01-01
We show that in 2+1 dimensional Quantum Electrodynamics an external magnetic field applied to a finite density of massless fermions is screened, due to a $2+1$-dimensional realization of the underlying $2$-dimensional axial anomaly of the space components of the electric current. This is shown to imply screening of the magnetic field, i.e., the Meissner effect. We discuss the physical implications of this result.
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field
Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in [Saha Institute of Nuclear Physics, Kolkata (India)
2015-07-15
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Topological aspects of classical and quantum (2+1)-dimensional gravity
In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g=0 and g=1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g=1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace model of (2+1)-dimensional gravity with the matter fields in the case of g=0 and g=1. For g=0, a wormhole solution is found but for g=1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g=1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity. (author)
In this Letter, We present a further generalized algebraic method to the (2 + 1)-dimensional dispersive long-wave equations (DLWS), As a result, we can obtain abundant new formal exact solutions of the equation. The method can also be applied to solve more (2 + 1)-dimensional (or (3 + 1)-dimensional) nonlinear partial differential equations (NPDEs)
Bulk-boundary correspondence in (3+1)-dimensional topological phases
Chen, Xiao; Tiwari, Apoorv; Ryu, Shinsei
2016-07-01
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level K , and its generalization. In particular, we put these theories on a flat (2+1)-dimensional torus T3 parameterized by its modular parameters, and compute the partition functions obeying various twisted boundary conditions. We show the partition functions are transformed into each other under S L (3 ,Z ) modular transformations, and furthermore establish the bulk-boundary correspondence in (3+1) dimensions by matching the modular S and T matrices computed from the boundary field theories with those computed in the bulk. We also propose the three-loop braiding statistics can be studied by constructing the modular S and T matrices from an appropriate boundary field theory.
Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry
We have studied the Hawking radiation from generalized rotating and static (2+1)-dimensional BTZ black holes. In this regard, we have benefited from the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized (2+1)-dimensional BTZ black holes are different from ordinary (2+1)-dimensional BTZ black holes due to the Noether symmetry. In other words, the Noether symmetry can change the tunneling rate and Hawking temperature of the BTZ black holes. This symmetry may cause the BTZ black holes to avoid evaporation and its breakdown may start the evaporation. (orig.)
Casana, R.; Ferreira, M.M., E-mail: manojr.ufma@gmail.com; Mouchrek-Santos, V.E.; Silva, Edilberto O.
2015-06-30
We have demonstrated that Lorentz-violating terms stemming from the fermion sector of the SME are able to generate geometrical phases on the wave function of electrons confined in 1-dimensional rings, as well as persistent spin currents, in the total absence of electromagnetic fields. We have explicitly evaluated the eigenenergies and eigenspinors of the electrons modified by the Lorentz-violating terms, using them to calculate the dynamic and the Aharonov–Anandan phases in the sequel. The total phase presents a pattern very similar to the Aharonov–Casher phase accumulated by electrons in rings under the action of the Rashba interaction. Finally, the persistent spin current were carried out and used to impose upper bounds on the Lorentz-violating parameters.
The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach
Lu, W F
1999-01-01
The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum in the field system is asymmetrical, which verifies an earlier conjecture. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for some portion of the aforementioned region. Besides, the masses of one particle and tow-particle bound state upon the symmetric vacuum are also calculated, and the resultant masses agree with the recent second-order results of fermion-mass perturbation for the massive Schwinger model.
One plotted the Green function of the Dirac equation within external constant and uniform field in terms of (2 + 1)-dimensional quantum electrodynamics (QRD2+1) with nonzero density of fermions. In terms of QRD2+1 single-loop approximation one derived expression for polarization operator within external constant and uniform magnetic field at nonzero chemical potential. One calculated contribution of the Chern-Simon induced term into polarization operator and efficient Lagrangian at fermion density corresponding to occupation of the Landau n relativistic levels by them in the external magnetic field. One derived expression for the Chern-Simon induced term in the magnetic field at end temperature and nonzero chemical potential
Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation
Zhengde Dai; Chuanjian Wang; Jun Liu
2014-10-01
A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.
Hypocycloidal throat for 2+1-dimensional thin-shell wormholes
Mazharimousavi, S Habib
2015-01-01
Recently we have shown that for $2+1-$dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider angular dependent throat geometry embedded in a $2+1-$dimensional flat spacetime in polar coordinates. It is shown that a generic, natural example of throat geometry is provided remarkably by a hypocycloid. That is, two flat $2+1-$dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one.
Hypocycloidal throat for 2+1-dimensional thin-shell wormholes
Mazharimousavi, S. Habib; Halilsoy, M.
2015-11-01
Recently we have shown that for 2+1-dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider an angular dependent throat geometry embedded in a 2+1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided by a hypocycloid. That is, two flat 2+1 dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one.
New Multi-soliton Solutions for the (2+1)-Dimensional Kadomtsev-Petviashvili Equation
LIU Yang-Kui; Zhaqilao; FANG Jian-Hui; LI Zhi-Bin; PANG Ting; LIN Peng
2008-01-01
In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a (1+1)-dimensional Broer Kaup (BK) equation and a (1+1)-dimensional high-order Broer Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new ba-sic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili (KP) equation are obtained.
Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation
A new (2+1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1+1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2+1)-dimensional lattice equation are explicitly obtained by the Darboux transformation.
A new hierarchy of (1 + 1)-dimensional soliton equations and its quasi-periodic solutions
A new spectral problem is proposed, from which a hierarchy of (1 + 1)-dimensional soliton equations is derived. With the help of nonlinearization approach, the soliton systems in the hierarchy are decomposed into two new compatible Hamiltonian systems of ordinary differential equations. The generating function flow method is used to prove the involutivity and the functional independence of the conserved integrals. The Abel-Jacobi coordinates are introduced to straighten out the associated flows. Using the Riemann-Jacobi inversion technique, the explicit quasi-periodic solutions for the (1 + 1)-dimensional soliton equations are obtained
Symmetry Reductions of (2 + 1-Dimensional CDGKS Equation and Its Reduced Lax Pairs
Na Lv
2014-01-01
Full Text Available With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.
The quantum interest conjecture in (3+1)-dimensional Minkowski space
Abreu, Gabriel
2010-01-01
The quantum inequalities, and the closely related quantum interest conjecture, impose restrictions on the distribution of the energy density measured by any time-like observer, potentially preventing the existence of exotic phenomena such as Alcubierre warp-drives or traversable wormholes. It has already been proved that both assertions can be reduced to statements concerning the existence or non-existence of bound states of a certain 1-dimensional quantum mechanical Hamiltonian. Using this approach, we will informally review a simple variational proof of one version of the Quantum Interest conjecture in (3+1)-dimensional Minkowski space.
Conservation laws for two (2 + 1)-dimensional differential-difference systems
Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080 (China) and Graduate School of the Chinese Academy of Sciences, Beijing (China)]. E-mail: gfyu@lsec.cc.ac.cn; Tam, H.-W. [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China)]. E-mail: tam@comp.hkbu.edu.hk
2006-10-15
Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced.
Chaotic solutions of(2+1)-dimensional Broek-Kaup equation with variable coefficients
Yang Zheng; Ma Song-Hua; Fang Jian-Ping
2011-01-01
In this paper, an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the(2+1)-dimensional Broek-Kaup equation with variable coefficients(VCBK). Based on the derived solitary wave solution and using a known chaotic system, some novel chaotic solutions are investigated.
Soliton Fission and Fusion in (2+1)-Dimensional Boiti-Leon-Pempinelli System
ZHENG Chun-Long; FANG Jian-Ping; CHEN Li-Qun
2005-01-01
By means of a special Painlevé-Backlund transformation and a multilinear variable separation approach,an exact solution with arbitrary functions of the (2+1)-dimensional Boiti-Leon-Pempinelli system (BLP) is derived.Based on the derived variable separation solution, we obtain some special soliton fission and fusion solutions for the higher dimensional BLP system.
Annihilation Solitons and Chaotic Solitons for the (2+1)-Dimensional Breaking Soliton System
无
2007-01-01
By means of an improved mapping method and a variable separation method, a scries of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
Variable Separation Solutions for the (2+1)-Dimensional Burgers Equation
唐晓艳; 楼森岳
2003-01-01
Considering that the multi-linear variable separation approach has been proved to be very useful to solve many (2+1)-dimensional integrable systems, we obtain the variable separation solutions of the Burgers equation with arbitrary number of variable separated functions. The Y-shaped soliton fusion phenomenon is revealed.
Nonpropagating Solitons in (2+1)-Dimensional Dispersive Long-Water Wave System
FANG Jian-Ping; ZHENG Chun-Long; LIU Qing
2005-01-01
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations
In this paper, two (3+1)-dimensional equations are investigated. Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types of exact solutions including some arbitrary functions. When these arbitrary functions are taken as some special functions, these solutions possess abundant structures. These solutions contain soliton-like solutions and rational solutions.
2+1-dimensional wormhole from a doublet of scalar fields
Mazharimousavi, S. Habib; Halilsoy, Mustafa
2015-01-01
We present a class of exact solutions in the framework of (2+1)-dimensional Einstein gravity coupled minimally to a doublet of scalar fields. Our solution can be interpreted upon the tuning of parameters as an asymptotically flat wormhole as well as a particle model in 2+1 dimensions.
Path Integral Evaluation of the Free Propagator on the (D-1)-dimensional Pseudosphere
Wospakrik, Hans J.
1999-01-01
We present an explicit path integral evaluation of the free Hamiltonian propagator on the (D-1)-dimensional pseudosphere, in the horicyclic coordinates, using the integral equation method. This method consists in deriving an integral equation for the propagator that turns out to be of Abel's type.
A Phase Space Path Integral for (2+1)-Dimensional Gravity
Carlip, Steven
1995-01-01
I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two approaches, and discuss some subtleties in the definition of the path integral necessary to prove this equivalence.
In this paper, by using symbolic and algebra computation, Chen and Wang's multiple Riccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the (2+1)-dimensional Breaking soliton equation are derived by using the extended multiple Riccati equations expansion method.
Linear superposition method for (2+1)-dimensional nonlinear wave equations
Lin Ji; Wang Rui-Min; Ye Li-Jun
2006-01-01
New forms of different-periodic travelling wave solutions for the(2+1)-dimensional Zakharov-Kuznetsov(ZK) equation and the Davey-Stewartson(DS)equation are obtained by the linear superposition approach of Jacobi elliptic function.A sequence of cyclic identities plays an important role in these procedures.
Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
Jean-Michel CORON; Jesús Ildefonso D（I）AZ; Abdelmalek DRICI; Tommaso MINGAZZINI
2013-01-01
The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control.They assume that the internal control is only time dependent.The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.
New soliton solutions of dissipative (2+1)-dimensional AKNS equation
Mohammad Najafi; Somayeh Najafi; Malihe Najafi
2013-01-01
We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of dissipative (2+1)-dimensional AKNS equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
Periodic Wave Solution to the (3+1)-Dimensional Boussinesq Equation
WU Yong-Qi
2008-01-01
@@ One- and two-periodic wave solutions for (3+1)-dimensional Boussinesq equation are presented by means of Hirota's bilinear method and the Riemann theta function. The soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.
New nonlocal symmetries and conservation laws of the (1+1)-dimensional Sine-Gordon equation
A system of linearized equations of the (1+1)-dimensional Sine-Gordon (SG) equation and its Bäcklund transformation are given to determine not only nonlocal symmetries but also nonlocal conservation laws of the SG equation. Through the parameter expansion procedure, a sequence of infinitely many nonlocal symmetries and a sequence of infinitely many nonlocal conservation laws are obtained
Solution for (1+1)-dimensional surface solitons in thermal nonlinear media
Ma, Xuekai; Yang, Zhenjun; Lu, Daquan; Guo, Qi; Hu, Wei
2011-03-01
Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.
Solution for (1+1)-dimensional surface solitons in thermal nonlinear media
Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.
New and More General Rational Formal Solutions to (2+1)-Dimensional Toda System
无
2007-01-01
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to (2+1)-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
On (2+1) Dimensional Topologically Massive Non-linear Electrodynamics
Slusarczyk, M.; Wereszczynski, A.
2002-01-01
The (2+1) dimensional non-linear electrodynamics, the so called Pagels--Tomboulis electrodynamics, with the Chern--Simons term is considered. We obtain "generalized self--dual equation" and find the corresponding generalized massive Chern--Simons Lagrangian. Similar results for (2+1) massive dilaton electrodynamics have been obtained.
Lattice versions with restricted suppersymmetry of simple (1+1)-dimensional supersymmetric models are numerically studied using a local hamiltonian Monte Carlo method. The pattern of supersymmetry breaking closely follows the expectations of Bartels and Bronzan obtain in an alternative lattice formulation. (orig.)
Evaluation of the performance of the WRF 1-Dimensional Lake model over the East Africa Great Lakes
Gudoshava, M.; Semazzi, F. H. M.
2015-12-01
This study seeks to investigate the performance of the 1-Dimensional lake model coupled to WRF over East Africa. The Africa Great lakes exert a great influence on the climate of the region and a number of studies have shown how the lake influences the circulation and the total precipitation over the region. The lakes have highly variable depths, with Lake Victoria having an average depth of 40m and Lake Tanganyika a depth of 450m. The Lake model for WRF was tested and calibrated for the Great lakes, however it was not tested for tropical lakes. We hypothesize that the inclusion of a 1-dimensional lake will reduce the precipitation bias as compared to the WRF model without the lake model. In addition initializing the lake temperature using a vertical temperature profile that closes resembles the one over these lakes will greatly reduce the spin up time. The simulations utilized three nested domains at 36, 12 and 4km. The 4km domain is centered over Lake Victoria Basin, while the 12 km domain includes all the lakes in East Africa. The Tropical Rainfall Measuring Mission (TRMM) datasets are used in evaluating the precipitation, and the following statistics were calculated: root mean square error, standard deviation of the model and observations and mean bias. The results show that the use of the 1-dimensional lake model improves the precipitation over the region considerably compared to an uncoupled model. The asymmetrical rainfall pattern is evident in the simulations. However using the default vertical temperature profile with a three-month spin up is not adequate to transfer heat to the bottom of the lake. Hence the temperatures are still very cold at the bottom. A nine-month spin up improves the lake surface temperatures and lake temperatures at the bottom. A two year spin up greatly improves the lake surface temperatures and hence the total precipitation over the lake. Thus longer spin up time allows for adequate heat transfer in the lake. Initializing the
Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations
Liu, Han-Ze; Xin, Xiang-Peng
2016-08-01
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. Supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009, and the doctorial foundation of Liaocheng University under Grant No. 31805
Periodic Wave Solutions to a (3+1)-Dimensional Soliton Equation
WANG Jun-Min
2012-01-01
Two classes of periodic wave solutions to the (3+1)-dimensional soliton equation are derived by employing the Hirota bilinear method and theta function identities.These solutions are expressed in terms of Riemann theta functions of genus one and can be converted into an elliptic function format,both their long wave limit and extremum value are discussed in detail.%Two classes of periodic wave solutions to the (3+1)-dimensional soliton equation are derived by employing the Hirota bilinear method and theta function identities. These solutions are expressed in terms of Riemann theta functions of genus one and can be converted into an elliptic function format, both their long wave limit and extremum value are discussed in detail.
Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry
Darabi, F.; Atazadeh, K.; Rezaei-Aghdam, A.
2014-01-01
We have studied the Hawking radiation from {\\it generalized} rotating and static $(2+1)$-dimensional BTZ black holes. In this regard, we have benefited the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized $(2+1)$-dim...
The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations
M Matinfar; M Eslami; S Roshandel
2015-10-01
In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.
Fission and Fusion of Solitons for the (1+1)-Dimensional Kupershmidt Equation
YING Jin-Ping
2001-01-01
By means of the heat conduction equation and the standard truncated Painlevé expansion, the (1+1) dimensional Kupershmidt equation is solved. Some significant exact multi-soliton solutions are given. Especially; for the interaction of the multi-solitons of the Kupershmidt equation, we find that a single (resonant) kink or bell soliton may be fissioned to several kink or bell solitons. Inversely, several kink or bell solitons may also be fused to one kink or bell soliton.
Exact solution of Dirac equation in 2+1 dimensional gravity
We find exact solutions of the Dirac equation in the 2+1 dimensional curved background by separation of variables. These solutions are given in terms of hypergeometric functions. We also perform the Gordon decomposition for the Dirac current to discuss the time dependence of the polarization densities and the magnetization density, and to show that the polarization densities are more effective than the magnetization density in the pair production in finite time intervals
Counter-rotational effects on stability of 2 + 1-dimensional thin-shell wormholes
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2014-09-15
The role of angular momentum in a 2 + 1-dimensional rotating thin-shell wormhole (TSW) is considered. Particular emphasis is given to stability when the shells (rings) are counter-rotating. We find that counter-rotating halves make the TSW supported by the equation of state of a linear gas more stable. Under a small velocity dependent perturbation, however, it becomes unstable. (orig.)
Expanding $(n+1)$-Dimensional Wormhole Solutions in Brans-Dicke Cosmology
Ebrahimi, E.; Riazi, N.
2009-01-01
We have obtained two classes of $(n+1)$-dimensional wormhole solutions using a traceless energy-momentum tensor in Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric spacetime also appear among the solutions as special cases. We have also considered the travesibility of the wormhole solutions...
Perturbation of higher-genus spatial surfaces in (2+1)-dimensional gravity
We study dynamical evolutions of spatial surfaces with genus g≥2 in (2+1)-dimensional pure Einstein gravity by the perturbation analysis around static moduli solutions. We find that an action of the perturbed Teichmueller parameters has a harmonic-oscillator form with a time-dependent mass and frequency. It is also shown that a set of the static moduli solutions is an attractor of nearby solutions
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time
Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)
2014-11-15
This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
Symbolic Computation Study of (2+1)-Dimensional Dispersive Long Wave Equations
Seeking exact analytical solutions of nonlinear evolution equations is of fundamental importance in mathematical physics. In this paper, based on a constructive algorithm and symbolic computation, abundant new exact solutions of the (2+1)-dimensional dispersive long wave equations are obtained, among which there are soliton-like solutions, mult-soliton-like solutions and formal periodic solutions, etc. Certain special solutions are considered and some interesting localized structures are revealed.
In this paper, the F-expansion method is extended and applied to construct the exact solutions of the (2 + 1)-dimensional generalized Wick-type stochastic Kadomtsev-Petviashvili equation by the aid of the symbolic computation system Maple. Some new stochastic exact solutions which include kink-shaped soliton solution, singular soliton solution and triangular periodic solutions are obtained via this method and Hermite transformation
The Multisoliton Solutions for the (2+1-Dimensional Sawada-Kotera Equation
Zhenhui Xu
2013-01-01
Full Text Available Applying bilinear form and extended three-wavetype of ansätz approach on the (2+1-dimensional Sawada-Kotera equation, we obtain new multisoliton solutions, including the double periodic-type three-wave solutions, the breather two-soliton solutions, the double breather soliton solutions, and the three-solitary solutions. These results show that the high-dimensional nonlinear evolution equation has rich dynamical behavior.
Painlevé Analysis and Some Solutions of(2+1)-Dimensional Generalized Burgers Equations
HONG Ke-Zhu; WU B-in; CHEN Xian-Feng
2003-01-01
Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e') analysis,the most generalized Painlev(e') integrable(2+1)-dimensional integrable Burgers systems are obtained.Some exact solutions of the generalized Burgers system are obtained via variable separation approach.
Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory
On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)
A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
Hongli An
2012-08-01
Full Text Available A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when γ=2 to a nonlinear dynamical subsystem with underlying integrable Hamiltonian-Ermakov structure. Exact solutions of the magnetogasdynamic system are thereby obtained which describe a rotating elliptic plasma cylinder. The semi-axes of the elliptical cross-section, remarkably, satisfy a Ermakov-Ray-Reid system.
A Bilinear B(a)cklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation
WU Jian-Ping
2008-01-01
@@ Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation.As an application, soliton solution and stationary rational solution for the (3+1)-dimensional soliton equation are presented.
Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei
Topological entanglement entropy of (2+1) dimensional Chern-Simons gauge theories on a general manifold is usually calculated with Witten's method of surgeries and replica trick, in which the spacetime manifold under consideration is very complicated. In this work, we develop an edge theory approach, which greatly simplifies the calculation of topological entanglement entropy of a Chern-Simons theory. Our approach applies to a general manifold with arbitrary genus. The effect of braiding and fusion of Wilson lines can be straightforwardly calculated within our framework. In addition, our method can be generalized to the study of other entanglement measures such as mutual information and entanglement negativity of a topological quantum field theory on a general manifold.
Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
Ammon, A.; T. Hartung; Jansen, K.; Leövey, H.; Volmer, J.
2016-01-01
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the c...
Strings and string breaking in 2+1 dimensional nonabelian theories
Kovner, Alex; Rosenstein, Baruch
1998-01-01
We consider properties of confining strings in 2+1 dimensional SU(2) nonabelian gauge theory with the Higgs field in adjoint representation. The analysis is carried out in the context of effective dual Lagrangian which describes the dynamics of t'Hooft's $Z_{N}$ vorices. We point out that the same Lagrangian should be interpreted as an effective Lagrangian for the lightest glueballs. It is shown how the string tension for a fundamental string arises in this description. We discuss the propert...
The Nernst theorem and statistical entropy in a (1+1)-dimensional charged black hole
It was derived that the bosonic and fermionic entropies in (1+1)-dimensional charged black hole directly by using the quantum statistical method. The result is the same as the integral expression obtained by solving the wave equation approximately. Then it is obtained the statistical entropy of the black hole by integration via the improved brick-wall method, membrane model. The derived entropy satisfies the thermodynamic relation. When the radiation temperature of the black hole tends to zero, so does the entropy. It obeys Nernst theorem. So it can be taken as Planck absolute entropy
Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation
Huang Wen-Hua
2009-01-01
A general solution,including three arbitrary functions,is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method.Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution,special types of periodic folded waves are derived.In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions of the periodic folded waves and the degenerated single folded solitary waves axe investigated graphically and found to be completely elastic.
Bolokhov, A A; Bolokhov, T A; Sherman, S G
1996-01-01
We present the analysis of the phase space geometry of 2 \\rightarrow 3 reaction for the general case of nonzero and unequal particle masses. Its purpose is to elaborate an alternative approach to the problem of integration over phase space which does not exploit the Monte Carlo principle. The fast and effective algorithm of integration based on Gauss method is developed for treating 1--dimensional distributions in two--particle invariant variables. The algorithm is characterized by significantly improved accuracy and it can meet requirements of interactive processing.
Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
Gecim, Ganim
2016-01-01
In this paper, we study early-time inflation and late-time acceleration of the universe in the presence of non-minimal coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background by using the Noether symmetry approach. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with the results obtained in the context of the 3+1 dimensional teleparallel gravity under Noether symmetry approach, and we see that the two models have similar physically results about the inflation of the universe.
Distributions of self-interactions and voids in (1+1)-dimensional directed percolation
We investigate the scaling of self-interactions and voids in (1+1)-dimensional directed percolation clusters and backbones. We verify that the meandering of the backbone scales like the directed cluster. A geometric relation between the size distribution and the fractal dimensions of a set of objects is applied to find the scaling properties of self-interactions in directed percolation. Lastly we connect the geometric properties of the backbone with the avalanche distribution generated by interface dynamics at the depinning transition
Distributions of self-interactions and voids in (1+1)-dimensional directed percolation
Huber, G.; Jensen, M.H.; Sneppen, K. [Center for Chaos and Turbulence Studies, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)
1995-09-01
We investigate the scaling of self-interactions and voids in (1+1)-dimensional directed percolation clusters and backbones. We verify that the meandering of the backbone scales like the directed cluster. A geometric relation between the size distribution and the fractal dimensions of a set of objects is applied to find the scaling properties of self-interactions in directed percolation. Lastly we connect the geometric properties of the backbone with the avalanche distribution generated by interface dynamics at the depinning transition.
LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS
张解放; 刘宇陆
2002-01-01
By using the extended homogeneous balance method, the localized coherentstructures are studied. A nonlinear transformation was first established, and then thelinearization form was obtained based on the extended homogeneous balance method for thehigher order ( 2 + 1 ) -dimensional Broer-Kaup equations. Starting from this linearizationform equation, a variable separation solution with the entrance of some arbitrary functionsand some arbitrary parameters was constructed. The quite rich localized coherent structureswere revealed. This method, which can be generalized to other (2 + 1 )-dimensionalnonlinear evolution equation, is simple and powerful.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
APPLICATION OF EXP-FUNCTION METHOD TO THE (2+1-DIMENSIONAL CALOGERO BOGOYAVLANSKII SCHIFF EQUATION
Z. AYATI
2009-07-01
Full Text Available In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1 -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving Calogero Bogoyavlanskii Schiff equation.
Exact periodic waves and their interactions for the (2+1)-dimensional KdV equation
Yan-Ze Peng
2005-08-01
By means of the singular manifold method we obtain a general solution involving three arbitrary functions for the (2+1)-dimensional KdV equation. Diverse periodic wave solutions may be produced by appropriately selecting these arbitrary functions as the Jacobi elliptic functions. The interaction properties of the periodic waves are investigated numerically and found to be nonelastic. The long wave limit yields some new types of solitary wave solutions. Especially the dromion and the solitoff solutions obtained in this paper possess new types of solution structures which are quite different from the basic dromion and solitoff ones reported previously in the literature.
Soliton solutions for (2+1-dimensional Breaking Soliton Equation: Three Wave Method
Somayeh Arbabi Mohammad-Abadi
2012-04-01
Full Text Available By means of the three-wave method one can solve some nonlinear partial differential equations (NLPDEs in their bilinear forms. When an NLPDE has no bilinear closed form we can not use this method. We modify the idea of three-wave method to obtain some analytic solutions for the (2+1-dimensional Breaking soliton equation by obtaining a bilinear closed form for it. By comparison of this method and other analytic methods, like HAM, HTA and EHTA, we can see that the new idea is very easy and straightforward.
Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation
ZHANG JieFang
2002-01-01
This article is concerned with the extended homogeneous balance method for studying thc abundantlocalized solution structures in the (2-k1)-dimensional dispersive long-wave equations uty + xx + (u2)xy/2 = 0, ηt +(u + u + uxy)x = 0. Starting from the homogeneous balance method, we find that the richness of the localized coherentstructures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selectionsof the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers,instantons and ring solitons.
Dai Chao-Qing; Zhou Guo-Quan
2007-01-01
Starting from the extended tanh-function method (ETM) based on the mapping method, the variable separation solutions of the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) system are derived. By further study, we find that these variable separation solutions are seemingly independent of but actually dependent on each other. Based on the variable separation solution and by choosing appropriate functions, some novel and interesting interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semifoldon, are investigated.
Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
Gecim, Ganim; Sucu, Yusuf(Department of Physics, Akdeniz University, 07058 Antalya, Turkey)
2016-01-01
In this paper, we study early-time inflation and late-time acceleration of the universe in the presence of non-minimal coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background by using the Noether symmetry approach. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with the results obtained in the context of the 3+1 dimensional teleparallel gr...
Effective actions of 2+1 dimensional gravity and BF theory
We develop the perturbation theory of the BF theory, which is equivalent to 2+1 dimensional gravity without a cosmological constant if we take SO(1,2) as the gauge group. We show that the BF theory, which may have a Chern-Simons term, has only tree- or one loop connected Feynman diagrams and that the theory is completely finite (at all orders). We evaluate the effective actions of the BF theory and the generalized BF theory which has a 'cosmological constant' and show that quantum corrections lead to 'Chern-Simons terms', using a BRST invariant regularization based on Pauli-Villars. (author). 19 refs, 4 figs, 2 tabs
Baskonus, Haci Mehmet; Bulut, Hasan
2016-04-01
In this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion.
无
2005-01-01
The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+ 1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-less system.Namely, by using a Backlund transformation and the MLVSA, we find a new general solution and define a new "universal formula". Then, some new (1+1)-dimensional coherent structures of this universal formula can be found by selecting corresponding functions appropriately. Specially, in some conditions, bell soliton and kink soliton can transform each other, which are illustrated graphically.
Zhao, Zhonglong; Han, Bo
2016-05-01
In this paper, we focus on a (2+1)-dimensional generalized breaking soliton equation, which describes the (2+1)-dimensional interaction of a Riemann wave propagating along the y -direction with a long wave along the x-direction. Based on a multidimensional Riemann theta function, the quasiperiodic wave solutions of a (2+1)-dimensional generalized breaking soliton equation are investigated by means of the bilinear Bäcklund transformation. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. The dynamical behaviors of the quasiperiodic wave solutions are discussed by presenting the numerical figures.
Quantum Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity
Pitelli, J P M
2016-01-01
In a recent paper [Phys. Rev. D 92:084012, 2015], the author studied the classical $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in Ho\\v{r}ava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will give one step further in the understanding of (1+1)-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with equation of state (EoS) $p=w\\rho$. The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schr\\"odinger equation for the wave function of the universe has the following properties: for $w=1$ (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for $w\
XU Chang-Zhi; ZHANG Jie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+ 1)-dimensional nonlinear models related to Schrodinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A (2+1)-dimensional multi-component DLW integrable hierarchy is obtained by using a (2+1)-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.
Bilinear Form and Two Bäcklund Transformations for the (3+1-Dimensional Jimbo-Miwa Equation
He Li
2015-01-01
Full Text Available With Bell polynomials and symbolic computation, this paper investigates the (3+1-dimensional Jimbo-Miwa equation, which is one of the equations in the Kadomtsev-Petviashvili hierarchy of integrable systems. We derive a bilinear form and construct a bilinear Bäcklund transformation (BT for the (3+1-dimensional Jimbo-Miwa equation, by virtue of which the soliton solutions are obtained. Bell-polynomial-typed BT is also constructed and cast into the bilinear BT.
2+1 Dimensional Quantum Gravity as a Gaussian Fermionic System and the 3D-Ising Model
Bonacina, G; Rasetti, M; Bonacina, Giuseppe; Martellini, Maurizio; Rasetti, Mario
1992-01-01
We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to $\\Sigma_g\\times\\RrR$ with $\\Sigma_g$ a closed and oriented Riemann surface of genus $g$, the corresponding 2+1-dimensional Euclidean quantum gravity may be related to the 3D-lattice Ising model before its thermodynamic limit.
Jin-Yuan, Li; Nian-Qiao, Fang; Ji, Zhang; Yu-Long, Xue; Xue-Mu, Wang; Xiao-Bo, Yuan
2016-04-01
In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given. Project supported by the National Natural Science Foundation of China (Grant No. 41406018).
RUAN Hang-Yu
2005-01-01
A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.
Consistent interactions of the 2+1 dimensional noncommutative Chern-Simons field
We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this happens only in a particular gauge
Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity
In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms
Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
Ammon, A; Jansen, K; Leövey, H; Volmer, J
2016-01-01
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that our new method leads to orders of magnitude reduced errors also in other regions of parameter space.
Extremal curves in 2+1-dimensional Yang-Mills theory
Orland, P; Orland, Peter; Semenoff, Gordon W.
2000-01-01
We examine the structure of the potential energy of 2+1-dimensional Yang-Mills theory on a torus with gauge group SU(2). We use a standard definition of distance on the space of gauge orbits. The curves of extremal potential energy in orbit space satisfy a certain partial differential equation. We argue that the energy spectrum is gapped because the extremal curves are of finite length. Though classical gluon waves satisfy our differential equation, they are not extremal curves. We construct examples of extremal curves and find how the length of these curves depends on the dimensions of the torus. The intersections with the Gribov horizon are determined explicitly. The results are discussed in the context of Feynman's ideas about the origin of the mass gap.
Neutron beam applications; development of texture measuring technique using 1-dimensional PSD
Park, No Jin; Lee, Moon Kyu; Joung, Tae Won; Lee, In Sung [Kumoh National University of Technology, Kumi (Korea)
2002-03-01
The new developed materials have often a low crystal symmetry or/and multi-phase state. Because the diffraction patterns of those materials are very complex and some peaks are overlapped, the measured pole figures with a conventional detector (0-dimensional detector) are not sufficient to use for the texture analysis. And also the widely broaden diffraction patterns caused by sever deformation, can only measured with lots of measuring errors using 0-dimensional detector. In this study the 1-dimensional and 2-dimensional position sensitive detector(PSD) is used such pattern to analyse. With PSD the more accurate pole figures can be measured, and the texture analysis, the estimation of the properties are determined more precisely. The measurement using PSD needs special technique for the analysis of the measured pattern. In this study the measuring and analysing technique is developed and compared with the conventional detector. 11 refs., 92 figs., 21 tabs. (Author)
Localized structures for (2+1)-dimensional Boiti–Leon–Pempinelli equation
Gui Mu; Zhengde Dai; Zhanhui Zhao
2013-09-01
It is shown that Painlevé integrability of (2+1)-dimensional Boiti–Leon–Pempinelli equation is easy to be verified using the standard Weiss–Tabor–Carnevale (WTC) approach after introducing the Kruskal’s simplification. Furthermore, by employing a singular manifold method based on Painlevé truncation, variable separation solutions are obtained explicitly in terms of two arbitrary functions. The two arbitrary functions provide us a way to study some interesting localized structures. The choice of rational functions leads to the rogue wave structure of Boiti–Leon–Pempinelli equation. In addition, for the other choices, it is observed that two solitons may evolve into breather after interaction. Also, the interaction between two kink compactons is investigated.
Quantum Probes of Timelike Naked Singularities in 2+1-Dimensional Power-Law Spacetimes
The formation of naked singularities in 2+1-dimensional power-law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field, respectively, are considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon and Dirac equations are used to probe the classical timelike naked singularities developed at r=0. We show that when the classically singular spacetimes probed with scalar waves, the considered spacetimes remain singular. However, the spinorial wave probe of the singularity in the metric of a self-interacting real scalar field remains quantum regular. The notable outcome in this study is that the quantum regularity/singularity cannot be associated with the energy conditions
Symmetry Reduction of the (2+1)-Dimensional Modified Dispersive Water-Wave System
Ma, Zheng-Yi; Fei, Jin-Xi; Du, Xiao-Yang
2015-08-01
Using the standard truncated Painlevé expansion, the residual symmetry of the (2+1)-dimensional modified dispersive water-wave system is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariances are derived by utilizing the obtained symmetries. The symmetries of the system are also derived through the Clarkson-Kruskal direct method, and several types of explicit reduction solutions relate to the trigonometric or the hyperbolic functions are obtained. Finally, some special solitons are depicted from one of the solutions. Supported by the National Natural Science Foundation of China under Grant No. 11447017 and the Natural Science Foundation of Zhejiang Province under Grant Nos. LY14A010005 and LQ13A010013
New Exact Solutions of (1 + 1)-Dimensional Coupled Integrable Dispersionless System
DAI Chao-Qing; YANG Qin; WANG Yue-Yue
2011-01-01
This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more general variable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) in our solutions, the annihilation phenomena of the flat-basin soliton,arch-basin soliton, and flat-top soliton are discussed.
Large phase shift of (1+1)-dimensional nonlocal spatial solitons in lead glass
Shou, Qian; Guo, Qi
2014-01-01
The large phase shift of strongly nonlocal spatial optical soliton(SNSOS) in the (1+1)-dimensional [(1+1)D] lead glass is investigated using the perturbation method. The fundamental soliton solution of the nonlocal nonlinear Schodinger equation(NNLSE) under the second approximation in strongly nonlocal case is obtained. It is found that the phase shift rate along the propagation direction of such soliton is proportional to the degree of nonlocality, which indicates that one can realize Pi-phase-shift within one Rayleigh distance in (1+1)D lead glass. A full comprehension of the nonlocality-enhancement to the phase shift rate of SNSOS is reached via quantitative comparisons of phase shift rates in different nonlocal systems.
Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation
ZHANG SHENG; TIAN CHI; QIAN WEI-YI
2016-06-01
The (4+1)-dimensional Fokas equation is derived in the process of extending the integrable Kadomtsev–Petviashvili and Davey–Stewartson equations to higher-dimensional nonlinear wave equations. This equation is under investigation in this paper. Hirota’s bilinear method is, for the first time, used to solve such a higher-dimensional equation. In order to bilinearize the Fokas equation, some appropriate transformations are adopted. As a result, single-soliton solution,double-soliton solution and three-soliton solution are obtained. A new uniform formula of n-soliton solution is derived from this. It is shown that the transformations adopted in this work play a key role in converting the Fokas equation into Hirota’s bilinear form.
Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity
Pitelli, J P M
2015-01-01
The $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid with equation of state $p=\\omega \\rho$ is analyzed through the view of Ho\\v rava-Lifshitz (HL) theory of gravity. In this theory, the anisotropic scaling of space and time breaks Lorentz invariance of General Relativity (GR) in such a way that the gravitational action is no longer a topological invariant and the theory becomes dynamical. With the introduction of a perfect fluid through Schutz formalism, it is shown that the resulting dynamical theory is very similar to the two-dimensional Jackiw-Teitelboim (JT) model, where a dilatonic degree of freedom is introduced to force a dynamical theory. However, in HL theory, the introduction of a dilaton field is not necessary.
Cosmology in (1 +1 ) -dimensional Hořava-Lifshitz theory of gravity
Pitelli, J. P. M.
2015-10-01
The (1 +1 )-dimensional Friedmann-Robertson-Walker universe filled with a perfect fluid with equation of state p =ω ρ is analyzed through the view of Hořava-Lifshitz (HL) theory of gravity. In this theory, the anisotropic scaling of space and time breaks Lorentz invariance of general relativity in such a way that the gravitational action is no longer a topological invariant and the theory becomes dynamical. With the introduction of a perfect fluid through Schutz formalism, it is shown that the resulting dynamical theory is very similar to the two-dimensional Jackiw-Teitelboim model, where a dilatonic degree of freedom is introduced to force a dynamical theory. However, in HL theory, the introduction of a dilaton field is not necessary.
Regularization strategy for an inverse problem for a 1 + 1 dimensional wave equation
Korpela, Jussi; Lassas, Matti; Oksanen, Lauri
2016-06-01
An inverse boundary value problem for a 1 + 1 dimensional wave equation with a wave speed c(x) is considered. We give a regularization strategy for inverting the map { A } :c\\mapsto {{Λ }}, where Λ is the hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed c. That is, we consider the case when we are given a perturbation of the Neumann-to-Dirichlet map \\tilde{{{Λ }}}={{Λ }}+{ E }, where { E } corresponds to the measurement errors, and reconstruct an approximative wave speed \\tilde{c}. We emphasize that \\tilde{{{Λ }}} may not be in the range of the map { A }. We show that the reconstructed wave speed \\tilde{c} satisfies \\parallel \\tilde{c}-c\\parallel ≤slant C\\parallel { E }{\\parallel }1/54. Our regularization strategy is based on a new formula to compute c from Λ.
Bellucci, S; Bragança, E; Saharian, A A
2016-01-01
We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even funct...
Dynamical formation and evolution of (2+1)-dimensional charged black holes
In this paper, we investigate the dynamical formation and evolution of (2 + 1)-dimensional charged black holes. We numerically study dynamical collapses of charged matter fields in an anti-de Sitter background and note the formation of black holes using the double-null formalism. Moreover, we include renormalized energy-momentum tensors assuming the S-wave approximation to determine thermodynamical back-reactions to the internal structures. If there are no semi-classical effects, the amount of charge determines the causal structures. If the charge is sufficiently small, the causal structure has a space-like singularity. However, as the charge increases, an inner Cauchy horizon appears. If we have sufficient charge, we see a space-like outer horizon and a time-like inner horizon, and if we give excessive charge, black hole horizons disappear. We have some circumstantial evidence that weak cosmic censorship is still satisfied, even for such excessive charge cases. Also, we confirm that there is mass inflation along the inner horizon, although the properties are quite different from those of four-dimensional cases. Semi-classical back-reactions will not affect the outer horizon, but they will affect the inner horizon. Near the center, there is a place where negative energy is concentrated. Thus, charged black holes in three dimensions have two types of curvature singularities in general: via mass inflation and via a concentration of negative energy. Finally, we classify possible causal structures. (paper)
A model of random center vortex lines in continuous 2+1-dimensional space-time
Altarawneh, Derar; Höllwieser, Roman
2016-01-01
A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining ph...
Expanding (n+1)-dimensional wormhole solutions in Brans-Dicke cosmology
We have obtained two classes of (n+1)-dimensional wormhole solutions using a traceless energy-momentum tensor in the Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry, while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric space-time also appear among the solutions as special cases. We have also considered the traversability of the wormhole solutions and have shown that they are indeed traversable. Finally, we have discussed the energy-momentum tensor which supports this geometry and have checked for the energy conditions. We have found that wormhole solutions in the first class of solutions violate the weak energy condition (WEC). In the second class, the wormhole geometries in a closed universe do violate the WEC, but in an open universe with a suitable choice of constants the supporting matter energy-momentum tensor can satisfy the WEC. However, even in this case the full effective energy-momentum tensor including the scalar field and the matter energy-momentum tensor still violates the WEC.
Verification of a 1-dimensional model for predicting shallow infiltration at Yucca Mountain
A characterization of net infiltration rates is needed for site-scale evaluation of groundwater flow at Yucca Mountain, Nevada. Shallow infiltration caused by precipitation may be a potential source of net infiltration. A 1-dimensional finite difference model of shallow infiltration with a moisture-dependent evapotranspiration function and a hypothetical root-zone was calibrated and verified using measured water content profiles, measured precipitation, and estimated potential evapotranspiration. Monthly water content profiles obtained from January 1990 through October 1993 were measured by geophysical logging of 3 boreholes located in the alluvium channel of Pagany Wash on Yucca Mountain. The profiles indicated seasonal wetting and drying of the alluvium in response to winter season precipitation and summer season evapotranspiration above a depth of 2.5 meters. A gradual drying trend below a depth of 2.5 meters was interpreted as long-term redistribution and/or evapotranspiration following a deep infiltration event caused by runoff in Pagany Wash during 1984. An initial model, calibrated using the 1990 to 1992 record, did not provide a satisfactory prediction of water content profiles measured in 1993 following a relatively wet winter season. A re-calibrated model using a modified, seasonally-dependent evapotranspiration function provided an improved fit to the total record. The new model provided a satisfactory verification using water content changes measured at a distance of 6 meters from the calibration site, but was less satisfactory in predicting changes at a distance of 18 meters
Vacuum energy is non-positive for (2 + 1)-dimensional holographic CFTs
Hickling, Andrew; Wiseman, Toby
2016-02-01
We consider a (2 + 1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial vacuum energy at zero temperature due to the Casimir effect. We assume a thermal state has an AdS/CFT dual description as a static smooth solution to gravity with a negative cosmological constant, which ends only on the conformal boundary or horizons. A bulk geometric argument then provides an upper bound on the ratio of CFT free energy to temperature. Considering the zero temperature limit of this bound implies the vacuum energy of the CFT is non-positive. Furthermore the vacuum energy must be negative unless the boundary metric is locally conformal to a product of time with a constant curvature space. We emphasise the argument does not require the zero temperature bulk geometry to be smooth, but only that singularities are ‘good’ so are hidden by horizons at finite temperature.
Vacuum energy is non-positive for (2+1)-dimensional holographic CFTs
Hickling, Andrew
2015-01-01
We consider a (2+1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial vacuum energy at zero temperature due to the Casimir effect. We assume a thermal state has an AdS/CFT dual description as a static smooth solution to gravity with a negative cosmological constant, which ends only on the conformal boundary or horizons. A bulk geometric argument then provides an upper bound on the ratio of CFT free energy to temperature. Considering the zero temperature limit of this bound implies the vacuum energy of the CFT is non-positive. Furthermore the vacuum energy must be negative unless the boundary metric is locally conformal to a product of time with a constant curvature space. We emphasise the argument does not require the zero temperature bulk geometry to be smooth, but only that singularities are `good' so are hidden by horizons at finite temperature.
A first look at transition amplitudes in (2 + 1)-dimensional causal dynamical triangulations
We study a lattice regularization of the gravitational path integral—causal dynamical triangulations—for (2 + 1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of fixed intrinsic geometries. For spatial topology of a 2-sphere, we determine the form of the Einstein–Hilbert action supplemented by the Gibbons–Hawking–York boundary terms within the Regge calculus of causal triangulations. Employing this action we numerically simulate a variety of transition amplitudes from the past boundary to the future boundary. To the extent that we have so far investigated them, these transition amplitudes appear consistent with the gravitational effective action previously found to characterize the ground state of quantum spacetime geometry within the Euclidean de Sitter-like phase. Certain of these transition amplitudes convincingly demonstrate that the so-called stalks present in this phase are numerical artifacts of the lattice regularization, seemingly indicate that the quantization technique of causal dynamical triangulations differs in detail from that of the no-boundary proposal of Hartle and Hawking, and possibly represent the first numerical simulations of portions of temporally unbounded quantum spacetime geometry within the causal dynamical triangulations approach. We also uncover tantalizing evidence suggesting that Lorentzian not Euclidean de Sitter spacetime dominates the ground state on sufficiently large scales. (paper)
Polar magneto-optical Kerr effect instrument for 1-dimensional magnetic nanostructures
Pathak, Sachin; Sharma, Manish
2014-01-01
The magneto-optical Kerr effect (MOKE) is a powerful technique to investigate the magnetization behaviour in magnetic nanostructures. We describe the design of a polar MOKE instrument for investigating the magnetization variation in MOKE signal observed in the exciting regime where the size of the magnetic nanostructures is around 20-350 nm. In particular, when the magnetization of the sample is perpendicular to its plane (i.e., along the axis of a cylindrical nanowire) we use polar MOKE configuration. The sign and magnitude of the small rotation measured in the signal is found proportional to the magnetization and its direction. The MOKE measurements indicate that the hysteresis depends on the shape as well as the density of nanostructures formed. The instrument is sensitive enough to clearly indicate the effect of magneto-static interaction on shape of M-H loop. We have observed the coercive field of ˜269 G for cylindrical nanowire grown in anodic aluminium oxide template and ˜135 G for "pin" shaped nanowire grown in polycarbonate track etched template. The magnetization reversal measurements are intricate in the case of "pin" or "X" shaped nanostructures as seen from the loop. These typical MOKE measurements on the 1-dimensional (1-D) nanostructures explore the effect of magneto-static interaction between the nanostructures.
Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories
This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability.
Verification of a 1-dimensional model for predicting shallow infiltration at Yucca Mountain
A characterization of net infiltration rates is needed for site-scale evaluation of groundwater flow at Yucca Mountain, Nevada. Shallow infiltration caused by precipitation may be a potential source of net infiltration. A 1-dimensional finite difference model of shallow infiltration with a moisture-dependant evapotranspiration function and a hypothetical root-zone was calibrated and verified using measured water content profiles, measured precipitation, and estimated potential evapotranspiration. Monthly water content profiles obtained from January 1990 through October 1993 were measured by geophysical logging of 3 boreholes located in the alluvium channel of Pagany Wash on Yucca Mountain. The profiles indicated seasonal wetting and drying of the alluvium in response to winter season precipitation and summer season evapotranspiration above a depth of 2.5 meters. A gradual drying trend below a depth of 2.5 meters was interpreted as long-term redistribution and/or evapotranspiration following a deep infiltration event caused by runoff in Pagany Wash during 1984. An initial model, calibrated using the 1990 to 1 992 record, did not provide a satisfactory prediction of water content profiles measured in 1993 following a relatively wet winter season. A re-calibrated model using a modified, seasonally-dependent evapotranspiration function provided an improved fit to the total record. The new model provided a satisfactory verification using water content changes measured at a distance of 6 meters from the calibration site, but was less satisfactory in predicting changes at a distance of 18 meters
Theta-function Solutions to the(2+1)-Dimensional Breaking Soliton Equation
WANG Jun-Min; YANG Xiao
2011-01-01
@@ A new periodic wave solution in terms of theta functions is presented for a kind of elliptic equation.Based on the results,with the help of Mathematica and the improved generalized F-expansion method,some periodic wave solutions in terms of theta functions are obtained for the(2+1)-dimensional breaking soliton equation.In addition,x-direction periodic wave solutions are derived,their properties and profiles are displayed in 3D figures.To our knowledge,these solutions are reported for the first time.%A new periodic wave solution in terms of theta functions is presented for a kind of elliptic equation. Based on the results, with the help of Mathematica and the improved generalized F-expansion method, some periodic wave solutions in terms of theta functions are obtained for the (2+l)-dimensional breaking soliton equation. In addition, x-direction periodic wave solutions are derived, their properties and proBles are displayed in 3D figures. To our knowledge, these solutions are reported for the first time.
Khalilov, V R
2015-01-01
The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in the QED$_{2+1}$ at the finite chemical potential, find the imaginary part of this Green function and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem to be likely to be revealed in a monolayer graphene sample in the presence of external constant uniform magnetic field $B$ perpendicular to it.
Khalilov, V.R.; Mamsurov, I.V. [M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow (Russian Federation)
2015-04-01
The polarization operator (tensor) for planar charged fermions in a constant uniform magnetic field is calculated in the one-loop approximation of 2 + 1-dimensional quantum electrodynamics (QED{sub 2+1}) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in QED{sub 2+1} at a finite chemical potential, find the imaginary part of this Green function, and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem likely to be revealed in a monolayer graphene sample in the presence of an external constant uniform magnetic field B perpendicular to it. (orig.)
Dromion and Multi-soliton Structures of the (2+1)-Dimensional Higher-Order Broer-Kaup System
林机
2002-01-01
Using the standard truncated Painlevé analysis and the Backlund transformation, we can obtain many significant exact soliton solutions of the (2+1)-dimensional higher-order Broer-Kaup (HBK) system. A special type of soliton solution is described by the variable coefficient heat-conduction-like equation. The inclusion of three arbitrary functions in the general expressions of the solitons makes the solitons of the (2+1)-dimensional HBK system possess abundant structures such as solitofT solutions, multi-dromion solutions, ring solitons and so on.
An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its solutions
Hu Xingbiao [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Li Chunxia [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Nimmo, Jonathan J C [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China)
2005-01-07
A symmetric (2+1)-dimensional Lotka-Volterra equation is proposed. By means of a dependent variable transformation, the equation is firstly transformed into multilinear form and further decoupled into bilinear form by introducing auxiliary independent variables. A bilinear Baecklund transformation is found and then the corresponding Lax pair is derived. Explicit solutions expressed in terms of pfaffian solutions of the bilinear form of the symmetric (2+1)-dimensional Lotka-Volterra equation are given. As a special case of the pfaffian solutions, we obtain soliton solutions and dromions.
YANG Qiu-Ying; MA Song-Hua; ZHANG Ying-Yue; FANG Jian-Ping; CHEN Tian-Lun; HONG Bi-Hai; ZHENG Chun-Long
2008-01-01
By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is derived. Based on the derived solitary wave solution, we obtain some special localized excitations and study the interactions between two solitary waves of the system.
In this paper, the Exp-function method is used to obtain generalized solitonary solutions and periodic solutions of the Generalized Zakharov system and (2 + 1)-dimensional Nizhnik-Novikov-Veselov system. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
WEN Xiao-Yong
2009-01-01
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.
XU Chang-Zhi
2006-01-01
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.
The double Wronskian solutions whose entries satisfy matrix equation for a (2+1)-dimensional breaking soliton equation ((2+1) DBSE) associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for (2+1) DBSE are obtained by taking special cases in general double Wronskian solutions. (general)
With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation are constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m → 0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions
The improved tanh function method [Chaos, Solitons and Fractals 2005;24:257] is further improved by constructing new ansatz solution of the considered equation. As its application, the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations are considered and abundant new exact non-travelling wave solutions are obtained
Jianping Shi; Jibin Li; Shumin Li
2013-11-01
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations.
Space-time-resolved quantum electrodynamics: A (1+1)-dimensional model
Glasgow, Scott; Smith, Dallas; Pritchett, Luke; Gardner, John; Ware, Michael J.
2016-06-01
We develop a model that reduces quantum electrodynamics (QED) in time plus three spatial dimensions to time plus a single spatial dimension, making it is possible to numerically calculate the dynamic behavior of simple QED systems. The dimensionality is restricted in such a way as to preserve the influence of spin and angular momentum. In contrast to the S -matrix scattering approach, these calculations are not perturbative within the zero- and one-photon sector of the relevant Hilbert space. The model restricts the electron occupation number to one and the photon occupation number to zero or one. We use this model to calculate the dynamics of a so-called bare electron that dresses itself by a photon field.
Entropy of 2+1 dimensional de Sitter space without cutoff
Kim, W; Park, Y J; Kim, Wontae; Kim, Yong-Wan; Park, Young-Jai
2006-01-01
By introducing the generalized uncertainty principle on the quantum state density, we calculate the statistical entropy of a scalar field on the background of three-dimensional de Sitter space without artificial cutoff. The desired entropy proportional to the horizon perimeter is obtained.
In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma–Tamborenea growth model, the (1+1)-dimensional Das Sarma–Tamborenea model is simulated on a large length scale by using the kinetic Monte–Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma–Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma–Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour. (general)
Lü, Xing; Tian, Bo; Zhang, Hai-Qiang; Xu, Tao; Li, He
2010-12-01
Gardner model describes certain nonlinear elastic structures, ion-acoustic waves in plasmas, and shear flows in ocean and atmosphere. In this paper, by virtue of the computerized symbolic computation, the integrability of a generalized (2+1)-dimensional variable-coefficient Gardner model is investigated. Painlevé integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to γ(t), the coefficient of the cubic nonlinear term u(2)u(x). Then, an independent transformation of the variable t transforms the reduced γ(t)-dependent equation into a constant-coefficient integrable one. Painlevé test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable. PMID:21198095
In this paper, the (2+1)-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, we prove that the (2+1)-dimensional generalization of shallow water wave equation possesses the Painlevé property under a certain condition, and its Lax pair is constructed by applying the singular manifold method. Based on the obtained Lax representation, the Darboux transformation (DT) is constructed. The first iterated solution, second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves in shallow water. (general)
Gardner model describes certain nonlinear elastic structures, ion-acoustic waves in plasmas, and shear flows in ocean and atmosphere. In this paper, by virtue of the computerized symbolic computation, the integrability of a generalized (2+1)-dimensional variable-coefficient Gardner model is investigated. Painleve integrability conditions are derived among the coefficient functions, which reduce all the coefficient functions to be proportional only to γ(t), the coefficient of the cubic nonlinear term u2ux. Then, an independent transformation of the variable t transforms the reduced γ(t)-dependent equation into a constant-coefficient integrable one. Painleve test shows that this is the only case when our original generalized (2+1)-dimensional variable-coefficient Gardner model is integrable.
The fermion in the gauge invariant formulation of the chiral Schwinger model and its relation to the fermion in the anomalous formulation is studied. A gauge invariant fermion operator is constructed that does not give rise to an asymptotic fermion field. It fits in the scheme prepared by generalized Schwinger models. Singularities in the short-distance limit of the chiral Schwinger model in the anomalous formulation lead to the conclusion that it is not a promising starting point for investigations towards realistic (3+1)-dimensional gauge theories with chiral fermion content. A new anomalous (1+1)-dimensional model is studied, the chiral quantum gravity. It is proven to be consistent if only a limited number of chiral fermions couple. The fermion propagator behaves analogously to the one in the massless Thirring model. A general rule is derived for the change of the fermion operator, which is induced by the breakdown of a gauge symmetry. (orig.)
Zitian Li
2014-09-01
A broad general variable separation solution with two arbitrary lower-dimensional functions of the (2+1)-dimensional Broer–Kaup (BK) equations was derived by means of a projective equation method and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as oscillating solitons, instantonlike and cross-like fractal structures are revealed by selecting appropriate functions of the general variable separation solution.
LI De-Sheng; LUO Cheng-Xin; ZHANG Hong-Qing
2004-01-01
Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t} in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach.
2015-01-01
Broad new families of rational form variable separation solutions with two arbitrary lower-dimensional functions of the (2 + 1)-dimensional Broer-Kaup system with variable coefficients are derived by means of an improved mapping approach and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as rouge wave, multidromion soliton, and soliton vanish phenomenon are revealed by selecting ap...
ZHANG Jie-Fang; MENG Jian-Ping; HUANG Wen-Hua
2004-01-01
From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.
A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)
Sachin Kumar
2012-10-01
Full Text Available Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1 dimensional ZK-BBM equations by using GG expansion method whereG G( satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions.
Layden, A.; S. MacCallum; Merchant, C.
2015-01-01
FLake, a 1-dimensional freshwater lake model, is tuned for 244 globally distributed large lakes using lake surface water temperatures (LSWTs) derived from Along-Track Scanning Radiometers (ATSRs). The model, tuned using only 3 lake properties; lake depth, albedo (snow and ice) and light extinction co-efficient, substantially improves the measured biases in various features of the LSWT annual cycle, including the LSWTs of saline and high altitude lakes. The daily ...
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
Teo, L. P.
2013-01-01
We consider the finite temperature Casimir free energy acting on a spherical shell in (D+1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar and electromagnetic fields. Dirichlet, Neumann, perfectly conducting and infinitely permeable boundary conditions are considered. The Casimir free energy is regularized using zeta functional regularization technique. To renormalize the Casimir free energy, we compute the heat kernel coefficients $c_n$, $0\\leq n\\leq D+1$, from the ...
Cong Sun; Bo Jiang
2015-01-01
We study the existence and orbital stability of smooth periodic traveling waves solutions of the (n +1)-dimensional coupled nonlinear Klein-Gordon equations. Such a system occurs in quantum mechanics, fluid mechanics, and optical fiber communication. Inspired by Angulo Pava’s results (2007), and by applying the stability theory established by Grillakis et al. (1987), we prove the existence of periodic traveling waves solutions and obtain the orbital stability of the solutions to this system.
Cong Sun
2015-01-01
Full Text Available We study the existence and orbital stability of smooth periodic traveling waves solutions of the (n +1-dimensional coupled nonlinear Klein-Gordon equations. Such a system occurs in quantum mechanics, fluid mechanics, and optical fiber communication. Inspired by Angulo Pava’s results (2007, and by applying the stability theory established by Grillakis et al. (1987, we prove the existence of periodic traveling waves solutions and obtain the orbital stability of the solutions to this system.
Ahmet Bekir; Özkan Güner
2013-08-01
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech$^{p}$ and tanh$^{p}$ functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Yan Wang; Zhenhui Wang
2013-01-01
By employing Hirota bilinear method, we mainly discuss the ( $3+1$ )-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get its $N$ exponential wave solutions. In virtue of some Riemann theta function formulas, we also construct its quasiperiodic solutions and analyze the asymptotic properties of these solutions. For the latter, by using certain variable transformations and identities of the theta functions, we explicitly...
Sperstad, Einar B. Stiansen. Iver B.; Sudbø, Asle
2012-01-01
We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range spatial ordering in the phase $\\theta$ of the superconducting order parameter, but temporal ordering only in spatial gradients $\\Delta \\theta$, not in $\\theta$. Significantly, the most ordered state therefore does not have 3D XY ordering. Rather, it featur...
In this paper, a detailed Lie symmetry analysis of the (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method, which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem. (general)
Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in (1+1)-Dimensional Spacetime
HE Xiao-Kai; LIU Wen-Biao; QIU Wei-Gang
2009-01-01
The Casimir energy of maesive scalar field with hybrid (Dirichlet-Neumann) boundary condition is calcu-lated. In order to regularize the model, the typical methods named as mode summation method and Green's function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field's mass. When the field is massless, the result is consistent with previous literatures.
In this paper, we consider a system of (2+1)-dimensional nonlinear models by using CK direct method and Hereman—Nuseir method generated by the Jaulent—Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation. (general)
SRD 166 MEMS Calculator (Web, free access) This MEMS Calculator determines the following thin film properties from data taken with an optical interferometer or comparable instrument: a) residual strain from fixed-fixed beams, b) strain gradient from cantilevers, c) step heights or thicknesses from step-height test structures, and d) in-plane lengths or deflections. Then, residual stress and stress gradient calculations can be made after an optical vibrometer or comparable instrument is used to obtain Young's modulus from resonating cantilevers or fixed-fixed beams. In addition, wafer bond strength is determined from micro-chevron test structures using a material test machine.
Groups Analysis and Localized Solutions of the (2+1)-Dimensional Ito Equation
Hu, Xiao-Rui; Chen, Jun-Chao; Chen, Yong
2015-07-01
Not Available Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ13A010014, the National Natural Science Foundation of China under Grant Nos 11326164, 11401528, 11435005 and 11375090, the Global Change Research Program of China (No 2015CB953904), the Research Fund for the Doctoral Program of Higher Education of China (No 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (No ZF1213), and Shanghai Minhang District Talents of High Level Scientific Research Project.
Thermodynamics of hot quantum scalar field in a (D+1) dimensional curved spacetime
C., W A Rojas
2016-01-01
We use the brick wall model to calculate the free energy of quantum scalar field in a curved spacetime (D +1) dimensions. We find the thermodynamics properties of quantum scalar field in several scenaries: Minkowski spacetime, Schwarzschild spacetime and BTZ spacetime. For the cases analysed, the thermodynamical properties of quantum scalar field is exactly with the reported. It was found that the entropy of the gas is proportional to the horizon area in a gravity field strong, which is consistent with the holographic principle.
(2+1)-dimensional QED with dynamically massive fermions in vacuum polarization
We study chiral symmetry breaking in three-dimensional QED with Nf flavors of four-component fermions. A closed system of Schwinger-Dyson equations for fermion and photon propagators and the full fermion-photon vertex is proposed, which is consistent with the Ward-Takahashi identity. A simplified version of that set of equations is reduced (in the nonlocal gauge) to the equation for a dynamical fermion mass function, where the one-loop vacuum polarization with dynamically massive fermions has been taken into account. The linearized equation for the fermion mass function is analyzed in real space. The analytical solution is compared with the results of numerical calculations of the nonlinear integral equation in momentum space. copyright 1996 The American Physical Society
Lakshminarayana, S.
Letters to the Editor Dynamic Ranking with n H11001 1 Dimensional Vector Space Models: An Alternative Search Mechanism for World Wide Web Sir: The World Wide Web (WWW) has grown both in depth and width of technology typically giving scope for new databases.../links based on the algo- rithm characteristics. To optimize the results we need to apply dynamically extendable vector based ranking techniques because of the properties that depend for ranking a page are growing and not finite. Kleinberg (1998) classified...
Harun-Or- Roshid
2014-01-01
Full Text Available Periodic and soliton solutions are presented for the (1+1-dimensional classical Boussinesq equation which governs the evolution of nonlinear dispersive long gravity wave traveling in two horizontal directions on shallow water of uniform depth. The equation is handled via the exp(−Φ(η-expansion method. It is worth declaring that the method is more effective and useful for solving the nonlinear evolution equations. In particular, mathematical analysis and numerical graph are provided for those solitons, periodic, singular kink and bell type solitary wave solutions to visualize the dynamics of the equation.
CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Based on the computerized symbolic system Maple, a new generalized expansion method of Riccatiequation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new generalansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, ut + buxxy + 4buvx +4buxv = 0, uy = vx, and obtain rich new families of the exact solutions of the breaking soliton equation, including thenon-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular functionsolutions.
$Q-\\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
Ma, Yu-Bo; Cao, Shuo
2016-01-01
In order to achieve a deeper understanding of gravity theories, it is important to further investigate the thermodynamic properties of black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose $T,Q,\\Phi$ as the state parameters and study the phase equilibrium problem of general $(n+1)$-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide theoretical foundation for studying the phase transition and phase structure of black hole systems.
ZHENHUI XU; HANLIN CHEN; ZHENGDE DAI
2016-08-01
In this paper, we obtained the exact breather-type kink soliton and breather-type periodic soliton solutions for the (3+1)-dimensional B-type Kadomtsev--Petviashvili (BKP) equation using the extended homoclinic test technique. Some new nonlinear phenomena, such as kink and periodic degeneracies, are investigated. Using the homoclinic breather limit method, some new rational breather solutions are found as well. Meanwhile, we also obtained the rational potential solution which is found to be just a rogue wave. These results enrich thevariety of the dynamics of higher-dimensional nonlinear wave field.
Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painlevé property of the (3+1)-dimensional Burgers equation, and then Bäcklund transformation is derived according to the truncated expansion of the obtained Painlevé analysis. Using the Bäcklund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we also give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures. (general)
Nikita AgasianITEP, Moscow; Dmitri Antonov
2015-01-01
Confining strings and RG flow at finite temperature are investigated in the (2+1)-dimensional Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of mass of the Higgs field, but much smaller than the vacuum expectation value of this field. The modification of the Debye mass of the dual photon with respect to the case when it is considered to be negligibly small compared to the Higgs mass, is found. Analogous modifications of ...
Storage and retrieval of (3+1)-dimensional weak-light bullets and vortices in a coherent atomic gas
Chen, Zhiming; Li, Hui-jun; Hang, Chao; Huang, Guoxiang
2016-01-01
A robust light storage and retrieval (LSR) in high dimensions is highly desirable for light and quantum information processing. However, most schemes on LSR realized up to now encounter problems due to not only dissipation, but also dispersion and diffraction, which make LSR with a very low fidelity. Here we propose a scheme to achieve a robust storage and retrieval of weak nonlinear high-dimensional light pulses in a coherent atomic gas via electromagnetically induced transparency. We show that it is available to produce stable (3+1)-dimensional light bullets and vortices, which have very attractive physical property and are suitable to obtain a robust LSR in high dimensions.
Full Symmetry Groups and Similar Reductions of a (2+1)-Dimensional Resonant Davey-Stewartson System
Applying the classical Lie symmetry method to the (2+1)-dimensional resonant Davey-Stewartson system introduced by Tang [X.Y. Tang et al., Chaos, Solitons and Fractals 42 (2007) 2707], a more general infinite dimensional Lie symmetry with Kac-Moody-Virasoro type Lie algebra is obtained, which involves four arbitrary functions of t. Alternatively, by a simple direct method, the full symmetry groups including Lie symmetry group and non-Lie symmetry group are gained straightly. In this way, the related Lie algebra can be easily found by a more simple limiting procedure. Lastly, via solving the characteristic equations, three types of the general similar reductions are derived. (general)
Öziş, Turgut; Aslan, İsmail
2008-11-01
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the ( 3+1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. Being less restrictive and concise, the method can be applied to many high-dimensional nonlinear evolution equations having wide applications in applied physical sciences.
Ozis, Turgut [Department of Mathematics, Ege University, 35100 Bornova, Izmir (Turkey)], E-mail: turgut.ozis@ege.edu.tr; Aslan, Ismail [Department of Mathematics, Izmir Institute of Technology, 35430 Urla, Izmir (Turkey)
2008-11-24
In this Letter, the Exp-function method, with the aid of a symbolic computation system such as Mathematica, is applied to the (3+1)-dimensional Jimbo-Miwa equation to show its effectiveness and reliability. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. Being less restrictive and concise, the method can be applied to many high-dimensional nonlinear evolution equations having wide applications in applied physical sciences.
Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge
Kotikov, A V; Teber, S
2016-01-01
The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N
In nonlinear optical fibres, the evolution of two polarization envelopes is governed by a system of coupled nonlinear Schroedinger (CNLS) equations. In this paper, with the aid of symbolic computation, the analytical bright one- and two-soliton solutions of the (2+1)-dimensional CNLS equations under certain constraints are presented by employing the Hirota method. We have discussed the head-on and overtaking interactions which include elastic and inelastic collisions between two parallel bright solitons. In the interaction process, the intensities of solitons can exhibit various redistributions. We also point out that these properties have important physical applications in constructing various logic gates and nonlinear optical fibers
In a cosmic dusty plasma, both azimuthal and height perturbations of a nonplanar cylindrical geometry are considered. For dust-ion-acoustic waves and with symbolic computation (3+1)-dimensional generalized Johnson [(3+1)DGJ] model is derived and analytic solutions are constructed. Supernova-shell-typed expanding bright (3+1)DGJ nebulons and Saturn-F-ring-type expanding dark (3+1)DGJ nebulons are both pictured and discussed. Essential difference of this letter from the existing literature is pointed out, with the relevant, possibly observable (3+1)DGJ-nebulonic structures for the future cosmic experiments proposed
Cloud of strings as source in 2 + 1-dimensional f(R) = R{sup n} gravity
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2016-02-15
We present three parameters exact solutions with possible black holes in 2 + 1-dimensional f(R) = R{sup n} modified gravity coupled minimally to a cloud of strings. These three parameters are n, the coupling constant of the cloud of strings ξ, and an integration constant C. Although in general one has to consider each set of parameters separately, for n an even integer greater than one we give a unified picture providing black holes. For n ≥ 1 we analyze a null/timelike geodesic within the context of particle confinement. (orig.)
Conformal invariance at a second-order phase transition yields an exact finite-size scaling theory on a two-dimensional cylinderical geometry. We combine this two-dimensional conformal field theory with a numerical investigation of the deconfinement phase transition of (2 + 1)-dimensional SU(2) lattice gauge theory. Results of this study and a more general finite-size scaling analysis on square lattices yield excellent agreement with d = 2 Ising critical behavior, as has been conjectured on the basis of universality. (orig.)
Conformal invariance at a 2nd order phase transition yields an exact finite size scaling theory on a 2-dimensional cylindrical geometry. We combine this two-dimensional conformal field theory with a numerical investigation of the deconfinement phase transition of (2+1)-dimensional SU(2) lattice gauge theory. Results of this study and a more general finite size scaling analysis on square lattices yield excellent agreement with d=2 Ising critical behavior, as has been conjectured on the basis of universality. (orig.)
Hitender Kumar
2013-03-01
Full Text Available The (2+1-dimensional Maccari and nonlinear Schrödinger equations are reduced to a nonlinear ordinary differential equation (ODE by using a simple transformation, various solutions of the nonlinear ODE are obtained by using extended F-expansion and projective Ricatti equation methods. With the aid of solutions of the nonlinear ODE more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Wen-guang Cheng
2014-01-01
Full Text Available The bilinear form, bilinear Bäcklund transformation, and Lax pair of a (2 + 1-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived through Bell polynomials. The integrable constraint conditions on variable coefficients can be naturally obtained in the procedure of applying the Bell polynomials approach. Moreover, the N-soliton solutions of the equation are constructed with the help of the Hirota bilinear method. Finally, the infinite conservation laws of this equation are obtained by decoupling binary Bell polynomials. All conserved densities and fluxes are illustrated with explicit recursion formulae.
Shaolin Li
2014-01-01
Full Text Available The bilinear operator and F-expansion method are applied jointly to study (2+1-dimensional Kadomtsev-Petviashvili (KP equation. An exact cusped solitary wave solution is obtained by using the extended single-soliton test function and its mechanical feature which blows up periodically in finite time for cusped solitary wave is investigated. By constructing the extended double-soliton test function, a new type of exact traveling wave solution describing the assimilation of solitary wave and periodic traveling wave is also presented. Our results validate the effectiveness for joint application of the bilinear operator and F-expansion method.
Chen Gang; Liu Zhan-Fang; Lan Ming-Jian
2011-01-01
The thermodynamic properties of a (2 + 1)-dimensional black hole with non-linear electrodynamics from the viewpoint of geometry is studied and some kinds of temperatures of the black hole have been obtained.Weinhold curvature and Ruppeiner curvature are explored as information geometry.Moreover,based on Quevedo's theory,the Legendre invariant geometry is investigated for the black hole. We also study the relationship between the scalar curvatures of the above several metrics and the phase transitions produced from the heat capacity.
Yan Wang
2013-01-01
Full Text Available By employing Hirota bilinear method, we mainly discuss the (3+1-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get its N exponential wave solutions. In virtue of some Riemann theta function formulas, we also construct its quasiperiodic solutions and analyze the asymptotic properties of these solutions. For the latter, by using certain variable transformations and identities of the theta functions, we explicitly investigate its periodic waves solutions in terms of one-theta function and two-theta functions.
We investigate the influence of the full vacuum polarization and vertex function on the fermion propagator, using the coupled Dyson-Schwinger equations for the photon and fermion propagator. We show that, within a range of vertex functions, the general behavior of the fermion propagator does not depend on the exact details of the vertex, both in the massless and in the massive phase. Independent of the precise vertex function, there is a critical number of fermion flavors for dynamical mass generation in (2+1)-dimensional QED. A consistent treatment of the vacuum polarization is essential for these results. copyright 1996 The American Physical Society
Petersen, Kurt Erling
1986-01-01
probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis...... of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested....
Jet propagation and Mach-cone formation in (3+1)-dimensional ideal hydrodynamics
This thesis investigates the jet-medium interactions in a Quark-Gluon Plasma using a hydrodynamical model. Such a Quark-Gluon Plasma represents a very early stage of our universe and is assumed to be created in heavy-ion collisions. Its properties are subject of current research. Since the comparison of measured data to model calculations suggests that the Quark-Gluon Plasma behaves like a nearly perfect liquid, the medium created in a heavy-ion collision can be described applying hydrodynamical simulations. One of the crucial questions in this context is if highly energetic particles (so-called jets), which are produced at the beginning of the collision and traverse the formed medium, may lead to the creation of a Mach cone. Such a Mach cone is always expected to develop if a jet moves with a velocity larger than the speed of sound relative to the medium. In that case, the measured angular particle distributions are supposed to exhibit a characteristic structure allowing for direct conclusions about the Equation of State and in particular about the speed of sound of the medium. Several different scenarios of jet energy loss are examined (the exact form of which is not known from first principles) and different mechanisms of energy and momentum loss are analyzed, ranging from weak interactions (based on calculations from perturbative Quantum Chromodynamics, pQCD) to strong interactions (formulated using the Anti-de-Sitter/Conformal Field Theory Correspondence, AdS/CFT). Though they result in different angular particle correlations which could in principle allow to distinguish the underlying processes (if it becomes possible to analyze single-jet events), it is shown that the characteristic structure observed in experimental data can be obtained due to the different contributions of several possible jet trajectories through an expanding medium. Such a structure cannot directly be connected to the Equation of State. In this context, the impact of a strong flow
Beguería, Santiago; Vicente Serrano, Sergio M.
2009-01-01
[EN] *Objectives: The program calculates time series of the Standardised Precipitation-Evapotransporation Index (SPEI). *Technical Characteristics: The program is executed from the Windows console. From an input data file containing monthly time series of precipitation and mean temperature, plus the geographic coordinates of the observatory, the program computes the SPEI accumulated at the time interval specified by the user, and generates a new data file with the SPEI time serie...
Reviewed is the effect of heat flux of different system parameters on critical density in order to give an initial view on the value of several parameters. A thorough analysis of different equations is carried out to calculate burnout is steam-water flows in uniformly heated tubes, annular, and rectangular channels and rod bundles. Effect of heat flux density distribution and flux twisting on burnout and storage determination according to burnout are commended
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2004-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave-short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.
McCarty, George
1982-01-01
How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...
Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested. (author)
LIN Mai-Mai; DUAN Wen-Shan
2007-01-01
In this paper,(2+1)-dimensional electron acoustic waves (EAW) in an unmagnetized collisionless plasma have been studied by the linearized method and the reductive perturbation technique,respectively.The dispersion relation and a modified Kadomtsev-Petviashvili (KP) equation have been obtained for the EAW in the plasma considering a cold electron fluid and a vortex-like hot electrons.It is found from some numerical results that the parameter β (the ratio of the free hot electron temperature to the hot trapped electron temperature) effects on the amplitude and the width of the electron acoustic solitary waves (EASW).It can be indicated that the free hot electron temperature and the hot trapped electron temperature have very important effect on the characters of the propagation for the EASW.
RUAN Hang-Yu; CHEN Yi-Xin
2006-01-01
Some new structures and interactions of solitons for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our results. Detailed behaviors of interaction are illustrated both analyticaily and in graphically. Our analysis shows that the interaction properties between two solitons are related to the form of interaction constant. The form of interaction constant and the dispersion relationship are related to the form of the seed solution {u0, v0, w0 } in Backlund transformation.
QIANG Ji-Ye; FEI Jin-Xi; CAI Gui-Ping; ZHENG Chun-Long
2007-01-01
With the aid of an improved projective approach and a linear variable separation method,new types of variable separation solutions (including solitary wave solutions,periodic wave solutions,and rational function solutions)with arbitrary functions for (2+1)-dimensional Korteweg-de Vries system are derived.Usually,in terms of solitary wave solutions and rational function solutions,one can find some important localized excitations.However,based on the derived periodic wave solution in this paper,we find that some novel and significant localized coherent excitations such as dromions,peakons,stochastic fractal patterns,regular fractal patterns,chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.
(2 + 1)-dimensional topological insulator described by the Kane–Mele model in the presence of Rashba spin–orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is accomplished within this model. The Hamiltonian methods are adopted to provide the coefficients appearing in the action. It is demonstrated straightforwardly that the coefficients of the Chern–Simons terms are given by the first Chern number attained through the related non-Abelian Berry gauge field. The effective theory which we obtain is in accord with the existence of the spin Hall phase where the value of the spin Hall conductivity is very close to the quantized one. (paper)
The investigation for (2+1)-dimensional Eckhaus-type extension of the dispersive long wave equation
The (2+1)-dimensional Eckhaus-type extension of the dispersive long wave (EEDLW) equation is investigated, which was obtained in the appropriate approximation from the basic equations of hydrodynamics. Though it has no Painleve property, we gain an auto-Baecklund transformation (aBT) by truncating the Laurent series expansion at O(w0). In particular, the special one of the aBT establishes a relationship between the EEDLW equation and a set of three linear partial differential equations involving the well-known heat equation. Finally many types of new exact solutions of the EEDLW equation are found from the obtained aBT and some proper ansaetze, which may be useful to explain some physical phenomena
By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.
Sun, Yan; Tian, Bo; Zhen, Hui-Ling; Wu, Xiao-Yu; Xie, Xi-Yang
2016-07-01
Under investigation in this paper is a (3 + 1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Hirota method and symbolic computation, we obtain the one-, two- and three-soliton solutions for such an equation. We graphically study the solitons related with the coefficient of the cubic nonlinearity M. Amplitude of the one soliton increases with increasing M, but the width of one soliton keeps unchanged as M increases. The two solitons and three solitons are parallel, and the amplitudes of the solitons increase with increasing M, but the widths of the solitons are unchanged. It is shown that the interactions between the two solitons and among the three solitons are elastic.
Sheng Zhang; Hong-Qing Zhang
2011-04-01
A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial differential equations.
Cheng, Xue-Ping; Wang, Jian-Yong; Ren, Bo; Yang, Yun-Qing
2016-08-01
The consistent tanh expansion (CTE) method is employed to the (2+1)-dimensional Caudrey—Dodd—Gibbon-Kotera—Sawada (CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters. Supported by the National Natural Science Foundation of China under Grant No. 11505154, the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ16A010003, and the Scientific Research Foundation for Doctoral Program of Zhejiang Ocean University under Grant No. Q1511
On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time
We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that in such a quantum field theory (i) a continuous symmetry of (pseudo)scalar field translations is spontaneously broken, (ii) Goldstone bosons appear as quanta of a free massless (pseudo)scalar field and (iii) there is a non-vanishing spontaneous magnetization. In spite of the existence of a spontaneous magnetization the main inequality between vacuum expectation values of certain operators which have been used for the derivation of the Mermin-Wagner-Hohenberg theorem (C. Itzykson and J.-M. Drouffe, Statistical field theory, Vol. I, 1989, pp. 219-224) is fulfilled. (orig.)
Guo Shimin [School of Mathematics and Statistics, Xi' an Jiaotong University, Xi' an 710049 (China); Research Group MAC 2, Centrum Wiskunde and Informatica, Amsterdam 1098XG (Netherlands); Wang Hongli [School of Business and Administration, Tongji University, Shanghai 200092 (China); Mei Liquan [School of Mathematics and Statistics, Xi' an Jiaotong University, Xi' an 710049 (China); Center for Computational Geosciences, Xi' an Jiaotong University, Xi' an 710049 (China)
2012-06-15
By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.
We analyze the (1+1)-dimensional Nambu - Jona-Lasinio (NJL) model nonperturbatively. In addition to its simple ground-state saddle points, the effective action of this model has a rich collection of nontrivial saddle points in which the composite fields σ(x)=left-angle bar ψψ right-angle and π(x)=left-angle bar ψiγ5ψ right-angle form static space-dependent configurations because of nontrivial dynamics. These configurations may be viewed as one-dimensional chiral open-quotes bags.close quotes We start our analysis of such configurations by asking what kind of initially static {σ(x),π(x)} background configurations will remain so under fermionic back reaction. By simply looking at the asymptotic spatial behavior of the expectation value of the fermion number current we show, independently of the large-N limit, that a necessary condition for this situation to occur is that {σ(x),π(x)} give rise to a reflectionless Dirac operator. We provide an explicit formula for the diagonal resolvent of the Dirac operator in a reflectionless {σ(x),π(x)} background which produces a prescribed number of bound states. We analyze in detail the cases of a single as well as two bound states. We explicitly check that these reflectionless backgrounds may be tuned such that the large- N saddle-point condition is satisfied. Thus, in the case of the NJL model, reflectionlessness is also sufficient to assure the time independence of the background. In our view, these facts make our work conceptually simpler than the previous work of Shei and of Dashen, Hasslacher, and Neveu which were based on the inverse scattering formalism. Our method of finding such nontrivial static configurations may be applied to other (1+1)-dimensional field theories. copyright 1997 The American Physical Society
Xiangrong Wang
2015-01-01
Full Text Available A generalized (2+1-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1-dimensional KdV equation. The N-soliton solutions of the (2+1-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method.
Cheng, Wenguang; Li, Biao
2016-04-01
The truncated Painlevé method is developed to obtain the nonlocal residual symmetry and the Bäcklund transformation for the (2+1)-dimensional KdV-mKdV equation. The residual symmetry is localised after embedding the (2+1)-dimensional KdV-mKdV equation to an enlarged one. The symmetry group transformation of the enlarged system is computed. Furthermore, the (2+1)-dimensional KdV-mKdV equation is proved to be consistent Riccati expansion (CRE) solvable. The soliton-cnoidal wave interaction solution in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral is obtained by using the consistent tanh expansion (CTE) method, which is a special form of CRE.
On a family of (1+1)-dimensional scalar field theory models: Kinks, stability, one-loop mass shifts
Alonso-Izquierdo, A., E-mail: alonsoiz@usal.es [Departamento de Matematica Aplicada and IUFFyM, Universidad de Salamanca (Spain); Mateos Guilarte, J. [Departamento de Fisica Fundamental and IUFFyM, Universidad de Salamanca (Spain)
2012-09-15
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and {phi}{sup 4} models, we look at all possible extensions such that the kink second-order fluctuation operators are Schroedinger differential operators with Poeschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and {phi}{sup 4} models. - Highlights: Black-Right-Pointing-Pointer We construct a family of scalar field theory models supporting kinks. Black-Right-Pointing-Pointer The second-order kink fluctuation operators involve Poeschl-Teller potential wells. Black-Right-Pointing-Pointer We compute the one-loop quantum correction to the kink mass with different methods.
LIN Ruihui
2014-02-01
Full Text Available We reconsider the thermal scalar Casimir effect for p-dimensional hypercubic cavity inside D+1-dimensional Minkowski space-time.The thermal Casimir free energy can be divided into the divergent zero-temperature part and the automatically finite temperature-dependent part through standard quantum field theory treatments.Due to the finiteness,the regularization of the temperature-dependent part,which is also required for the convergency of the Casimir energy and the vanishing of the Casimir force with the separation increasing to infinity,is neglected in some literatures.We derive rigorously the regularization of the zero temperature part as well as the temperature-dependent part of the free energy by making use of the zeta function technique and the Abel-Plana formula.In the cases of D=3,p=1 and D=3,p=3,we precisely recover the results of parallel plates and three-dimensional box in the literature.And explicit expressions of the Casimir free energy in both low temperature (small separations and high temperature (large separations regimes are given,through which we find that after the regularization of both parts,with the side length going to infinity the force always tends to zero for different boundary conditions.Our study may be helpful in providing a comprehensive and complete understanding of this old problem.
Lie, Donald Y. C.; Lopez, J.
2011-04-01
A fully monolithic 1-Dimensional (1-D) AC-coupled Voltage-Controlled-Oscillators (VCOs) phased-array network design will be presented in this paper. This radio-frequency (RF) VCO array integrates on-chip inductors, varactors and bias current sources and it contains an odd number of VCOs AC-coupled through on-chip switchable resistor networks using MOSFETs. The measured results and SPICE simulated performance of the monolithic unit cell VCO agree reasonably well. Realistic circuit simulations in IBM 7HP 0.18 um BiCMOS design kit indicate promising results of the 1-D coupled-VCO array by showing the design can control the phasing of this on-chip VCO-array by means of tuning the edge elements and/or by varying the coupling strength via different resistor values using the on-chip MOSFET switches. Simulation data shows that it can offer high directivity and a possible element-to-element phase tuning arrangement that allows a ˜±20-30° degree coverage from broadside without the need for phase shifters or additional circuitry complexity. This AC-coupled 1-D VCO array, therefore, shows great potential for RF active antennas applications to perform wide angle beam steering for the highly used S-band.
David L. Chichester; Scott M. Watson; James T. Johnson
2012-10-01
One-dimensional fiber-bundle arrays may prove useful in a number of radiation sensing applications where radiation detection over large areas is needed. Tests have been performed to evaluate the light generation and transmission characteristics of 15-meter long, 10-fiber bundles of BCF-10, BCF-12, and BCF-20 scintillating fibers (Saint Gobain) exposed to collimated gamma-ray sources. The test set-up used one R9800 (Hamamatsu) photomultiplier tube (PMT) at each end, with a high-speed waveform digitizer to collect data. Time constraints were imposed on the waveform data to perform time-of-flight analysis of the events in the fiber bundles, eliminating spurious noise pulses in the high gain PMTs and also allowing 1-dimensional localization of interactions along the lengths of the fiber bundles. This paper will present the results of these measurements including the attenuation coefficients of the two fiber types and the timing resolution (position uncertainty) possible for each fiber bundle when using the R9800 PMTs.
A new (2+1)-dimensional variant Boussinesq system with its spectral problems is presented in this paper, which has a close connection with the Whitham-Broer-Kaup soliton hierarchy describing long waves in shallow water. Based on the associated spectral problems, the Darboux transformation (DT) with multi-parameters was firstly constructed with the help of symbolic computation. Then, by using the DT, some new one- and two-soliton solutions of the (2+1)-dimensional variant Boussinesq system were obtained and graphically represented. These solutions might be of some value in fluid dynamics.
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
Based on a new intermediate transformation, a variable-coefficient hyperbola function method is proposed.Being concise and straightforward, it is applied to the (2+1)-dimensional variable-coefficient Broer Kaup system. As a result, several new families of exact soliton-like solutions are obtained, besides the travelling wave. When imposing some conditions on them, the new exact solitary wave solutions of the (2+1)-dimensional Broer-Kaup system are given. The method can be applied to other variable-coefficient nonlinear evolution equations in mathematical physics.
In the paper, the generalized projective Riccati equation method is extended to construct some non-travelling wave solutions to a (3 + 1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures. When some arbitrary functions included in these solutions are taken as some special functions, these solutions possess abundant structures
HUANG Wen-Hua; ZHANG Jie-Fang
2004-01-01
Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.
SHEN Shou-Feng; ZHANG Jun; PAN Zu-Liang
2005-01-01
By using a Backlund transformation and the multi-linear variable separation approach, we find a new generalsolution ofa (2+1)-dimensional generalization of the nonlinear Schrodinger system. The new "universal" formula is defined, and then, rich coherent structures can be found by selecting corresponding functions appropriately.
BAI Cheng-Jie; BAI Cheng-Lin; HAN Ji-Guang; ZHAO Hong
2005-01-01
By the application of the extended homogeneous balance method, we derive an auto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KP equations. Based on the BT, in which there are two homogeneity equations to be solved, we obtain some exact solutions containing single solitary waves.
The improved tanh function method [Commun. Theor. Phys. (Beijing, China) 43 (2005) 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the (2+1)-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.
Rooman, M.; Spindel, Ph.
1999-01-01
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de Sitter geometries.
The objective of this work was to provide experimental heat transfer boundary condition and reactor pressure vessel (RPV) section thermal response data that can be used to benchmark computer codes that simulate thermal annealing of RPVS. This specific protect was designed to provide the Electric Power Research Institute (EPRI) with experimental data that could be used to support the development of a thermal annealing model. A secondary benefit is to provide additional experimental data (e.g., thermal response of concrete reactor cavity wall) that could be of use in an annealing demonstration project. The setup comprised a heater assembly, a 1.2 in x 1.2 m x 17.1 cm thick [4 ft x 4 ft x 6.75 in] section of an RPV (A533B ferritic steel with stainless steel cladding), a mockup of the open-quotes mirrorclose quotes insulation between the RPV and the concrete reactor cavity wall, and a 25.4 cm [10 in] thick concrete wall, 2.1 in x 2.1 in [10 ft x 10 ft] square. Experiments were performed at temperature heat-up/cooldown rates of 7, 14, and 28 degrees C/hr [12.5, 25, and 50 degrees F/hr] as measured on the heated face. A peak temperature of 454 degrees C [850 degrees F] was maintained on the heated face until the concrete wall temperature reached equilibrium. Results are most representative of those RPV locations where the heat transfer would be 1-dimensional. Temperature was measured at multiple locations on the heated and unheated faces of the RPV section and the concrete wall. Incident heat flux was measured on the heated face, and absorbed heat flux estimates were generated from temperature measurements and an inverse heat conduction code. Through-wall temperature differences, concrete wall temperature response, heat flux absorbed into the RPV surface and incident on the surface are presented. All of these data are useful to modelers developing codes to simulate RPV annealing
A. Layden
2015-10-01
Full Text Available FLake, a 1-dimensional freshwater lake model, is tuned for 244 globally distributed large lakes using lake surface water temperatures (LSWTs derived from Along-Track Scanning Radiometers (ATSRs. The model, tuned using only 3 lake properties; lake depth, albedo (snow and ice and light extinction co-efficient, substantially improves the measured biases in various features of the LSWT annual cycle, including the LSWTs of saline and high altitude lakes. The daily mean absolute differences (MAD and the spread of differences (±2 standard deviations across the trial seasonally ice covered lakes (lakes with a lake-mean LSWT remaining below 1 °C for part of the annual cycle is reduced from 3.01± 2.25 °C (pre-tuning to 0.84 ± 0.51 °C (post-tuning. For non-seasonally ice-covered trial lakes (lakes with a lake-mean LSWT remaining above 1 °C throughout its annual cycle, the average daily mean absolute difference (MAD is reduced from 3.55 ± 3.20 °C to 0.96 ± 0.63 °C. The post tuning results for the trial lakes (35 lakes are highly representative of the post tuning results of the 244 lakes. The sensitivity of the summer LSWTs of deeper lakes to changes in the timing of ice-off is demonstrated. The modelled summer LSWT response to changes in ice-off timing is found to be strongly affected by lake depth and latitude, explaining 0.50 (R2adj, p = 0.001 of the inter-lake variance in summer LSWTs. Lake depth alone explains 0.35 (p =0.003 of the variance. The tuning approach undertaken in this study, overcomes the obstacle of the lack of available lake characteristic information (snow and ice albedo and light extinction co-efficient for individual lakes. Furthermore, the tuned values for lake depth, snow and ice albedo and light extinction co-efficient for the 244 lakes provide guidance for improving LSWTs modelling in FLake.
On-Site was developed to provide modelers and model reviewers with prepackaged tools ("calculators") for performing site assessment calculations. The philosophy behind OnSite is that the convenience of the prepackaged calculators helps provide consistency for simple calculations,...
Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong
2015-11-01
Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.
Banerjee, Ayan; Rahaman, Farook; Jotania, Kanti; Sharma, Ranjan; Rahaman, Mosiur
2014-01-01
Gravitational analyzes in lower dimensions has become a field of active research interest ever since Banados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69, 1849, 1992) proved the existence of a black hole solution in (2 + 1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2 + 1)-dimensional anisotropic star in anti-de ...
Mohammad Najafi; Maliheh Najafi; M. T. Darvishi
2012-01-01
By means of modification of the extended homoclinic test approach (mEHTA), we obtain some new exact soliton solutions for the (2+l)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation by obtaining a bilinear closed form for it.%By means of modification of the extended homoclinic test approach (mEHTA),we obtain some new exact soliton solutions for the (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation by obtaining a bilinear closed form for it.
Ma Hong-Cai; Deng Ai-Ping; Qin Zhen-Yun
2009-01-01
@@ With the help of the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to obtain the Jacobi doubly periodic wave solutions of the (2+1)-dimensionai B-type Kadomtsev-Petviashvili (BKP) equation and the generalized Klein-Gordon equation. The method is also valid for other (1+1)-dimensional and higher dimensional systems.
Fusion and fission phenomena for solitary waves have been discovered theoretically and experimentally. In this paper, the (2 + 1)-dimensional variable-coefficient Broer-Kaup system is symbolically investigated. By employing the bilinear method, new solitary solutions with arbitrary functions are obtained. At the same time, the non-elastic interactions of solitary solutions are graphically studied. Furthermore, soliton fusion and fission phenomena are revealed by choosing appropriate functions.
This paper is to investigate the extended (2+1)-dimensional Konopelchenko-Dubrovsky equations, which can be applied to describing certain phenomena in the stratified shear flow, the internal and shallow-water waves, plasmas and other fields. Painleve analysis is passed through via symbolic computation. Bilinear-form equations are constructed and soliton solutions are derived. Soliton solutions and interactions are illustrated. Bilinear-form Baecklund transformation and a type of solutions are obtained. (general)
(3+1)维ZK方程的孤立波解%Multi-solitary wave solutions of the (3 +1)-dimensional ZK equation
石玉仁; 周志刚; 张娟; 杨红娟
2012-01-01
采用变换和拟设相结合的方法得到了(3+1)维Zakharov-Kuznetsov (ZK)方程的几组精确解,包括周期波解、单孤子解和双孤子解.%Some exact solution, involving the periodical solution, single soliton solution and doublesoliton solution are obtained for the (3 ~t~ 1 )-dimensional Zakharov-Kuznetsov (ZK) equation by usingtransformations.
Chiral Anomaly in Euclidean (2+1)-DIMENSIONAL Space and AN Application to the Quantum Hall Effect
Bracken, Paul
The chiral anomaly in (2+1)-dimensions and its relationship to the zero mode of the Dirac equation in the massless case is studied. Solutions are obtained for the Dirac equation under a vector potential which generates a constant magnetic field. It is shown that there is an anomaly term associated with the corresponding chiral transformation. It can be calculated by using the regularization procedure of Fujikawa. The results are applied to the quantum Hall effect.
Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in 2+1 dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm potential which is highly singular at the origin, producing divergences in a perturbative expansion around the usual solution of the free Dirac equation. This problem is surmounted by using a perturbative expansion around the exact solution of the commutative Aharonov-Bohm problem. We calculate, in this setting, the scattering amplitude and the corrections to the differential and total cross sections for a spin 1/2 particle, in the small-flux limit
We study the parity breaking effective action in 2+1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. There are two classes of such actions that arise: namely, terms that do not manifestly depend on E(vector sign) and ones that do. We derive the exact effective action that is not manifestly dependent on E(vector sign). For the other class that depends explicitly on E(vector sign), there are families of terms that can be determined order by order in perturbation theory. We attempt to generalize our results to nonstatic backgrounds through the use of time ordered exponentials and prove gauge invariance, both small and large, of the resulting effective action. We also point out some open questions that need to be further understood
Distillation Calculations with a Programmable Calculator.
Walker, Charles A.; Halpern, Bret L.
1983-01-01
Describes a three-step approach for teaching multicomponent distillation to undergraduates, emphasizing patterns of distribution as an aid to understanding the separation processes. Indicates that the second step can be carried out by programmable calculators. (A more complete set of programs for additional calculations is available from the…
WANG Shuang; WU Shuang-Qing; XIE Fei; DAN Lin
2006-01-01
@@ We investigate the first law of thermodynamics in the case of the (2 + 1)-dimensional Banados-Teitelboim-Zanelli black holes and Kerr-de Sitter spacetimes. In particular, we focus on the integral mass formulas. It is found that by assuming the cosmological constant as a variable state parameter, both the differential and integral mass formulas of the first law of black hole thermodynamics in the asymptotic flat spacetimes can be directly extended to those of rotating black holes in anti-de Sitter and de Sitter backgrounds. It should be pointed that these formulae come into existence in any dimensions.
The (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation with linear and parabolic traps is studied, and an exact Kuznetsov–Ma soliton solution in certain parameter conditions is derived. These precise expressions indicate that diffraction and chirp factors influence phase, center and widths, while the gain/loss parameter only affects peaks. By adjusting the relation between the maximum accumulated time Tm and the accumulated time T0 based on maximum amplitude of Kuznetsov–Ma soliton, postpone, maintenance and restraint of superposed Kuznetsov–Ma solitons are investigated
Ebert, D; Klimenko, K G; Zhukovsky, V C
2016-01-01
In this paper the duality correspondence between fermion-antifermion and difermion interaction channels is established in two (2+1)-dimensional Gross-Neveu type models with a fermion number chemical potential $\\mu$ and a chiral chemical potential $\\mu_5$. The role and influence of this property on the phase structure of the models are investigated. In particular, it is shown that the chemical potential $\\mu_5$ promotes the appearance of dynamical chiral symmetry breaking, whereas the chemical potential $\\mu$ contributes to the emergence of superconductivity.
Karsch, F.; Laermann, E.; Lütgemeier, M.
1994-01-01
We establish a close relation between the spatial string tension of the (3+1)-dimensional $SU(3)$ gauge theory at finite temperature ($\\sigma_s$) and the string tension of the 3-dimensional $SU(3)$ gauge theory ($\\sigma_3$) which is similar to what has been found previously for $SU(2)$. We obtain $\\sqrt{\\sigma_3} = (0.554 \\pm 0.004) g_3^2$ and $\\sqrt{\\sigma_s} = (0.586 \\pm 0.045)g^2(T) T$, respectively. For temperatures larger than twice the critical temperature results are consistent with a ...
Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum
2014-01-01
In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics. PMID:25674431
Based on a new general ansaetz, a new general algebraic method named improved Riccati equation rational expansion method is devised for constructing multiple nontravelling wave solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. With the aid of symbolic computation, we choose the (2 + 1)-dimensional cubic nonlinear Schroedinger equation to illustrate the method. As a result, six families of new exact analytical solutions for this equation are found, which include some new and more general exact rational form soliton-like solutions and triangular periodic-like solutions
Lukierski, Jerzy; Stichel, Peter C.; Zakrzewski, Wojtek J.
1996-01-01
We consider a new D=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we provide the dynamical interpretation of the second central charge of the (2+1)-dimensional Galilean algebra. We discuss also the interpretation of k as describing the noncommutativity of D=2 space coordinates. The model is quantized in two ways: using the Os...
Spin-orbit gap of graphene: First-principles calculations
Yao, Yugui; Ye, Fei; Qi, Xiao-Liang; Zhang, Shou-Cheng; Fang, Zhong
2006-01-01
Even though graphene is a low energy system consisting of the two dimensional honeycomb lattice of carbon atoms, its quasi-particle excitations are fully described by the 2+1 dimensional relativistic Dirac equation. In this paper we show that while the spin-orbit interaction in graphene is of the order of $4 meV$, it opens up a gap of the order of $10^{-3} meV$ at the Dirac points. We present the first principle calculation of the spin-orbit gap, and explain the behavior in terms of a simple ...
Autistic Savant Calendar Calculators.
Patti, Paul J.
This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these calculators. Three…
张福伟; 刘进生
2012-01-01
By using the variational method and critical point theory, especially critical group and Morse theory, combined with the matrix theory and space dimension, taking into account the critical points of both positive and negative energy functional, the multiplicity of solutions of 1-dimensional nonlinear discrete elliptic resonant problem was investigated. Under some assumptions, two kinds of new sufficient conditions were obtained under which there exist at least two nonzero solutions. An example was given to verify the obtained results. The results showed that, under the same assumptions, the number of known solutions of 1-dimensional resonant problem is more than that of multidimensional resonant problem.%利用变分方法与临界点理论,特别是临界群与Morse理论,结合矩阵理论与空间维数,同时考虑正、负能量泛函的临界点,研究了一维非线性离散椭圆共振问题解的多重性.在一定的假设条件下,得到了此类问题至少存在两个非零解的两类新的充分条件,并给出了具体应用的实例.结果表明:在相同的假设条件下,一维共振问题比多维共振问题得到的解更多.
In this paper, a (3+1)-dimensional generalized Kadomtsev—Petviashvili (GKP) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves (quasi-periodic waves) for the (3+1)-dimensional GKP equation. Interestingly, the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure. (general)
Heterogeneous Calculation of ε
A heterogeneous method of calculating the fast fission factor given by Naudet has been applied to the Carlvik - Pershagen definition of ε. An exact calculation of the collision probabilities is included in the programme developed for the Ferranti - Mercury computer
Personal Finance Calculations.
Argo, Mark
1982-01-01
Contains explanations and examples of mathematical calculations for a secondary level course on personal finance. How to calculate total monetary cost of an item, monthly payments, different types of interest, annual percentage rates, and unit pricing is explained. (RM)
Consolidated fuel shielding calculations
Irradiated fuel radiation dose rate and radiation shielding requirements are calculated using a validated ISOSHLD-II model. Comparisons are made to experimental measurements. ISOSHLD-11 calculations are documented
Calculating Clearances for Manipulators
Copeland, E. L.; Peticolas, J. D.; Ray, L. D.
1983-01-01
Set of algorithms rapidly calculates minimum safe clearances for remote manipulators. Such calculations are used in design of trajectories for manipulators to ensure they do not accidentally strike surrounding objects. Structural parts are considered as cylindrical shells having circular plane areas for ends. Clearance calculation method offers special benefits in industrial robotics, particularly in automated machining.
A point-kernel integral technique code, PKN, and the related data library have been developed to calculate neutron and secondary gamma-ray dose equivalents in water, concrete and iron shields for neutron sources in 3-dimensional geometry. The comparison between calculational results of the present code and those of the 1-dimensional transport code ANISN = JR, and the 2-dimensional transport code DOT4.2 showed a sufficient accuracy, and the availability of the PKN code has been confirmed. (author)
How Do Calculators Calculate Trigonometric Functions?
Underwood, Jeremy M.; Edwards, Bruce H.
How does your calculator quickly produce values of trigonometric functions? You might be surprised to learn that it does not use series or polynomial approximations, but rather the so-called CORDIC method. This paper will focus on the geometry of the CORDIC method, as originally developed by Volder in 1959. This algorithm is a wonderful…
In this paper, we investigate a (3+1)-dimensional generalized variable-coefficient Kadomtsev—Petviashvili equation, which can describe the nonlinear phenomena in fluids or plasmas. Painlevé analysis is performed for us to study the integrability and we find that the equation is not completely integrable. By virtue of the binary Bell polynomials, bilinear form and soliton solutions are obtained, and Bäcklund transformation in the binary-Bell-polynomial form and bilinear form are derived. Soliton collisions are graphically discussed: the solitons keep their original shapes unchanged after the collision except for the phase shifts. Variable coefficients are seen to affect the motion of solitons: when the variable coefficients are chosen as the constants, solitons keep their directions unchanged during the collision; with the variable coefficients as the functions of the temporal coordinate, the one soliton changes its direction. (general)
Under investigation in this paper is a (2+1)-dimensional nonlinear evolution equation generated via the Jaulent–Miodek hierarchy for nonlinear water waves. With the aid of binary Bell polynomials and symbolic computation, bilinear forms and a Bäcklund transformations are derived. N-soliton solutions are obtained through the Hirota method. Soliton propagation is discussed analytically. The bell-shaped soliton, anti-bell-shaped soliton and shock wave can be seen with some parameters selected. Soliton interactions are analyzed graphically: four kinds of elastic interactions are presented: two parallel bell-shaped solitons, two parallel anti-bell-shaped solitons, three parallel bell-shaped solitons and three parallel anti-bell-shaped solitons. We see that (1) the solitons maintain their original amplitudes, widths and directions except for some phase shifts after each interaction, and (2) the smaller the soliton amplitude is, the faster the soliton travels. (papers)
TANG Xiao-Yan; LOU Sen-Yue
2002-01-01
We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.
We study the (2+1)-dimensional nonlinear Schrödinger equation with different forms of distributed transverse diffraction in anisotropic graded-index grating waveguides, and obtain an exact two-breather solution for certain functional relations. From this solution, both Akhmediev breathers and Kuznetsov–Ma solitons can be constructed. A mechanism for controlling these localized solutions is presented. Two different transverse forms of diffraction and chirp factors play important roles in the evolutional characteristics such as phase, center and widths, while the gain/loss parameter only affects the evolution of their peaks. The propagation type of Akhmediev breathers and Kuznetsov–Ma solitons is determined by the relation between the maximum effective propagation distance, Zm, and the effective propagation distance, Z0, based on the center of the breathers. By adjusting this relation, partial excitation, maintenance and limitation of superposed Akhmediev breathers and Kuznetsov–Ma solitons are investigated for a waveguide with decreasing exponential diffraction.
Banerjee, Ayan; Jotania, Kanti; Sharma, Ranjan; Rahaman, Mosiur
2014-01-01
Gravitational analyzes in lower dimensions has become a field of active research interest ever since Banados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69, 1849, 1992) proved the existence of a black hole solution in (2 + 1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2 + 1)-dimensional anisotropic star in anti-de Sitter background space-time which have been obtained by assuming that the equation of state (EOS) describing the material composition of the star could either be linear or non-linear in nature. By matching the interior solution to the BTZ exterior metric with zero spin, we have demonstrated that the solutions provided here are regular and well-behaved at the stellar interior.
Gao, Xin-Yi
2016-06-01
Liquids with gas bubbles are commonly seen in medical science, natural science, daily life and engineering. Nonlinear-wave symbolic computation on the (3+1)-dimensional variable-coefficient Kudryashov-Sinelshchikov model for a bubbly liquid is hereby performed. An auto-Bäcklund transformation and with some solitonic solutions are obtained. With respect to the density fluctuation of the bubble-liquid mixture, both the auto-Bäcklund transformation and solitonic solutions depend on the bubble-liquid-viscosity, transverse-perturbation, bubble-liquid-nonlinearity and bubble-liquid-dispersion coefficient functions. We note that some shock waves given by our solutions have been observed by the gas-bubble/liquid-mixture experiments. Effects on a bubbly liquid with respect to the bubble-liquid-viscosity, transverse-perturbation, bubble-liquid-nonlinearity and bubble-liquid-dispersion coefficient functions might be detected by the future gas-bubble/liquid-mixture experiments.
In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, which describe the interactions of the Riemann waves with the long waves. With symbolic computation, the Hirota bilinear forms and Baecklund transformations are derived for those two systems. Furthermore, multisoliton solutions in terms of the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions into the bilinear equations. Via the Wronskian technique, it is proved that the Baecklund transformations obtained are the ones between the (N - 1)- and N-soliton solutions. Propagations and interactions of the kink-/bell-shaped solitons are presented. It is shown that the Riemann waves possess the solitonic properties, and maintain the amplitudes and velocities in the collisions only with some phase shifts. (general)
李玉红; 王鸿章; 刁群
2012-01-01
给出椭圆方程的一组Theta周期波解,结合它的一个Backlund变换,得到这个椭圆方程的无穷序列Theta函数周期波解,最后利用这个椭圆方程作为辅助方程,借助于计算机符号计算软件Mathematica,得到了(2+1)维Zakharov-Kuznetsov方程的无穷序列Theta函数周期波解.%Based on some theta periodic wave solutions to a elliptical equation, together with its Backlund transformation, infinite sequences theta periodic wave solutions are derived; then regarding this elliptical equation as an auxiliary equation, with the help of computer software Mathematica, infinite sequences theta periodic wave solutions to (2 + 1)-dimensional Zakha-rov- Kuznetsov equation are obtained.
We consider the domains of those pseudoorthogonal coordinate systems in flat 2+1 - dimensional space-time which allow for separation of the Klein-Gordon equation by a product ansatz and which were characterized by Kalnins and Miller in connection with the symmetry group of the wave equation. The horizons of these domains which were constructed as enveloping surfaces of the common lightlike tangent planes of the coordinate surfaces turn out to be lightlike rule surfaces, generated by the totality of tangents of a lightlike curve. Consideration of the possible relations between the coordinate surfaces and the lightcone at infinity helped to complete the list of families of confocal quadrics appearing as coordinate surfaces in the work of Kalnins and Miller. The article aims at providing preliminary work for an investigation of field quantizations based on different coordinate systems, that is, for a search for possible generalizations of the Unruh-effect. (author)
To calculate total dose effect on semi-conductor devices in satellite for a period of space mission effectively, two approximate calculation models for a comic radiation shielding were proposed. They are a sectoring method and a chord-length distribution method. When an approximate method was applied in this study, complex structure of satellite was described into multiple 1-dimensional slabs, structural materials were converted to reference material(aluminum), and the pre-calculated dose-depth conversion function was introduced to simplify the calculation process. Verification calculation was performed for orbit location and structure geometry of KITSAT-1 and compared with detailed 3-dimensional calculation results and experimental values. The calculation results from approximate method were estimated conservatively with acceptable error. However, results for satellite mission simulation were underestimated in total dose rate compared with experimental values
Nagao, Yoshiharu [Japan Atomic Energy Research Inst., Oarai, Ibaraki (Japan). Oarai Research Establishment
1998-03-01
In material testing reactors like the JMTR (Japan Material Testing Reactor) of 50 MW in Japan Atomic Energy Research Institute, the neutron flux and neutron energy spectra of irradiated samples show complex distributions. It is necessary to assess the neutron flux and neutron energy spectra of an irradiation field by carrying out the nuclear calculation of the core for every operation cycle. In order to advance core calculation, in the JMTR, the application of MCNP to the assessment of core reactivity and neutron flux and spectra has been investigated. In this study, in order to reduce the time for calculation and variance, the comparison of the results of the calculations by the use of K code and fixed source and the use of Weight Window were investigated. As to the calculation method, the modeling of the total JMTR core, the conditions for calculation and the adopted variance reduction technique are explained. The results of calculation are shown. Significant difference was not observed in the results of neutron flux calculations according to the difference of the modeling of fuel region in the calculations by K code and fixed source. The method of assessing the results of neutron flux calculation is described. (K.I.)
Electrical installation calculations advanced
Kitcher, Christopher
2013-01-01
All the essential calculations required for advanced electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practiceA step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3For apprentices and electrical installatio
Electronics Environmental Benefits Calculator
U.S. Environmental Protection Agency — The Electronics Environmental Benefits Calculator (EEBC) was developed to assist organizations in estimating the environmental benefits of greening their purchase,...
Electrical installation calculations basic
Kitcher, Christopher
2013-01-01
All the essential calculations required for basic electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practice. A step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3Fo
Waste Package Lifting Calculation
The objective of this calculation is to evaluate the structural response of the waste package during the horizontal and vertical lifting operations in order to support the waste package lifting feature design. The scope of this calculation includes the evaluation of the 21 PWR UCF (pressurized water reactor uncanistered fuel) waste package, naval waste package, 5 DHLW/DOE SNF (defense high-level waste/Department of Energy spent nuclear fuel)--short waste package, and 44 BWR (boiling water reactor) UCF waste package. Procedure AP-3.12Q, Revision 0, ICN 0, calculations, is used to develop and document this calculation
Mohammed Abdulrahim Hamdi
2012-02-01
Full Text Available The mobile and wireless industry is entering an exciting time. Demand for mobile technology is growing at a tremendous rate. Corporations are deploying mobile applications that provide substantial business benefits, and consumers are readily adopting mobile data applications. We present scientific application for mobile phone in steps of software engineering project starting from data gathering, data analysis, designing, coding, packaging, testing and deploying, Mobile Scientific Calculator (MSC enable user to compute any mathematical operation by using this application in mobile phone without needing to use the calculator. Scientific calculator offers three keys the four mathematic operations, the four systems of digits and offering many of functions such as angles functions, power, factorial and other functions. Scientific calculator is suitable for many mobile phones which don t have scientific calculator in its applications, it provide simple design for dealing with its functions for all users. It operated on more than one mobile phone model.
Harun Or ROSHID
2015-01-01
Full Text Available By using exp(-Phi-expansion method, abundant exact traveling wave solutions for the fifth order (1+1-dimensional Kaup-Keperschmidt equation have been obtained in a uniform way. The obtained solutions in this work are imperative and significant for the explanation of some practical physical phenomena. It is shown that the exp(-Phi-expansion method together with the first order ordinary differential equation, provides a progress mathematical tool for solving nonlinear partial differential equations. Numerical results, together with graphical representation, explicitly reveal the complete reliability and high efficiency of the proposed algorithm. Normal 0 false false false EN-US X-NONE TH v\\:* {behavior:url(#default#VML;} o\\:* {behavior:url(#default#VML;} w\\:* {behavior:url(#default#VML;} .shape {behavior:url(#default#VML;} By using the -expansion method, abundant exact traveling wave solutions for the fifth order (1+1-dimensional Kaup-Kupershmidt equation are obtained in a uniform way. The obtained solutions in this work are imperative and significant for explanation of some practical physical phenomena. It is shown that the -expansion method, together with the first order ordinary differential equation, provides a progress mathematical tool for solving nonlinear partial differential equations. Numerical results, together with graphical representation, explicitly reveal the complete reliability and high efficiency of the proposed algorithm. Normal 0 false false false EN-US X-NONE TH /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif"; mso-fareast-font-family:"Times New Roman"; mso
Collection of CASIM calculations
Monte Carlo calculations of hadronic cascades at Fermilab have usually been done using the code CASIM written by A. Van Ginneken. These calculations are often performed to determine the quantity of shielding required for radiation protection purposes. A number of examples of such calculations have been presented previously. Several years of practical experience have led the author to develop the collection of additional cases included in the present report. These results along with those given earlier will serve as a useful reference. No attempt was made here to consider all possibilities; rather, the purpose was to develop a useful set of examples. Exceptionally intricate cases should, of course, receive individualized attention as appropriate
We present GW calculations of molecules, ordered and disordered solids and interfaces, which employ an efficient contour deformation technique for frequency integration and do not require the explicit evaluation of virtual electronic states nor the inversion of dielectric matrices. We also present a parallel implementation of the algorithm, which takes advantage of separable expressions of both the single particle Green's function and the screened Coulomb interaction. The method can be used starting from density functional theory calculations performed with semilocal or hybrid functionals. The newly developed technique was applied to GW calculations of systems of unprecedented size, including water/semiconductor interfaces with thousands of electrons
Radioactive cloud dose calculations
Radiological dosage principles, as well as methods for calculating external and internal dose rates, following dispersion and deposition of radioactive materials in the atmosphere are described. Emphasis has been placed on analytical solutions that are appropriate for hand calculations. In addition, the methods for calculating dose rates from ingestion are discussed. A brief description of several computer programs are included for information on radionuclides. There has been no attempt to be comprehensive, and only a sampling of programs has been selected to illustrate the variety available
Geogebra: Calculation of Centroid
Qamil Kllogjeri; Pellumb Kllogjeri
2012-01-01
Our paper is result of the research done in a special direction for solving problems of physics by using GeoGebra programme: calculation of centroid. Lots of simulations of physical phenomena from the class of Mechanics can be performed and computational problems can be solved with GeoGebra. GeoGebra offers many commands and one of them is the command “centroid” to calculate the coordinates of the centroid of a polygon but, we have created a new tool to calculate the coordinates of the centr...
nuclear reactor design calculations
In this work , the sensitivity of different reactor calculation methods, and the effect of different assumptions and/or approximation are evaluated . A new concept named error map is developed to determine the relative importance of different factors affecting the accuracy of calculations. To achieve this goal a generalized, multigroup, multi dimension code UAR-DEPLETION is developed to calculate the spatial distribution of neutron flux, effective multiplication factor and the spatial composition of a reactor core for a period of time and for specified reactor operating conditions. The code also investigates the fuel management strategies and policies for the entire fuel cycle to meet the constraints of material and operating limitations
Faria da Veiga, Paulo A.; O'Carroll, Michael; Valencia Alvites, José C.
2016-03-01
Considering a 3 + 1 dimensional lattice quantum chromodynamics (QCD) model defined with the improved Wilson action, three flavors, and 4 × 4 Dirac spin matrices, in the strong coupling regime, we reanalyze the question of the existence of the eightfold way baryons and complete our previous work where the existence of isospin octet baryons was rigorously solved. Here, we show the existence of isospin decuplet baryons which are associated with isolated dispersion curves in the subspace of the underlying quantum mechanical Hilbert space with vectors constructed with an odd number of fermion and antifermion basic quark and antiquark fields. Moreover, smoothness properties for these curves are obtained. The present work deals with a case for which the traditional method to solve the implicit equation for the dispersion curves, based on the use of the analytic implicit function theorem, cannot be applied. We do not have only one but two solutions for each one-baryon decuplet sector with fixed spin third component. Instead, we apply the Weierstrass preparation theorem, which also provides a general method for the general degenerate case. This work is completed by analyzing a spectral representation for the two-baryon correlations and providing the leading behaviors of the field strength normalization and the mass of the spectral contributions with more than one-particle. These are needed results for a rigorous analysis of the two-baryon and meson-baryon particle spectra.
A Simple Calculator Algorithm.
Cook, Lyle; McWilliam, James
1983-01-01
The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)
Frederiksen, Morten
2014-01-01
Williamson’s characterisation of calculativeness as inimical to trust contradicts most sociological trust research. However, a similar argument is found within trust phenomenology. This paper re-investigates Williamson’s argument from the perspective of Løgstrup’s phenomenological theory of trust....... Contrary to Williamson, however, Løgstrup’s contention is that trust, not calculativeness, is the default attitude and only when suspicion is awoken does trust falter. The paper argues that while Williamson’s distinction between calculativeness and trust is supported by phenomenology, the analysis needs to...... take actual subjective experience into consideration. It points out that, first, Løgstrup places trust alongside calculativeness as a different mode of engaging in social interaction, rather conceiving of trust as a state or the outcome of a decision-making process. Secondly, the analysis must take...
Handout on shielding calculation
In order to avoid the difficulties of the radioprotection supervisors in the tasks related to shielding calculations, is presented in this paper the basic concepts of shielding theory. It also includes exercises and examples. (author)
IRIS core criticality calculations
Three-dimensional Monte Carlo computer code KENO-VI of CSAS26 sequence of SCALE-4.4 code system was applied for pin-by-pin calculations of the effective multiplication factor for the first cycle IRIS reactor core. The effective multiplication factors obtained by the above mentioned Monte Carlo calculations using 27-group ENDF/B-IV library and 238-group ENDF/B-V library have been compared with the effective multiplication factors achieved by HELIOS/NESTLE, CASMO/SIMULATE, and modified CORD-2 nodal calculations. The results of Monte Carlo calculations are found to be in good agreement with the results obtained by the nodal codes. The discrepancies in effective multiplication factor are typically within 1%. (author)
Unit Cost Compendium Calculations
U.S. Environmental Protection Agency — The Unit Cost Compendium (UCC) Calculations raw data set was designed to provide for greater accuracy and consistency in the use of unit costs across the USEPA...
Shielding calculations for SSC
Monte Carlo calculations of hadron and muon shielding for SSC are reviewed with emphasis on their application to radiation safety and environmental protection. Models and algorithms for simulation of hadronic and electromagnetic showers, and for production and transport of muons in the TeV regime are briefly discussed. Capabilities and limitations of these calculations are described and illustrated with a few examples. 12 refs., 3 figs
Current interruption transients calculation
Peelo, David F
2014-01-01
Provides an original, detailed and practical description of current interruption transients, origins, and the circuits involved, and how they can be calculated Current Interruption Transients Calculationis a comprehensive resource for the understanding, calculation and analysis of the transient recovery voltages (TRVs) and related re-ignition or re-striking transients associated with fault current interruption and the switching of inductive and capacitive load currents in circuits. This book provides an original, detailed and practical description of current interruption transients, origins,
Reactor lattice transport calculations
The present lecture is a continuation of the lecture on Introduction to the Neutron Transport Phenomena. It comprises three aspects of lattice calculations. First the idea of a reactor lattice is introduced. Then the main definitions used in reactor lattice analysis are given, and finally two basic methods applied for solution of the transport equations are defined. Several remarks on secondary results from lattice transport calculations are added. (author)
Electrical installation calculations
Watkins, AJ
2006-01-01
Designed to provide a step by step guide to successful application of the electrical installation calculations required in day to day electrical engineering practice, the Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike.Now in its seventh edition, Volume 1 has been fully updated to meet the requirements of the 2330 Level 2 Certificate in Electrotechnical Technology from City & Guilds, and will also prove a vi
Geometric unsharpness calculations
Anderson, D.J. [International Training and Education Group (INTEG), Oakville, Ontario (Canada)
2008-07-15
The majority of radiographers' geometric unsharpness calculations are normally performed with a mathematical formula. However, a majority of codes and standards refer to the use of a nomograph for this calculation. Upon first review, the use of a nomograph appears more complicated but with a few minutes of study and practice it can be just as effective. A review of this article should provide enlightenment. (author)
Uncertainty calculations made easier
Hogenbirk, A.
1994-07-01
The results are presented of a neutron cross section sensitivity/uncertainty analysis performed in a complicated 2D model of the NET shielding blanket design inside the ITER torus design, surrounded by the cryostat/biological shield as planned for ITER. The calculations were performed with a code system developed at ECN Petten, with which sensitivity/uncertainty calculations become relatively simple. In order to check the deterministic neutron transport calculations (performed with DORT), calculations were also performed with the Monte Carlo code MCNP. Care was taken to model the 2.0 cm wide gaps between two blanket segments, as the neutron flux behind the vacuum vessel is largely determined by neutrons streaming through these gaps. The resulting neutron flux spectra are in excellent agreement up to the end of the cryostat. It is noted, that at this position the attenuation of the neutron flux is about 1 l orders of magnitude. The uncertainty in the energy integrated flux at the beginning of the vacuum vessel and at the beginning of the cryostat was determined in the calculations. The uncertainty appears to be strongly dependent on the exact geometry: if the gaps are filled with stainless steel, the neutron spectrum changes strongly, which results in an uncertainty of 70% in the energy integrated flux at the beginning of the cryostat in the no-gap-geometry, compared to an uncertainty of only 5% in the gap-geometry. Therefore, it is essential to take into account the exact geometry in sensitivity/uncertainty calculations. Furthermore, this study shows that an improvement of the covariance data is urgently needed in order to obtain reliable estimates of the uncertainties in response parameters in neutron transport calculations. (orig./GL).
Uncertainty calculations made easier
The results are presented of a neutron cross section sensitivity/uncertainty analysis performed in a complicated 2D model of the NET shielding blanket design inside the ITER torus design, surrounded by the cryostat/biological shield as planned for ITER. The calculations were performed with a code system developed at ECN Petten, with which sensitivity/uncertainty calculations become relatively simple. In order to check the deterministic neutron transport calculations (performed with DORT), calculations were also performed with the Monte Carlo code MCNP. Care was taken to model the 2.0 cm wide gaps between two blanket segments, as the neutron flux behind the vacuum vessel is largely determined by neutrons streaming through these gaps. The resulting neutron flux spectra are in excellent agreement up to the end of the cryostat. It is noted, that at this position the attenuation of the neutron flux is about 1 l orders of magnitude. The uncertainty in the energy integrated flux at the beginning of the vacuum vessel and at the beginning of the cryostat was determined in the calculations. The uncertainty appears to be strongly dependent on the exact geometry: if the gaps are filled with stainless steel, the neutron spectrum changes strongly, which results in an uncertainty of 70% in the energy integrated flux at the beginning of the cryostat in the no-gap-geometry, compared to an uncertainty of only 5% in the gap-geometry. Therefore, it is essential to take into account the exact geometry in sensitivity/uncertainty calculations. Furthermore, this study shows that an improvement of the covariance data is urgently needed in order to obtain reliable estimates of the uncertainties in response parameters in neutron transport calculations. (orig./GL)
Neutron spectra calculation in material in order to compute irradiation damage
This short presentation will be on neutron spectra calculation methods in order to compute the damage rate formation in irradiated structure. Three computation schemes are used in the French C.E.A.: (1) 3-dimensional calculations using the line of sight attenuation method (MERCURE IV code), the removal cross section being obtained from an adjustment on a 1-dimensional transport calculation with the discrete ordinate code ANISN; (2) 2-dimensional calculations using the discrete ordinates method (DOT 3.5 code), 20 to 30 group library obtained by collapsing the 100 group a library on fluxes computed by ANISN; (3) 3-dimensional calculations using the Monte Carlo method (TRIPOLI system). The cross sections which originally came from UKNDL 73 and ENDF/B3 are now processed from ENDF B IV. (author)
Progress on theoretical calculation
The calculation program NPPD-2 of neutron reaction data in the energy region from 10-11 to 20 MeV has been researched with extending the energy from 5 to 20 MeV. In this program, the cascade γ-de-excitations of the compound nucleus and residual nucleus are described by means of the Troubetzkoy's statistical model and the conservation relations of angular momentum and parity are are considered. This program may be used for the calculations of the natural element, with the number of isotopes less than 10. The program has been finished and the calculations for oxygen are being done in order to test the program. The reaction channels in n + 40Ca, which considered in NPPD-2, are presented
Daylight calculations in practice
Iversen, Anne; Roy, Nicolas; Hvass, Mette;
The aim of the project was to obtain a better understanding of what daylight calculations show and also to gain knowledge of how the different daylight simulation programs perform compared with each other. Experience has shown that results for the same room, obtained from two daylight simulation...... programs can give different results. This can be due to restrictions in the program itself and/or be due to the skills of the persons setting up the models. This is crucial as daylight calculations are used to document that the demands and recommendations to daylight levels outlined by building authorities....... The aim of the project was to obtain a better understanding of what daylight calculations show and also to gain knowledge of how the different daylight simulation programs perform compared with each other. Furthermore the aim was to provide knowledge of how to build up the 3D models that were to be...
Geogebra: Calculation of Centroid
Qamil Kllogjeri
2012-09-01
Full Text Available Our paper is result of the research done in a special direction for solving problems of physics by using GeoGebra programme: calculation of centroid. Lots of simulations of physical phenomena from the class of Mechanics can be performed and computational problems can be solved with GeoGebra. GeoGebra offers many commands and one of them is the command “centroid” to calculate the coordinates of the centroid of a polygon but, we have created a new tool to calculate the coordinates of the centroid of a plane region bounded by curves. Our work is part of the passionate work of many GeoGebra users which will result with a very rich fund of GeoGebra virtual tools, examples and experiences that will be worldwidely available for many teachers and practioners.
Population dose calculation technique
An original method is suggested for calculating the population doses from gas and aerosol radioactive releases. The method is based on the assumption of uniform population and arable land distribution. The validity of this assumption has been proved for a rather large condition range. Though, some modified formulae are given to take into account the non-uniformity of population distribution, connected with large cities, on the one hand, and with woods, shores, regional borders, on the other hand. Employment of the suggested method results in an apriciable calculation accuracy rise for the long-living slowly precipitating radionuclides as compared with the existing methods
Big Bang Nucleosynthesis Calculation
Kurki-Suonio, H
2001-01-01
I review standard big bang nucleosynthesis and some versions of nonstandard BBN. The abundances of the primordial isotopes D, He-3, and Li-7 produced in standard BBN can be calculated as a function of the baryon density with an accuracy of about 10%. For He-4 the accuracy is better than 1%. The calculated abundances agree fairly well with observations, but the baryon density of the universe cannot be determined with high precision. Possibilities for nonstandard BBN include inhomogeneous and antimatter BBN and nonzero neutrino chemical potentials.
Electrical installation calculations
Watkins, AJ
2006-01-01
Designed to provide a step by step guide to successful application of the electrical installation calculations required in day to day electrical engineering practice, the Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both Foundation and Modern Apprentices, and professional electrical installation engineers alike.Now in its sixth edition, Volume 2 has been fully updated to meet the requirements of the 2330 Level 3 Certificate in Electrotechnical Technology from City & Guilds, and will also prove a vital purchase for students of Level 3
Djouadi, Abdelhak
2002-01-01
I discuss the various available tools for the study of the properties of the new particles predicted in the Minimal Supersymmetric extension of the Standard Model. Emphasis will be put on the codes for the determination of the sparticle and Higgs boson spectrum. Codes for the calculation of production cross sections, decay widths and branching ratios, Dark Matter relic density and detection rates, as well as codes for automatic analytical calculations and Monte-Carlo event generators for Supersymmetric processes will be briefly discussed.
Three recent TDHF calculations
Three applications of TDHF are discussed. First, vibrational spectra of a post grazing collision 40Ca nucleus is examined and found to contain many high energy components, qualitatively consistent with recent Orsay experiments. Second, the fusion cross section in energy and angular momentum are calculated for 16O + 24Mg to exhibit the parameters of the low l window for this system. A sensitivity of the fusion cross section to the effective two body potential is discussed. Last, a preliminary analysis of 86Kr + 139La at E/sub lab/ = 505 MeV calculated in the frozen approximation is displayed, compared to experiment and discussed
Noordzij, Marlies; Dekker, Friedo W.; Zoccali, Carmine; Jager, Kitty J.
2011-01-01
The sample size is the number of patients or other experimental units that need to be included in a study to answer the research question. Pre-study calculation of the sample size is important; if a sample size is too small, one will not be able to detect an effect, while a sample that is too large may be a waste of time and money. Methods to calculate the sample size are explained in statistical textbooks, but because there are many different formulas available, it can be difficult for inves...
无
2011-01-01
Compared with ellipse cavity, the spoke cavity has many advantages, especially for the low and medium beam energy. It will be used in the superconductor accelerator popular in the future. Based on the spoke cavity, we design and calculate an accelerator
Water vapor pressure calculation.
Hall, J R; Brouillard, R G
1985-06-01
Accurate calculation of water vapor pressure for systems saturated with water vapor can be performed using the Goff-Gratch equation. A form of the equation that can be adapted for computer programming and for use in electronic databases is provided. PMID:4008425
Languages for structural calculations
The differences between human and computing languages are recalled. It is argued that they are to some extent structured in antagonistic ways. Languages in structural calculation, in the past, present, and future, are considered. The contribution of artificial intelligence is stressed
Calendrical Calculation and Intelligence.
O'Connor, Neil; Cowan, Richard; Samella, Katerina
2000-01-01
Studied the ability to name the days of the week for dates in the past and future (calendrical calculation) of 10 calendrical savants with Wechlser Adult Intelligence Scale scores from 50 to 97. Results suggest that although low intelligence does not prevent the development of this skill, the talent depends on general intelligence. (SLD)
PIC: Protein Interactions Calculator
Tina, KG; Bhadra, R.; Srinivasan, N.
2007-01-01
Interactions within a protein structure and interactions between proteins in an assembly are essential considerations in understanding molecular basis of stability and functions of proteins and their complexes. There are several weak and strong interactions that render stability to a protein structure or an assembly. Protein Interactions Calculator (PIC) is a server which, given the coordinate set of 3D structure of a protein or an assembly, computes various interactions such as disulphide bo...
Calculations in furnace technology
Davies, Clive; Hopkins, DW; Owen, WS
2013-01-01
Calculations in Furnace Technology presents the theoretical and practical aspects of furnace technology. This book provides information pertinent to the development, application, and efficiency of furnace technology. Organized into eight chapters, this book begins with an overview of the exothermic reactions that occur when carbon, hydrogen, and sulfur are burned to release the energy available in the fuel. This text then evaluates the efficiencies to measure the quantity of fuel used, of flue gases leaving the plant, of air entering, and the heat lost to the surroundings. Other chapters consi
Zero Temperature Hope Calculations
The primary purpose of the HOPE code is to calculate opacities over a wide temperature and density range. It can also produce equation of state (EOS) data. Since the experimental data at the high temperature region are scarce, comparisons of predictions with the ample zero temperature data provide a valuable physics check of the code. In this report we show a selected few examples across the periodic table. Below we give a brief general information about the physics of the HOPE code. The HOPE code is an ''average atom'' (AA) Dirac-Slater self-consistent code. The AA label in the case of finite temperature means that the one-electron levels are populated according to the Fermi statistics, at zero temperature it means that the ''aufbau'' principle works, i.e. no a priory electronic configuration is set, although it can be done. As such, it is a one-particle model (any Hartree-Fock model is a one particle model). The code is an ''ion-sphere'' model, meaning that the atom under investigation is neutral within the ion-sphere radius. Furthermore, the boundary conditions for the bound states are also set at the ion-sphere radius, which distinguishes the code from the INFERNO, OPAL and STA codes. Once the self-consistent AA state is obtained, the code proceeds to generate many-electron configurations and proceeds to calculate photoabsorption in the ''detailed configuration accounting'' (DCA) scheme. However, this last feature is meaningless at zero temperature. There is one important feature in the HOPE code which should be noted; any self-consistent model is self-consistent in the space of the occupied orbitals. The unoccupied orbitals, where electrons are lifted via photoexcitation, are unphysical. The rigorous way to deal with that problem is to carry out complete self-consistent calculations both in the initial and final states connecting photoexcitations, an enormous computational task. The Amaldi correction is an attempt to address this problem by distorting the
Linewidth calculations and simulations
Strandberg, Ingrid
2016-01-01
We are currently developing a new technique to further enhance the sensitivity of collinear laser spectroscopy in order to study the most exotic nuclides available at radioactive ion beam facilities, such as ISOLDE at CERN. The overall goal is to evaluate the feasibility of the new method. This report will focus on the determination of the expected linewidth (hence resolution) of this approach. Different effects which could lead to a broadening of the linewidth, e.g. the ions' energy spread and their trajectories inside the trap, are studied with theoretical calculations as well as simulations.
Lopez, Cesar
2015-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. This book is designed for use as a scientific/business calculator so that you can get numerical solutions to problems involving a wide array of mathematics using MATLAB. Just look up the function y
In this paper, excerpts of the 'Core Design', 'Computational Chains' and 'Qualification of Computational Chains' lectures are presented. Nuclear reactor design basic concepts as power distribution and reactivity are defined and analyzed both from the theoretical and the computational point of view. Emphasis is put on the physical meaning and sensitivity of both 'observables' to design parameters. Computational aspects, mainly as regards the effects of the heterogeneity in space and energy in reactor calculations, are afforded too. Structure and qualification of computational code packages are discussed and a practical application to the FRAMATOME SCIENCE advanced computational chain is supplied. (author)
Several Monte Carlo techniques are compared in the transport of neutrons of different source energies through two different deep-penetration problems each with two parts. The first problem involves transmission through a 200-cm concrete slab. The second problem is a 900 bent pipe jacketed by concrete. In one case the pipe is void, and in the other it is filled with liquid sodium. Calculations are made with two different Los Alamos Monte Carlo codes: the continuous-energy code MCNP and the multigroup code MCMG
Configuration space Faddeev calculations
The detailed study of few-body systems provides one of the most effective means for studying nuclear physics at subnucleon distance scales. For few-body systems the model equations can be solved numerically with errors less than the experimental uncertainties. We have used such systems to investigate the size of relativistic effects, the role of meson-exchange currents, and the importance of quark degrees of freedom in the nucleus. Complete calculations for momentum-dependent potentials have been performed, and the properties of the three-body bound state for these potentials have been studied. Few-body calculations of the electromagnetic form factors of the deuteron and pion have been carried out using a front-form formulation of relativistic quantum mechanics. The decomposition of the operators transforming convariantly under the Poincare group into kinematical and dynamical parts has been studies. New ways for constructing interactions between particles, as well as interactions which lead to the production of particles, have been constructed in the context of a relativistic quantum mechanics. To compute scattering amplitudes in a nonperturbative way, classes of operators have been generated out of which the phase operator may be constructed. Finally, we have worked out procedures for computing Clebsch-Gordan and Racah coefficients on a computer, as well as giving procedures for dealing with the multiplicity problem
Weldon Spring dose calculations
In response to a request by the Oak Ridge Operations (ORO) Office of the Department of Energy (DOE) for assistance to the Department of the Army (DA) on the decommissioning of the Weldon Spring Chemical Plant, the Health and Safety Research Division of the Oak Ridge National Laboratory (ORNL) performed limited dose assessment calculations for that site. Based upon radiological measurements from a number of soil samples analyzed by ORNL and from previously acquired radiological data for the Weldon Spring site, source terms were derived to calculate radiation doses for three specific site scenarios. These three hypothetical scenarios are: a wildlife refuge for hunting, fishing, and general outdoor recreation; a school with 40 hr per week occupancy by students and a custodian; and a truck farm producing fruits, vegetables, meat, and dairy products which may be consumed on site. Radiation doses are reported for each of these scenarios both for measured uranium daughter equilibrium ratios and for assumed secular equilibrium. Doses are lower for the nonequilibrium case
Multilayer optical calculations
Byrnes, Steven J
2016-01-01
When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain aspects of it are difficult to find explicitly and consistently worked out in the literature. Here, we derive the formulas underlying the transfer-matrix method of calculating the optical properties of these stacks, including oblique-angle incidence, absorption-vs-position profiles, and ellipsometry parameters. We discuss and explain some strange consequences of the formulas in the situation where the incident and/or final (semi-infinite) medium are absorptive, such as calculating $T>1$ in the absence of gain. We also discuss some implementation details like complex-plane branch cuts. Finally, we derive modified formulas for including one or more "incoherent" layers, i.e. very thick layers in which interference can be neglected. This document was written in conjunction with ...
Molecular Dynamics Calculations
1996-01-01
The development of thermodynamics and statistical mechanics is very important in the history of physics, and it underlines the difficulty in dealing with systems involving many bodies, even if those bodies are identical. Macroscopic systems of atoms typically contain so many particles that it would be virtually impossible to follow the behavior of all of the particles involved. Therefore, the behavior of a complete system can only be described or predicted in statistical ways. Under a grant to the NASA Lewis Research Center, scientists at the Case Western Reserve University have been examining the use of modern computing techniques that may be able to investigate and find the behavior of complete systems that have a large number of particles by tracking each particle individually. This is the study of molecular dynamics. In contrast to Monte Carlo techniques, which incorporate uncertainty from the outset, molecular dynamics calculations are fully deterministic. Although it is still impossible to track, even on high-speed computers, each particle in a system of a trillion trillion particles, it has been found that such systems can be well simulated by calculating the trajectories of a few thousand particles. Modern computers and efficient computing strategies have been used to calculate the behavior of a few physical systems and are now being employed to study important problems such as supersonic flows in the laboratory and in space. In particular, an animated video (available in mpeg format--4.4 MB) was produced by Dr. M.J. Woo, now a National Research Council fellow at Lewis, and the G-VIS laboratory at Lewis. This video shows the behavior of supersonic shocks produced by pistons in enclosed cylinders by following exactly the behavior of thousands of particles. The major assumptions made were that the particles involved were hard spheres and that all collisions with the walls and with other particles were fully elastic. The animated video was voted one of two
I took only few topics to investigate, some on which I had some personal interest, and others that I felt rather crucial for the design. In this document I report my calculations on these various subjects. Therefore this document represents my tangible contribution to TRISTAN design. I give in the following the list of the topics which are discussed in this document. 1. Increase of the vertical betatron emmitance by skew quadrupoles in the electron storage ring. 2. Bremsstrahlung. 3. Dipole correcting system for electron ring. 4. Wigglers at low energies 5. Steady state compensation of beam loading in the single beam mode in the electron storage ring. 6. Coupled bunch longitudinal instability for electron ring. 7. Ion production and trapping in the electron storage ring for TRISTAN. 8. Estimate of the longitudinal impedance for the TRISTAN electron storage ring. (author)
Our work is dedicated to the assessment of the heat released in the Jet tokamak divertor tiles. We have performed the computation of the heat flux from temperature data collected by thermo-couples through a 1 dimensional linear model. This method has implied solving an inverse problem whose matrix is singular, we have succeeded in using Tikhonov's regularization technique. Then we have compared these values of the heat flux with those deduced from infra-red measurements. Infra-red measurements are impaired by the deposition of particles on the surface. Both methods give unrealistic negative values at the end of the plasma discharge. The use of a non-linear 1-dimensional model that would allow the diffusion coefficient to vary is expected to improve the calculation. (A.C.)
Exoplanet Equilibrium Chemistry Calculations
Blumenthal, Sarah; Harrington, J.; Bowman, M.; Blecic, J.
2013-10-01
Recently, Agundez et al. (2012, A&A 548, A73) used a chemical kinetics code to study a model HD 209458b (equilibrium temperature of 1450 K, assuming full redistribution and 0 albedo). They found that thermochemistry dominates most of the dayside, but that significant compositional gradients may exist across the dayside. We calculate equilibrium-chemistry molecular abundances for several model exoplanets, using NASA's open-source Chemical Equilibrium Abundances code (McBride and Gordon 1996). We vary the degree of radiation redistribution to the dark side, ranging from total redistribution to instantaneous reradiation. Atomically, both the solar abundance multiple and the carbon fraction vary. Planet substellar temperatures range from just above 1200 K, where photochemistry should no longer be important, to those of hot planets (3000 K). We present synthetic abundance images for the key spectroscopic molecules CO, CH4, and H2O for several hot-Jupiter model planets. This work was supported by the NASA Planetary Atmospheres grant NNX12AI69G.
Relative Hazard Calculation Methodology
The methodology presented in this document was developed to provide a means of calculating the RH ratios to use in developing useful graphic illustrations. The RH equation, as presented in this methodology, is primarily a collection of key factors relevant to understanding the hazards and risks associated with projected risk management activities. The RH equation has the potential for much broader application than generating risk profiles. For example, it can be used to compare one risk management activity with another, instead of just comparing it to a fixed baseline as was done for the risk profiles. If the appropriate source term data are available, it could be used in its non-ratio form to estimate absolute values of the associated hazards. These estimated values of hazard could then be examined to help understand which risk management activities are addressing the higher hazard conditions at a site. Graphics could be generated from these absolute hazard values to compare high-hazard conditions. If the RH equation is used in this manner, care must be taken to specifically define and qualify the estimated absolute hazard values (e.g., identify which factors were considered and which ones tended to drive the hazard estimation)
Parallel nearest neighbor calculations
Trease, Harold
We are just starting to parallelize the nearest neighbor portion of our free-Lagrange code. Our implementation of the nearest neighbor reconnection algorithm has not been parallelizable (i.e., we just flip one connection at a time). In this paper we consider what sort of nearest neighbor algorithms lend themselves to being parallelized. For example, the construction of the Voronoi mesh can be parallelized, but the construction of the Delaunay mesh (dual to the Voronoi mesh) cannot because of degenerate connections. We will show our most recent attempt to tessellate space with triangles or tetrahedrons with a new nearest neighbor construction algorithm called DAM (Dial-A-Mesh). This method has the characteristics of a parallel algorithm and produces a better tessellation of space than the Delaunay mesh. Parallel processing is becoming an everyday reality for us at Los Alamos. Our current production machines are Cray YMPs with 8 processors that can run independently or combined to work on one job. We are also exploring massive parallelism through the use of two 64K processor Connection Machines (CM2), where all the processors run in lock step mode. The effective application of 3-D computer models requires the use of parallel processing to achieve reasonable "turn around" times for our calculations.
Configuration space Faddeev calculations
The detailed study of few-body systems provides one of the most precise tools for studying the dynamics of nuclei. Our research program consists of a careful theoretical study of the nuclear few-body systems. During the past year we have completed several aspects of this program. We have continued our program of using the trinucleon system to investigate the validity of various realistic nucleon-nucleon potentials. Also, the effects of meson-exchange currents in nuclear systems have been studied. Initial calculations using the configuration-space Faddeev equations for nucleon-deuteron scattering have been completed. With modifications to treat relativistic systems, few-body methods can be applied to phenomena that are sensitive to the structure of the individual hadrons. We have completed a review of Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics for Advances in Nuclear Physics. Although it is called a review, it is a large document that contains a significant amount of new research
One of the most important aspects in relation to the quality assurance in any analytical activity is the estimation of measurement uncertainty. There is general agreement that 'the expression of the result of a measurement is not complete without specifying its associated uncertainty'. An analytical process is the mechanism for obtaining methodological information (measurand) of a material system (population). This implies the need for the definition of the problem, the choice of methods for sampling and measurement and proper execution of these activities for obtaining information. The result of a measurement is only an approximation or estimate of the value of the measurand, which is complete only when accompanied by an estimate of the uncertainty of the analytical process. According to the 'Vocabulary of Basic and General Terms in Metrology' measurement uncertainty' is the parameter associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand (or magnitude). This parameter could be a standard deviation or a confidence interval. The uncertainty evaluation requires detailed look at all possible sources, but not disproportionately. We can make a good estimate of the uncertainty concentrating efforts on the largest contributions. The key steps of the process of determining the uncertainty in the measurements are: - the specification of the measurand; - identification of the sources of uncertainty - the quantification of individual components of uncertainty, - calculate the combined standard uncertainty; - report of uncertainty.
Relativistic few body calculations
A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ5γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs
Ahrens, Thomas J.
2001-01-01
We examined the von Mises and Mohr-Coulomb strength models with and without damage effects and developed a model for dilatancy. The models and results are given in O'Keefe et al. We found that by incorporating damage into the models that we could in a single integrated impact calculation, starting with the bolide in the atmosphere produce final crater profiles having the major features found in the field measurements. These features included a central uplift, an inner ring, circular terracing and faulting. This was accomplished with undamaged surface strengths of approximately 0.1 GPa and at depth strengths of approximately 1.0 GPa. We modeled the damage in geologic materials using a phenomenological approach, which coupled the Johnson-Cook damage model with the CTH code geologic strength model. The objective here was not to determine the distribution of fragment sizes, but rather to determine the effect of brecciated and comminuted material on the crater evolution, fault production, ejecta distribution, and final crater morphology.
The rating reliability calculator
Solomon David J
2004-04-01
Full Text Available Abstract Background Rating scales form an important means of gathering evaluation data. Since important decisions are often based on these evaluations, determining the reliability of rating data can be critical. Most commonly used methods of estimating reliability require a complete set of ratings i.e. every subject being rated must be rated by each judge. Over fifty years ago Ebel described an algorithm for estimating the reliability of ratings based on incomplete data. While his article has been widely cited over the years, software based on the algorithm is not readily available. This paper describes an easy-to-use Web-based utility for estimating the reliability of ratings based on incomplete data using Ebel's algorithm. Methods The program is available public use on our server and the source code is freely available under GNU General Public License. The utility is written in PHP, a common open source imbedded scripting language. The rating data can be entered in a convenient format on the user's personal computer that the program will upload to the server for calculating the reliability and other statistics describing the ratings. Results When the program is run it displays the reliability, number of subject rated, harmonic mean number of judges rating each subject, the mean and standard deviation of the averaged ratings per subject. The program also displays the mean, standard deviation and number of ratings for each subject rated. Additionally the program will estimate the reliability of an average of a number of ratings for each subject via the Spearman-Brown prophecy formula. Conclusion This simple web-based program provides a convenient means of estimating the reliability of rating data without the need to conduct special studies in order to provide complete rating data. I would welcome other researchers revising and enhancing the program.
Surface retention capacity calculation
David, Vaclav; Dostal, Tomas
2010-05-01
Flood wave transformation in the floodplain is the phenomenon which is researched within interdisciplinary project NIVA - Water Retention in Floodplains and Possibilities of Retention Capacity Increase. The project focuses on broad range of floodplain ecosystem services and mitigation of flooding is one of them. Despite main influence on flood wave transformation is due to flow retardation, retention in surface depressions within floodplain has been analyzed to get better overview of whole transformation process. Detail digital relief model (DRM) has been used for given purposes to be able to analyze terrain depressions volumes. The model was developed with use of stereophotogrammetric evaluation of airborne images with high resolution of 10 cm. It was essential for purposes of presented analysis not to apply pit removal routines which are often used for generation of DRM for hydrological modelling purposes. First, the methodology of analysis was prepared and tested on artificial surface. This surface was created using random raster generation, filtration and resampling with final resolution of 1000 x 1000 units and height of maximum 10 units above datum. The methodology itself is based on analysis of areas inundated by water at different elevation levels. Volume is than calculated for each depression using extraction of terrain elevations under corresponding water level. The method was then applied on the area of Lužnice River floodplain section to assess retention capacity of real floodplain. The floodplain had to be cut into sections perpendicular to main river orientation for analyses as the method was tested for square shaped area without any significant inclination. Results obtained by mentioned analysis are presented in this paper. Acknowledgement Presented research was accomplished within national project NIVA - Water Retention in Floodplains and Possibilities of Retention Capacity Increase, nr. QH82078. The project is funded by Ministry of Agriculture of
Focusing on the numerical aspects and accuracy we study a class of bulk viscosity driven expansion scenarios using the relativistic Navier-Stokes and truncated Israel-Stewart form of the equations of relativistic dissipative fluids in 1+1 dimensions. The numerical calculations of conservation and transport equations are performed using the numerical framework of flux corrected transport. We show that the results of the Israel-Stewart causal fluid dynamics are numerically much more stable and smoother than the results of the standard relativistic Navier-Stokes equations. (orig.)
Calculation of e- H scattering processes using hyperspherical coordinates
A method is presented for accurately solving the Schroedinger equation of the scattering of an electron from a hydrogen atom in three dimensions, which uses hyperspherical coordinates. The motivation for using this new technique is that previous methods - the coupled channel expansions using target atom eigenfunctions, polarization functions and pseudostates, and variational methods have all proven unsatisfactory. The coupled channel calculations tend to have difficulty obtaining convergence with respect to basis set size, and the variational method interjects spurious resonances. Previous applications of hyperspherical coordinates have used methods that, while adequate for computing the energy level of the sound state of H-, are not appropriate to full scattering calculations. Converged surface functions were obtained at a set of discrete values of the hyperradius, which acts as a parameter. The surface functions are further expanded in a basis set that involves 1-dimensional functions of the hyperspherical angle, which are obtained by a finite difference method. The surface functions were used to expand the scattering functions. The resulting coupled equations are solved numerically. The wave functions are obtained separately at each energy and are converged with respect to the number of basis functions used
Calculation of multiphoton ionization processes
Chang, T. N.; Poe, R. T.
1976-01-01
We propose an accurate and efficient procedure in the calculation of multiphoton ionization processes. In addition to the calculational advantage, this procedure also enables us to study the relative contributions of the resonant and nonresonant intermediate states.
HEU benchmark calculations and LEU preliminary calculations for IRR-1
We performed neutronics calculations for the Soreq Research Reactor, IRR-1. The calculations were done for the purpose of upgrading and benchmarking our codes and methods. The codes used were mainly WIMS-D/4 for cell calculations and the three dimensional diffusion code CITATION for full core calculations. The experimental flux was obtained by gold wire activation methods and compared with our calculated flux profile. The IRR-1 is loaded with highly enriched uranium fuel assemblies, of the plate type. In the framework of preparation for conversion to low enrichment fuel, additional calculations were done assuming the presence of LEU fresh fuel. In these preliminary calculations we investigated the effect on the criticality and flux distributions of the increase of U-238 loading, and the corresponding uranium density.(author)
A comparison of carbon calculators
International attention to carbon dioxide emissions is turning to an individual's contribution, or 'carbon footprint.' Calculators that estimate an individual's CO2 emissions have become more prevalent on the internet. Even with similar inputs, however, these calculators can generate varying results, often by as much as several metric tons per annum per individual activity. This paper examines the similarities and differences among ten US-based calculators. Overall, the calculators lack consistency, especially for estimates of CO2 emissions from household electricity consumption. In addition, most calculators lack information about their methods and estimates, which impedes comparison and validation. Although carbon calculators can promote public awareness of carbon emissions from individual behavior, this paper reveals the need for improved consistency and transparency in the calculators
杨征; 马松华; 方建平
2011-01-01
With the help of the symbolic computation system Maple and an improved Riccati equation mapping approach, a series of exact solutions of the (2 + 1 ) -dimensional Zakharov-Kuznetsov equation (ZK) is derived. Based on the derived solution, we obtain some special soliton structures.%在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解.根据得到的解,研究了ZK方程的特殊孤子结构.
张解放; 刘宇陆
2002-01-01
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation. A Backlund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable-separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons.
Invert Effective Thermal Conductivity Calculation
The objective of this calculation is to evaluate the temperature-dependent effective thermal conductivities of a repository-emplaced invert steel set and surrounding ballast material. The scope of this calculation analyzes a ballast-material thermal conductivity range of 0.10 to 0.70 W/m · K, a transverse beam spacing range of 0.75 to 1.50 meters, and beam compositions of A 516 carbon steel and plain carbon steel. Results from this calculation are intended to support calculations that identify waste package and repository thermal characteristics for Site Recommendation (SR). This calculation was developed by Waste Package Department (WPD) under Office of Civilian Radioactive Waste Management (OCRWM) procedure AP-3.12Q, Revision 1, ICN 0, Calculations
Global nuclear-structure calculations
The revival of interest in nuclear ground-state octupole deformations that occurred in the 1980's was stimulated by observations in 1980 of particularly large deviations between calculated and experimental masses in the Ra region, in a global calculation of nuclear ground-state masses. By minimizing the total potential energy with respect to octupole shape degrees of freedom in addition to ε2 and ε4 used originally, a vastly improved agreement between calculated and experimental masses was obtained. To study the global behavior and interrelationships between other nuclear properties, we calculate nuclear ground-state masses, spins, pairing gaps and Β-decay and half-lives and compare the results to experimental qualities. The calculations are based on the macroscopic-microscopic approach, with the microscopic contributions calculated in a folded-Yukawa single-particle potential
Measurement and calculation of evaporation
Plesničar, Leja
2015-01-01
The thesis presents three selected methods of measurement and calculation of the evapotranspiration on research plot at Hajdrihova 28 in Ljubljana. First method is measurement by evaporation pan type A and the other two methods are empirical equations for potential evapotranspiration calculation: FAO Penman-Monteith equation and Thornthwait equation. The results obtained for all three methods are compared with each other. Calculated results according to the FAO Penman-Monteith equation wer...
Calculation of Spectra of Solids:
Lindgård, Per-Anker
1975-01-01
The Gilat-Raubenheimer method simplified to tetrahedron division is used to calculate the real and imaginary part of the dynamical response function for electrons. A frequency expansion for the real part is discussed. The Lindhard function is calculated as a test for numerical accuracy....... The conduction electron susceptibility is calculated for Gd, Tb and Dy using the RAPW energy bands by Keeton and Louks....
Manikandan, K; Senthilvelan, M
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields. PMID:27475076
殷京津; 王丽真
2015-01-01
利用不变子空间方法研究了(3+1)维短波方程的不变子空间和精确解。在(2+1)维短波方程增加一维的情形下，构造了更加广泛的精确解，同时也得到了超曲面的爆破解。主要结果不仅推广了不变子空间理论在高维非线性偏微分方程中的应用，而且对研究高维方程的动力系统有重要意义。%Considered herein is invariant spaces and exact solutions of (3+1) dimensional short wave equation with the invariant spaces method. More exact solution and hyperspace blow-up solution are obtained in case of increasing one dimension for (2+1) dimensional short wave equation. The results not only extend the application of the theory of invariant subspace in high-dimensional nonlinear partial differential equations, but also have a great meaning for study high-dimensional dynamical system equations.
CAVEAT calculations of shock interactions
CAVEAT is a computer code for calculating the time-varying fluid dynamics of several adjacent materials in two or three space dimensions. Using an extended Godunov technique and adaptive meshing, the code allows for large slippage at material interfaces. To exhibit the capability for calculating strong distortions we have performed a variety of calculations describing the interaction of shocks with rigid wedges, cylinders, and spheres and deformable cylindrical, spherical, and conical shells in two space dimensions. Comparison of the results with experimental data and analytical solutions demonstrates the considerable accuracy that can be expected from calculations with this code
Calculations of effective atomic number
Kaliman, Z. [Department of Physics, Faculty of Arts and Sciences, Omladinska 14, Rijeka (Croatia); Orlic, N. [Department of Physics, Faculty of Arts and Sciences, Omladinska 14, Rijeka (Croatia)], E-mail: norlic@ffri.hr; Jelovica, I. [Department of Physics, Faculty of Arts and Sciences, Omladinska 14, Rijeka (Croatia)
2007-09-21
We present and discuss effective atomic number (Z{sub eff}) obtained by different methods of calculations. There is no unique relation between the computed values. This observation led us to the conclusion that any Z{sub eff} is valid only for given process. We illustrate calculations for different subshells of atom Z=72 and for M3 subshell of several other atoms.
Calculation of two Belyi pairs
Dremov, V. A.
2008-01-01
We calculate two Belyi pairs using the properties of Mulase-Penkava differential. Details are provided including accurate construction of coordinates, variables and equations. The calculation is a part of the work which results in a catalogue arXiv:0710.2658
CELSS scenario analysis: Breakeven calculations
Mason, R. M.
1980-01-01
A model of the relative mass requirements of food production components in a controlled ecological life support system (CELSS) based on regenerative concepts is described. Included are a discussion of model scope, structure, and example calculations. Computer programs for cultivar and breakeven calculations are also included.
Shielding calculational system for plutonium
A computer calculational system has been developed and assembled specifically for calculating dose rates in AEC plutonium fabrication facilities. The system consists of two computer codes and all nuclear data necessary for calculation of neutron and gamma dose rates from plutonium. The codes include the multigroup version of the Battelle Monte Carlo code for solution of general neutron and gamma shielding problems and the PUSHLD code for solution of shielding problems where low energy gamma and x-rays are important. The nuclear data consists of built in neutron and gamma yields and spectra for various plutonium compounds, an automatic calculation of age effects and all cross-sections commonly used. Experimental correlations have been performed to verify portions of the calculational system. (23 tables, 7 figs, 16 refs) (U.S.)
Closure and Sealing Design Calculation
T. Lahnalampi; J. Case
2005-08-26
The purpose of the ''Closure and Sealing Design Calculation'' is to illustrate closure and sealing methods for sealing shafts, ramps, and identify boreholes that require sealing in order to limit the potential of water infiltration. In addition, this calculation will provide a description of the magma that can reduce the consequences of an igneous event intersecting the repository. This calculation will also include a listing of the project requirements related to closure and sealing. The scope of this calculation is to: summarize applicable project requirements and codes relating to backfilling nonemplacement openings, removal of uncommitted materials from the subsurface, installation of drip shields, and erecting monuments; compile an inventory of boreholes that are found in the area of the subsurface repository; describe the magma bulkhead feature and location; and include figures for the proposed shaft and ramp seals. The objective of this calculation is to: categorize the boreholes for sealing by depth and proximity to the subsurface repository; develop drawing figures which show the location and geometry for the magma bulkhead; include the shaft seal figures and a proposed construction sequence; and include the ramp seal figure and a proposed construction sequence. The intent of this closure and sealing calculation is to support the License Application by providing a description of the closure and sealing methods for the Safety Analysis Report. The closure and sealing calculation will also provide input for Post Closure Activities by describing the location of the magma bulkhead. This calculation is limited to describing the final configuration of the sealing and backfill systems for the underground area. The methods and procedures used to place the backfill and remove uncommitted materials (such as concrete) from the repository and detailed design of the magma bulkhead will be the subject of separate analyses or calculations. Post
Closure and Sealing Design Calculation
The purpose of the ''Closure and Sealing Design Calculation'' is to illustrate closure and sealing methods for sealing shafts, ramps, and identify boreholes that require sealing in order to limit the potential of water infiltration. In addition, this calculation will provide a description of the magma that can reduce the consequences of an igneous event intersecting the repository. This calculation will also include a listing of the project requirements related to closure and sealing. The scope of this calculation is to: summarize applicable project requirements and codes relating to backfilling nonemplacement openings, removal of uncommitted materials from the subsurface, installation of drip shields, and erecting monuments; compile an inventory of boreholes that are found in the area of the subsurface repository; describe the magma bulkhead feature and location; and include figures for the proposed shaft and ramp seals. The objective of this calculation is to: categorize the boreholes for sealing by depth and proximity to the subsurface repository; develop drawing figures which show the location and geometry for the magma bulkhead; include the shaft seal figures and a proposed construction sequence; and include the ramp seal figure and a proposed construction sequence. The intent of this closure and sealing calculation is to support the License Application by providing a description of the closure and sealing methods for the Safety Analysis Report. The closure and sealing calculation will also provide input for Post Closure Activities by describing the location of the magma bulkhead. This calculation is limited to describing the final configuration of the sealing and backfill systems for the underground area. The methods and procedures used to place the backfill and remove uncommitted materials (such as concrete) from the repository and detailed design of the magma bulkhead will be the subject of separate analyses or calculations. Post-closure monitoring will not
Computer calculation of Witten's 3-manifold invariant
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Computer calculation of Witten's 3-manifold invariant
Freed, Daniel S.; Gompf, Robert E.
1991-10-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.
The code system which is a compilation of well known codes NJOY, AMPX, ANISN and DOT-3 adapted for NDP Fortran on IBM PC/AT is described. The 171-group library DLC-41/VITAMIN-C with Bondarenko Factors based on the ENDF/B-4 is introduced to the system as a main data library. Modification and development of this library are realized by NJOY code on the base of ENDF/B-6 files. A 171-group problem-oriented data library is usually used in 1 dimensional calculations by the code ANISN. This library is being generated by the AMPX modules (BONAMI and others). Data libraries with smaller number of groups are being used in 2 dimensional calculations by DOT-3. These libraries have been gotten from 171-group problem-oriented libraries which are averaged by corresponding spectra from 1 dimensional calculations. Using of the described system is being demonstrated with two examples. (authors). 6 refs., 2 tabs., 5 figs
Practical astronomy with your calculator
Duffett-Smith, Peter
1989-01-01
Practical Astronomy with your Calculator, first published in 1979, has enjoyed immense success. The author's clear and easy to follow routines enable you to solve a variety of practical and recreational problems in astronomy using a scientific calculator. Mathematical complexity is kept firmly in the background, leaving just the elements necessary for swiftly making calculations. The major topics are: time, coordinate systems, the Sun, the planetary system, binary stars, the Moon, and eclipses. In the third edition there are entirely new sections on generalised coordinate transformations, nutr
Calculation of thermal diffuse scattering
Wakabayashi, N.; Nicklow, R. M.; Katano, S.; Ishii, Y.; Child, H. R.; Smith, H. G.; Fernandez-Baca, J. A.
We have developed a computer program to calculate the thermal diffuse scattering (TDS) intensity distribution for single-crystal specimens in a diffractometer with no energy analysis. We assumed that the phonon frequencies are approximated by those of elastic waves and that the elastic constants, density and lattice parameters of the system under study are known. The results of the calculations were compared to experimental data obtain for single crystals of Si, diamond and NiAl at the wide-angle neutron diffractometer (WAND) at the HFIR at Oak Ridge National Laboratory. Excellent agreement was found between the calculations and the experimental observations.
Calculation of thermal diffuse scattering
The authors developed a computer program to calculate the thermal diffuse scattering (TDS) intensity distribution for single crystal specimens in a diffractometer with no energy analysis. They assumed that the phonon frequencies are approximated by those of elastic waves and that the elastic constants, density and lattice parameters of the system under study are known. The results of the calculations were compared to experimental data obtained for single crystals of Si, diamond and NiAl at the Wide Angle neutron Diffractometer at the HFIR at Oak Ridge National Laboratory. Excellent agreement was found between the calculations and the experimental observations
Relativistic calculations of atomic structure
Fricke, Burkhard
1984-01-01
A review of relativistic atomic structure calculations is given with a emphasis on the Multiconfigurational-Dirac-Fock method. Its problems and deficiencies are discussed together with the contributions which go beyond the Dirac-Fock procedure.
Calculations of turbulent separated flows
Zhu, J.; Shih, T. H.
1993-01-01
A numerical study of incompressible turbulent separated flows is carried out by using two-equation turbulence models of the K-epsilon type. On the basis of realizability analysis, a new formulation of the eddy-viscosity is proposed which ensures the positiveness of turbulent normal stresses - a realizability condition that most existing two-equation turbulence models are unable to satisfy. The present model is applied to calculate two backward-facing step flows. Calculations with the standard K-epsilon model and a recently developed RNG-based K-epsilon model are also made for comparison. The calculations are performed with a finite-volume method. A second-order accurate differencing scheme and sufficiently fine grids are used to ensure the numerical accuracy of solutions. The calculated results are compared with the experimental data for both mean and turbulent quantities. The comparison shows that the present model performs quite well for separated flows.
罗琳; 桂胜华
2012-01-01
Binary Bell polynomials are applied to construct the bilinear forms for a (3+1)-dimensional nonlinear equation. The authors obtain its Backlund transformations and corresponding Lax pair. In the meantime, the periodic wave solution to the nonlinear equation is constructed by using the bilinear equations and a proper Riemann theta function.%利用双Bell多项式方法构造了一个(3+1)维非线性方程的双线性形式,得到了该方程的双线性B(a)cklund变换和相应的Lax对.同时利用Riemann theta函数,获得了该方程的周期波解.
Calculation method of Tesla coil
Коломієць, Роман Олександрович
2015-01-01
Tesla coil, despite the simplicity of its design may be called one of the least studied electronic devices. The article is an attempt to bring in various experimental results of general theoretical framework, which is the basis of exact calculation method of Tesla coils. Such calculation should be the starting point to create devices based on it. In order to develop such methods were considered the general principles of designing Tesla coil, reviewed the most famous mathematical models of its...
Hydraulic calculation of pressure pipes
Mikhalev, M. A.
2012-01-01
In the present time there is only one classic method for hydraulic calculation of pressure pipes. In it fluid flow velocity and pipeline diameter are considered as given values.The paper proposes a procedure for physical modeling and hydraulic calculation of pressure pipes, based on the theory of similarity. Methods for obtaining similarity criteria from combinations of similarity numbers were discussed. Similarity numbers and criteria and criteria equations were defined.
Multifragmentation calculated with relativistic forces
A saturating hamiltonian is presented in a relativistically covariant formalism. The interaction is described by scalar and vector mesons, with coupling strengths adjusted to the nuclear matter. No explicit density dependence is assumed. The hamiltonian is applied in a QMD calculation to determine the fragment distribution in O + Br collision at different energies (50 - 200 MeV/u) to test the applicability of the model at low energies. The results are compared with experiment and with previous non-relativistic calculations. (orig.)
The calculation of pressure vessels
The calculation guidelines of the Arbeitsgemeinschaft Druckbehaelter (task group for pressure vessels) have been revised with the following objective: conversion to international standards (SI), adaption to the latest state of guidelines for production and testing, revision of the contents of individual regulations. Another target of the cooperating interest groups of producers, operators, and supervisory bodies was a harmonization of the approaches for calculation with other German guidelines, in particular the Technische Regeln fuer Dampfkessel (technical regulations for steam boilers). (orig./RW)
Methods of core neutronic calculation
Core neutronic calculations lead to the determination of geometry, composition, controls systems and to the core exploitation limits in agreement with the expected performances, with safety rules, technological choices and fuel management methods. Neutronic calculations object are described with physics justifications of hypothesis and approximations. A description and a definition of reactivity and power distribution are also given. A panorama of calculation methods used in the conception of fast breeder and pressure water reactors, are described with numerical aspects and general interest considerations related to the field of these methods and to the industrial options chosen. A complete industrial uses panorama of methods derived from the classical or generalized perturbation theory is followed by the qualification and the definition of the validity field of numerical codes.(A.B.). 88 refs., 6 figs
Insertion device calculations with mathematica
Carr, R. [Stanford Synchrotron Radiation Lab., CA (United States); Lidia, S. [Univ. of California, Davis, CA (United States)
1995-02-01
The design of accelerator insertion devices such as wigglers and undulators has usually been aided by numerical modeling on digital computers, using code in high level languages like Fortran. In the present era, there are higher level programming environments like IDL{reg_sign}, MatLab{reg_sign}, and Mathematica{reg_sign} in which these calculations may be performed by writing much less code, and in which standard mathematical techniques are very easily used. The authors present a suite of standard insertion device modeling routines in Mathematica to illustrate the new techniques. These routines include a simple way to generate magnetic fields using blocks of CSEM materials, trajectory solutions from the Lorentz force equations for given magnetic fields, Bessel function calculations of radiation for wigglers and undulators and general radiation calculations for undulators.
PHEBUS-FPTO Benchmark calculations
This report summarizes a set of pre-test predictions made for the first Phebus-FP test, FPT-O. There were many different calculations, performed by various organizations and they represent the first attempt to calculate the whole experimental sequence, from bundle to containment. Quantitative agreement between the various calculations was not good but the particular models in the code responsible for disagreements were mostly identified. A consensus view was formed as to how the test would proceed. It was found that a successful execution of the test will require a different operating procedure than had been assumed here. Critical areas which require close attention are the need to devize a strategy for the power and flow in the bundle that takes account of uncertainties in the modelling and the shroud conductivity and the necessity to develop a reliable method to achieve the desired thermalhydraulic conditions in the containment
Parameters calculation of shielding experiment
The radiation transport methodology comparing the calculated reactions and dose rates for neutrons and gama-rays, with experimental measurements obtained on iron shield, irradiated in the YAYOI reactor is evaluated. The ENDF/B-IV and VITAMIN-C libraries and the AMPX-II modular system, for cross sections generation collapsed by the ANISN code were used. The transport calculations were made using the DOT 3.5 code, adjusting the boundary iron shield source spectrum to the reactions and dose rates, measured at the beginning of shield. The neutron and gamma ray distributions calculated on the iron shield presented reasonable agreement with experimental measurements. An experimental arrangement using the IEA-R1 reactor to determine a shielding benchmark is proposed. (Author)
Canister Transfer Facility Criticality Calculations
J.E. Monroe-Rammsy
2000-10-13
The objective of this calculation is to evaluate the criticality risk in the surface facility for design basis events (DBE) involving Department of Energy (DOE) Spent Nuclear Fuel (SNF) standardized canisters (Civilian Radioactive Waste Management System [CRWMS] Management and Operating Contractor [M&O] 2000a). Since some of the canisters will be stored in the surface facility before they are loaded in the waste package (WP), this calculation supports the demonstration of concept viability related to the Surface Facility environment. The scope of this calculation is limited to the consideration of three DOE SNF fuels, specifically Enrico Fermi SNF, Training Research Isotope General Atomic (TRIGA) SNF, and Mixed Oxide (MOX) Fast Flux Test Facility (FFTF) SNF.
The (2+1)-dimensional gravastars
We propose a new model of a gravastar in (2+1) anti-de Sitter spacetime. This new three-dimensional configuration has three different regions with different equations of state: [I] Interior: 0⩽r1, ρ=-p; [II] Shell: r1⩽r2, ρ=p; [III] Exterior: r2< r, ρ=p=0. The outer region of this gravastar corresponds to the exterior (2+1) anti-de Sitter spacetime, popularly known as the BTZ spacetime. Like BTZ model, Λ is taken to be negative, which at the junction turns out to be positive as required by stability of gravastar and mathematical consistency. After investigating the Interior spacetime, Shell and Exterior spacetime we have highlighted different physical features in terms of Length and Energy, Entropy, and Junction conditions of the spherical distribution. It is shown that the present model of charge-free gravastar in connection to the exterior (2+1) anti-de Sitter spacetime or the BTZ spacetime is non-singular.
Ab Initio Calculations of Oxosulfatovanadates
Frøberg, Torben; Johansen, Helge
1996-01-01
Restricted Hartree-Fock and multi-configurational self-consistent-field calculations together with secondorder perturbation theory have been used to study the geometry, the electron density, and the electronicspectrum of (VO2SO4)-. A bidentate sulphate attachment to vanadium was found to be stable...... with anO-V-O angle of 72.5 degrees . The calculated spectrum shows bands in reasonable agreement with anexperimental spectrum which has been attributed to (VO2SO4)-. The geometry and the electron density fortwo binuclear vanadium complexes proposed as intermediates in the vanadium catalyzed SO2...
Data Acquisition and Flux Calculations
Rebmann, C.; Kolle, O; Heinesch, B;
2012-01-01
In this chapter, the basic theory and the procedures used to obtain turbulent fluxes of energy, mass, and momentum with the eddy covariance technique will be detailed. This includes a description of data acquisition, pretreatment of high-frequency data and flux calculation.......In this chapter, the basic theory and the procedures used to obtain turbulent fluxes of energy, mass, and momentum with the eddy covariance technique will be detailed. This includes a description of data acquisition, pretreatment of high-frequency data and flux calculation....
Design basis accident calculation problems
Sudden failures of the primary circuit is the design basis accident of pressurized water reactors, being liable to affect the other two barriers separating the fission products from the environment. The calculation of the thermohydraulic behavior of the core and primary circuit is at present based, for the CEA, on the RELAP 4 code. However a second-generation code, POSEIDON, is being developed by the CEA, EDF and FRAMATOME to obtain a better description of the physical phenomena and a better estimate of safety margins. Other difficult problems arise in connection with the calculation of structural stresses and the behavior of the vessel during decompression
Friction and wear calculation methods
Kragelsky, I V; Kombalov, V S
1981-01-01
Friction and Wear: Calculation Methods provides an introduction to the main theories of a new branch of mechanics known as """"contact interaction of solids in relative motion."""" This branch is closely bound up with other sciences, especially physics and chemistry. The book analyzes the nature of friction and wear, and some theoretical relationships that link the characteristics of the processes and the properties of the contacting bodies essential for practical application of the theories in calculating friction forces and wear values. The effect of the environment on friction and wear is a
Molecular calculations with B functions
Steinborn, E O; Ema, I; López, R; Ramírez, G
1998-01-01
A program for molecular calculations with B functions is reported and its performance is analyzed. All the one- and two-center integrals, and the three-center nuclear attraction integrals are computed by direct procedures, using previously developed algorithms. The three- and four-center electron repulsion integrals are computed by means of Gaussian expansions of the B functions. A new procedure for obtaining these expansions is also reported. Some results on full molecular calculations are included to show the capabilities of the program and the quality of the B functions to represent the electronic functions in molecules.
ITER Port Interspace Pressure Calculations
Carbajo, Juan J [ORNL; Van Hove, Walter A [ORNL
2016-01-01
The ITER Vacuum Vessel (VV) is equipped with 54 access ports. Each of these ports has an opening in the bioshield that communicates with a dedicated port cell. During Tokamak operation, the bioshield opening must be closed with a concrete plug to shield the radiation coming from the plasma. This port plug separates the port cell into a Port Interspace (between VV closure lid and Port Plug) on the inner side and the Port Cell on the outer side. This paper presents calculations of pressures and temperatures in the ITER (Ref. 1) Port Interspace after a double-ended guillotine break (DEGB) of a pipe of the Tokamak Cooling Water System (TCWS) with high temperature water. It is assumed that this DEGB occurs during the worst possible conditions, which are during water baking operation, with water at a temperature of 523 K (250 C) and at a pressure of 4.4 MPa. These conditions are more severe than during normal Tokamak operation, with the water at 398 K (125 C) and 2 MPa. Two computer codes are employed in these calculations: RELAP5-3D Version 4.2.1 (Ref. 2) to calculate the blowdown releases from the pipe break, and MELCOR, Version 1.8.6 (Ref. 3) to calculate the pressures and temperatures in the Port Interspace. A sensitivity study has been performed to optimize some flow areas.
On calculation of photoneutron yields
A simple analytical expression has been obtained for the photon track lengths in the region of nuclei giant resonance by summing the cross-sections of the bremsstrahlung from thin layers. The photoneutron yields from thick Cu and Pb targets calculated for verifying this expression are in a good agreement with the experimental results obtained by other authors
Dead reckoning calculating without instruments
Doerfler, Ronald W
1993-01-01
No author has gone as far as Doerfler in covering methods of mental calculation beyond simple arithmetic. Even if you have no interest in competing with computers you'll learn a great deal about number theory and the art of efficient computer programming. -Martin Gardner
Sparsifying preconditioner for soliton calculations
Lu, Jianfeng; Ying, Lexing
2016-06-01
We develop a robust and efficient method for soliton calculations for nonlinear Schrödinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of the method is demonstrated by numerical examples of gap solitons in the context of nonlinear optics.
Relativistic multiple scattering Xα calculations
A one component relativistic theory has recently been developed and tested on isolated atoms and on molecules through the molecular scattered-wave formalism of Johnson, while its application to energy-band calculations (through a relativistic augmented-plane-wave program) has also been considered
CALCULATION OF MAGNETIC OIL CLARIFIER
Puzik, S. O.; National Aviation University; Shevchuk, V. S.; National Aviation University; Baranivskiy, Y. O.; National Aviation University; Mykhailenko, O. O.; National Aviation University
2013-01-01
Technology of oil cleaning from iron-containing impurities that shows the feasibility of magnetic cleaners applying was investigated. Comparative analysis of the types of magnetic clarifier was carried out. Procedure of calculating the dimension type of oil clarifier, which makes it possible to obtain high purity grade oil, was offered.
Sparsifying preconditioner for soliton calculations
Lu, Jianfeng
2015-01-01
We develop a robust and efficient method for soliton calculations for nonlinear Schr\\"odinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of the method is demonstrated by numerical examples of gap solitons in the context of nonlinear optics.
Giavitto, Jean-Louis; Reichenmann, François
2012-01-01
Alan Turing a non seulement défini l'objet d'étude de l'informatique, le calcul, mais aussi révolutionné notre rapport aux machines. Il a fondé l'informatique comme un domaine scientifique autonome et a ouvert le chemin vers un nouveau continent à explorer et à habiter.
Professional Growth & Support Spending Calculator
Education Resource Strategies, 2013
2013-01-01
This "Professional Growth & Support Spending Calculator" helps school systems quantify all current spending aimed at improving teaching effectiveness. Part I provides worksheets to analyze total investment. Part II provides a system for evaluating investments based on purpose, target group, and delivery. In this Spending Calculator…
Prenatal radiation exposure. Dose calculation
The unborn child requires special protection. In this context, the indication for an X-ray examination is to be checked critically. If thereupon radiation of the lower abdomen including the uterus cannot be avoided, the examination should be postponed until the end of pregnancy or alternative examination techniques should be considered. Under certain circumstances, either accidental or in unavoidable cases after a thorough risk assessment, radiation exposure of the unborn may take place. In some of these cases an expert radiation hygiene consultation may be required. This consultation should comprise the expected risks for the unborn while not perturbing the mother or the involved medical staff. For the risk assessment in case of an in-utero X-ray exposition deterministic damages with a defined threshold dose are distinguished from stochastic damages without a definable threshold dose. The occurrence of deterministic damages depends on the dose and the developmental stage of the unborn at the time of radiation. To calculate the risks of an in-utero radiation exposure a three-stage concept is commonly applied. Depending on the amount of radiation, the radiation dose is either estimated, roughly calculated using standard tables or, in critical cases, accurately calculated based on the individual event. The complexity of the calculation thereby increases from stage to stage. An estimation based on stage one is easily feasible whereas calculations based on stages two and especially three are more complex and often necessitate execution by specialists. This article demonstrates in detail the risks for the unborn child pertaining to its developmental phase and explains the three-stage concept as an evaluation scheme. It should be noted, that all risk estimations are subject to considerable uncertainties.
AGING FACILITY CRITICALITY SAFETY CALCULATIONS
The purpose of this design calculation is to revise and update the previous criticality calculation for the Aging Facility (documented in BSC 2004a). This design calculation will also demonstrate and ensure that the storage and aging operations to be performed in the Aging Facility meet the criticality safety design criteria in the ''Project Design Criteria Document'' (Doraswamy 2004, Section 4.9.2.2), and the functional nuclear criticality safety requirement described in the ''SNF Aging System Description Document'' (BSC [Bechtel SAIC Company] 2004f, p. 3-12). The scope of this design calculation covers the systems and processes for aging commercial spent nuclear fuel (SNF) and staging Department of Energy (DOE) SNF/High-Level Waste (HLW) prior to its placement in the final waste package (WP) (BSC 2004f, p. 1-1). Aging commercial SNF is a thermal management strategy, while staging DOE SNF/HLW will make loading of WPs more efficient (note that aging DOE SNF/HLW is not needed since these wastes are not expected to exceed the thermal limits form emplacement) (BSC 2004f, p. 1-2). The description of the changes in this revised document is as follows: (1) Include DOE SNF/HLW in addition to commercial SNF per the current ''SNF Aging System Description Document'' (BSC 2004f). (2) Update the evaluation of Category 1 and 2 event sequences for the Aging Facility as identified in the ''Categorization of Event Sequences for License Application'' (BSC 2004c, Section 7). (3) Further evaluate the design and criticality controls required for a storage/aging cask, referred to as MGR Site-specific Cask (MSC), to accommodate commercial fuel outside the content specification in the Certificate of Compliance for the existing NRC-certified storage casks. In addition, evaluate the design required for the MSC that will accommodate DOE SNF/HLW. This design calculation will achieve the objective of providing the criticality safety results to support the preliminary design of the Aging
Calculation of potassium critical temperature
The paper describes the algorithm of the functional prediction which is based on the selforganization of nonlinear algebraic models. The calculation procedure includes the module for the recognition of the dependence type hitch allows to restrict the number of choice of the prediction functions at the each step of the model building. The characteristic property of this algorithm is bootstrap method application as the external criteria of the selforganization. The calculation module is built using APL*PLUS and the user-friendly interface is implemented using Clipper 5.01 under Windows control. When using the algorithm and the programs, the critical point of potassium has been predicted on the base of the solubility curves of liquid and steam. 9 refs.; 1 fig.; 1 tab
Algorithm project weight calculation aircraft
Г. В. Абрамова
2013-07-01
Full Text Available The paper describes the process of a complex technical object design on the example of the aircraft, using information technology such as CAD/CAM/CAE-systems, presents the basic models of aircraft which are developed in the process of designing and reflect the different aspects of its structure and function. The idea of control parametric model at complex technical object design is entered, which is a set of initial data for the development of design stations and enables the optimal complex technical object control at all stages of design using modern computer technology. The paper discloses a process of weight design, which is associated with all stages of development aircraft and its production. Usage of a scheduling algorithm that allows to organize weight calculations are carried out at various stages of planning and weighing options to optimize the use of available database of formulas and methods of calculation
CONTRIBUTION FOR MINING ATMOSPHERE CALCULATION
Franica Trojanović
1989-12-01
Full Text Available Humid air is an unavoidable feature of mining atmosphere, which plays a significant role in defining the climate conditions as well as permitted circumstances for normal mining work. Saturated humid air prevents heat conduction from the human body by means of evaporation. Consequently, it is of primary interest in the mining practice to establish the relative air humidity either by means of direct or indirect methods. Percentage of water in the surrounding air may be determined in various procedures including tables, diagrams or particular calculations, where each technique has its specific advantages and disadvantages. Classical calculation is done according to Sprung's formula, in which case partial steam pressure should also be taken from the steam table. The new method without the use of diagram or tables, established on the functional relation of pressure and temperature on saturated line, is presented here for the first time (the paper is published in Croatian.
Consolidated fuel decay heat calculations
Wittekind, W.D.
1994-06-24
The radiological decay heat generated from all irradiated fuel presently in K East (KE) and K West (KW) Basins was calculated in support of consolidated fuel storage. There are four sources of heat inflow into the fuel storage basins: (1) radiological decay heat from irradiated fuel; (2) mechanical heat from operating machinery (e.g., pumps); (3) heat flow from surroundings (mainly the ground through the concrete walls into the basin water if it is maintained below ambient); and (4) exothermic chemical reactions of uranium oxidation (although at basin temperatures this reaction rate is slow). This report details the radiological decay heat from irradiated fuel source in the K basins. Decay heat calculations using ORIGEN2 (Wittekind 1994 and Schmittroth 1993) for irradiated fuel presently (April 1994) in KE and KW Basins gave results for January 31 of each year.
Calculation of Hilbert Borcherds Products
Mayer, Sebastian
2010-01-01
In Brunier and Bundschuh, “On Borcherds Products Associated with Lattices of Prime Discriminant.” Ramanujan Journal 7 (2003), 49–61, the authors use Borcherds lifts to obtain Hilbert modular forms. Another approach is to calculate Hilbert modular forms using the Jacquet--Langlands correspondence, which was implemented by Lassina Dembele in "Magma". In Mayer, "Rings of Hilbert Modular Forms for the Fields $\\Q(\\sqrt{13})$ and $\\Q(\\sqrt{17})$,'' To appear, 2009, we use Brunier and...
Numerical calculation of Casimir forces
Kilen, Isak Ragnvald
2012-01-01
In this thesis a set of regularized boundary integral equation are introduced that can be used to calculate the Casimir force induced by a two dimensional scalar field. The boundary integral method is compared to the functional integral method and mode summation where possible. Comparisons are done for the case of two parallel plates, two concentric circles and two adjacent circles. The results indicate that the boundary integral method correctly predicts the geometry dependence of the C...
Calculations of the Wigner angle
Two new methods to determine Wigner's angle in special relativity are presented. The first one consists in calculating the angle between the compositions u-bar x ν-bar and ν-bar x u-bar of the two non-collinear velocities u-bar and ν-bar. In another method we introduce a generalization in the complex plane of Einstein's addition law of parallel velocities. (author)
Archimedes' calculations of square roots
Davies, E B
2011-01-01
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide internal evidence that he probably used an interpolation technique. The conclusions are relevant to the precise calculations by which he obtained upper and lower bounds on pi.
Parallel plasma fluid turbulence calculations
The study of plasma turbulence and transport is a complex problem of critical importance for fusion-relevant plasmas. To this day, the fluid treatment of plasma dynamics is the best approach to realistic physics at the high resolution required for certain experimentally relevant calculations. Core and edge turbulence in a magnetic fusion device have been modeled using state-of-the-art, nonlinear, three-dimensional, initial-value fluid and gyrofluid codes. Parallel implementation of these models on diverse platforms--vector parallel (National Energy Research Supercomputer Center's CRAY Y-MP C90), massively parallel (Intel Paragon XP/S 35), and serial parallel (clusters of high-performance workstations using the Parallel Virtual Machine protocol)--offers a variety of paths to high resolution and significant improvements in real-time efficiency, each with its own advantages. The largest and most efficient calculations have been performed at the 200 Mword memory limit on the C90 in dedicated mode, where an overlap of 12 to 13 out of a maximum of 16 processors has been achieved with a gyrofluid model of core fluctuations. The richness of the physics captured by these calculations is commensurate with the increased resolution and efficiency and is limited only by the ingenuity brought to the analysis of the massive amounts of data generated
Decay heat calculations for reactors
Estimation of release of energy (decay heat) over an extended period of time after termination of neutron induced fission is necessary for determining the heat removal requirements when the reactor is shutdown, and for fuel storage and transport facilities as well as for accident studies. The method of decay heat estimation relies on the measurements over practical time intervals as well as on calculation for predictions over very long time intervals. Neutron cross-sections, fission yields and decay data together with operational history are the basic inputs to such. A code used to calculate decay heat would require to generate isotopic inventory that would be present at the shutdown based on operational history of the reactor and follow up the decay over an extended period of time. Aspects of decay heat estimation based on standards like ANS 5.1 and by fuel cycle analysis codes shall be discussed. A Fuel Cycle Analysis Code, ADWITA (Activation, Decay, Waste Incineration and Transmutation Analysis) which can generate inventory based on irradiation history and calculate radioactivity and decay heat for extended period of cooling, has been written. The method and data involved in Fuel Cycle Analysis Code ADWITA and some results obtained shall also be presented. (author)
Calculation of groundwater travel time
Pre-waste-emplacement groundwater travel time is one indicator of the isolation capability of the geologic system surrounding a repository. Two distinct modeling approaches exist for prediction of groundwater flow paths and travel times from the repository location to the designated accessible environment boundary. These two approaches are: (1) the deterministic approach which calculates a single value prediction of groundwater travel time based on average values for input parameters and (2) the stochastic approach which yields a distribution of possible groundwater travel times as a function of the nature and magnitude of uncertainties in the model inputs. The purposes of this report are to (1) document the theoretical (i.e., mathematical) basis used to calculate groundwater pathlines and travel times in a basalt system, (2) outline limitations and ranges of applicability of the deterministic modeling approach, and (3) explain the motivation for the use of the stochastic modeling approach currently being used to predict groundwater pathlines and travel times for the Hanford Site. Example calculations of groundwater travel times are presented to highlight and compare the differences between the deterministic and stochastic modeling approaches. 28 refs
[IOL calculation for high ametropia].
Haigis, W
2008-11-01
Long and short eyes are connected with high ametropia and constitute special problems for biometry and IOL calculations. Ultrasound measurements on these eyes, which often have altered geometries, are frequently more difficult than in normal eyes. This holds especially for long eyes, which significantly benefit from optical biometry. Measurement errors, IOL manufacturing tolerances and uncertainties regarding the effective lens position affect short eyes much more than normal eyes. The selection of a suitable IOL formula is of special importance for the refractive outcome. For short eyes, Holladay-2, HofferQ and Haigis are recommended, for long eyes Holladay-1, Holladay-2 and Haigis. In each case, optimized IOL constants must be used. If minus lenses for extremely long eyes are calculated with the same constants as plus lenses, a hyperopic refractive error is created, which can be avoided by a separate set of constants for minus lenses. For extremely short eyes the commonly used approximation of thinner lenses fails necessitating a thick lens calculation or raytracing. PMID:18998145
The (3 + 1)-dimensional superspace approach is applied to describe and refine a series of sheared compounds related to layered high Tc superconducting oxides. Two commensurate members (m = 4, 5) of the 2212 stair-like [Bi2Sr3Fe2O9]m[Bi4Sr6Fe2O16] family of compounds, previously studied using single-crystal diffraction data, are analyzed. A common average unit cell has been identified and a composition-dependent modulation wavevector is proposed. The model is built using only three independent atomic domains, one for the metal atoms and two for the O atoms. The three Sr, Bi and Fe species are described using close-connected crenel-like functions forming a continuous atomic domain along the internal space. The two oxygen domains are represented by crenel functions and the displacive modulation functions are built up by Legendre polynomials recently implemented in the program JANA2006. Surprisingly, the results of the refinements show a striking similarity of the displacive modulations for the two compounds analyzed, indicating that a unique model can be used to describe the correlations between the atomic displacements of the 2212 stair-like series. This final model is then applied to predict the structure of new members of the family. (orig.)
王倩
2013-01-01
T he method of constructing approximate conserved vectors and conserved law s for perturbed (2+1)-dimensional Boussinesq equation are concretely described .In terms of the partial Lagrangian ap-proach ,the conserved law s are constructed by using approximate Noether method ,then the approximate Noether-type symmetry operators and approximate conserved law s are obtained .%利用近似Noether-type对称算子构造了具有扰动项的（2＋1）维Boussinesq方程的近似守恒向量和近似守恒律，在（2＋1）维Boussinesq方程允许的拉格朗日函数的情况下，利用近似Noether法研究了该方程的守恒律，给出了（2＋1）维扰动Boussinesq方程的近似Noether对称算子、近似守恒向量以及近似守恒律。
Two kinds of Gaussian-type light bullet (LB) solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically obtained. The phase switches, powers and transverse power-flow densities of these solutions in homogeneous media are studied. The linear stability analysis of these LB solutions and the direct numerical simulation indicate that LB solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media. Moreover, the broadened and compressed behaviors of LBs in the exponential periodic amplification system and diffraction decreasing system are discussed. Results indicate that LB is more stable for the sign-changing nonlinearity in the exponential periodic amplification system than for the non-sign-changing nonlinearity in the diffraction decreasing system at the same propagation distances
AGING FACILITY CRITICALITY SAFETY CALCULATIONS
C.E. Sanders
2004-09-10
The purpose of this design calculation is to revise and update the previous criticality calculation for the Aging Facility (documented in BSC 2004a). This design calculation will also demonstrate and ensure that the storage and aging operations to be performed in the Aging Facility meet the criticality safety design criteria in the ''Project Design Criteria Document'' (Doraswamy 2004, Section 4.9.2.2), and the functional nuclear criticality safety requirement described in the ''SNF Aging System Description Document'' (BSC [Bechtel SAIC Company] 2004f, p. 3-12). The scope of this design calculation covers the systems and processes for aging commercial spent nuclear fuel (SNF) and staging Department of Energy (DOE) SNF/High-Level Waste (HLW) prior to its placement in the final waste package (WP) (BSC 2004f, p. 1-1). Aging commercial SNF is a thermal management strategy, while staging DOE SNF/HLW will make loading of WPs more efficient (note that aging DOE SNF/HLW is not needed since these wastes are not expected to exceed the thermal limits form emplacement) (BSC 2004f, p. 1-2). The description of the changes in this revised document is as follows: (1) Include DOE SNF/HLW in addition to commercial SNF per the current ''SNF Aging System Description Document'' (BSC 2004f). (2) Update the evaluation of Category 1 and 2 event sequences for the Aging Facility as identified in the ''Categorization of Event Sequences for License Application'' (BSC 2004c, Section 7). (3) Further evaluate the design and criticality controls required for a storage/aging cask, referred to as MGR Site-specific Cask (MSC), to accommodate commercial fuel outside the content specification in the Certificate of Compliance for the existing NRC-certified storage casks. In addition, evaluate the design required for the MSC that will accommodate DOE SNF/HLW. This design calculation will achieve the objective of providing the
Calculation of gas turbine characteristic
Mamaev, B. I.; Murashko, V. L.
2016-04-01
The reasons and regularities of vapor flow and turbine parameter variation depending on the total pressure drop rate π* and rotor rotation frequency n are studied, as exemplified by a two-stage compressor turbine of a power-generating gas turbine installation. The turbine characteristic is calculated in a wide range of mode parameters using the method in which analytical dependences provide high accuracy for the calculated flow output angle and different types of gas dynamic losses are determined with account of the influence of blade row geometry, blade surface roughness, angles, compressibility, Reynolds number, and flow turbulence. The method provides satisfactory agreement of results of calculation and turbine testing. In the design mode, the operation conditions for the blade rows are favorable, the flow output velocities are close to the optimal ones, the angles of incidence are small, and the flow "choking" modes (with respect to consumption) in the rows are absent. High performance and a nearly axial flow behind the turbine are obtained. Reduction of the rotor rotation frequency and variation of the pressure drop change the flow parameters, the parameters of the stages and the turbine, as well as the form of the characteristic. In particular, for decreased n, nonmonotonic variation of the second stage reactivity with increasing π* is observed. It is demonstrated that the turbine characteristic is mainly determined by the influence of the angles of incidence and the velocity at the output of the rows on the losses and the flow output angle. The account of the growing flow output angle due to the positive angle of incidence for decreased rotation frequencies results in a considerable change of the characteristic: poorer performance, redistribution of the pressure drop at the stages, and change of reactivities, growth of the turbine capacity, and change of the angle and flow velocity behind the turbine.
Calculation of Thermal Scattering Kernels
A long-standing programme at General Atomic has been the development of physical models to describe the scattering of slow neutrons from the various moderators and the numerical methods necessary for the computation of thermal neutron cross-sections and scattering kernels. This paper contains a review of the recent developments and improvements in the scattering descriptions and subsequent kernels for the moderators Be, C, H2O, D2O, CH2, H2 and D2. In particular for the moderators Be and C accurate phonon spectra, obtained by the root sampling technique, are presented along with comparisons to demonstrate how well the scattering models can predict the results of cross-section and spectral measurements. While the treatment of H2O is essentially that of Nelkin, curves of calculated and experimental neutron spectra are shown, which demonstrate that the inclusion of anisotropic effects for the molecular vibrations improve the agreement between theory and experiment. Following Butler's description of neutron scattering by D2O, a scattering kernel has been obtained which predicts quite accurately integral quantities such as neutron spectra and angular as well as total scattering cross-sections. An interesting result of the curves shown is that the inter- and intramolecular interference effects tend to cancel so that an incoherent approximation is quite adequate to calculate neutron spectra in D2O for the case of infinite media or weakly space-dependent problems. By utilizing the treatment by Lin and Koenig of the vibrational modes of infinite CH2 chains, a scattering kernel has been obtained which results in very good agreement between the predicted and experimental total cross-section and neutron spectra. Curves are presented to demonstrate this agreement between theory and experiment. Neutron spectra have been calculated for liquid hydrogen at boiling using a very accurate scattering description. These spectra are shown in the paper to be very sensitive both to
Calculational Tool for Skin Contamination Dose Assessment
Hill, R L
2002-01-01
Spreadsheet calculational tool was developed to automate the calculations preformed for dose assessment of skin contamination. This document reports on the design and testing of the spreadsheet calculational tool.
Calculation of sound propagation in fibrous materials
Tarnow, Viggo
Calculations of attenuation and velocity of audible sound waves in glass wools are presented. The calculations use only the diameters of fibres and the mass density of glass wools as parameters. The calculations are compared with measurements....
Atomic physics: computer calculations and theoretical analysis
Drukarev, E. G.
2004-01-01
It is demonstrated, how the theoretical analysis preceding the numerical calculations helps to calculate the energy of the ground state of helium atom, and enables to avoid qualitative errors in the calculations of the characteristics of the double photoionization.
The Dental Trauma Internet Calculator
Gerds, Thomas Alexander; Lauridsen, Eva Fejerskov; Christensen, Søren Steno Ahrensburg;
2012-01-01
Background/Aim Prediction tools are increasingly used to inform patients about the future dental health outcome. Advanced statistical methods are required to arrive at unbiased predictions based on follow-up studies. Material and Methods The Internet risk calculator at the Dental Trauma Guide...... provides prognoses for teeth with traumatic injuries based on the Copenhagen trauma database: http://www.dentaltraumaguide.org The database includes 2191 traumatized permanent teeth from 1282 patients that were treated at the dental trauma unit at the University Hospital in Copenhagen (Denmark...
Three-dimensional cavity calculations
The existence of a code that solves for the resonant electromagnetic modes of oscillation in arbitrarily-shaped three-dimensional cavities opens new possibilities in rf-structure analysis and research. The URMEL-3D code, the product of a multi-year collaboration between DESY, KFA-Juelich, and Los Alamos, has been used in some exploratory studies to determine the feasibility of using a 3-D code to calculate the properties of several practical rf structures. The results are reported here for three cases: the jungle gym, two coupled cavities, and a waveguide-cavity coupling problem
Optimization calculations at TR-2
Full text: The main objective of the optimization calculations at TR-2 is to increase the radioisotope production (Tc-99m, I-131). Irradiation time and location were optimized separately. A second objective of this study is to obtain similar activities in the irradiated samples irrespective of the irradiation positions. This study also includes the maximization of the discharge burnup levels of the HEU elements in a mixed HEU-LEU core, so both safe and economical usage of the reactor is attained. Five group structure is used for the burnup dependent cross-section libraries that are generated by EPRI-CELL code. The RABANL integral transport option of MC2-2 code was used to accurately account for the resonance self-shielding of U-238. Transport corrected effective cross sections were used for the control rod regions. The data for Mo, Tc and Te isotopes were not available in this library, so new data were generated using GGC-4 and ANISN codes. In order to have a better understanding of the neutronic interactions, especially in the epithermal energy range, 9 group structure for the cross-section libraries of all the isotopes in the core have been generated with the fore mentioned codes. 2D diffusion-depletion code GEREBUS is used for the reactivity and burnup calculations. The 9 group calculations gave higher activity values then 5 group results, but the relative variations between different core positions remained the same, as could be expected. Many new core designs and various irradiation positions have been investigated for the above mentioned purposes. The reactor core was designed as compact as possible, in order to have higher fluxes for the irradiation samples. New graphite and Be reflectors have been added to the periphery of the core to enhance the reactivity and the discharge burnup levels. The water boxes which are used for the irradiation purposes have been moved from periphery to the inside of the reactor core. These modifications have yielded higher
Calculation of transonic aileron buzz
Steger, J. L.; Bailey, H. E.
1979-01-01
An implicit finite-difference computer code that uses a two-layer algebraic eddy viscosity model and exact geometric specification of the airfoil has been used to simulate transonic aileron buzz. The calculated results, which were performed on both the Illiac IV parallel computer processor and the Control Data 7600 computer, are in essential agreement with the original expository wind-tunnel data taken in the Ames 16-Foot Wind Tunnel just after World War II. These results and a description of the pertinent numerical techniques are included.
Rate calculation with colored noise
Bartsch, Thomas; Benito, R M; Borondo, F
2016-01-01
The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a new method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.
Digital calculations of engine cycles
Starkman, E S; Taylor, C Fayette
1964-01-01
Digital Calculations of Engine Cycles is a collection of seven papers which were presented before technical meetings of the Society of Automotive Engineers during 1962 and 1963. The papers cover the spectrum of the subject of engine cycle events, ranging from an examination of composition and properties of the working fluid to simulation of the pressure-time events in the combustion chamber. The volume has been organized to present the material in a logical sequence. The first two chapters are concerned with the equilibrium states of the working fluid. These include the concentrations of var
Electronics reliability calculation and design
Dummer, Geoffrey W A; Hiller, N
1966-01-01
Electronics Reliability-Calculation and Design provides an introduction to the fundamental concepts of reliability. The increasing complexity of electronic equipment has made problems in designing and manufacturing a reliable product more and more difficult. Specific techniques have been developed that enable designers to integrate reliability into their products, and reliability has become a science in its own right. The book begins with a discussion of basic mathematical and statistical concepts, including arithmetic mean, frequency distribution, median and mode, scatter or dispersion of mea
Perturbation calculations with Wilson loop
We present perturbative calculations with the Wilson loop (WL). The dimensional regularization method is used with a special attention concerning to the problem of divergences in the WL expansion in second and fourth orders, in three and four dimensions. We show that the residue in the pole, in 4d, of the fourth order graphs contribution sum is important for the charge renormalization. We compute up to second order the exact expression of the WL, in three-dimensional gauge theories with topological mass as well as its assimptotic behaviour for small and large distances. the author
The "intelligence" of calendrical calculators.
Young, R L; Nettelbeck, T
1994-09-01
Strategies of 4 men (WAIS-R range 65 to 76) when making calendar calculations were investigated. Each subject completed a battery of standardized psychological tests. Results suggested that subjects were aware of rules and regularities associated with the calendar, including knowledge of the 14 different calendar templates, one of which describes any calendar year. Their strategies were rigidly applied and could not be modified easily, even when doing so would have facilitated performance. The involvement of practice, memory, anchor dates, eidetic imagery, and mathematical algorithms were discussed. We concluded that these savants relied heavily on memory, with little manipulation of cognitive input, as opposed to transforming stimuli. PMID:7803035
Calculation of sound propagation in fibrous materials
Tarnow, Viggo
1996-01-01
Calculations of attenuation and velocity of audible sound waves in glass wools are presented. The calculations use only the diameters of fibres and the mass density of glass wools as parameters. The calculations are compared with measurements.......Calculations of attenuation and velocity of audible sound waves in glass wools are presented. The calculations use only the diameters of fibres and the mass density of glass wools as parameters. The calculations are compared with measurements....
Light Pipe Energy Savings Calculator
Owens, Erin; Behringer, Ernest R.
2009-04-01
Dependence on fossil fuels is unsustainable and therefore a shift to renewable energy sources such as sunlight is required. Light pipes provide a way to utilize sunlight for interior lighting, and can reduce the need for fossil fuel-generated electrical energy. Because consumers considering light pipe installation may be more strongly motivated by cost considerations than by sustainability arguments, an easy means to examine the corresponding costs and benefits is needed to facilitate informed decision-making. The purpose of this American Physical Society Physics and Society Fellowship project is to create a Web-based calculator to allow users to quantify the possible cost savings for their specific light pipe application. Initial calculations show that the illumination provided by light pipes can replace electric light use during the day, and in many cases can supply greater illumination levels than those typically given by electric lighting. While the installation cost of a light pipe is significantly greater than the avoided cost of electricity over the lifetime of the light pipe at current prices, savings may be realized if electricity prices increase.
SR 97 - Radionuclide transport calculations
Lindgren, Maria [Kemakta Konsult AB, Stockholm (Sweden); Lindstroem, Fredrik [Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden)
1999-12-01
An essential component of a safety assessment is to calculate radionuclide release and dose consequences for different scenarios and cases. The SKB tools for such a quantitative assessment are used to calculate the maximum releases and doses for the hypothetical repository sites Aberg, Beberg and Ceberg for the initial canister defect scenario and also for the glacial melting case for Aberg. The reasonable cases, i.e. all parameters take reasonable values, results in maximum biosphere doses of 5x10{sup -8} Sv/yr for Aberg, 3x10{sup -8} Sv/yr for Beberg and 1x10{sup -8} Sv/yr for Ceberg for peat area. These doses lie significantly below 0.15 mSv/yr. (A dose of 0.15 mSv/yr for unit probability corresponds to the risk limit of 10{sup -5} per year for the most exposed individuals recommended in regulations.) The conclusion that the maximum risk would lie well below 10{sup -5} per year is also demonstrated by results from the probabilistic calculations, which directly assess the resulting risk by combining dose and probability estimates. The analyses indicate that the risk is 2x10{sup -5} Sv/yr for Aberg, 8x10{sup -7} Sv/yr for Beberg and 3x10{sup -8} Sv/yr for Ceberg. The analysis shows that the most important parameters in the near field are the number of defective canisters and the instant release fraction. The influence from varying one parameter never changes the doses as much as an order of magnitude. In the far field the most important uncertainties affecting release and retention are associated with permeability and connectivity of the fractures in the rock. These properties affect several parameters. Highly permeable and well connected fractures imply high groundwater fluxes and short groundwater travel times. Sparsely connected or highly variable fracture properties implies low flow wetted surface along migration paths. It should, however, be remembered that the far-field parameters have little importance if the near-field parameters take their reasonable
Fung, Jimmy [Los Alamos National Laboratory; Schofield, Sam [LLNL; Shashkov, Mikhail J. [Los Alamos National Laboratory
2012-06-25
We did not run with a 'cylindrically painted region'. However, we did compute two general variants of the original problem. Refinement studies where a single zone at each level of refinement contains the entire internal energy at t=0 or A 'finite' energy source which has the same physical dimensions as that for the 91 x 46 mesh, but consisting of increasing numbers of zones with refinement. Nominal mesh resolution: 91 x 46. Other mesh resolutions: 181 x 92 and 361 x 184. Note, not identical to the original specification. To maintain symmetry for the 'fixed' energy source, the mesh resolution was adjusted slightly. FLAG Lagrange or full (Eulerian) ALE was used with various options for each simulation. Observation - for either Lagrange or ALE, point or 'fixed' source, calculations converge on density and pressure with mesh resolution, but not energy, (not vorticity either).
Langage C++ et calcul scientifique
Saramito, Pierre
2005-01-01
La simulation numérique est devenue essentielle dans de nombreux domaines tels que la mécanique des fluides et des solides, la météo, l'évolution du climat, la biologie ou les semi-conducteurs. Elle permet de comprendre, de prévoir, d'accéder là où les instruments de mesures s'arrêtent. Ce livre présente des méthodes performantes du calcul scientifique : matrices creuses, résolution efficace des grands systèmes linéaires, ainsi que de nombreuses applications à la résolution par éléments fini...
On Calculation of Amplitudes in Quantum Electrodynamics
Karplyuk, Kostyantyn; Zhmudsky, Oleksandr
2012-01-01
A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation of cross sections for different processes. The effectiveness of the method is shown on the cross-section calculation of Coulomb scattering, Compton scattering and electron-positron annihilation.
Calculating system reliability with SRFYDO
Morzinski, Jerome [Los Alamos National Laboratory; Anderson - Cook, Christine M [Los Alamos National Laboratory; Klamann, Richard M [Los Alamos National Laboratory
2010-01-01
SRFYDO is a process for estimating reliability of complex systems. Using information from all applicable sources, including full-system (flight) data, component test data, and expert (engineering) judgment, SRFYDO produces reliability estimates and predictions. It is appropriate for series systems with possibly several versions of the system which share some common components. It models reliability as a function of age and up to 2 other lifecycle (usage) covariates. Initial output from its Exploratory Data Analysis mode consists of plots and numerical summaries so that the user can check data entry and model assumptions, and help determine a final form for the system model. The System Reliability mode runs a complete reliability calculation using Bayesian methodology. This mode produces results that estimate reliability at the component, sub-system, and system level. The results include estimates of uncertainty, and can predict reliability at some not-too-distant time in the future. This paper presents an overview of the underlying statistical model for the analysis, discusses model assumptions, and demonstrates usage of SRFYDO.
RTU Comparison Calculator Enhancement Plan
Miller, James D.; Wang, Weimin; Katipamula, Srinivas
2014-03-31
Over the past two years, Department of Energy’s Building Technologies Office (BTO) has been investigating ways to increase the operating efficiency of the packaged rooftop units (RTUs) in the field. First, by issuing a challenge to the RTU manufactures to increase the integrated energy efficiency ratio (IEER) by 60% over the existing ASHRAE 90.1-2010 standard. Second, by evaluating the performance of an advanced RTU controller that reduces the energy consumption by over 40%. BTO has previously also funded development of a RTU comparison calculator (RTUCC). RTUCC is a web-based tool that provides the user a way to compare energy and cost savings for two units with different efficiencies. However, the RTUCC currently cannot compare savings associated with either the RTU Challenge unit or the advanced RTU controls retrofit. Therefore, BTO has asked PNNL to enhance the tool so building owners can compare energy and savings associated with this new class of products. This document provides the details of the enhancements that are required to support estimating energy savings from use of RTU challenge units or advanced controls on existing RTUs.
Benchmark calculations for EGS5
In the past few years, EGS4 has undergone an extensive upgrade to EGS5, in particularly in the areas of low-energy electron physics, low-energy photon physics, PEGS cross section generation, and the coding from Mortran to Fortran programming. Benchmark calculations have been made to assure the accuracy, reliability and high quality of the EGS5 code system. This study reports three benchmark examples that show the successful upgrade from EGS4 to EGS5 based on the excellent agreements among EGS4, EGS5 and measurements. The first benchmark example is the 1969 Crannell Experiment to measure the three-dimensional distribution of energy deposition for 1-GeV electrons shower in water and aluminum tanks. The second example is the 1995 Compton-scattered spectra measurements for 20-40 keV, linearly polarized photon by Namito et. al., in KEK, which was a main part of the low-energy photon expansion work for both EGS4 and EGS5. The third example is the 1986 heterogeneity benchmark experiment by Shortt et. al., who used a monoenergetic 20-MeV electron beam to hit the front face of a water tank containing both air and aluminum cylinders and measured spatial depth dose distribution using a small solid-state detector. (author)
RTU Comparison Calculator Enhancement Plan
Miller, James D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Wang, Weimin [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Katipamula, Srinivas [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2015-07-01
Over the past two years, Department of Energy’s Building Technologies Office (BTO) has been investigating ways to increase the operating efficiency of the packaged rooftop units (RTUs) in the field. First, by issuing a challenge to the RTU manufactures to increase the integrated energy efficiency ratio (IEER) by 60% over the existing ASHRAE 90.1-2010 standard. Second, by evaluating the performance of an advanced RTU controller that reduces the energy consumption by over 40%. BTO has previously also funded development of a RTU comparison calculator (RTUCC). RTUCC is a web-based tool that provides the user a way to compare energy and cost savings for two units with different efficiencies. However, the RTUCC currently cannot compare savings associated with either the RTU Challenge unit or the advanced RTU controls retrofit. Therefore, BTO has asked PNNL to enhance the tool so building owners can compare energy and savings associated with this new class of products. This document provides the details of the enhancements that are required to support estimating energy savings from use of RTU challenge units or advanced controls on existing RTUs.
Selfconsistent calculations for hyperdeformed nuclei
Molique, H.; Dobaczewski, J.; Dudek, J.; Luo, W.D. [Universite Louis Pasteur, Strasbourg (France)
1996-12-31
Properties of the hyperdeformed nuclei in the A {approximately} 170 mass range are re-examined using the self-consistent Hartree-Fock method with the SOP parametrization. A comparison with the previous predictions that were based on a non-selfconsistent approach is made. The existence of the {open_quotes}hyper-deformed shell closures{close_quotes} at the proton and neutron numbers Z=70 and N=100 and their very weak dependence on the rotational frequency is suggested; the corresponding single-particle energy gaps are predicted to play a role similar to that of the Z=66 and N=86 gaps in the super-deformed nuclei of the A {approximately} 150 mass range. Selfconsistent calculations suggest also that the A {approximately} 170 hyperdeformed structures have neglegible mass asymmetry in their shapes. Very importantly for the experimental studies, both the fission barriers and the {open_quotes}inner{close_quotes} barriers (that separate the hyperdeformed structures from those with smaller deformations) are predicted to be relatively high, up to the factor of {approximately}2 higher than the corresponding ones in the {sup 152}Dy superdeformed nucleus used as a reference.
The Reactor Physics Committee of the Nuclear Energy Agency has set up a series of benchmark calculations to compare the performance of the various codes used in shielding calculations for fuel transport flasks. For one benchmark the calculations are to be compared with dose-rates measured outside a French TN-12 flask loaded with 12 irradiated fuel elements from a PWR. Neutron dose-rate measurements were made with a Helium-3 detector encased in paraffin with an unknown response. It did not produce measurements of equivalent dose-rates therefore standard flux to dose conversion factors could not be used in the calculations. A 1-dimensional adjoint calculation was carried out by the CEA at Saclay to determine the response function for the detector and this was used to calculate neutron dose-rates for the flask. However the dose-rates calculated away from the surface of the flask were underestimated suggesting that there was an angular dependence of the response. This report describes MCBEND calculations which have been performed to produce an angular response function for the detector, which was used to provide revised dose-rates. (author)
Locke, H.F.
1991-11-01
The Reactor Physics Committee of the Nuclear Energy Agency has set up a series of benchmark calculations to compare the performance of the various codes used in shielding calculations for fuel transport flasks. For one benchmark the calculations are to be compared with dose-rates measured outside a French TN-12 flask loaded with 12 irradiated fuel elements from a PWR. Neutron dose-rate measurements were made with a Helium-3 detector encased in paraffin with an unknown response. It did not produce measurements of equivalent dose-rates therefore standard flux to dose conversion factors could not be used in the calculations. A 1-dimensional adjoint calculation was carried out by the CEA at Saclay to determine the response function for the detector and this was used to calculate neutron dose-rates for the flask. However the dose-rates calculated away from the surface of the flask were underestimated suggesting that there was an angular dependence of the response. This report describes MCBEND calculations which have been performed to produce an angular response function for the detector, which was used to provide revised dose-rates. (author).
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC)
2014-02-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a{sup N}, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Ablinger, Jakob [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Blümlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Wißbrock, Fabian [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)
2014-08-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version of the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∼30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N∈C. Integrals with a power-like divergence in N-space ∝a{sup N},a∈R,a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝aN, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution
Fog, Agner
2008-01-01
conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...
76 FR 71431 - Civil Penalty Calculation Methodology
2011-11-17
... TRANSPORTATION Federal Motor Carrier Safety Administration Civil Penalty Calculation Methodology AGENCY: Federal... its civil penalty methodology. Part of this evaluation includes a forthcoming explanation of the Uniform Fine Assessment (UFA) algorithm, which FMCSA currently uses for calculation of civil...
Dynamics Calculation of Travel Wave Tube
无
2011-01-01
During the dynamics calculating of the travel tube, we must obtain the field map in the tube. The field map can be affected by not only the beam loading, but also the attenuation coefficient. The calculation of the attenuation coefficient
A New Approach for Calculating Vacuum Susceptibility
宗红石; 平加伦; 顾建中
2004-01-01
Based on the Dyson-Schwinger approach, we propose a new method for calculating vacuum susceptibilities. As an example, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is presented.
Carbon cycle modeling calculations for the IPCC
We carried out essentially all the carbon cycle modeling calculations that were required by the IPCC Working Group 1. Specifically, IPCC required two types of calculations, namely, ''inverse calculations'' (input was CO2 concentrations and the output was CO2 emissions), and the ''forward calculations'' (input was CO2 emissions and output was CO2 concentrations). In particular, we have derived carbon dioxide concentrations and/or emissions for several scenarios using our coupled climate-carbon cycle modelling system
Lattice Dynamics Calculation in MGB2
In Present report, We have introduced a new theoretical results for MgB2 by using home design programme Lattice Dynamics. we have calculated partial and total density of states (PDOS, TDOS), infrared and Raman spectrums and specific heat capacity. Dispersion curves in different symmetry points are calculated and found that there is agreement with other calculations. Also we have tried to investigate the Boron Isotope effect on the calculated properties
CORRECTED CALCULATION OF HORIZONTAL GATING SYSTEMS
I. A. Zayatz
2015-05-01
Full Text Available In the course of fulfillment of work the specified calculations of horizontal gating systems for various parts produced in dispensable molds were carried out. The results of work showed that the weight removal value in gating systems fluctuates in big intervals and the specified calculation of horizontal gating systems enables to calculate precisely their weight that allows to calculate quantity of metal in metal charge.
Final disposal room structural response calculations
Finite element calculations have been performed to determine the structural response of waste-filled disposal rooms at the WIPP for a period of 10,000 years after emplacement of the waste. The calculations were performed to generate the porosity surface data for the final set of compliance calculations. The most recent reference data for the stratigraphy, waste characterization, gas generation potential, and nonlinear material response have been brought together for this final set of calculations
Thermohydraulic calculation of WWER-type NPP
Technique of thermohydraulic calculation of the WWER-type NPP in unsteady processes is described. Effective algorithm for solving hydrodynamics equations without regard for acoustic effects permitting to use enough large time integration step is given. Calculation of two-dimensional temperature fields in fuel element is considered. Method for calculating a pressurizer, steam generators and pumps is described as well
Quantum Transport Calculations Using Periodic Boundary Conditions
Wang, Lin-Wang
2004-01-01
An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This method allows the use of conventional ground state ab initio programs without big changes. The computational effort is only a few times of a normal ground state calculations, thus is makes accurate quantum transport calculations for large systems possible.
47 CFR 1.1623 - Probability calculation.
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall...