WorldWideScience

Sample records for 1-dimensional calculations

  1. Spacetime Singularities in (2+1)-Dimensional Quantum Gravity

    CERN Document Server

    Minassian, E A

    2002-01-01

    The effects of spacetime quantization on black hole and big bang/big crunch singularities can be studied using new tools from (2+1)-dimensional quantum gravity. I investigate effects of spacetime quantization on singularities of the (2+1)-dimensional BTZ black hole and the (2+1)-dimensional torus universe. Hosoya has considered the BTZ black hole, and using a ``quantum generalized affine parameter'' (QGAP), has shown that, for some specific paths, quantum effects ``smear'' the singularity. Using generic gaussian wave functions, I show that both BTZ black hole and the torus universe contain families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, further support this conclusion.

  2. Spacetime singularities in (2 + 1)-dimensional quantum gravity

    Science.gov (United States)

    Minassian, Eric

    2002-12-01

    The effects of spacetime quantization on black-hole and big-bang/big-crunch singularities can be studied using new tools from (2 + 1)-dimensional quantum gravity. I investigate effects of spacetime quantization on the singularities of the (2 + 1)-dimensional BTZ black hole and the (2 + 1)-dimensional torus universe. Hosoya has considered the BTZ black hole, and using a 'quantum-generalized affine parameter' (QGAP), has shown that, for some specific paths, quantum effects 'smear' the singularity. Using generic Gaussian wavefunctions, I show that both the BTZ black hole and the torus universe contain families of paths that still reach the singularities with finite QGAPs, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular-invariant wavefunctions of Carlip and Nelson for the torus universe, further support this conclusion.

  3. (2+1)-dimensional supersymmetric integrable equations

    Science.gov (United States)

    Yan, Zhao-Wen; Tala; Chen, Fang; Liu, Tao-Ran; Han, Jing-Min

    2017-09-01

    By means of two different approaches, we construct the (2+1)-dimensional supersymmetric integrable equations based on the super Lie algebra osp(3/2). We relax the constraint condition of homogenous space of super Lie algebra osp(3/2) in the first approach. In another one, the technique of extending the dimension of the systems is used. Furthermore for the (2 + 1)-dimensional supersymmetric integrable equations, we also derive their Bäcklund transformations.

  4. Teleparallel equivalent theory of (1+ 1)-dimensional gravity

    Institute of Scientific and Technical Information of China (English)

    Gamal G.L. Nashed

    2010-01-01

    A theory of (1 +1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei~' and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy-momentum formula.

  5. New Interaction Solutions of (3+1-Dimensional KP and (2+1-Dimensional Boussinesq Equations

    Directory of Open Access Journals (Sweden)

    Bo Ren

    2015-01-01

    Full Text Available The consistent tanh expansion (CTE method has been succeeded to apply to the nonintegrable (3+1-dimensional Kadomtsev-Petviashvili (KP and (2+1-dimensional Boussinesq equations. The interaction solution between one soliton and one resonant soliton solution for the (3+1-dimensional KP equation is obtained with CTE method. The interaction solutions among one soliton and cnoidal waves for these two equations are also explicitly given. These interaction solutions are investigated in both analytical and graphical ways. It demonstrates that the interactions between one soliton and cnoidal waves are elastic with phase shifts.

  6. Holographic duality between (2 +1 ) -dimensional quantum anomalous Hall state and (3 +1 ) -dimensional topological insulators

    Science.gov (United States)

    Gu, Yingfei; Lee, Ching Hua; Wen, Xueda; Cho, Gil Young; Ryu, Shinsei; Qi, Xiao-Liang

    2016-09-01

    In this paper, we study (2 +1 ) -dimensional quantum anomalous Hall states, i.e., band insulators with quantized Hall conductance, using exact holographic mapping. Exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in (3 +1 ) -dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a (3 +1 ) -dimensional topological insulator. The dual description enables a characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.

  7. Rainich conditions in (2 + 1)-dimensional gravity

    Science.gov (United States)

    Krongos, D. S.; Torre, C. G.

    2017-01-01

    In (3 + 1) spacetime dimensions, the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the analogous conditions for (2 + 1)-dimensional gravity coupled to electromagnetism. Both the non-null and null cases are treated. The construction of these conditions is based upon reducing the problem to that of gravity coupled to a scalar field, which we have treated elsewhere. These conditions can be easily extended to other theories of (2 + 1)-dimensional gravity. For example, we apply the geometrization conditions to topologically massive gravity coupled to the electromagnetic field and obtain a family of plane-fronted wave solutions.

  8. Connectivity of Random 1-Dimensional Networks

    OpenAIRE

    Kurlin, V.; Mihaylova, L.

    2007-01-01

    An important problem in wireless sensor networks is to find the minimal number of randomly deployed sensors making a network connected with a given probability. In practice sensors are often deployed one by one along a trajectory of a vehicle, so it is natural to assume that arbitrary probability density functions of distances between successive sensors in a segment are given. The paper computes the probability of connectivity and coverage of 1-dimensional networks and gives estimates for a m...

  9. Exact Periodic-Wave Solutions for (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional KP Equation

    Institute of Scientific and Technical Information of China (English)

    ZHAO Qiang; LIU Shi-Kuo; FU Zun-Tao

    2004-01-01

    The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.

  10. Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations

    Indian Academy of Sciences (India)

    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.

  11. Exploration of Similarity Renormalization Group Generators in 1-Dimensional Potentials

    Science.gov (United States)

    Heinz, Matthias

    2016-09-01

    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. The user input into the SRG evolution is a matrix called the generator, which determines to what form the Hamiltonian is transformed. As it is currently used, the SRG evolves Hamiltonian into a band diagonal form. However, due to many-body forces induced by the evolution, the SRG introduces errors when used to renormalize many-body potentials. This makes it unfit for calculations with nuclei larger than a certain size. A recent paper suggests that alternate generators may induce smaller many-body forces. Smaller many-body force induction would allow SRG use to be extended to larger nuclei. I use 1-dimensional systems of two, three, and four bosons to further study the SRG evolution and how alternate generators affect many-body forces induced.

  12. Variable Separation Solutions in (1+1)-Dimensional and (3+1)-Dimensional Systems via Entangled Mapping Approach

    Institute of Scientific and Technical Information of China (English)

    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.

  13. Kink manifolds in (1+1)-dimensional scalar field theory

    Energy Technology Data Exchange (ETDEWEB)

    Alonso Izquierdo, A.; Gonzalez Leon, M.A. [Departamento de Estadistica y Matematica Aplicadas, Facultad de Ciencias, Universidad de Salamanca, Salamanca (Spain); Mateos Guilarte, J. [Departamento de Fisica, Facultad de Ciencias, Universidad de Salamanca, Salamanca (Spain)

    1998-01-09

    The general structure of kink manifolds in (1+1)-dimensional complex scalar field theory is described by analysing three special models. New solitary waves are reported. Kink energy sum rules arise between different types of solitary waves. (author)

  14. Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories

    Science.gov (United States)

    Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

    2017-04-01

    We calculate the multipoint Green's functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z2 Ising model, sinh-Gordon model and Z3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.

  15. Multipoint Green's functions in 1+1 dimensional integrable quantum field theories

    Directory of Open Access Journals (Sweden)

    H.M. Babujian

    2017-04-01

    Full Text Available We calculate the multipoint Green's functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z2 Ising model, sinh-Gordon model and Z3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.

  16. Hypocycloidal throat for 2 + 1-dimensional thin-shell wormholes

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  17. High energy scattering in (2+1)-dimensional QCD A dipole picture

    CERN Document Server

    Li, Maozhen; Miao Li; Chung-I Tan

    1995-01-01

    A dipole picture of high energy scattering is developed in the 2+1 dimensional QCD, following Mueller. A generalized integral equation for the dipole density with a given separation and center of mass position is derived, and meson-meson non-forward scattering amplitude is therefore calculated. We also calculate the amplitude due to two pomeron exchange, and the triple pomeron coupling. We compare the result obtained by this method to our previous result based on an effective action approach, and find the two results agree at the one pomeron exchange level.

  18. Upon Generating (2+1)-dimensional Dynamical Systems

    Science.gov (United States)

    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.

  19. Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation using the new approach of generalized (′/)-expansion method

    Indian Academy of Sciences (India)

    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.

  20. Rainich Conditions in (2+1)-Dimensional Gravity

    CERN Document Server

    Krongos, D S

    2016-01-01

    In (3 + 1) spacetime dimensions the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the analogous conditions for (2 + 1)-dimensional gravity coupled to electromagnetism. Both the non-null and null cases are treated. The construction of these conditions is based upon reducing the problem to that of gravity coupled to a scalar field, which we have treated elsewhere. These conditions can be easily extended to other theories of (2 + 1)-dimensional gravity. For example, we apply the geometrization conditions to topologically massive gravity coupled to the electromagnetic field and obtain a family of plane-fronted wave solutions.

  1. Exact solutions of atmospheric (3+1-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations with viscosity

    Directory of Open Access Journals (Sweden)

    Ping Liu

    2015-08-01

    Full Text Available The symmetry reduction equations, similarity solutions, sub-groups and exact solutions of the (3+1-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations with viscosity (INHBV equations, which describe the atmospheric gravity waves, are researched in this paper. Calculation on symmetry shows that the equations are invariant under the Galilean transformations, scaling transformations, rotational transformations and space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1-dimensional INHBV equations are proposed. Traveling wave solutions of the INHBV equations are demonstrated by means of symmetry method. The evolutions on the wind velocities and temperature perturbation are demonstrated by figures.

  2. Exact solutions of atmospheric (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations with viscosity

    Science.gov (United States)

    Liu, Ping; Zeng, Bao-Qing; Deng, Bo-Bo; Yang, Jian-Rong

    2015-08-01

    The symmetry reduction equations, similarity solutions, sub-groups and exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations with viscosity (INHBV equations), which describe the atmospheric gravity waves, are researched in this paper. Calculation on symmetry shows that the equations are invariant under the Galilean transformations, scaling transformations, rotational transformations and space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHBV equations are proposed. Traveling wave solutions of the INHBV equations are demonstrated by means of symmetry method. The evolutions on the wind velocities and temperature perturbation are demonstrated by figures.

  3. Ruppeiner Geometry of (2 + 1)-Dimensional Spinning Dilaton Black Hole*

    Institute of Scientific and Technical Information of China (English)

    CHEN Xiu-Wu; WEI Shao-Wen; LIU Yu-Xiao

    2011-01-01

    In this paper, we study the geometrothermodynamics of (2 + 1)-dimensional spinning dilaton black hole.We show that the Ruppeiner curvature vanishes, which implies that there exist no phase transitions and thermodynamic interactions. However when the thermodynamics fluctuation is included, the geometry structure is reconsidered. The non-vanishing Ruppeiner curvature is obtained, which means the phase space is non-flat. We also study the phase transitions and show that it can indeed take place at some points.

  4. (N+1)-dimensional Lorentzian evolving wormholes supported by polytropic matter

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  5. Exact solutions of (3 + 1)-dimensional stochastic Burgers equation

    Energy Technology Data Exchange (ETDEWEB)

    Wang Tieying [Department of Applied Mathematics and Physics, Dalian Nationalities for University, Dalian 116600 (China)]. E-mail: wangty@dlnu.edu.cn; Ren Yonghong [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Zhao Yali [Department of Mathematics, Chaoyang Teachers College, Chaoyang 122000 (China)

    2006-08-15

    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.

  6. Causality in 1+1-dimensional Yukawa model-II

    Indian Academy of Sciences (India)

    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.

  7. Exact interior solutions in 2 + 1-dimensional spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)

    2014-04-15

    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.)

  8. Integrable lattice hierarchies associated with two new (2+1)-dimensional discrete spectral problems

    Energy Technology Data Exchange (ETDEWEB)

    Pickering, Andrew [Dpto. de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos C/ Tulipan s/n, 28933 Mostoles, Madrid (Spain); Zhu Zuonong, E-mail: znzhu2@yahoo.com.c [Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240 (China)

    2009-10-19

    In this Letter, by considering two new (2+1)-dimensional discrete linear spectral problems, new (2+1)-dimensional integrable lattice hierarchies are constructed. It is shown that the two new (2+1)-dimensional integrable lattice hierarchies are extensions (to nonisospectral and (2+1)-dimensional cases) of a (1+1)-dimensional 3-field lattice hierarchy of Zhang et al. and a (1+1)-dimensional 2-field lattice hierarchy due to Merola, Ragnisco and Tu. We also obtain new (1+1)-dimensional nonisospectral lattice hierarchies which include a nonisospectral relativistic Toda lattice hierarchy.

  9. (2+1)-Dimensional Gravity in Weyl Integrable Spacetime

    CERN Document Server

    Aguilar, J E Madriz; Fonseca-Neto, J B; Almeida, T S; Formiga, J B

    2015-01-01

    We investigate (2+1)-dimensional gravity in a Weyl integrable spacetime (WIST). We show that, unlike general relativity, this scalar-tensor theory has a Newtonian limit for any dimension and that in three dimensions the congruence of world lines of particles of a pressureless fluid has a non-vanishing geodesic deviation. We present and discuss a class of static vacuum solutions generated by a circularly symmetric matter distribution that for certain values of the parameter w corresponds to a space-time with a naked singularity at the center of the matter distribution. We interpret all these results as being a direct consequence of the space-time geometry.

  10. 1+1 dimensional compactifications of string theory.

    Science.gov (United States)

    Goheer, Naureen; Kleban, Matthew; Susskind, Leonard

    2004-05-14

    We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.

  11. Lump Solution of (2+1)-Dimensional Boussinesq Equation

    Science.gov (United States)

    Ma, Hong-Cai; Deng, Ai-Ping

    2016-05-01

    A class of lump solutions of (2+1)-dimensional Boussinesq equation are obtained with the help of Maple by using Hirota bilinear method. Some contour plots with different determinant values are sequentially made to show that the corresponding lump solution tends to zero when the determinant approaches zero. The particular lump solutions with specific values of the involved parameters are plotted, as illustrative examples. Supported by the National Natural Science Foundation of China under Grant No. 10647112 and the Fund of Science and Technology Commission of Shanghai Municipality under Grant No. ZX201307000014

  12. Quench Dynamics in Confined 1+1-Dimensional Systems

    CERN Document Server

    Engelhardt, Dalit

    2015-01-01

    We present a scheme for investigating the response of confined 1+1-dimensional systems to a quantum quench and consider the extent to which a system whose post-quench dynamics are near-integrable may be analyzed by an application of boundary CFT techniques. As the main example we present a model of a split-momentum quench in a finite 1D geometry, a setup analogous to that of the experiment of Kinoshita, Wenger, and Weiss [Nature 440, 900 (2006)]. We analytically derive the form of the expected momentum distributions and describe how such information may be used to assess the extent of integrability breaking in realistic systems.

  13. Tipping Points in 1-Dimensional Schelling Models with Switching Agents

    Science.gov (United States)

    Barmpalias, George; Elwes, Richard; Lewis-Pye, Andy

    2015-02-01

    Schelling's spacial proximity model was an early agent-based model, illustrating how ethnic segregation can emerge, unwanted, from the actions of citizens acting according to individual local preferences. Here a 1-dimensional unperturbed variant is studied under switching agent dynamics, interpretable as being open in that agents may enter and exit the model. Following the authors' work (Barmpalias et al., FOCS, 2014) and that of Brandt et al. (Proceedings of the 44th ACM Symposium on Theory of Computing (STOC 2012), 2012), rigorous asymptotic results are established. The dynamic allows either type to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a generalization of the models considered in [1] and [3], the model's parameters comprise the initial proportions of the two types, along with independent values of the tolerance for each type. This model comprises a 1-dimensional spin-1 model with spin dependent external field, as well as providing an example of cascading behaviour within a network.

  14. Topology and incompleteness for 2+1-dimensional cosmological spacetimes

    Science.gov (United States)

    Fajman, David

    2016-12-01

    We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.

  15. Generalized (2+1) dimensional black hole by Noether symmetry

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  16. Entanglement entropy after partial projective measurement in $1+1$ dimensional conformal field theories: exact results

    CERN Document Server

    Rajabpour, M A

    2015-01-01

    We calculate analytically the R\\'enyi bipartite entanglement entropy $S_{\\alpha}$ of the ground state of $1+1$ dimensional conformal field theories (CFT) after performing projective measurement in a part of the system. Using Cardy's method we show that the entanglement entropy in this setup is dependent on the central charge and the operator content of the system. When due to the measured region the two parts are disconnected, the entanglement entropy decreases like a power-law with respect to the characteristic distance of the two regions with an exponent which is dependent on the rank $\\alpha$ of the R\\'enyi entanglement entropy and the smallest scaling dimension present in the system. We check our findings by making numerical calculations on the Klein-Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators. We also comment on the post-measurement entanglement entropy in the massive quantum field theories.

  17. Aspects of noncommutative (1+1)-dimensional black holes

    Science.gov (United States)

    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.

  18. Aspects of noncommutative (1+1)-dimensional black holes

    CERN Document Server

    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.

  19. Non-trivial 2+1-Dimensional Gravity

    CERN Document Server

    Grigore, D R

    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. However, in addition to Einstein and Chern-Simons coupling we need coupling to fermionic ghost and anti-ghost fields and to a vector-graviton field with the same mass as the graviton.

  20. Entanglement and majorization in (1+1)-dimensional quantum systems

    CERN Document Server

    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.

  1. Schramm-Loewner evolution theory of the asymptotic behaviors of (2 + 1) -dimensional Wolf-Villain model

    Science.gov (United States)

    Chen, Yili; Tang, Gang; Xun, Zhipeng; Zhu, Lei; Zhang, Zhe

    2017-01-01

    Although extensive analytical and numerical work has focus on investigating the (2+1)-dimensional Wolf-Villain (WV) model, some problems concerning its asymptotical behaviors, such as the universality class to which it belongs remain controversial. The Schramm-Loewner evolution (SLE) theory is an attractive approach to describe the fluctuation phenomena and random processes, and has also been applied to the analysis of the stochastic growth of surfaces. In this work, we applied SLE theory to the analysis of the saturated surface to conduct in-depth research, with a new perspective, on the asymptotical behaviors of the (2+1)-dimensional WV model. On the basis of the analysis of the saturated surface contour lines, we determine that the diffusion coefficient calculated for (2+1)-dimensional WV model is κ = 2.91 ± 0.01, and that for Family model is κ = 2.88 ± 0.01. Accordingly we can conclude from the view of SLE theory, that the (2+1)-dimensional WV model, similar to the Family model, also belongs to the Edwards-Wilkinson universality class.

  2. Nonlocal symmetry and exact solutions of the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation

    Science.gov (United States)

    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).

  3. Quantum cosmology in (1 +1 )-dimensional Hořava-Lifshitz theory of gravity

    Science.gov (United States)

    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.

  4. A (2+1)-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings

    Institute of Scientific and Technical Information of China (English)

    Huanhe Dong

    2007-01-01

    Under the frame of the (2+1)-dimensional zero curvature equation and Tu model,the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.

  5. Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model

    Science.gov (United States)

    Banerjee, Santo; Misra, Amar P.; Rondoni, L.

    2012-01-01

    Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type, with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to steady-states, to divergencies in a finite time as well as to the formation of spatiotemporal irregular patterns. The latter, in particular, appears to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady-states are achieved with sufficiently large values of the chemotactic coefficient (χ) and/or with growth rates r below a critical value rc. For r>rc, the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime, for different values of χ, r and of the diffusion coefficient D.

  6. Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model

    CERN Document Server

    Banerjee, S; Rondoni, L

    2011-01-01

    Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to a steady-state, divergence in a finite time as well as the formation of spatiotemporal irregular patterns. The latter, in particular, appear to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady states are achieved with sufficiently large values of the chemotactic coefficient $(\\chi)$ and/or with growth rates $r$ below a critical value $r_c$. For $r > r_c$, the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime for different values of $\\chi$, $r$ and the diffusion coefficient $D$.

  7. 2 + 1-dimensional traversable wormholes supported by positive energy

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  8. Rotating thin shells in (2+1)-dimensional asymptotically AdS spacetimes: Mechanical properties, Machian effects, and energy conditions

    CERN Document Server

    Lemos, José P S; Minamitsuji, Masato

    2015-01-01

    A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2+1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

  9. Solutions and Conservation Laws of a (2+1-Dimensional Boussinesq Equation

    Directory of Open Access Journals (Sweden)

    Letlhogonolo Daddy Moleleki

    2013-01-01

    Full Text Available We study a nonlinear evolution partial differential equation, namely, the (2+1-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1-dimensional Boussinesq equation. Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1-dimensional Boussinesq equation.

  10. Study of (2+1)-Dimensional Higher-Order Broer-Kaup System

    Institute of Scientific and Technical Information of China (English)

    WANG Ling; LIU Xi-Qiang; DONG Zhong-Zhou

    2007-01-01

    Painlevé property and infinite symmetries of the (2+1)-dimensional higher-order Broer-Kaup (HBK) system are studied in this paper.Using the modified direct method,we derive the theorem of general symmetry groups to (2+1)-dimensional HBK system.Based on our theorem,some new forms of solutions are obtained.We also find infinite number of conservation laws of the (2+1)-dimensional HBK system.

  11. Symmetries, Traveling Wave Solutions, and Conservation Laws of a (3+1-Dimensional Boussinesq Equation

    Directory of Open Access Journals (Sweden)

    Letlhogonolo Daddy Moleleki

    2014-01-01

    Full Text Available We analyze the (3+1-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the (3+1-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the (3+1-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.

  12. Baicklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation

    Institute of Scientific and Technical Information of China (English)

    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.

  13. (1 + 1) dimensional hydrodynamics for high-energy heavy-ion collisions

    Science.gov (United States)

    Satarov, L. M.; Mishustin, I. N.; Merdeev, A. V.; Stöcker, H.

    2007-10-01

    A (1 + 1)-dimensional hydrodynamical model in the light-cone coordinates is used to describe central heavy-ion collisions at ultrarelativistic bombarding energies. Deviations from Bjorken scaling are taken into account by choosing finite-size profiles for the initial energy density. The sensitivity of fluid-dynamical evolution to the equation of state and the parameters of initial state are investigated. Experimental constraints on the total energy of produced particles are used to reduce the number of model parameters. Spectra of secondary particles are calculated under the assumption that the transition from the hydrodynamical stage to the collisionless expansion of matter occurs at a certain freeze-out temperature. An important role of resonances in the formation of observed hadronic spectra is demonstrated. The calculated rapidity distributions of pions, kaons, and antiprotons in central Au + Au collisions at √s NN = 200 GeV are compared with experimental data of the BRAHMS Collaboration. Parameters of the initial state are reconstructed for different choices of the equation of state. The best fit of these data is obtained for a soft equation of state and Gaussian-like initial profiles of the energy density, intermediate between the Landau and Bjorken limits.

  14. Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hong; BAI Cheng-Lin

    2004-01-01

    Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+ 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.

  15. Abundant Multisoliton Structure of the (3+1)-Dimensional Nizhnik-Novikov-Veselov Equation

    Institute of Scientific and Technical Information of China (English)

    BAI Cheng-Lin

    2004-01-01

    Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, the nonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of single solitary wave solution and the multisoliton solutions are constructed.

  16. N-Soliton Solutions of (2+1)-Dimensional Non-isospectral AKNS System

    Institute of Scientific and Technical Information of China (English)

    ZHANG Xiao-Xian; SUN Ye-Peng

    2008-01-01

    The bilinear form of the (2+1)-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a (2+1)-dimensional non-isospectral Schrodinger equation and its N-soliton solutions are constructed.

  17. Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations

    Science.gov (United States)

    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

  18. NEW EXPLICIT SOLUTIONS TO THE (2+1)-DIMENSIONAL BROER-KAUP EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Liu Xiqiang

    2004-01-01

    Applying the homogeneous balance method, we have found the explicit and soliton solutions and given a successive formula of finding explicit solutions to the (2+1)-dimensional Broer-Kaup equations. Moreover, by using the Lie group method, we have discussed the similarity solutions to the (2+1)-dimensional Broer-Kaup equations.

  19. (2+1-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves

    Directory of Open Access Journals (Sweden)

    Chunlei Wang

    2015-01-01

    Full Text Available 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 equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.

  20. Horizons in 2+1-dimensional collapse of particles

    Indian Academy of Sciences (India)

    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.

  1. Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model

    CERN Document Server

    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...

  2. Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge

    CERN Document Server

    Reinhardt, H

    2008-01-01

    We study the Hamiltonian approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the ...

  3. Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids

    Indian Academy of Sciences (India)

    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.

  4. Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations

    Directory of Open Access Journals (Sweden)

    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.

  5. Integrability and Solutions of the (2 + 1)-dimensional Hunter-Saxton Equation

    Science.gov (United States)

    Cai, Hong-Liu; Qu, Chang-Zheng

    2016-04-01

    In this paper, the (2 + 1)-dimensional Hunter-Saxton equation is proposed and studied. It is shown that the (2 + 1)-dimensional Hunter-Saxton equation can be transformed to the Calogero-Bogoyavlenskii-Schiff equation by reciprocal transformations. Based on the Lax-pair of the Calogero-Bogoyavlenskii-Schiff equation, a non-isospectral Lax-pair of the (2 + 1)-dimensional Hunter-Saxton equation is derived. In addition, exact singular solutions with a finite number of corners are obtained. Furthermore, the (2 + 1)-dimensional μ-Hunter-Saxton equation is presented, and its exact peaked traveling wave solutions are derived. Supported by National Natural Science Foundation of China under Grant No. 11471174 and NSF of Ningbo under Grant No. 2014A610018

  6. Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation

    Institute of Scientific and Technical Information of China (English)

    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.

  7. Feedback Equivalence of 1-dimensional Control Systems of the 1-st Order

    OpenAIRE

    2008-01-01

    The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

  8. Exact Solutions of the (3+1)-Dimensional KP and KdV-Type Equations

    Institute of Scientific and Technical Information of China (English)

    LI De-Sheng; Lü Zhuo-Sheng; ZHANG Hong-Qing

    2003-01-01

    Abundant new soliton-like and period form solutions for certain (3+1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system, Maple.

  9. Construction of Perturbatively Correct Light Front Hamiltonian for (2+1)-Dimensional Gauge Theory

    CERN Document Server

    Malyshev, M Yu; Zubov, R A; Franke, V A

    2016-01-01

    In this paper we consider (2+1)-dimensional SU(N)-symmetric gauge theory within light front perturbation theory, regularized by the method analogous to Pauli-Villars regularization. This enables us to construct correct renormalized light front Hamiltonian.

  10. Determinant Solutions to a (3+1)-Dimensional Generalized KP Equation with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    Alrazi ABDELJABBAR; Wenxiu MA; Ahmet YILDIRIM

    2012-01-01

    A system of linear conditions is presented for Wronskian and Grammian solutions to a (3+1)-dimensional generalized vcKP equation. The formulations of these solutions require a constraint on variable coefficients.

  11. Lie symmetry group of (2+1-dimensional Jaulent-Miodek equation

    Directory of Open Access Journals (Sweden)

    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.

  12. Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity

    CERN Document Server

    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.

  13. Particle Collision near 1+1 Dimensional Horava-Lifshitz Black Holes

    CERN Document Server

    Halilsoy, M

    2015-01-01

    The unbounded center-of-mass (CM) energy of colliding particles near horizon of a black hole emerges even in 1+1- dimensional Horava-Lifshitz gravity. The latter has imprints of renormalizable quantum gravity characteristics in accordance with simple power counting. The result obtained is valid also for a 1- dimensional Compton process between a massive/massless Hawking photon emaneting from the black hole and an in falling massless/massive particle.

  14. Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes

    OpenAIRE

    Clarkson, R.; Fatibene, L.; Mann, R. B.

    2002-01-01

    We consider the thermodynamic properties of $(d+1)$-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either $(d-1)$-dimensional (called "bolts") or of lower dimensionality (pure "NUTs"). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge meth...

  15. Improving the thin-disk models of circumstellar disk evolution. The 2+1-dimensional model

    Science.gov (United States)

    Vorobyov, Eduard I.; Pavlyuchenkov, Yaroslav N.

    2017-09-01

    Context. Circumstellar disks of gas and dust are naturally formed from contracting pre-stellar molecular cores during the star formation process. To study various dynamical and chemical processes that take place in circumstellar disks prior to their dissipation and transition to debris disks, the appropriate numerical models capable of studying the long-term disk chemodynamical evolution are required. Aims: We improve the frequently used 2D hydrodynamical model for disk evolution in the thin-disk limit by employing a better calculation of the disk thermal balance and adding a reconstruction of the disk vertical structure. Together with the hydrodynamical processes, the thermal evolution is of great importance since it influences the strength of gravitational instability and the chemical evolution of the disk. Methods: We present a new 2+1-dimensional numerical hydrodynamics model of circumstellar disk evolution, where the thin-disk model is complemented with the procedure for calculating the vertical distributions of gas volume density and temperature in the disk. The reconstruction of the disk vertical structure is performed at every time step via the solution of the time-dependent radiative transfer equations coupled to the equation of the vertical hydrostatic equilibrium. Results: We perform a detailed comparison between circumstellar disks produced with our previous 2D model and with the improved 2+1D approach. The structure and evolution of resulting disks, including the differences in temperatures, densities, disk masses, and protostellar accretion rates, are discussed in detail. Conclusions: The new 2+1D model yields systematically colder disks, while the in-falling parental clouds are warmer. Both effects act to increase the strength of disk gravitational instability and, as a result, the number of gravitationally bound fragments that form in the disk via gravitational fragmentation as compared to the purely 2D thin-disk simulations with a simplified

  16. Series of (2+1)-dimensional stable self-dual interacting conformal field theories

    Science.gov (United States)

    Cheng, Meng; Xu, Cenke

    2016-12-01

    Using the duality between seemingly different (2+1)-dimensional [(2 +1 )d ] conformal field theories (CFT) proposed recently [D. T. Son, Phys. Rev. X 5, 031027 (2015), 10.1103/PhysRevX.5.031027; M. A. Metlitski and A. Vishwanath, Phys. Rev. B 93, 245151 (2016), 10.1103/PhysRevB.93.245151; C. Wang and T. Senthil, Phys. Rev. X 6, 011034 (2015), 10.1103/PhysRevX.6.011034; C. Wang and T. Senthil, Phys. Rev. X 5, 041031 (2015), 10.1103/PhysRevX.5.041031; C. Wang and T. Senthil, Phys. Rev. B 93, 085110 (2016), 10.1103/PhysRevB.93.085110; C. Xu and Y.-Z. You, Phys. Rev. B 92, 220416 (2015), 10.1103/PhysRevB.92.220416; D. F. Mross et al., Phys. Rev. Lett. 117, 016802 (2016), 10.1103/PhysRevLett.117.016802; A. Karch and D. Tong, arXiv:1606.01893; N. Seiberg et al., arXiv:1606.01989; P.-S. Hsin and N. Seiberg, arXiv:1607.07457], we study a series of (2 +1 )d stable self-dual interacting CFTs. These CFTs can be realized (for instance) on the boundary of the 3 d bosonic topological insulator protected by U(1) and time-reversal symmetry (T ), and they remain stable as long as these symmetries are preserved. When realized as a boundary system, these CFTs can be driven into anomalous fractional quantum Hall states once T is broken. We demonstrate that the newly proposed dualities allow us to study these CFTs quantitatively through a controlled calculation, without relying on a large flavor number of matter fields. We also propose a numerical test for our results, which would provide strong evidence for the originally proposed duality between Dirac fermion and QED.

  17. Bulk-boundary correspondence in (3+1)-dimensional topological phases

    Science.gov (United States)

    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.

  18. Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Darabi, F. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Atazadeh, K.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of)

    2014-07-15

    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.)

  19. Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms

    CERN Document Server

    Casana, R; Mouchrek-Santos, V E; Silva, Edilberto O

    2015-01-01

    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.

  20. Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms

    Directory of Open Access Journals (Sweden)

    R. Casana

    2015-06-01

    Full Text Available 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.

  1. Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms

    Energy Technology Data Exchange (ETDEWEB)

    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.

  2. Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms

    Science.gov (United States)

    Casana, R.; Ferreira, M. M.; Mouchrek-Santos, V. E.; Silva, Edilberto O.

    2015-06-01

    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.

  3. The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

    CERN Document Server

    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.

  4. Symmetry Reductions of (2 + 1-Dimensional CDGKS Equation and Its Reduced Lax Pairs

    Directory of Open Access Journals (Sweden)

    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.

  5. Chaos and Fractals in a (2+1)-Dimensional Soliton System

    Institute of Scientific and Technical Information of China (English)

    郑春龙; 张解放; 盛正卯

    2003-01-01

    Considering that there are abundant coherent soliton excitations in high dimensions, we reveal a novel phenomenon that the localized excitations possess chaotic and fractal behaviour in some (2+1)-dimensional soliton systems. To clarify the interesting phenomenon, we take the generalized (2+1)-dimensional Nizhnik-NovikovVesselov system as a concrete example. A quite general variable separation solutions of this system is derived via a variable separation approach first, then some new excitations like chaos and fractals are derived by introducing some types of lower-dimensional chaotic and fractal patterns.

  6. Multisoliton Solutions of the (2+1)-Dimensional KdV Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jie-Fang; HUANG Wen-Hua

    2001-01-01

    Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2+1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations.``

  7. Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation

    Indian Academy of Sciences (India)

    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.

  8. Compacton, Peakon, and Foldon Structures in the (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jie-Fang; MENG Jian-Ping; WU Feng-Min; SI Jian-Qing

    2004-01-01

    By the use of the extended homogenous balance method, the Backlund transformation for a (2+1)-dimensional integrable model, the(2+ 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation, is obtained, and then the NNV equation is transformed into three equations of linear, bilinear, and tri-linear forms, respectively. From the above three equations, a rather general variable separation solution of the model is obtained. Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.

  9. Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation

    Institute of Scientific and Technical Information of China (English)

    JIANG Qiao-Yun; ZHOU Ru-Guang

    2006-01-01

    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.

  10. A new method to the(2+1)-dimensional modified KP equation

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    By means of the auxiliary ordinary differential equation method,we have obtained many solitary wave solutions,periodic wave solutions and variable separation solutions for the (2+1)-dimensional KP equation.Using a mixed method,many exact solutions have been obtained.

  11. Abundant new travelling wave solutions for the (2 + 1)-dimensional Sine-Gordon equation

    Energy Technology Data Exchange (ETDEWEB)

    Li Zhu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000 (China)], E-mail: lizhu1813@163.com; Dong Huanhe [College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510 (China)

    2008-07-15

    Abundant new travelling wave solutions of the (2 + 1)-dimensional Sine-Gordon equation are obtained by the generalized Jacobi elliptic function method. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions.

  12. Study on (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation by Using Extended Mapping Approach

    Institute of Scientific and Technical Information of China (English)

    XU Chang-Zhi; HE Bao-Gang

    2006-01-01

    Extended mapping approach is introduced to solve (2+1)-dimensional Nizhnik-Novikov-Veselov equation.A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation,rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.

  13. Symmetry Analysis of (2+1)-Dimensional Nonlinear Klein-Gordon Equations

    Institute of Scientific and Technical Information of China (English)

    唐晓艳; 楼森岳

    2002-01-01

    We have obtained two types of two-dimensional similarity reductions for the (2 +1)-dimensional Klein-Gordon system using the standard classical Lie group approach with computer algebra. The well-known one-dimensional reductions, radial and travelling reductions are equivalent to the two special cases of our general two-dimensional reductions.

  14. Variable Separation for (1+1)-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives

    Institute of Scientific and Technical Information of China (English)

    WANG Peng-Zhou; ZHANG Shun-Li

    2008-01-01

    We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A(u, ux)uxxx + B(u, ux) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.

  15. The exact solutions to (2+1)-dimensional nonlinear Schrǒdinger equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jin-liang; WANG Ming-liang; FANG Zong-de

    2004-01-01

    By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrǒdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.

  16. Folded localized excitations in the (2+1)-dimensional modified dispersive water-wave system

    Institute of Scientific and Technical Information of China (English)

    Lei Yan; Ma Song-Hua; Fang Jian-Ping

    2013-01-01

    By using a mapping approach and a linear variable separation approach,a new family of solitary wave solutions with arbitrary functions for the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived.Based on the derived solutions and using some multi-valued functions,we obtain some novel folded localized excitations of the system.

  17. Nonpropagating Solitons in (2+1)-Dimensional Dispersive Long-Water Wave System

    Institute of Scientific and Technical Information of China (English)

    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.

  18. Peakon Excitations and Fractal Dromions for General (2+1)-Dimensional Korteweg de Vries System

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived. Based on the derived solitary wave excitation, we obtain some special peakon excitations and fractal dromions in this short note.

  19. New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    CHEN Huai-Tang; ZHANG Hong-Qing

    2004-01-01

    A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+ 1 )-dimensional Burgers equation with variable coefficients.

  20. Exact Solutions of Some (1+1)-Dimensional Nonlinear Evolution Equations

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    By means of the variable separation method, new exact solutions of some (1+1)-dimensional nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.

  1. Localized Excitations in a Sixth-Order (1+1)-Dimensional Nonlinear Evolution Equation

    Institute of Scientific and Technical Information of China (English)

    SHEN Shou-Feng

    2005-01-01

    In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.

  2. Variable Separation Solutions for the (2+1)-Dimensional Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  3. New and More General Rational Formal Solutions to (2+1)-Dimensional Toda System

    Institute of Scientific and Technical Information of China (English)

    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.

  4. Symbolic Computation and q-Deformed Function Solutions of (2+1)-Dimensional Breaking Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    CAO Li-Na; WANG Deng-Shan; CHEN Lan-Xin

    2007-01-01

    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.

  5. Methods of numerical analysis of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics

    Science.gov (United States)

    Klimenko, S. V.; Nikitin, I. N.; Urazmetov, W. F.

    2000-04-01

    Numerical methods for solution of differential equations with deviating arguments describing 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with half-retarded/halfadvanced interaction (Wheeler and Feynman, 1949) are developed. A bifurcation of solutions and violation of their reflectional symmetries in the region of velocities v>0.937c are found in numerical analysis.

  6. Quantization of point particles in (2+1)-dimensional gravity and spacetime discreteness

    NARCIS (Netherlands)

    Hooft, G. 't

    1996-01-01

    By investigating the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world it is found that these particles live on a space-time lattice. The space-time lattice points can be characterized by three integers. Various representations are possible, the details depen

  7. New Exact Solutions of the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces

    Institute of Scientific and Technical Information of China (English)

    LI De-Sheng; ZHANG Hong-Qing

    2004-01-01

    In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.

  8. New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations

    Institute of Scientific and Technical Information of China (English)

    BAI Cheng-Lin; LIU Xi-Qiang; ZHAO Hong

    2005-01-01

    In this paper, two (3+1)-dimensional equations are investigated. A uto-Backlund 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.

  9. Periodic Homoclinic Wave of (1+1)-Dimensional Long-Short Wave Equation

    Institute of Scientific and Technical Information of China (English)

    LI Dong-Long; DAI Zheng-De; GUO Yan-Feng

    2008-01-01

    @@ The exact periodic homoclinic wave of (1+1) D long-short wave equation is obtained using an extended homoclinic test technique.This result shows complexity and variety of dynamical behaviour for a (1+1)-dimensional longshort wave equation.

  10. Annihilation Solitons and Chaotic Solitons for the (2+1)-Dimensional Breaking Soliton System

    Institute of Scientific and Technical Information of China (English)

    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.

  11. New Exact Solutions and Localized Structures for (3+1)-Dimensional Burgers System

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jing-Shang; LI Jiang-Bo; MA Song-Hua; REN Qing-Bao; FANG Jian-Ping; ZHENG Chun-Long

    2008-01-01

    With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensional Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.

  12. Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  13. A note on the Painleve analysis of a (2 + 1) dimensional Camassa-Holm equation

    Energy Technology Data Exchange (ETDEWEB)

    Gordoa, P.R. [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, C/Tulipan s/n, 28933 Mostoles, Madrid (Spain); Pickering, A. [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, C/Tulipan s/n, 28933 Mostoles, Madrid (Spain); Senthilvelan, M. [Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirappalli 620 024 (India)]. E-mail: senthilvelan@cnld.bdu.ac.in

    2006-06-15

    We investigate the Painleve analysis for a (2 + 1) dimensional Camassa-Holm equation. Our results show that it admits only weak Painleve expansions. This then confirms the limitations of the Painleve test as a test for complete integrability when applied to non-semilinear partial differential equations.

  14. New Families of Exact Solutions for (2+1)-Dimensional Broer-Kaup System

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hong; BAI Cheng-Lin; HAN Ji-Guang

    2005-01-01

    Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.

  15. Conservation laws for two (2 + 1)-dimensional differential-difference systems

    Energy Technology Data Exchange (ETDEWEB)

    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.

  16. Backlünd transformation and multiple soliton solutions for the (3+1)-dimensional Nizhnik Novikov-Veselov equation

    Institute of Scientific and Technical Information of China (English)

    Bai Cheng-Lin

    2004-01-01

    @@ We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions.

  17. Investigation of 1-Dimensional ultrasonic vibration compliance mechanism based on finite element analysis

    Science.gov (United States)

    Latif, A. Afiff; Ibrahim, M. Rasidi; Rahim, E. A.; Cheng, K.

    2017-04-01

    The conventional milling has many difficulties in the processing of hard and brittle material. Hence, ultrasonic vibration assisted milling (UVAM) was proposed to overcome this problem. The objective of this research is to study the behavior of compliance mechanism (CM) as the critical part affect the performance of the UVAM. The design of the CM was investigated and focuses on 1-Dimensional. Experimental result was obtained from a portable laser digital vibrometer. While the 1-Dimensional value such as safety factor, deformation of hinges and stress analysis are obtained from finite elements simulation. Finally, the findings help to find the best design judging from the most travelled distance of the piezoelectric actuators. In addition, this paper would provide a clear picture the behavior of the CM embedded in the UVAM, which can provide good data and to improve the machining on reducing tool wear, and lower cutting force on the workpiece surface roughness.

  18. Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations

    Science.gov (United States)

    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

  19. (3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material

    Institute of Scientific and Technical Information of China (English)

    Hu Yong-Hua; Fu Xi-Quan; Wen Shuang-Chun; Su Wen-Hua; Fan Dian-Yuan

    2006-01-01

    In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized (3+1)-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material (RHM) and left-handed material (LHM) is derived. By the commonly used Drude dispersive model for LHM, a (3+1)-dimensional nonlinear Schr(o)dinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.

  20. New periodic wave solutions, localized excitations and their interaction for (2+1)-dimensional Burgers equation

    Institute of Scientific and Technical Information of China (English)

    Ma Hong-Cai; Ge Dong-Jie; Yu Yao-Dong

    2008-01-01

    Based on the B(a)cklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+1)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution).

  1. Integrability and chemical potential in the (3 + 1)-dimensional Skyrme model

    Science.gov (United States)

    Alvarez, P. D.; Canfora, F.; Dimakis, N.; Paliathanasis, A.

    2017-10-01

    Using a remarkable mapping from the original (3 + 1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions-anti-Skyrmions bound states within a finite box in 3 + 1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions-anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.

  2. Interactions Among Peakons,Dromions,and Compactons for a (2+1)-Dimensional Soliton System

    Institute of Scientific and Technical Information of China (English)

    ZHENG Chun-Long

    2004-01-01

    Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary waves like peakons,dromions,and compactons are investigated and some novel features or interesting behaviors are revealed.The results show that the interactions for peakon-dromion,compacton-dromion,and peakon-compacton may be completely nonelastic or completely elastic.

  3. Embed-Solitons and Their Evolutional Behaviors of (3+1)-Dimensional Burgers System

    Institute of Scientific and Technical Information of China (English)

    ZHU Hai-Ping; ZHENG Chun-Long

    2007-01-01

    With the help of an extended mapping approach and a linear variable separation method, new families of variable separation solutions with arbitrary functions for the (3+1)-dimensional Burgers system are derived. Based on thc derived exact solutions, some novel and interesting localized coherent excitations such as embed-solitons are revealed by selecting appropriate boundary conditions and/or initial qualifications. The time evolutional properties of the novel localized excitation are also briefly investigated.

  4. Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation

    Science.gov (United States)

    Aksoy, Esin; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.

    2016-06-01

    Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation are studied by the generalized Kudryashov method, the exp-function method and the (G'/G)-expansion method. The solutions obtained include the form of hyperbolic functions, trigonometric and rational functions. These methods are effective, simple, and many types of solutions can be obtained at the same time.

  5. New Complexiton Solutions of (1+1)-Dimensional Dispersive Long Wave Equation

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1 )-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.

  6. New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yuan-Yuan; ZHENG Ying; ZHANG Hong-Qing

    2006-01-01

    In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.

  7. Double Elliptic Equation Expansion Approach and Novel Solutions of (2+1)-Dimensional Break Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    ZHAO Xue-Qin; SUN Wei-Kun; ZHI Hong-Yan; CAO Nan-Bin; SHEN Ya-Liang

    2008-01-01

    In this paper, by means of double elliptic equation expansion approach, the novel double nonlinear wave solutions of the (2+1)-dimensional break soliton equation are obtained. These double nonlinear wave solutions contain the double Jacobi elliptic function-like solutions, the double solitary wave-like solutions, and so on. The method is also powerful to some other nonlinear wave equations in (2+1) dimensions.

  8. New Types of Travelling Wave Solutions From (2+1)-Dimensional Davey-Stewartson Equation

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hong

    2006-01-01

    In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixth-degree nonlinear term, we study the (2+1)-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.

  9. A study of geodesic motion in a (2+1)-dimensional charged BTZ black hole

    CERN Document Server

    Soroushfar, Saheb; Jafari, Afsaneh

    2015-01-01

    This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions. Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential.

  10. Interaction between compacton an danticompacton,peakon and antipeakon in(2+1)-dimensional spaces

    Institute of Scientific and Technical Information of China (English)

    韩平; 张解放; 孟剑平

    2003-01-01

    Starting from the variable separation solution obtained by using the extended homogenous balance method, a class of novel localized coherent structures such as the multi-peakon-antipeakons solution and the multi-compactonanticompactons solution of the (2 + 1)-dimensional dispersive long wave equation are found by selecting appropriate functions. These new structures exhibit some novel interaction features that are different from one of the known results.Their interaction behaviour is very similar to the completely elastic collisions between two classical particles.

  11. Symmetry Analysis and Exact Solutions of (2+1)-Dimensional Sawada-Kotera Equation

    Institute of Scientific and Technical Information of China (English)

    YU Jian-Ping; ZHI Hong-Yan; SUN Yong-Li; ZHANG Hong-Qing

    2008-01-01

    Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the (2+1)-dimensional Sawada Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou's direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada Kotera and Konopelchenko Dubrovsky equations, respectively.

  12. (3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator

    Institute of Scientific and Technical Information of China (English)

    LUO Xiang-Qian; XU Hao; YANG Jie-Chao; WANG Yu-Li; CHANG Di; LIN Yin; Helmut Kroger

    2001-01-01

    In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``

  13. Extended Complex tanh-Function Method and Exact Solutions to (2+1)-Dimensional Hirota Equation

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hong

    2007-01-01

    In this paper,a new extended complex tanh-function method is presented for constructing traveling wave,non-traveling wave,and coefficient functions' soliton-like solutions of nonlinear equations.This method is nore powerful than the complex tanh-function method [Chaos,Solitons and Fractals 20 (2004) 1037].Abundant new solutions of (2+1)-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.

  14. Painlevé Analysis and Some Solutions of(2+1)-Dimensional Generalized Burgers Equations

    Institute of Scientific and Technical Information of China (English)

    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.

  15. Doubly Periodic Propagating Wave for (2+1)-Dimensional Breaking Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    WANG Yi-Hong; HUANG Wen-Hua; WANG Sheng-Kui; LIU Yu-Lu; ZHANG Jie-Fang

    2008-01-01

    Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two famines of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi e11iptic function waves are graphically considered and found to be nonelastic.

  16. Rich Localized Coherent Structures of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation

    Institute of Scientific and Technical Information of China (English)

    LI Hua-Mei

    2003-01-01

    Using a Backlund transformation and the variable separation approach, we find there exist abundant localized coherent structures for the (2 + 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system. The abundance of the localized structures for the model is introduced by the entrance of an arbitrary function of the seed solution. For some specialselections of the arbitrary function, it is shown that the localized structures of the BKK equation may be dromions, lumps, ring solitons, peakons, or fractal solitons etc.

  17. New Similarity Reduction Solutions for the (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation

    Institute of Scientific and Technical Information of China (English)

    ZHI Hong-Yan

    2013-01-01

    In this paper,some new formal similarity reduction solutions for the (2+ 1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.

  18. Quasi-periodic and Non-periodic Waves in (2+1)-Dimensional Nonlinear Systems

    Institute of Scientific and Technical Information of China (English)

    TANG Xiao-Yan; LOU Sen-Yue

    2005-01-01

    New exact quasi-periodic and non-periodic solutions for the (2 + 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.

  19. New Exact Solutions to (2+1)-Dimensional Variable Coefficients Broer-Kaup Equations

    Institute of Scientific and Technical Information of China (English)

    ZHU Jia-Min; MA Zheng-Yi

    2006-01-01

    In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions.Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.

  20. The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation

    Institute of Scientific and Technical Information of China (English)

    CHENG Zhi-long; HAO Xiao-hong

    2015-01-01

    Based on the travelling wave method, a (2+1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.

  1. Counter-rotational effects on stability of 2 + 1-dimensional thin-shell wormholes

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  2. A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction

    Directory of Open Access Journals (Sweden)

    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.

  3. Fission and Fusion of Solitons for the (1+1)-Dimensional Kupershmidt Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  4. Pair production of Dirac particles in a d+1-dimensional noncommutative space-time

    CERN Document Server

    Samary, Dine Ousmane; Hounkonnou, Mahouton Norbert

    2014-01-01

    This work addresses the exact computation of the propability of fermionic particle pair production in $(d+1)-$ dimensional noncommutative Moyal space. Using the Seiberg-Witten maps that establish relations between noncommutative and commutative field variables, to first order in the noncommutative parameter $\\theta$, 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.

  5. Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  6. Non-completely elastic interactions in a (2+1)-dimensional dispersive long wave equation

    Institute of Scientific and Technical Information of China (English)

    Chen Wei-Lu; Zhang Wen-Ting; Zhang Li-Pu; Dai Chao-Qing

    2012-01-01

    With the help of a modified mapping method,we obtain two kinds of variable separation solutions with two arbitrary functions for the (2+1)-dimensional dispersive long wave equation.When selecting appropriate multi-valued functions in the variable separation solution,we investigate the interactions among special multi-dromions,dromion-like multi-peakons,and dromion-like multi-semifoldons,which all demonstrate non-completely elastic properties.

  7. Interaction Behaviors Between Special Dromions in the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation

    Institute of Scientific and Technical Information of China (English)

    CHEN Wei-Lu; ZHANG Wen-Ting; ZHANG Li-Pu; DAI Chao-Qing

    2013-01-01

    A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting appropriate functions,we discuss the completely elastic head-on collision between two dromion-lattices,non-completely elastic "chase and collision" between two multi-dromion-pairs and completely non-elastic interaction phenomenon between anti-dromion and dromion-pair.

  8. Relaxation of 2+1 dimensional classical O(2) symmetric scalar fields

    CERN Document Server

    Borsanyi, S; Borsanyi, Sz.; Szep, Zs.

    2001-01-01

    Real time thermalization and relaxation phenomena are studied in the low energy density phase of the 2+1 dimensional classical O(2) symmetric scalar theory by solving numerically its dynamics. The near-equilibrium decay rate of on-shell waves and the power law governing the large time asymptotics of the off-shell relaxation agree with the analytic results based on linear response theory. The realisation of the Mermin-Wagner theorem is also studied in the final equilibrium ensemble.

  9. The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations

    Indian Academy of Sciences (India)

    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.

  10. Searching for the (3+1)-Dimensional Painlevé Integrable Model and its Solitary Wave Solution

    Institute of Scientific and Technical Information of China (English)

    李画眉

    2002-01-01

    A (3+1)-dimensional integrable model constructed by conformal invariants is proven to be integrable. The solitary wave solution of the model is obtained by a simple algebraic transformation relation between the (3 + 1)-dimensional Harry-Dym equation and the cubic nonlinear Klein-Gordon equation.

  11. A Bilinear B(a)cklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  12. New Multiple Soliton-like and Periodic Solutions for (2+1)-Dimensional Canonical Generalized KP Equation with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    ZHANG Li-Hua; LIU Xi-Qiang; BAI Cheng-Lin

    2006-01-01

    In this paper, the generalized tanh function method is extended to (2+1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional CGKP equation with variable coefficients.

  13. Critical behavior of (2 +1 )-dimensional QED: 1 /Nf corrections in the Landau gauge

    Science.gov (United States)

    Kotikov, A. V.; Shilin, V. I.; Teber, S.

    2016-09-01

    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 flavor number, Nc. It is found that the dynamical fermion mass appears for N

  14. Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  15. Complexiton solutions of the (2+1)-dimensional dispersive long wave equation

    Institute of Scientific and Technical Information of China (English)

    Chen Yong; Fan En-Gui

    2007-01-01

    In this pager a pure algebraic method implemented in a computer algebraic system, named multiple Riccati equations rational expansion method, is presented to construct a novel class of complexiton solutions to integrable equations and nonintegrable equations. By solving the (2+1)-dimensional dispersive long wave equation, it obtains many new types of complexiton solutions such as various combination of trigonometric periodic and hyperbolic function solutions,various combination of trigonometric periodic and rational function solutions, various combination of hyperbolic and rational function solutions, etc.

  16. (2+1)-Dimensional Combined Structures of Various Solitons with Completely Nonelastic Interaction Properties

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jie-Fang; MENG Jian-Ping

    2004-01-01

    Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidromion solution, multi-peakon and multi-compacton solution, for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are found by selecting appropriate functions. These new structures exhibit novel interaction features. Their interaction behavior is very similar to the completely nonelastic collisions between two classical particles.

  17. Canonical Formulation of A Bosonic Matter Field in 1+1 Dimensional Curved Space

    CERN Document Server

    Ghalati, R N; Sherry, T N

    2006-01-01

    We study a Bosonic scalar in 1+1 dimensional curved space that is coupled to a dynamical metric field. This metric, along with the affine connection, also appears in the Einstein-Hilbert action when written in first order form. After illustrating the Dirac constraint analysis in Yang-Mills theory, we apply this formulation to the Einstein-Hilbert action and the action of the Bosonic scalar field, first separately and then together. Only in the latter case does a dynamical degree of freedom emerge.

  18. Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime

    CERN Document Server

    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.

  19. Lump Solutions for the (3+1)-Dimensional Kadomtsev-Petviashvili Equation

    Science.gov (United States)

    Liu, De-Yin; Tian, Bo; Xie, Xi-Yang

    2016-12-01

    In this article, we investigate the lump solutions for the Kadomtsev-Petviashvili equation in (3+1) dimensions that describe the dynamics of plasmas or fluids. Via the symbolic computation, lump solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are derived based on the bilinear forms. The conditions to guarantee analyticity and rational localisation of the lump solutions are presented. The lump solutions contain eight parameters, two of which are totally free, and the other six of which need to satisfy the presented conditions. Plots with particular choices of the involved parameters are made to show the lump solutions and their energy distributions.

  20. APPLICATION OF EXP-FUNCTION METHOD TO THE (2+1-DIMENSIONAL CALOGERO BOGOYAVLANSKII SCHIFF EQUATION

    Directory of Open Access Journals (Sweden)

    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.

  1. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn

    2013-12-06

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.

  2. Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity

    CERN Document Server

    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.

  3. Dirac Field as a Source of the Inflation in 2+1 Dimensional Teleparallel Gravity

    Directory of Open Access Journals (Sweden)

    Ganim Gecim

    2017-01-01

    Full Text Available In this paper, we study early-time inflation and late-time acceleration of the universe by nonminimally coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW cosmological model background. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with that of the 3+1 dimensional teleparallel gravity under Noether symmetry approach. And we see that the study explains early-time inflation and late-time acceleration of the universe.

  4. A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

    Energy Technology Data Exchange (ETDEWEB)

    Wang Qi [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China); Chen Yong [M.M. Key Lab, Chinese Academy of Sciences, Beijing 100080 (China); Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China); E-mail: chenyong@dlut.edu.cn; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)

    2005-09-01

    In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution 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. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation.

  5. Holographic conductivity of 1+1 dimensional systems in soft wall model

    CERN Document Server

    Bhatnagar, Neha

    2016-01-01

    We study the optical conductivity of 1+1 dimensional systems using soft wall model in the bottom up approach of AdS/CFT (anti-de Sitter/conformal field theory) duality. We find the numerical results for optical conductivity and investigate the system using holographic model in the probe limit. The dependence of conductivity on chemical potential is also investigated. Further, we extend the soft wall model as a `no-wall' model by eliminating the dilaton background and study the response of the system in a simplified approach.

  6. Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model

    CERN Document Server

    Kelling, Jeffrey; Gemming, Sibylle

    2016-01-01

    Local Scale-Invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2+1 dimensional Kardar-Parisi-Zhang surfaces. Very precise measurements of the universal autoresponse function enabled us to perform nonlinear fitting with the scaling forms, suggested by local scale-invariance (LSI). While the simple LSI ansatz does not seem to work, forms based on logarithmic extension of LSI provide satisfactory description of the full (measured) time evolution of the autoresponse function.

  7. Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

    Institute of Scientific and Technical Information of China (English)

    Wang Yun-Hu; Chen Yong

    2013-01-01

    We investigate the extended (2+1)-dimensional shallow water wave equation.The binary Bell polynomials are used to construct bilinear equation,bilinear B(a)cklund transformation,Lax pair,and Darboux covariant Lax pair for this equation.Moreover,the infinite conservation laws of this equation are found by using its Lax pair.All conserved densities and fluxes are given with explicit recursion formulas.The N-soliton solutions are also presented by means of the Hirota bilinear method.

  8. Periodic Semifolded Solitary Waves for (2+1)-Dimensional Variable Coefficient Broer-Kaup System

    Institute of Scientific and Technical Information of China (English)

    JI Jie; HUANG Wen-Hua

    2008-01-01

    Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the (2+1)-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.

  9. Lump and lump-soliton solutions to the (2+1) -dimensional Ito equation

    Science.gov (United States)

    Yang, Jin-Yun; Ma, Wen-Xiu; Qin, Zhenyun

    2017-06-01

    Based on the Hirota bilinear form of the (2+1) -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.

  10. Interaction Solutions for (1+1)-Dimensional Higher-Order Broer—Kaup System

    Science.gov (United States)

    Xin, Xiang-Peng; Liu, Xi-Qiang

    2016-11-01

    The (1+1)-dimensional higher-order Broer—Kaup (HBK) system is studied by consistent tanh expansion (CTE) method in this paper. It is proved that the HBK system is CTE solvable, and some exact interaction solutions among different nonlinear excitations such as solitons, rational waves, periodic waves, corresponding images are explicitly given. Supported by National Natural Science Foundation of China under Grant Nos. 11505090, 11171041, 11405103, 11447220, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009

  11. A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation

    Institute of Scientific and Technical Information of China (English)

    YANG Zong-Hang

    2006-01-01

    An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guideline to classify the various types of the solution according to some parameters.

  12. Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation

    Institute of Scientific and Technical Information of China (English)

    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.

  13. Lorentz contraction of bound states in 1+1 dimensional gauge theory

    Science.gov (United States)

    Järvinen, M.

    2004-09-01

    We consider the Lorentz contraction of a fermion-antifermion bound state in 1+1 dimensional QED. In 1+1 dimensions the absence of physical, propagating photons allows us to explicitly solve the weak coupling limit α≪m2 of the Bethe-Salpeter bound state equation in any Lorentz frame. In a time-ordered formalism it is seen that all pair production is suppressed in this limit. The wave function is shown to contract while the mass spectrum is invariant under boosts.

  14. Embedded-Soliton and Complex Wave Excitations of (3+1)-Dimensional Burgers System

    Institute of Scientific and Technical Information of China (English)

    ZHAO Ren; ZHU Hai-Ping; ZHANG Li-Chun; PAN Zhen-Huan; WU Yue-Qin; ZHENG Chun-Long; LI Huai-Fan

    2008-01-01

    Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the (3+1 )-dimensional Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.

  15. Gauss integration over relativistic 3-body phase space for 1-dimensional distributions of 2 --> 3 reaction

    CERN Document Server

    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.

  16. LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    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.

  17. Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation

    Institute of Scientific and Technical Information of China (English)

    Zhang Wen-Ting; Dai Chao-Qing; Chen Wei-Lu

    2013-01-01

    With the help of a modified mapping method and a new mapping method,we re-study the (3+ 1)-dimensional Burgers equation,and derive two families of variable separation solutions.By selecting appropriate functions in the variable separation solution,we discuss the interaction behaviors among taper-like,plateau-type rings,and rectangle-type embed-solitons in the periodic wave background.All the interaction behaviors are completely elastic,and no phase shift appears after interaction.

  18. Symmetry Groups and Exact Solutions of New (4+1)-Dimensional Fokas Equation

    Institute of Scientific and Technical Information of China (English)

    YANG Zheng-Zheng; YAN Zhen-Ya

    2009-01-01

    In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symme-tries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries and some constructive methods to get some doubly periodic wave solutions and other solutions of the Fokas equation. In particular, some solitary wave solutions are also given.

  19. Dynamics of Nth-order rogue waves in $(2 + 1)$-dimensional Hirota equation

    Indian Academy of Sciences (India)

    HANG GAO

    2017-06-01

    Inspired by the works of Ohta and Yang, we construct general high-order rogue wave solutions for the $(2 + 1)$-dimensional Hirota equation using the bilinear transformation method. The formula of the solutions can be represented in terms of determinants. It is shown that the order of rogue waves will depend on the roots of determinants. These rogue waves are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. In addition, some interesting dynamic patterns of rogue waves are exhibited in the $(x, y)$ and $(x, t)$ planes.

  20. (2+1)-Dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory

    Science.gov (United States)

    Xu, Wei; Zou, De-Cheng

    2017-06-01

    In (2+1)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter k=1 and k≠1), in the Einstein-Power-Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with k≠1, we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.

  1. Exact periodic waves and their interactions for the (2+1)-dimensional KdV equation

    Indian Academy of Sciences (India)

    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.

  2. Quantum Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity

    CERN Document Server

    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\

  3. Thermodynamics of (d+1)-dimensional NUT-charged AdS spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Clarkson, R. E-mail: rick@avatar.uwaterloo.ca; Fatibene, L. E-mail: fatibene@dm.unito.it; Mann, R.B. E-mail: mann@avatar.uwaterloo.ca

    2003-03-03

    We consider the thermodynamic properties of (d+1)-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti-de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either (d-1)-dimensional (called 'bolts') or of lower dimensionality (pure 'NUTs'). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge methods and the AdS/CFT-inspired counterterm approach. We then generalize these results to arbitrary dimensionality. We find in 4k+2 dimensions that there are no regions in parameter space in the pure NUT case for which the entropy and specific heat are both positive, and so all such spacetimes are thermodynamically unstable. For the pure NUT case in 4k dimensions a region of stability exists in parameter space that decreases in size with increasing dimensionality. All bolt cases have some region of parameter space for which thermodynamic stability can be realized.

  4. Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes

    CERN Document Server

    Clarkson, R; Mann, R B

    2003-01-01

    We consider the thermodynamic properties of $(d+1)$-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either $(d-1)$-dimensional (called "bolts") or of lower dimensionality (pure "NUTs"). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge methods and the AdS/CFT-inspired counterterm approach. We then generalize these results to arbitrary dimensionality. We find in $4k+2$ dimensions that there are no regions in parameter space in the pure NUT case for which the entropy and specific heat are both positive, and so all such spacetimes are thermodynamically unstable. For the pure NUT case in $4k$ dimensions a region of stability exists in parameter space that decreases in size with increasing dimensionality. All bolt cases have some region of parameter space for wh...

  5. Lump Solutions and Interaction Phenomenon for (2+1)-Dimensional Sawada-Kotera Equation

    Science.gov (United States)

    Huang, Li-Li; Chen, Yong

    2017-05-01

    In this paper, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the (2+1)-dimensional Sawada-Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11675054 and 11435005, Outstanding Doctoral Dissertation Cultivation Plan of Action under Grant No. YB2016039, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213

  6. Some New Exact Solutions to the Dispersive Long-Wave Equation in(2+1)-Dimensional Spaces

    Institute of Scientific and Technical Information of China (English)

    LI De-Sheng; ZHANG Hong-Qing

    2003-01-01

    In this paper, by using a further extended tanh method and symbolic computation system, some newsoliton-like and period form solutions of the dispersive long-wave equation in (2+1)-dimensional spaces are obtained.

  7. Exact Solutions of Generalized Boussinesq-Burgers Equations and (2+1-Dimensional Davey-Stewartson Equations

    Directory of Open Access Journals (Sweden)

    Isaiah Elvis Mhlanga

    2012-01-01

    Full Text Available We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and (2+1-dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+1-dimensional Davey-Stewartson equations.

  8. AUTO-BÄCKLUND Transformation and New Exact Solutions of the (2 + 1)-DIMENSIONAL Nizhnik-Novikov Equation

    Science.gov (United States)

    Wang, Dengshan; Zhang, Hong-Qing

    In this paper, making use of the truncated Laurent series expansion method and symbolic computation we get the auto-Bäcklund transformation of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation. As a result, single soliton solution, single soliton-like solution, multi-soliton solution, multi-soliton-like solution, the rational solution and other exact solutions of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation are found. These solutions may be useful to explain some physical phenomena.

  9. Variable Separation Solution for (1+1)-Dimensional Nonlinear Models Related to Schr(o)dinger Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  10. Declination Calculator

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — Declination is calculated using the current International Geomagnetic Reference Field (IGRF) model. Declination is calculated using the current World Magnetic Model...

  11. Casimir interaction between spheres in $\\boldsymbol{(D+1)}$-dimensional Minkowski spacetime

    CERN Document Server

    Teo, L P

    2014-01-01

    We consider the Casimir interaction between two spheres in $(D+1)$-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coordinate frames differ by a translation, we generalize the operator approach employed in [IEEE Trans. Antennas Propag. \\textbf{36}, 1078 (1988)]. The result is expressed in terms of an integral over Gegenbauer polynomials. Using our expression for the Casimir interaction energy, we derive the large separation and small separation asymptotic expansions of the Casimir interaction energy. In the large separation regime, we find that the Casimir interaction energy is of order $L^{-2D+3}$, $L^{-2D+1}$ and $L^{-2D-1}$ respectively for Dirichlet-Di...

  12. Painlevé Integrability and New Exact Solutions of the (4 + 1-Dimensional Fokas Equation

    Directory of Open Access Journals (Sweden)

    Sheng Zhang

    2015-01-01

    Full Text Available The Painlevé integrability of the (4+1-dimensional Fokas equation is verified by the WTC method of Painlevé analysis combined with a new and more general transformation. By virtue of the truncated Painlevé expansion, two new exact solutions with arbitrary differentiable functions are obtained. Thanks to the arbitrariness of the included functions, the obtained exact solutions not only possess rich spatial structures but also help to bring about two-wave solutions and three-wave solutions. It is shown that the transformation adopted in this work plays a key role in testing the Painlevé integrability and constructing the exact solutions of the Fokas equation.

  13. Regularization strategy for an inverse problem for a 1 + 1 dimensional wave equation

    Science.gov (United States)

    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.

  14. Critical behavior of (2 +1 )-dimensional QED: 1 /Nf corrections in an arbitrary nonlocal gauge

    Science.gov (United States)

    Kotikov, A. V.; Teber, S.

    2016-12-01

    Dynamical chiral symmetry breaking (D χ SB ) is studied within (2 +1 )-dimensional QED with N four-component fermions. The leading and next-to-leading orders of the 1 /N expansion are computed exactly. The analysis is carried out in an arbitrary nonlocal gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavor number, Nc(ξ ), where ξ is the gauge-fixing parameter, which is such that D χ SB takes place for N Feynman gauge, Nc(0 )=3.0844 in the Landau gauge, and Nc(2 /3 )=3.0377 in the ξ =2 /3 gauge where the leading order fermion wave function is finite. These results suggest that D χ SB should take place for integer values N ≤3 .

  15. The GUP effect on Hawking radiation of the 2 + 1 dimensional black hole

    Science.gov (United States)

    Gecim, Ganim; Sucu, Yusuf

    2017-10-01

    We investigate the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation of the 2 + 1 dimensional Martinez-Zanelli black hole by using the Hamilton-Jacobi method. In this connection, we discuss the tunneling probabilities and Hawking temperature of the spin-1/2 and spin-0 particles for the black hole. Therefore, we use the modified Klein-Gordon and Dirac equations based on the GUP. Then, we observe that the Hawking temperature of the scalar and Dirac particles depend on not only the black hole properties, but also the properties of the tunneling particle, such as angular momentum, energy and mass. And, in this situation, we see that the tunneling probability and the Hawking radiation of the Dirac particle is different from that of the scalar particle.

  16. Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation

    Indian Academy of Sciences (India)

    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.

  17. Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness

    Energy Technology Data Exchange (ETDEWEB)

    Ammon, A. [IVU-Traffic Technologies AG, Berlin (Germany); Hartung, T. [King' s College London (United Kingdom). Dept. of Mathematics; Jansen, K.; Volmer, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leoevey, H. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik

    2016-08-15

    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≤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.

  18. Noether Gauge Symmetry of Dirac Field in (2 + 1-Dimensional Gravity

    Directory of Open Access Journals (Sweden)

    Ganim Gecim

    2015-01-01

    Full Text Available We consider a gravitational theory including a Dirac field that is nonminimally coupled to gravity in 2 + 1 dimensions. Noether gauge symmetry approach can be used to fix the form of coupling function F(Ψ and the potential V(Ψ of the Dirac field and to obtain a constant of motion for the dynamical equations. In the context of (2 + 1-dimensional gravity, we investigate cosmological solutions of the field equations using these forms obtained by the existence of Noether gauge symmetry. In this picture, it is shown that, for the nonminimal coupling case, the cosmological solutions indicate both an early-time inflation and late-time acceleration for the universe.

  19. $(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory

    CERN Document Server

    Xu, Wei

    2014-01-01

    We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.

  20. Gravitational collapse in 2+1 dimensional AdS spacetime

    CERN Document Server

    Pretorius, F; Pretorius, Frans; Choptuik, Matthew W.

    2000-01-01

    We present results of numerical simulations of the formation of black holes from the gravitational collapse of a massless, minimally-coupled scalar field in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The geometry exterior to the event horizon approaches the BTZ solution, showing no evidence of scalar `hair'. To study the interior structure we implement a variant of black-hole excision, which we call singularity excision. We find that interior to the event horizon a strong, spacelike curvature singularity develops. We study the critical behavior at the threshold of black hole formation, and find a continuously self-similar solution and corresponding mass-scaling exponent of approximately 1.2. The critical solution is universal to within a phase that is related to the angle deficit of the spacetime.

  1. Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

    Science.gov (United States)

    Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

    2016-12-01

    Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

  2. An Eternal Time Machine in 2+1 Dimensional anti-de Sitter Space

    CERN Document Server

    De Deo, S

    2002-01-01

    2+1 dimensional anti-de Sitter space has been the subject of much recent investigation. Studies of the behaviour of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological identification of adS isometries. In this paper, we present a new configuration of two orbiting massive point particles that leads to an ``eternal'' time machine, where closed timelike curves fill the entire space. In contrast to previous solutions, this configuration has no event or chronology horizons. Another interesting feature is that there is no lower bound on the relative velocities of the point masses used to construct the time machine; as long as the particles exceed a certain mass threshold, an eternal time machine will be produced.

  3. Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness

    CERN Document Server

    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.

  4. BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term

    CERN Document Server

    Huang, Yong-Chang; Lee, Xi-Guo

    2006-01-01

    We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

  5. (N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

    Science.gov (United States)

    Arshad, Muhammad; Lu, Dianchen; Wang, Jun

    2017-07-01

    In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

  6. Chiral density wave versus pion condensation in the 1+1 dimensional NJL model

    CERN Document Server

    Adhikari, Prabal

    2016-01-01

    In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $\\mu$ using dimensional regularization. The phase diagram in the $\\mu$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $\\mu>\\mu_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential $\\mu_I$. The phase diagram in the $\\mu_I$--$\\mu$ plane is mapped out and shows a rich phase structure.

  7. A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations

    CERN Document Server

    Cooperman, Joshua H; Miller, Jonah M

    2016-01-01

    Studying transition amplitudes in (2+1)-dimensional causal dynamical triangulations, Cooperman and Miller discovered speculative evidence for Lorentzian quantum geometries emerging from its Euclidean path integral. On the basis of this evidence, Cooperman and Miller conjectured that Lorentzian de Sitter spacetime, not Euclidean de Sitter space, dominates the ground state of the quantum geometry of causal dynamical triangulations on large scales, a scenario akin to that of the Hartle-Hawking no-boundary proposal in which Lorentzian spacetimes dominate a Euclidean path integral. We argue against this conjecture: we propose a more straightforward explanation of their findings, and we proffer evidence for the Euclidean nature of these seemingly Lorentzian quantum geometries. This explanation reveals another manner in which the Euclidean path integral of causal dynamical triangulations behaves correctly in its semiclassical limit--the implementation and interaction of multiple constraints.

  8. Analytical, 1-Dimensional Impedance Model of a Composite Solid Oxide Fuel Cell Cathode

    DEFF Research Database (Denmark)

    Mortensen, Jakob Egeberg; Søgaard, Martin; Jacobsen, Torben

    2014-01-01

    An analytical, 1-dimensional impedance model for a composite solid oxide fuel cell cathode is derived. It includes geometrical parameters of the cathode, e.g., the internal surface area and the electrode thickness, and also material parameters, e.g., the surface reaction rate and the vacancy...... diffusion coefficient. The model is successfully applied to a total of 42 impedance spectra, obtained in the temperature range 555°C–852°C and in the oxygen partial pressure range 0.028 atm–1.00 atm for a cathode consisting of a 50/50 wt% mixture of (La0.6Sr0.4)0.99CoO3 − δ and Ce0.9Gd0.1O1.95 − δ...... and providing both qualitative and quantitative information on the evolution of the impedance spectra of cathodes with changing parameters....

  9. Localized structures for (2+1)-dimensional Boiti–Leon–Pempinelli equation

    Indian Academy of Sciences (India)

    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.

  10. Multiwave solutions of time-fractional (2 + 1)-dimensional Nizhnik–Novikov–Veselov equations

    Indian Academy of Sciences (India)

    M S OSMAN

    2017-04-01

    In this paper, we present a generalized unified method for finding multiwave solutions of the timefractional (2+1)-dimensional Nizhnik–Novikov–Veselov equations. The fractional derivatives are described in the modified Riemann–Liouville sense. The fractional complex transform has been suggested to convert fractional order differential equations with modified Riemann–Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation. Multiauxiliary equations have been introduced in this method to obtain not only multisoliton solutions but also multiperiodic or multielliptic solutions. It is shown that the considered method is very effective and convenient for solving wide classes of nonlinear partial differential equations of fractional order.

  11. Exact solutions of the (2+1-dimensional cubic Klein–Gordon equation and the (3+1-dimensional Zakharov–Kuznetsov equation using the modified simple equation method

    Directory of Open Access Journals (Sweden)

    Kamruzzaman Khan

    2014-04-01

    Full Text Available Exact solutions of nonlinear evolution equations (NLEEs play a vital role to reveal the internal mechanism of complex physical phenomena. In this article, we implemented the modified simple equation (MSE method for finding the exact solutions of NLEEs via the (2+1-dimensional cubic Klein–Gordon (cKG equation and the (3+1-dimensional Zakharov–Kuznetsov (ZK equation and achieve exact solutions involving parameters. When the parameters are assigned special values, solitary wave solutions are originated from the exact solutions. It is established that the MSE method offers a further influential mathematical tool for constructing exact solutions of NLEEs in mathematical physics.

  12. Model of random center vortex lines in continuous 2 +1 -dimensional spacetime

    Science.gov (United States)

    Altarawneh, Derar; Engelhardt, Michael; Höllwieser, Roman

    2016-12-01

    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 piecewise 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 phase transition. We study both vortex percolation and the potential V (R ) between the quark and antiquark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions, and at different temperatures. We find three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature.

  13. A model of random center vortex lines in continuous 2+1-dimensional space-time

    CERN Document Server

    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...

  14. Smooth and sharp creation of a pointlike source for a $(3+1)$-dimensional quantum field

    CERN Document Server

    Zhou, L J; Kunstatter, Gabor; Louko, Jorma

    2016-01-01

    We analyse the smooth and sharp creation of a pointlike source for a quantised massless scalar field in $(3+1)$-dimensional Minkowski spacetime, as a model for the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. After a smooth creation, the renormalised energy density $\\langle T_{00} \\rangle$ is well defined away from the source, but it is time dependent, and it is so large near the source that the total energy transmitted into the field during the source creation is infinite. In the sharp creation limit, $\\langle T_{00} \\rangle$ diverges everywhere in the causal future of the creation event, and so does the response of an Unruh-DeWitt detector that operates in the causal future of the creation event. The source creation is hence significantly more singular than the corresponding process in $1+1$ dimensions, and may be sufficiently singular to break down quantum correlations in the way which has been proposed to happen in the spacetime of an evaporating b...

  15. Verification of a 1-dimensional model for predicting shallow infiltration at Yucca Mountain

    Energy Technology Data Exchange (ETDEWEB)

    Hevesi, J.A.; Flint, A.L. [Geological Survey, Mercury, NV (United States); Flint, L.E. [Foothill Engineering Consultants, Mercury, Nevada (United States)

    1994-12-31

    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.

  16. Verification of a 1-dimensional model for predicting shallow infiltration at Yucca Mountain

    Energy Technology Data Exchange (ETDEWEB)

    Hevesi, J.; Flint, A.L. [Geological Survey, Mercury, NV (United States); Flint, L.E. [Foothill Eng. Consultants, Mercury, NV (United States)

    1994-12-31

    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.

  17. Vacuum energy is non-positive for (2+1)-dimensional holographic CFTs

    CERN Document Server

    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.

  18. Characteristics of the breathers, rogue waves and solitary waves in a generalized (2+1)-dimensional Boussinesq equation

    Science.gov (United States)

    Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

    2016-07-01

    Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.

  19. The multicomponent (2+1)-dimensional Glachette-Johnson (GJ) equation hierarchy and its super-integrable coupling system

    Institute of Scientific and Technical Information of China (English)

    Yu Fa-Jun; Zhang Hong-Qing

    2008-01-01

    This paper presents a set of multicomponent matrix Lie algebra,which is used to construct a new loop algebra (A)M.By using the Tu scheme,a Liouville integrable multicomponent equation hierarchy is generated,which possesses the Hamiltonian structure.As its reduction cases,the multicomponent (2+1)-dimensional Glaehette-Johnson (GJ) hierarchy is given.Finally,the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem.

  20. An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its solutions

    Energy Technology Data Exchange (ETDEWEB)

    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.

  1. Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space

    Energy Technology Data Exchange (ETDEWEB)

    Bellucci, S. [INFN, Laboratori Nazionali di Frascati, Frascati (Italy); Bezerra de Mello, E.R. [Universidade Federal da Parai ba, Departamento de Fisica, 58.059-970, Joao Pessoa, PB (Brazil); Braganca, E. [INFN, Laboratori Nazionali di Frascati, Frascati (Italy); Universidade Federal da Parai ba, Departamento de Fisica, 58.059-970, Joao Pessoa, PB (Brazil); Saharian, A.A. [Yerevan State University, Department of Physics, Yerevan (Armenia)

    2016-06-15

    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 function of the chemical potential. The behavior of the expectation values in various asymptotic regions of the parameters are discussed in detail. In particular, we show that for points near the cone apex the vacuum parts dominate. For a massless field with zero chemical potential the fermion condensate and charge density vanish. Simple expressions are derived for the part in the total charge induced by the planar angle deficit and magnetic flux. Combining the results for separate irreducible representations, we also consider the fermion condensate, charge and current densities in parity and time-reversal symmetric models. Possible applications to graphitic nanocones are discussed. (orig.)

  2. Magnetic catalysis effect in the (2+1-dimensional Gross–Neveu model with Zeeman interaction

    Directory of Open Access Journals (Sweden)

    Klimenko K.G.

    2015-01-01

    Full Text Available Magnetic catalysis of the chiral symmetry breaking and other magnetic properties of the (2+1-dimensional Gross–Neveu model are studied taking into account the Zeeman interaction of spin-1/2 quasi-particles (electrons with tilted (with respect to a system plane external magnetic field B→ = B→⊥ + B→∥$\\vec B\\, = \\,{\\vec B_ \\bot }\\, + \\,{\\vec B_\\parallel }$. The Zeeman interaction is proportional to magnetic moment μB of electrons. For simplicity, temperature and chemical potential are equal to zero throughout the paper. We compare in the framework of the model the above mentioned phenomena both at μB = 0 and μB ≠ 0. It is shown that at μB ≠ 0 the magnetic catalysis effect is drastically changed in comparison with the μB = 0 case. Namely, at μB ≠ 0 the chiral symmetry, being spontaneously broken by B→$\\vec B$ at subcritical coupling constants, is always restored at |B→$\\vec B$| → ∞ (even at B→∥$\\vec B_\\parallel$ = 0. Moreover, it is proved in this case that chiral symmetry can be restored simply by tilting B→$\\vec B$ to a system plane, and in the region B⊥ → 0 the de Haas – van Alphen oscillations of the magnetization are observed. At supercritical values of coupling constant we have found two chirally non-invariant phases which respond differently on the action of B→$\\vec B$. The first (at rather small values of |B→$\\vec B$| is a diamagnetic phase, in which there is an enhancement of chiral condensate, whereas the second is a paramagnetic chirally broken phase. Numerical estimates show that phase transitions described in the paper can be achieved at low enough laboratory magnetic fields.

  3. Lie symmetry and exact solution of (2+1-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients

    Directory of Open Access Journals (Sweden)

    Ma Hong-Cai

    2013-01-01

    Full Text Available The simple direct method is adopted to find Non-Auto-Backlund transformation for variable coefficient non-linear systems. The (2+1-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients is used as an example to elucidate the solution procedure, and its symmetry transformation and exact solutions are obtained.

  4. New exact excitations and soliton fission and fusion for the (2+1)-dimensional Broer-Kaup-Kupershmidt system

    Institute of Scientific and Technical Information of China (English)

    Fang Jian-Ping; Zheng Chun-Long

    2005-01-01

    With the help of an extended mapping approach, a series of new types of exact excitations with two arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific soliton fission and fusion solutions of the higher-dimensional BKK system are also obtained.

  5. Symbolic Computation and Construction of New Exact Travelling Wave Solutions to (3+1)-Dimensional KP Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Xiao-Xian; WEN Xiao-Yong; SUN Ye-Peng

    2008-01-01

    With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation axe 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.

  6. The (2+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions

    Science.gov (United States)

    Wazwaz, Abdul-Majid

    2010-03-01

    In this work, the generalized (2+1) and (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equations are studied. We employ the Cole-Hopf transformation and the Hirota bilinear method to derive multiple-soliton solutions and multiple singular soliton solutions for these equations. The necessary conditions for complete integrability of each equation are derived

  7. Spatiotemporal soliton clusters in the $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity

    Indian Academy of Sciences (India)

    HONG-YU WU; LI-HONG JIANG

    2017-09-01

    From a generic transformation, a $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter $m = 0$, Gaussian solitons are constructed. For the modulation depth $q = 1$ and the azimuthal parameter $m \

  8. Spatiotemporal soliton clusters in the (3+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity

    Science.gov (United States)

    Wu, Hong-Yu; Jiang, Li-Hong

    2017-09-01

    From a generic transformation, a (3+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter m = 0, Gaussian solitons are constructed. For the modulation depth q = 1 and the azimuthal parameter m\

  9. Analytical travelling wave solutions and parameter analysis for the (2+1)-dimensional Davey–Stewartson-type equations

    Indian Academy of Sciences (India)

    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.

  10. Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

    Institute of Scientific and Technical Information of China (English)

    Tang Ya-Ning; Ma Wen-Xiu; Xu Wei

    2012-01-01

    Based on the Grammian and Pfaffian derivative formulae,Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form.Moreover,a Pfaffian extension ismade for the equation by means of the Pfaffianization procedure,the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.

  11. A Series of Variable Separation Solutions and New Soliton Structures of (2+1)-Dimensional Korteweg-de Vries Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  12. New Exact Solutions and Interactions Between Two Solitary Waves for (3+1)-Dimensional Jimbo-Miwa System

    Institute of Scientific and Technical Information of China (English)

    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.

  13. A Series of Exact Solutions for a New (2+1)-Dimensional Calogero KdV Equation

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    An algebraic method is proposed to solve a new (2+1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions.

  14. New Families of Rational Form Variable Separation Solutions to (2+1)-Dimensional Dispersive Long Wave Equations

    Institute of Scientific and Technical Information of China (English)

    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.

  15. New Families of Rational Form Solitary Wave Solutions to (2+1)-Dimensional Broer-Kaup-Kupershmidt System

    Institute of Scientific and Technical Information of China (English)

    WANG Qi; CHEN Yong; LI Biao; ZHANG Hong-Qing

    2005-01-01

    Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.

  16. New Families of Exact Excitations to (2+1)-Dimensional Toda Lattice System via an Extended Projective Approach

    Institute of Scientific and Technical Information of China (English)

    FANG Jian-Ping; FEI Jin-Xi; ZHENG Chun-Long

    2006-01-01

    In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems (DDEs).As a concrete example, new families of exact solutions to the (2+1)-dimensional Toda lattice system are obtained by the extended projective approach.

  17. On the First Law of Thermodynamics for (2+1) Dimensional Charged BTZ Black Hole and Charged de Sitter Space

    OpenAIRE

    LARRAÑAGA, Eduard Alexis

    2008-01-01

    In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1) dimensional charged BTZ black holes and charged de Sitter space.

  18. New Exact Solutions for the Generalized (2+1)-dimensional Nonlinear Schr(o)dinger Equation with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    JIANG Zhi-ping

    2012-01-01

    With the help of the variable-coefficient generalized projected Ricatti equation expansion method,we present exact solutions for the generalized (2+1)-dimensional nonlinear Schr(o)dinger equation with variable coefficients.These solutions include solitary wave solutions,soliton-like solutions and trigonometric function solutions.Among these solutions,some are found for the first time.

  19. A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions

    Science.gov (United States)

    Karpenko, Iu.; Huovinen, P.; Bleicher, M.

    2014-11-01

    We describe the details of 3+1 dimensional relativistic hydrodynamic code for the simulations of quark-gluon/hadron matter expansion in ultra-relativistic heavy ion collisions. The code solves the equations of relativistic viscous hydrodynamics in the Israel-Stewart framework. With the help of ideal-viscous splitting, we keep the ability to solve the equations of ideal hydrodynamics in the limit of zero viscosities using a Godunov-type algorithm. Milne coordinates are used to treat the predominant expansion in longitudinal (beam) direction effectively. The results are successfully tested against known analytical relativistic inviscid and viscous solutions, as well as against existing 2+1D relativistic viscous code. Catalogue identifier: AETZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 13 825 No. of bytes in distributed program, including test data, etc.: 92 750 Distribution format: tar.gz Programming language: C++. Computer: any with a C++ compiler and the CERN ROOT libraries. Operating system: tested on GNU/Linux Ubuntu 12.04 x64 (gcc 4.6.3), GNU/Linux Ubuntu 13.10 (gcc 4.8.2), Red Hat Linux 6 (gcc 4.4.7). RAM: scales with the number of cells in hydrodynamic grid; 1900 Mbytes for 3D 160×160×100 grid. Classification: 1.5, 4.3, 12. External routines: CERN ROOT (http://root.cern.ch), Gnuplot (http://www.gnuplot.info/) for plotting the results. Nature of problem: relativistic hydrodynamical description of the 3-dimensional quark-gluon/hadron matter expansion in ultra-relativistic heavy ion collisions. Solution method: finite volume Godunov-type method. Running time: scales with the number of hydrodynamic cells; typical running times on Intel(R) Core(TM) i7-3770 CPU @ 3.40 GHz, single thread mode, 160

  20. Exact traveling wave solutions to the (3+1-dimensional mKdV–ZK and the (2+1-dimensional Burgers equations via exp(−Φ(η-expansion method

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2015-09-01

    Full Text Available In this work, the exact traveling wave solutions to the (3+1-dimensional mKdV–ZK equation and the (2+1-dimensional Burgers equation are studied using the exp(-Φ(η-expansion method. The traveling wave solutions are expressed in terms of the exponential functions, the hyperbolic functions, the trigonometric functions and the rational functions. This method is one of the powerful methods that appear in recent time in establishing some new exact traveling wave solutions to the nonlinear partial differential equations. It is shown that the exp(-Φ(η-expansion method is simple and valuable mathematical instrument for solving nonlinear evolution equations in mathematical physics and engineering.

  1. Calculator calculus

    CERN Document Server

    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...

  2. Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation

    Institute of Scientific and Technical Information of China (English)

    WEN Xiao-Yong; MENG Xiang-Hua

    2013-01-01

    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.

  3. Particle Collision Near 1 + 1-Dimensional Horava-Lifshitz Black Hole and Naked Singularity

    Directory of Open Access Journals (Sweden)

    M. Halilsoy

    2017-01-01

    Full Text Available The unbounded center-of-mass (CM energy of oppositely moving colliding particles near horizon emerges also in 1+1-dimensional Horava-Lifshitz gravity. This theory has imprints of renormalizable quantum gravity characteristics in accordance with the method of simple power counting. Surprisingly the result obtained is not valid for a 1-dimensional Compton-like process between an outgoing photon and an infalling massless/massive particle. It is possible to achieve unbounded CM energy due to collision between infalling photons and particles. The source of outgoing particles may be attributed to an explosive process just outside the horizon for a black hole and the naturally repulsive character for the case of a naked singularity. It is found that absence of angular momenta in 1+1-dimension does not yield unbounded energy for collisions in the vicinity of naked singularities.

  4. New exact travelling wave solutions of generalised sinh- Gordon and (2 + 1-dimensional ZK-BBM equations

    Directory of Open Access Journals (Sweden)

    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.

  5. Localized Structures on Periodic Background Wave of (2+1)-Dimensional Boiti-Leon-Pempinelli System via an Object Reduction

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, we present an object reduction for nonlinear partial differential equations. As a concrete example of its applications in physical problems, this method is applied to the (2+1)-dimensional Boiti-Leon-Pempinelli system, which has the extensive physics background, and an abundance of exact solutions is derived from some reduction equations. Based on the derived solutions, the localized structures under the periodic wave background are obtained.

  6. Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients

    Institute of Scientific and Technical Information of China (English)

    Liu Xiao-Bei; Li Biao

    2011-01-01

    We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters.Different shapes of bright solitons,a train of bright solitons and dark solitons are observed.The obtained results may raise the possibilities of relevant experiments and potential applications.

  7. New doubly periodic and multiple soliton solutions of the generalized (3+1)-dimensional KP equation with variable coefficients

    Institute of Scientific and Technical Information of China (English)

    陈怀堂; 张鸿庆

    2003-01-01

    A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients.

  8. Extended Jacobi elliptic function method and its applications to (2+1)-dimensional dispersive long-wave equation

    Institute of Scientific and Technical Information of China (English)

    Chen Yong; Li Biao; Zhang Hong-Qing

    2004-01-01

    @@ An extended Jacobi elliptic function method is proposed for constructing the exact double periodic solutions of nonlinear partial differential equations (PDEs) in a unified way. It is shown that these solutions exactly degenerate to the many types of soliton solutions in a limited condition. The Wu-Zhang equation (which describes the (2+1)-dimensional dispersive long wave) is investigated by this means and more formal double periodic solutions are obtained.

  9. Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to (2+1)-Dimensional Stochastic Dispersive Long Wave System

    Institute of Scientific and Technical Information of China (English)

    SONG Li-Na; ZHANG Hong-Qing

    2007-01-01

    In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

  10. New localized excitations and cross-like fractal structures to the (2+1)-dimensional Broer–Kaup system

    Indian Academy of Sciences (India)

    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.

  11. Complex wave excitations and chaotic patterns for a general (2+1)-dimensional Korteweg-de Vries system

    Institute of Scientific and Technical Information of China (English)

    Ma Song-Hua; Fang Jian-Ping; Zheng Chun-Long

    2008-01-01

    Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for a general (2+1)-dimensional Korteweg de Vries system (GKdV) is derived. According to the derived solutions, we obtain some novel dromion-lattice solitons, complex wave excitations and chaotic patterns for the GKdV system.

  12. Bright and dark soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation and generalized Benjamin equation

    Indian Academy of Sciences (India)

    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.

  13. Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to(1+1)-Dimensional Dispersive Long Wave Equation

    Institute of Scientific and Technical Information of China (English)

    WANG Qi; CHEN Yong; ZHANG Hong-Qing

    2005-01-01

    In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.

  14. Coherent soliton structures of the (2+1)-dimensional long-wave-short-wave resonance interaction equation

    Institute of Scientific and Technical Information of China (English)

    黄文华; 张解放; 盛正卯

    2002-01-01

    The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave-short-waveresonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by theentrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shownthat the coherent soliton structures may be dromions, solitoffs, etc.

  15. A Generalized Variable-Coefficient Algebraic Method Exactly Solving (3+1)-Dimensional Kadomtsev-Petviashvilli Equation

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interestfor (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.

  16. Using Symbolic Computation to Exactly Solve the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces

    Institute of Scientific and Technical Information of China (English)

    XIE Fu-Ding; CHEN Jing; L(U) Zhuo-Sheng

    2005-01-01

    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.

  17. Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation

    Institute of Scientific and Technical Information of China (English)

    Wei-Peng Hu; Zi-Chen Deng; Yu-Yue Qin; Wen-Rong Zhang

    2012-01-01

    In the present paper,a general solution involving three arbitrary functions for the generalized (2+1)-dimensional KdV-mKdV equation,which is derived from the generalized (l+l)-dimensional KdV-mKdV equation,is first introduced by means of the Wiess,Tabor,Carnevale (WTC) truncation method.And then multisymplectic fonmulations with several conservation laws taken into account are presented for the generalized (2+1)-dimensional KdV-mKdV equation based on the multisymplectic theory of Bridges.Subsequently,in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from the general solution,a semi-implicit multi-symplectic scheme is constructed that is equivalent to the Preissmann scheme.From the results of the numerical experiments,we can conclude that the multi-symplectic schemes can accurately simulate the periodic wave solutions of the generalized (2+ 1)-dimensional KdV-mKdV equation while preserve approximately the conservation laws.

  18. Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in (1+1)-Dimensional Spacetime

    Institute of Scientific and Technical Information of China (English)

    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.

  19. Statistical Entropy and Superradiance in 2+1 Dimensional Acoustic Black Holes

    CERN Document Server

    Kim, W T; Yoon, M S; Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok

    2005-01-01

    We study ``draining bathtub'' as an acoustic analogue of a three-dimensional rotating black hole. Rotating fluid near the sonic horizon necessarily gives rise to the superradiant modes, which are partially responsible for the thermodynamic quantities in this rotating vortex-like hole. Using the recently suggested thin-layer method overcoming some difficulties from the well-known brick-wall method, we explicitly calculate the free energy of the system by treating the superradiance carefully and obtain the desirable entropy formula.

  20. Massive vector bosons tunnelled from the (2+1)-dimensional black holes

    Science.gov (United States)

    Gecim, Ganim; Sucu, Yusuf

    2017-03-01

    In this study, we investigate the Hawking radiation from three-dimensional New-type black hole and Warped-AdS3 black hole by using the quantum tunnelling properties of a massive spin-1 particle, i.e. a massive vector boson. Using the Hamilton-Jacobi method, we calculate the tunnelling probabilities and the Hawking temperature of the escaping massive spin-1 vector particle from the black holes. From these results, we see that the massive vector boson tunnels the same as a scalar and a Dirac particle from these black holes.

  1. Thermodynamics of hot quantum scalar field in a (D+1) dimensional curved spacetime

    CERN Document Server

    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. The 4-Body Problem in a (1+1)-Dimensional Self-Gravitating System

    CERN Document Server

    Laurtizen, Andrew; Mann, Robert B

    2013-01-01

    We report on the results of a study of the motion of a four particle non-relativistic one-dimensional self-gravitating system. We show that the system can be visualized in terms of a single particle moving within a potential whose equipotential surfaces are shaped like a box of pyramid-shaped sides. As such this is the largest $N$-body system that can be visualized in this way. We describe how to classify possible states of motion in terms of Braid Group operators, generalizing this to $N$ bodies. We find that the structure of the phase\\textcolor{black}{{} space of each of these systems yields a large variety of interesting dynamics, containing regions of quasiperiodicity and chaos. Lyapunov exponents are calculated for many trajectories to measure stochasticity and previously unseen phenomena in the Lyapunov graphs are observed.

  3. Joint Application of Bilinear Operator and F-Expansion Method for (2+1-Dimensional Kadomtsev-Petviashvili Equation

    Directory of Open Access Journals (Sweden)

    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.

  4. A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions.The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions,and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on (2+1)-dimensional dispersive long-wave equation.

  5. Fractal Dromion, Fractal Lump, and Multiple Peakon Excitations in a New (2+1)-Dimensional Long Dispersive Wave System

    Institute of Scientific and Technical Information of China (English)

    ZHENG Chun-Long; ZHU Jia-Min; ZHANG Jie-Fang; CHEN Li-Qun

    2003-01-01

    By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: λqt + qxx - 2q ∫ (qr)xdy = 0, λrt - rxx + 2r ∫(qr)xdy = 0, is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, farctal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.

  6. New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation

    Institute of Scientific and Technical Information of China (English)

    WANG Qi; CHEN Yong; LI Biao; ZHANG Hong-Qing

    2004-01-01

    Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e.,the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.

  7. Applications of extended F-expansion and projective Ricatti equation methods to (2+1-dimensional soliton equations

    Directory of Open Access Journals (Sweden)

    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.

  8. Storage and retrieval of (3+1)-dimensional weak-light bullets and vortices in a coherent atomic gas

    CERN Document Server

    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.

  9. The exp(−Φ(η-expansion method with application in the (1+1-dimensional classical Boussinesq equations

    Directory of Open Access Journals (Sweden)

    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.

  10. Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory

    CERN Document Server

    Chamizo, Fernando

    2016-01-01

    We consider the $2+1$ dimensional Yang-Mills theory with gauge group $\\text{SU}(N)$ on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when $N$ and the volume vary and certain chromomagnetic flux associated to the topology of the bundle can be adjusted. Under natural assumptions about how to match the perturbative regime and the expected confinement, we prove that the absence of tachyonic instabilities is related to some problems in number theory, namely the Diophantine approximation of irreducible fractions by other fractions of smaller denominator.

  11. Critical Coupling in (1+1)-Dimensional Light-Front $\\phi^{4}$ Theory; 2, effects of non-diagonal interactions

    CERN Document Server

    Oshima, K

    2001-01-01

    Spontaneous symmetry breaking in (1+1)-dimensional $\\phi^{4}$ theory is studied with discretized light-front quantization. Taking effects of non-diagonal interactions into account, the first few terms of the commutation relations $[a_{0},a_{n}]$ are recalculated in the $\\hbar$ expansion. Our result of the critical coupling is still consistent with the equal-time result $22\\mu^{2}/\\hbar \\le \\lambda_{\\rm{cr}} \\le 55.5\\mu^{2}/\\hbar$. We also have examined effects of regarding the ratio of the bare coupling constant to a renormalized mass as an independent parameter in the $\\hbar$ expansion.

  12. Exact Solutions for (4+1-Dimensional Nonlinear Fokas Equation Using Extended F-Expansion Method and Its Variant

    Directory of Open Access Journals (Sweden)

    Yinghui He

    2014-01-01

    Full Text Available The construction of exact solution for higher-dimensional nonlinear equation plays an important role in knowing some facts that are not simply understood through common observations. In our work, (4+1-dimensional nonlinear Fokas equation, which is an important physical model, is discussed by using the extended F-expansion method and its variant. And some new exact solutions expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.

  13. $Q-\\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes

    CERN Document Server

    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.

  14. Nonlocal symmetries, consistent Riccati expansion integrability, and their applications of the (2+1)-dimensional Broer-Kaup-Kupershmidt system

    Science.gov (United States)

    Hu, Xiao-Rui; Chen, Yong

    2015-09-01

    For the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion (CRE) is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied. Project supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ13A010014) and the National Natural Science Foundation of China (Grant Nos. 11326164, 11401528, 11435005, and 11375090).

  15. Exact and explicit solutions to the (3+1)-dimensional Jimbo-Miwa equation via the Exp-function method

    Energy Technology Data Exchange (ETDEWEB)

    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.

  16. Thermodynamic and geometric framework of a (2+1)-dimensional black hole with non-linear electrodynamics

    Institute of Scientific and Technical Information of China (English)

    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.

  17. Local scale-invariance of the 2  +  1 dimensional Kardar–Parisi–Zhang model

    Science.gov (United States)

    Kelling, Jeffrey; Ódor, Géza; Gemming, Sibylle

    2017-03-01

    Local scale-invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2  +  1 dimensional Kardar–Parisi–Zhang surfaces. Very precise measurements of the universal autoresponse function enabled us to perform nonlinear fitting with the scaling forms, suggested by local scale-invariance (LSI). While the simple LSI ansatz does not seem to work, forms based on logarithmic extension of LSI provide satisfactory description of the full (measured) time evolution of the autoresponse function.

  18. Cloud of strings as source in 2 + 1-dimensional f(R) = R{sup n} gravity

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  19. Generalized and improved (G'/G)-expansion method for (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation.

    Science.gov (United States)

    Naher, Hasibun; Abdullah, Farah Aini; Akbar, M Ali

    2013-01-01

    The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple.

  20. Generalized and Improved (G′/G)-Expansion Method for (3+1)-Dimensional Modified KdV-Zakharov-Kuznetsev Equation

    Science.gov (United States)

    Naher, Hasibun; Abdullah, Farah Aini; Akbar, M. Ali

    2013-01-01

    The generalized and improved -expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple. PMID:23741355

  1. Hierarchy of the low-lying excitations for the (2 + 1)-dimensional q = 3 Potts model in the ordered phase

    Science.gov (United States)

    Nishiyama, Yoshihiro

    2017-03-01

    The (2 + 1)-dimensional q = 3 Potts model was simulated with the exact diagonalization method. In the ordered phase, the elementary excitations (magnons) are attractive, forming a series of bound states in the low-energy spectrum. We investigate the low-lying spectrum through a dynamical susceptibility, which is readily tractable with the exact diagonalization method via the continued-fraction expansion. As a result, we estimate the series of (scaled) mass gaps, m 2 , 3 , 4 /m1 (m1: single-magnon mass), in proximity to the transition point.

  2. Kink degeneracy and rogue potential solution for the (3+1)-dimensional B-type Kadomtsev--Petviashvili equation

    Indian Academy of Sciences (India)

    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.

  3. Entanglement entropy and mutual information of circular entangling surfaces in the 2  +  1-dimensional quantum Lifshitz model

    Science.gov (United States)

    Zhou, Tianci; Chen, Xiao; Faulkner, Thomas; Fradkin, Eduardo

    2016-09-01

    We investigate the entanglement entropy (EE) of circular entangling cuts in the 2  +  1-dimensional quantum Lifshitz model. The ground state in this model is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose amplitude 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 also scales at long distance with a power determined by the lowest scaling dimension local operator in the theory.

  4. Thermodynamics of (2 +1 )-dimensional black holes in Einstein-Maxwell-dilaton gravity

    Science.gov (United States)

    Dehghani, M.

    2017-08-01

    In this paper, the linearly charged three-dimensional Einstein's theory coupled to a dilatonic field has been considered. It has been shown that the dilatonic potential must be considered in a form of generalized Liouville-type potential. Two new classes of charged dilatonic black hole solutions, as the exact solutions to the Einstein-Maxwell-dilaton (EMd) gravity, have been obtained and their properties have been studied. The conserved charge and mass related to both of the new EMd black holes have been calculated. Through comparison of the thermodynamical extensive quantities (i.e., temperature and entropy) obtained from both, the geometrical and the thermodynamical methods, the validity of first law of black hole thermodynamics has been investigated for both of the new black holes we just obtained. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new black hole solutions have been analyzed. It has been shown that there is a specific range for the horizon radius in such a way that the black holes with the horizon radius in that range are locally stable. Otherwise, they are unstable and may undergo type one or type two phase transitions to be stabilized.

  5. Thermodynamics of (2 +1 )-dimensional charged black holes with power-law Maxwell field

    Science.gov (United States)

    Dehghani, M.

    2016-11-01

    In this work, the three-dimensional nonlinearly charged black holes have been considered with a power-law modified electromagnetic theory. The black hole solutions to Einstein's three-dimensional field equations with a negative cosmological constant have been constructed in the presence of power-law nonlinear electrodynamics. Through the physical and mathematical interpretation of the solutions, a new class of asymptotically anti-de Sitter (AdS) black hole solutions has been introduced. The area law, surface gravity, and Gauss's law are utilized to obtain the entropy, temperature, and electric charge of the new AdS black holes, respectively. The quasilocal mass of the solutions has been calculated based on the counterterm method. A Smarr-type formula for the mass as a function of entropy and charge has been obtained. It has been shown that the thermodynamical quantities satisfy the first law of thermodynamics for the new AdS black holes. Also, it has been found that in order for the Smarr mass formula to be compatible with the first law of black hole thermodynamics, the cosmological parameter Λ should be treated as a thermodynamical variable and the generalized first law of thermodynamics has been introduced. Through the canonical ensemble method, the black hole remnant or phase transitions have been investigated regarding the black hole heat capacity. It has been found that the AdS black hole solutions we just obtained are thermodynamically stable.

  6. New Compacton-Like and Solitary Pattern-Like Solutions of (2+1)-Dimensional Generalization of Modified KdV Equation

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of (2+1)-dimensional generalization of mKd V equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this (2+ 1)-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions.

  7. Traveling wave solutions of the (2 + 1-dimensional Zoomeron equation and the Burgers equations via the MSE method and the Exp-function method

    Directory of Open Access Journals (Sweden)

    Kamruzzaman Khan

    2014-03-01

    Full Text Available The modified simple equation (MSE method is promising for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs in mathematical physics. In this letter, we investigate solutions of the (2 + 1-dimensional Zoomeron equation and the (2 + 1-dimensional Burgers equation by using the MSE method and the Exp-function method. The competence of the methods for constructing exact solutions has been established.

  8. Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave-short-wave resonant interaction

    Institute of Scientific and Technical Information of China (English)

    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.

  9. Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Zheng Xuedong; Chen Yong; Zhang Hongqing

    2003-05-12

    Making use of a new generalized ansatzes, we present the generalized extended tanh-function method for constructing the exact solutions of nonlinear partial differential equations (NPDEs) in a unified way. Applying the generalized method, with the aid of MAPLE, we consider the Wu-Zhang equation (which describes (1+1)-dimensional dispersive long wave). As a result, we can successfully obtain the solitary wave solutions that can be found by the extended tanh-function method and the modified extended tanh-function method. More importantly, for the equation, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary wave solutions, bell-profile solitary wave solutions, periodic wave solutions, rational solutions, singular solutions and other new formal solutions. As an illustrative sample, the properties of some soliton solutions for Wu-Zhang equation are shown by some figures.

  10. Symmetry Reduction, Exact Solutions, and Conservation Laws of (2+1)-Dimensional Burgers Korteweg-de Vries Equation

    Institute of Scientific and Technical Information of China (English)

    DONG Zhong-Zhou; LIU Xi-Qiang; BAI Cheng-Lin

    2006-01-01

    Using the classical Lie method of infinitesimals, we first obtain the symmetry of the (2+1)-dimensional Burgers-Korteweg-de-Vries (3D-BKdV) equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.

  11. New Modified Jacobi Elliptic Function Expansion Method and Its Application to (3+1)-Dimensional KP Equation

    Institute of Scientific and Technical Information of China (English)

    DOU Fu-Quan; SUN Jian-An; DUAN Wen-Shan; SHI Yu-Ren; L(U) Ke-Pu; HONG Xue-Ren

    2006-01-01

    With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional Kadomtsev-Petviashvili equation to illustrate our method. As a result, twenty families of periodic solutions are obtained. Of course, more solitary wave solutions, shock wave solutions or triangular function formal solutions can be obtained at their limit condition.

  12. Q-Φ criticality in the extended phase space of (n+1)-dimensional RN-AdS black holes

    Science.gov (United States)

    Ma, Yu-Bo; Zhao, Ren; Cao, Shuo

    2016-12-01

    In order to achieve a deeper understanding of gravity theories, i.e., the quantum properties of gravity theories and the statistical explanation of gravitational entropy, it is important to further investigate the thermodynamic properties of a 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,Φ as the state parameters and study the phase equilibrium problem of a 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 a theoretical foundation for studying the phase transition and phase structure of black hole systems.

  13. A transformed rational function method for (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

    Indian Academy of Sciences (India)

    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.

  14. Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation

    Science.gov (United States)

    Xu, Gui-Qiong; Deng, Shu-Fang

    2016-11-01

    Under investigation in this paper is a (2 + 1)-dimensional generalized NNV equation, which includes as many important nonlinear models as its particular cases. First, we perform the Painlevé test for the generalized NNV equation with the help of symbolic computation, and it is shown that this generalized equation admits the Painlevé property for one set of parametric choices. For the newly obtained integrable equation, we then employ the binary Bell polynomial method to construct the bilinear form, N-soliton solution, bilinear Bäcklund transformation and Lax pair in a systematic way. In addition, some new doubly periodic wave solutions with two arbitrary functions are obtained by means of truncated Painlevé expansions. Finally, the collisions of multiple solitons and periodic waves are interesting and shown by some graphs.

  15. Bäcklund Transformation and Soliton Solutions for a (3+1)-Dimensional Variable-Coefficient Breaking Soliton Equation

    Science.gov (United States)

    Zhao, Chen; Gao, Yi-Tian; Lan, Zhong-Zhou; Yang, Jin-Wei

    2016-09-01

    In this article, a (3+1)-dimensional variable-coefficient breaking soliton equation is investigated. Based on the Bell polynomials and symbolic computation, the bilinear forms and Bäcklund transformation for the equation are derived. One-, two-, and three-soliton solutions are obtained via the Hirota method. N-soliton solutions are also constructed. Propagation characteristics and interaction behaviors of the solitons are discussed graphically: (i) solitonic direction and position depend on the sign of the wave numbers; (ii) shapes of the multisoliton interactions in the scaled space and time coordinates are affected by the variable coefficients; (iii) multisoliton interactions are elastic for that the velocity and amplitude of each soliton remain unchanged after each interaction except for a phase shift.

  16. New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2+1-Dimensional Evolution Equation

    Directory of Open Access Journals (Sweden)

    Hasibun Naher

    2012-01-01

    Full Text Available The generalized Riccati equation mapping is extended with the basic (G′/G-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G′(η=w+uG(η+vG2(η is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.

  17. Soliton solutions for a (3 + 1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a plasma

    Science.gov (United States)

    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.

  18. (3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

    Energy Technology Data Exchange (ETDEWEB)

    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.

  19. 2 + 1 dimensional de Sitter universe emerging from the gauge structure of a nonlinear quantum system.

    Science.gov (United States)

    Kam, Chon-Fai; Liu, Ren-Bao

    2017-08-29

    Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical surfaces in the parameter space. We find that these critical surfaces result in a new type of gauge field singularity, namely, a conic singularity that resembles the big bang of a 2 + 1 dimensional de Sitter universe, with the fundamental frequency of Bogoliubov excitations acting as the cosmic scale, and mode softening at the critical surface, where the fundamental frequency vanishes, causing a causal singularity. Such conic singularity may be observed in various systems such as Bose-Einstein condensates and molecular magnets. This finding offers a new approach to quantum simulation of fundamental physics.

  20. Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

    Science.gov (United States)

    Wen, Xiao-Yong; Yan, Zhenya

    2017-02-01

    The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.

  1. The Interactions of N-Soliton Solutions for the Generalized (2+1-Dimensional Variable-Coefficient Fifth-Order KdV Equation

    Directory of Open Access Journals (Sweden)

    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.

  2. Residual Symmetry and Explicit Soliton-Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV-mKdV Equation

    Science.gov (United States)

    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.

  3. Comparison of BCF-10, BCF-12, and BCF-20 Scintillating Fibers for Use in a 1-Dimensional Linear Sensor

    Energy Technology Data Exchange (ETDEWEB)

    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.

  4. Predicting the performances of a CAMPRO engine retrofitted with liquefied petroleum gas (LPG system using 1-dimensional software

    Directory of Open Access Journals (Sweden)

    Kamaruddin M. Hazeem

    2017-01-01

    Full Text Available Recently, the depletion of petroleum resources and the impact of exhaust emission caused by combustion towards environmental has been forced to all researchers to come out with an alternative ways to prevent this situation become worse. Liquefied petroleum gas (LPG is the most compatible and have a potential to become a source of energy for internal combustion engine. Unfortunately, the investigation of LPG in internal combustion engine among researcher still have a gap in research. Thus, in this study a 1-Dimensional simulation CAMPRO 1.6L engine model using GT-Power is developed to predict the performances of engines that using LPG as a fuel for internal combustion engine. The constructed model simulation will throughout the validation process with the experimental data to make sure the precision of this model. The validation process shows that the results have a good agreement between the simulation model and the experimental data. As a result, the performance of LPG simulation model shows that a Brake Torque (BT, Brake Power (BP and Brake Mean Effective Pressure (BMEP were significantly improved in average of 7% in comparison with gasoline model. In addition, Brake Specific Fuel Consumption (BSFC also shows an improvement by 5%, which is become more economic. Therefore, the developed GT-Power model offer a successful fuel conversion to LPG systems via retrofit technology to provide comprehensive support for implementation of energy efficient and environmental friendly vehicles.

  5. Regularization of Casimir free energy for p-dimensional Hypercubic Cavities inside D+1-dimensional Minkowski Spacetime

    Directory of Open Access Journals (Sweden)

    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.

  6. A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation

    Science.gov (United States)

    Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao

    2017-06-01

    With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University

  7. Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge

    CERN Document Server

    Kotikov, A V

    2016-01-01

    Dynamical chiral symmetry breaking (D$\\chi$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $1/N$ expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, $N_c(\\xi)$ where $\\xi$ is the gauge fixing parameter, which is such that D$\\chi$SB takes place for $N

  8. Assessment of reduced-order unscented Kalman filter for parameter identification in 1-dimensional blood flow models using experimental data.

    Science.gov (United States)

    Caiazzo, A; Caforio, Federica; Montecinos, Gino; Muller, Lucas O; Blanco, Pablo J; Toro, Eluterio F

    2016-10-25

    This work presents a detailed investigation of a parameter estimation approach on the basis of the reduced-order unscented Kalman filter (ROUKF) in the context of 1-dimensional blood flow models. In particular, the main aims of this study are (1) to investigate the effects of using real measurements versus synthetic data for the estimation procedure (i.e., numerical results of the same in silico model, perturbed with noise) and (2) to identify potential difficulties and limitations of the approach in clinically realistic applications to assess the applicability of the filter to such setups. For these purposes, the present numerical study is based on a recently published in vitro model of the arterial network, for which experimental flow and pressure measurements are available at few selected locations. To mimic clinically relevant situations, we focus on the estimation of terminal resistances and arterial wall parameters related to vessel mechanics (Young's modulus and wall thickness) using few experimental observations (at most a single pressure or flow measurement per vessel). In all cases, we first perform a theoretical identifiability analysis on the basis of the generalized sensitivity function, comparing then the results owith the ROUKF, using either synthetic or experimental data, to results obtained using reference parameters and to available measurements.

  9. Variable-Coefficient Hyperbola Function Method and Its Application to (2+1)-Dimensional Variable-Coefficient Broer-Kaup System

    Institute of Scientific and Technical Information of China (English)

    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.

  10. Exact periodic cross-kink wave solutions for the new (2+1)-dimensional KdV equation in fluid flows and plasma physics

    Science.gov (United States)

    Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping

    2016-10-01

    The Korteweg-de Vries (KdV)-type models have been shown to describe many important physical situations such as fluid flows, plasma physics, and solid state physics. In this paper, a new (2 + 1)-dimensional KdV equation is discussed. Based on the Hirota's bilinear form and a generalized three-wave approach, we obtain new exact solutions for the new (2 + 1)-dimensional KdV equation. With the help of symbolic computation, the properties for some new solutions are presented with some figures.

  11. Variable-coefficient projective Riccati equation method and its application to a new (2 + 1)-dimensional simplified generalized Broer-Kaup system

    Energy Technology Data Exchange (ETDEWEB)

    Huang Dingjiang E-mail: hdj8116@163.com; Zhang Hongqing

    2005-01-01

    In this paper, based on a new intermediate transformation, a variable-coefficient projective Riccati equation method is proposed. Being concise and straightforward, it is applied to a new (2 + 1)-dimensional simplified generalized Broer-Kaup (SGBK) system. As a result, several new families of exact soliton-like solutions are obtained, beyond the travelling wave. When imposing some condition on them, the new exact solitary wave solutions of the (2 + 1)-dimensional SGBK system are given. The method can be applied to other nonlinear evolution equations in mathematical physics.

  12. On an Auto-B(a)cklund Transformation for (2+1)-Dimensional Variable Coefficient Generalized KP Equations and Exact Solutions

    Institute of Scientific and Technical Information of China (English)

    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.

  13. Non-travelling wave solutions to a (3 + 1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Tingxuan [Huaian University of Radio and TV, Huaian, Jiangsu 223005 (China); Xuan, Heng-Nong [School of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210003 (China)]. E-mail: hn_xuan@yahoo.com.cn; Zhang Dafang [School of Software, Hunan University, Changsha 410082 (China); Wang Changji [Computer Science Department, Sun Yet-Sen University, Guangzhou 510275 (China)

    2007-11-15

    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.

  14. New Exact Solutions and Evolution of Solitons in Background Waves for (2+1)-Dimensional Modified Dispersive Water-Wave System

    Institute of Scientific and Technical Information of China (English)

    MA Song-Hua; JIANG Yong-Qing; FANG Jian-Ping

    2008-01-01

    With the help of the conditional similarity reduction method, some new exact solutions of the (2+1)-dimensional modified dispersive water-wave system (MDWW) are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.

  15. Asymptotic Behaviour of Solitons with a Double Spectral Parameter for the Bogomolny Equation in (2+1)-Dimensional Anti de Sitter Space

    Institute of Scientific and Technical Information of China (English)

    JI Xue-Feng; ZHOU Zi-Xiang

    2005-01-01

    @@ The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)-dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.

  16. Magnetic Field Calculator

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Calculator will calculate the total magnetic field, including components (declination, inclination, horizontal intensity, northerly intensity,...

  17. 1-Dimensional simulation of thermal annealing in a commercial nuclear power plant reactor pressure vessel wall section

    Energy Technology Data Exchange (ETDEWEB)

    Nakos, J.T.; Rosinski, S.T.; Acton, R.U.

    1994-11-01

    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 {times} 1.2 m {times} 17.1 cm thick [4 ft {times} 4 ft {times} 6.75 in] section of an RPV (A533B ferritic steel with stainless steel cladding), a mockup of the {open_quotes}mirror{close_quotes} insulation between the RPV and the concrete reactor cavity wall, and a 25.4 cm [10 in] thick concrete wall, 2.1 in {times} 2.1 in [10 ft {times} 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.

  18. 1-Dimensional simulation of thermal annealing in a commercial nuclear power plant reactor pressure vessel wall section

    Energy Technology Data Exchange (ETDEWEB)

    Nakos, J.T.; Rosinski, S.T.; Acton, R.U.

    1994-11-01

    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 {times} 1.2 m {times} 17.1 cm thick [4 ft {times} 4 ft {times} 6.75 in] section of an RPV (A533B ferritic steel with stainless steel cladding), a mockup of the {open_quotes}mirror{close_quotes} insulation between the RPV and the concrete reactor cavity wall, and a 25.4 cm [10 in] thick concrete wall, 2.1 in {times} 2.1 in [10 ft {times} 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.

  19. Determining lake surface water temperatures (LSWTs worldwide using a tuned 1-dimensional lake model (FLake, v1

    Directory of Open Access Journals (Sweden)

    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.

  20. Exact solutions to the (3+1-dimensional coupled Klein–Gordon–Zakharov equation using exp(−Φ(ξ-expansion method

    Directory of Open Access Journals (Sweden)

    M.G. Hafez

    2016-06-01

    Full Text Available In this article, the exp(-Φ(ξ-expansion method is modified for (3+1-dimensional space–time coordinate system and successfully implemented to construct the new exact traveling wave solutions of the (3+1-dimensional coupled Klein–Gordon–Zakharov equation. The solutions of this equation are expressed in terms of hyperbolic, trigonometric, exponential and rational functions. The results illustrate its effectiveness for solving nonlinear coupled partial differential equations arises in mathematical physics and engineering. The annihilation phenomena of the wave propagation in the x–y plane are also investigated. Furthermore, the three-dimensional surface plots due to the obtained solutions are also given to make the dynamics of the equation visible.

  1. New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer-Kaup-Kupershmidt system

    Institute of Scientific and Technical Information of China (English)

    Yang Xian-Lin; Tang Jia-Shi

    2007-01-01

    Some new exact solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji et al in their auxiliary equation method. By using this method and these new solutions the combined Korteweg-de Vries (KdV) and modified KdV (mKdV) equation and (2+1)-dimensional Broer Kaup-Kupershmidt system are investigated and abundant exact travelling wave solutions are obtained that include new solitary wave solutions and triangular periodic wave solutions.

  2. Painleve Analysis, Soliton Solutions and B(a)cklund Transformation for Extended (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations in Fluid Mechanics via Symbolic Computation

    Institute of Scientific and Technical Information of China (English)

    XU Peng-Bo; GAO Yi-Tian; YU Xin; WANG Lei; LIN Guo-Dong

    2011-01-01

    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. Painlevé 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 B(a)cklund transformation and a type of solutions are obtained.

  3. A modified variable-coefficient projective Riccati equation method and its application to (2 + 1)-dimensional simplified generalized Broer-Kaup system

    Energy Technology Data Exchange (ETDEWEB)

    Liu Qing [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)], E-mail: lsxylq@163.com; Zhu Jiamin; Hong Bihai [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)

    2008-09-15

    A modified variable-coefficient projective Riccati equation method is proposed and applied to a (2 + 1)-dimensional simplified and generalized Broer-Kaup system. It is shown that the method presented by Huang and Zhang [Huang DJ, Zhang HQ. Chaos, Solitons and Fractals 2005; 23:601] is a special case of our method. The results obtained in the paper include many new formal solutions besides the all solutions found by Huang and Zhang.

  4. The generalizing Riccati equation mapping method in non-linear evolution equation: application to (2 + 1)-dimensional Boiti-Leon-Pempinelle equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhu Shundong [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)], E-mail: zhusd1965@sina.com

    2008-09-15

    The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by the generalizing Riccati equation mapping method and picking up its new solutions. In order to test the validity of this approach, the (2 + 1)-dimensional Boiti-Leon-Pempinelle equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.

  5. A new compound Riccati equations rational expansion method and its application to the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov system

    Energy Technology Data Exchange (ETDEWEB)

    Song Lina [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)], E-mail: songlina1981@yahoo.com.cn; Wang Qi; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)

    2008-06-15

    In this paper, based on a new general ansaetze and symbolic computation, a new compound Riccati equations rational expansion method is proposed. Being concise and straightforward, it is applied to the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov system. It is shown that more complexiton solutions can be found by this new method. The method can be applied to other nonlinear partial differential equations in mathematical physics.

  6. New Exact Solutions to the (2+1)-Dimensional Ablowitz-Kaup-Newell-Segur Equation: Modification of the Extended Homoclinic Test Approach

    Institute of Scientific and Technical Information of China (English)

    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.

  7. Flexible Mental Calculation.

    Science.gov (United States)

    Threlfall, John

    2002-01-01

    Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…

  8. Geochemical Calculations Using Spreadsheets.

    Science.gov (United States)

    Dutch, Steven Ian

    1991-01-01

    Spreadsheets are well suited to many geochemical calculations, especially those that are highly repetitive. Some of the kinds of problems that can be conveniently solved with spreadsheets include elemental abundance calculations, equilibrium abundances in nuclear decay chains, and isochron calculations. (Author/PR)

  9. Autistic Savant Calendar Calculators.

    Science.gov (United States)

    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…

  10. How Do Calculators Calculate Trigonometric Functions?

    Science.gov (United States)

    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…

  11. Core calculations of JMTR

    Energy Technology Data Exchange (ETDEWEB)

    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.)

  12. Calculating correct compilers

    DEFF Research Database (Denmark)

    Bahr, Patrick; Hutton, Graham

    2015-01-01

    In this article, we present a new approach to the problem of calculating compilers. In particular, we develop a simple but general technique that allows us to derive correct compilers from high-level semantics by systematic calculation, with all details of the implementation of the compilers...... falling naturally out of the calculation process. Our approach is based upon the use of standard equational reasoning techniques, and has been applied to calculate compilers for a wide range of language features and their combination, including arithmetic expressions, exceptions, state, various forms...

  13. Radar Signature Calculation Facility

    Data.gov (United States)

    Federal Laboratory Consortium — FUNCTION: The calculation, analysis, and visualization of the spatially extended radar signatures of complex objects such as ships in a sea multipath environment and...

  14. Electrical installation calculations basic

    CERN Document Server

    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

  15. Electrical installation calculations advanced

    CERN Document Server

    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

  16. Electronics Environmental Benefits Calculator

    Data.gov (United States)

    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,...

  17. Enhanced many-body effects in 2- and 1-dimensional ZnO structures: a Green's function perturbation theory study.

    Science.gov (United States)

    Wei, Wei; Dai, Ying; Huang, Baibiao; Jacob, Timo

    2013-10-14

    In order to study many-body effects in ZnO structures with reduced-dimensionality, electronic and optical absorption properties of ZnO monolayer and armchair ZnO nanoribbons (AZnONRs) are studied by means of Green's function perturbation theory using the GW+Bethe-Salpeter equation approach. In both ZnO monolayer and AZnONRs, as a consequence of enhanced quantum confinement, the quasi-particle corrections are significant and the optical absorption properties are dominated by strong excitonic effects with considerable binding energies (1-2 eV) assigned to the lowest-energy bound excitons. It reveals that inclusion of excitonic effects, which are neglected in calculations at single-particle approximation, is crucial to qualitatively and quantitatively describe the optical properties of such materials with reduced-dimensionality.

  18. Calculators and Polynomial Evaluation.

    Science.gov (United States)

    Weaver, J. F.

    The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized.…

  19. Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the $\\delta$-Function Potential in 1-dimensional Relativistic Quantum Mechanics

    CERN Document Server

    Al-Hashimi, M H; Wiese, U -J

    2014-01-01

    We consider the Schr\\"odinger equation for a relativistic point particle in an external 1-dimensional $\\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \\sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

  20. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    Energy Technology Data Exchange (ETDEWEB)

    Kong Cuicui [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)], E-mail: cuicuikong@yahoo.com.cn; Wang Dan; Song Lina; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)

    2009-01-30

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  1. Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length

    CERN Document Server

    Menculini, L; Roy, P

    2013-01-01

    We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (\\beta -->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene.

  2. Competition and duality correspondence between chiral and superconducting channels in (2+1)-dimensional four-fermion models with fermion number and chiral chemical potentials

    CERN Document Server

    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.

  3. The First Law of Thermodynamics of the (2+1)-Dimensional Banados-Teitelboim-Zanelli Black Holes and Kerr-de Sitter Spacetimes

    Institute of Scientific and Technical Information of China (English)

    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.

  4. A Series of Soliton-like and Double-like Periodic Solutions of a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

    Institute of Scientific and Technical Information of China (English)

    CHEN Yong; WANG Qi; LI Biao

    2004-01-01

    We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.

  5. Hierarchy of the low-lying excitations for the (2+1-dimensional q=3 Potts model in the ordered phase

    Directory of Open Access Journals (Sweden)

    Yoshihiro Nishiyama

    2017-03-01

    Full Text Available The (2+1-dimensional q=3 Potts model was simulated with the exact diagonalization method. In the ordered phase, the elementary excitations (magnons are attractive, forming a series of bound states in the low-energy spectrum. We investigate the low-lying spectrum through a dynamical susceptibility, which is readily tractable with the exact diagonalization method via the continued-fraction expansion. As a result, we estimate the series of (scaled mass gaps, m2,3,4/m1 (m1: single-magnon mass, in proximity to the transition point.

  6. Development of approximate shielding calculation method for high energy cosmic radiation on LEO satellites

    Energy Technology Data Exchange (ETDEWEB)

    Sin, M. W.; Kim, M. H. [Kyunghee Univ., Yongin (Korea, Republic of)

    2002-10-01

    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.

  7. Baryons and Low-Density Baryonic Matter in 1+1 Dimensional Large N_c QCD with Heavy Quarks

    CERN Document Server

    Adhikari, Prabal; Jamgochian, Arec; Kumar, Nilay

    2012-01-01

    This paper studies baryons and baryonic matter in the combined large N_c and heavy quark mass limits of QCD in 1+1 dimension. In this non-relativistic limit, baryons are composed of N_c quarks that interact, at leading order in N_c, through a color Coulomb potential. Using variational techniques, very accurate calculations of single baryon masses and interaction energies of low-density baryon crystal are performed. These results are used to cross-check a general numerical approach applicable for arbitrary quark masses and baryon densities recently proposed by Bringoltz, which is based on a lattice in a finite box with periodic boundary conditions. The Bringoltz method differs from a previous approach of Salcedo, et al. in its treatment of a finite box effect - namely gauge configurations that wind around the box. One might expect these effects to be small for large enough boxes, in which the baryon density approaches zero to high accuracy at the edges. However, the effects of these windings appear to be quite...

  8. The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

    Science.gov (United States)

    Menezes, Natália; Alves, Van Sérgio; Smith, Cristiane Morais

    2016-12-01

    The experimental observation of the renormalization of the Fermi velocity v F as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field B, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in B, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity for the massive case arises due to electronic interactions. In addition, for gapped systems, we observe a running of the mass parameter.

  9. Tensor RG calculations and quantum simulations near criticality

    CERN Document Server

    Meurice, Y; Tsai, Shan-Wen; Unmuth-Yockey, J; Yang, Li-Ping; Zhang, Jin

    2016-01-01

    We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models.

  10. 一维离散椭圆共振问题解的多重性%The Multiplicity of Solutions of 1-Dimensional Discrete Elliptic Problem with Resonance

    Institute of Scientific and Technical Information of China (English)

    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.

  11. Interval arithmetic in calculations

    Science.gov (United States)

    Bairbekova, Gaziza; Mazakov, Talgat; Djomartova, Sholpan; Nugmanova, Salima

    2016-10-01

    Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.

  12. Unit Cost Compendium Calculations

    Data.gov (United States)

    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...

  13. EFFECTIVE DISCHARGE CALCULATION GUIDE

    Institute of Scientific and Technical Information of China (English)

    D.S.BIEDENHARN; C.R.THORNE; P.J.SOAR; R.D.HEY; C.C.WATSON

    2001-01-01

    This paper presents a procedure for calculating the effective discharge for rivers with alluvial channels.An alluvial river adjusts the bankfull shape and dimensions of its channel to the wide range of flows that mobilize the boundary sediments. It has been shown that time-averaged river morphology is adjusted to the flow that, over a prolonged period, transports most sediment. This is termed the effective discharge.The effective discharge may be calculated provided that the necessary data are available or can be synthesized. The procedure for effective discharge calculation presented here is designed to have general applicability, have the capability to be applied consistently, and represent the effects of physical processes responsible for determining the channel, dimensions. An example of the calculations necessary and applications of the effective discharge concept are presented.

  14. Calculativeness and trust

    DEFF Research Database (Denmark)

    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...

  15. Magnetic Field Grid Calculator

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Properties Calculator will computes the estimated values of Earth's magnetic field(declination, inclination, vertical component, northerly...

  16. Scientific calculating peripheral

    Energy Technology Data Exchange (ETDEWEB)

    Ethridge, C.D.; Nickell, J.D. Jr.; Hanna, W.H.

    1979-09-01

    A scientific calculating peripheral for small intelligent data acquisition and instrumentation systems and for distributed-task processing systems is established with a number-oriented microprocessor controlled by a single component universal peripheral interface microcontroller. A MOS/LSI number-oriented microprocessor provides the scientific calculating capability with Reverse Polish Notation data format. Master processor task definition storage, input data sequencing, computation processing, result reporting, and interface protocol is managed by a single component universal peripheral interface microcontroller.

  17. Current interruption transients calculation

    CERN Document Server

    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,

  18. Shielding calculations for SSC

    Energy Technology Data Exchange (ETDEWEB)

    Van Ginneken, A.

    1990-03-01

    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.

  19. Geometric unsharpness calculations

    Energy Technology Data Exchange (ETDEWEB)

    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)

  20. Source and replica calculations

    Energy Technology Data Exchange (ETDEWEB)

    Whalen, P.P.

    1994-02-01

    The starting point of the Hiroshima-Nagasaki Dose Reevaluation Program is the energy and directional distributions of the prompt neutron and gamma-ray radiation emitted from the exploding bombs. A brief introduction to the neutron source calculations is presented. The development of our current understanding of the source problem is outlined. It is recommended that adjoint calculations be used to modify source spectra to resolve the neutron discrepancy problem.

  1. INVAP's Nuclear Calculation System

    OpenAIRE

    Ignacio Mochi

    2011-01-01

    Since its origins in 1976, INVAP has been on continuous development of the calculation system used for design and optimization of nuclear reactors. The calculation codes have been polished and enhanced with new capabilities as they were needed or useful for the new challenges that the market imposed. The actual state of the code packages enables INVAP to design nuclear installations with complex geometries using a set of easy-to-use input files that minimize user errors due to confusion or mi...

  2. Calculations in apheresis.

    Science.gov (United States)

    Neyrinck, Marleen M; Vrielink, Hans

    2015-02-01

    It's important to work smoothly with your apheresis equipment when you are an apheresis nurse. Attention should be paid to your donor/patient and the product you're collecting. It gives additional value to your work when you are able to calculate the efficiency of your procedures. You must be capable to obtain an optimal product without putting your donor/patient at risk. Not only the total blood volume (TBV) of the donor/patient plays an important role, but also specific blood values influence the apheresis procedure. Therefore, not all donors/patients should be addressed in the same way. Calculation of TBV, extracorporeal volume, and total plasma volume is needed. Many issues determine your procedure time. By knowing the collection efficiency (CE) of your apheresis machine, you can calculate the number of blood volumes to be processed to obtain specific results. You can calculate whether you need one procedure to obtain specific results or more. It's not always needed to process 3× the TBV. In this way, it can be avoided that the donor/patient is needless long connected to the apheresis device. By calculating the CE of each device, you can also compare the various devices for quality control reasons, but also nurses/operators.

  3. OFTIFEL PERSONALIZED NUTRITIONAL CALCULATOR

    Directory of Open Access Journals (Sweden)

    Malte BETHKE

    2016-11-01

    Full Text Available A food calculator for elderly people was elaborated by Centiv GmbH, an active partner in the European FP7 OPTIFEL Project, based on the functional requirement specifications and the existing recommendations for daily allowances across Europe, data which were synthetized and used to give aims in amounts per portion. The OPTIFEL Personalised Nutritional Calculator is the only available online tool which allows to determine on a personalised level the required nutrients for elderly people (65+. It has been developed mainly to support nursing homes providing best possible (personalised nutrient enriched food to their patients. The European FP7 OPTIFEL project “Optimised Food Products for Elderly Populations” aims to develop innovative products based on vegetables and fruits for elderly populations to increase length of independence. The OPTIFEL Personalised Nutritional Calculator is recommended to be used by nursing homes.

  4. INVAP's Nuclear Calculation System

    Directory of Open Access Journals (Sweden)

    Ignacio Mochi

    2011-01-01

    Full Text Available Since its origins in 1976, INVAP has been on continuous development of the calculation system used for design and optimization of nuclear reactors. The calculation codes have been polished and enhanced with new capabilities as they were needed or useful for the new challenges that the market imposed. The actual state of the code packages enables INVAP to design nuclear installations with complex geometries using a set of easy-to-use input files that minimize user errors due to confusion or misinterpretation. A set of intuitive graphic postprocessors have also been developed providing a fast and complete visualization tool for the parameters obtained in the calculations. The capabilities and general characteristics of this deterministic software package are presented throughout the paper including several examples of its recent application.

  5. Calculating Quenching Weights

    CERN Document Server

    Salgado, C A; Salgado, Carlos A.; Wiedemann, Urs Achim

    2003-01-01

    We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus colli...

  6. Spin Resonance Strength Calculations

    Science.gov (United States)

    Courant, E. D.

    2009-08-01

    In calculating the strengths of depolarizing resonances it may be convenient to reformulate the equations of spin motion in a coordinate system based on the actual trajectory of the particle, as introduced by Kondratenko, rather than the conventional one based on a reference orbit. It is shown that resonance strengths calculated by the conventional and the revised formalisms are identical. Resonances induced by radiofrequency dipoles or solenoids are also treated; with rf dipoles it is essential to consider not only the direct effect of the dipole but also the contribution from oscillations induced by it.

  7. Spin resonance strength calculations

    Energy Technology Data Exchange (ETDEWEB)

    Courant,E.D.

    2008-10-06

    In calculating the strengths of depolarizing resonances it may be convenient to reformulate the equations of spin motion in a coordinate system based on the actual trajectory of the particle, as introduced by Kondratenko, rather than the conventional one based on a reference orbit. It is shown that resonance strengths calculated by the conventional and the revised formalisms are identical. Resonances induced by radiofrequency dipoles or solenoids are also treated; with rf dipoles it is essential to consider not only the direct effect of the dipole but also the contribution from oscillations induced by it.

  8. A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time

    CERN Document Server

    Brihaye, Y

    2011-01-01

    We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct "hairy" black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.

  9. Nonlinear Self-Adjointness, Conservation Laws and Soliton-Cnoidal Wave Interaction Solutions of (2+1)-Dimensional Modified Dispersive Water-Wave System

    Science.gov (United States)

    Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li

    2017-01-01

    This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41

  10. New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

    Science.gov (United States)

    Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

    In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

  11. The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

    Science.gov (United States)

    Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef

    2013-01-01

    Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

  12. A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

    Institute of Scientific and Technical Information of China (English)

    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.

  13. Density-fluctuation symbolic computation on the (3+1)-dimensional variable-coefficient Kudryashov-Sinelshchikov equation for a bubbly liquid with experimental support

    Science.gov (United States)

    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.

  14. Finite Genus Solutions to the Generalised Kaup-Newell Hierarchy and Two 2+1 Dimensional Modified Korteweg-de Vries Equations

    Science.gov (United States)

    Yang, Xiao; Han, Jiayan

    2017-07-01

    A generalised Kaup-Newell (gKN) hierarchy is introduced, which starts with a system of first-order ordinary differential equations and includes the Gerdjikov-Ivanov equation. By introducing an appropriate generating function, its related Hamiltonian systems and algebraic curve are given. The Hamiltonian systems are proved to be integrable, then the gKN hierarchy is solved by Hamiltonian flows. The algebraic curve is provided with suitable genus, then based on the trace formula and Riemann-Jacobi inversion theorem, finite genus solutions of the gKN hierarchy are obtained. Besides, two 2+1 dimensional modified Korteweg-de Vries (mKdV) equations are also solved.

  15. LiZn(4 - x) (x = 0.825) as a (3 + 1)-dimensional modulated derivative of hexagonal close packing.

    Science.gov (United States)

    Pavlyuk, Volodymyr; Chumak, Ihor; Akselrud, Lev; Lidin, Sven; Ehrenberg, Helmut

    2014-04-01

    The (3+1)-dimensional modulated structure of the LiZn(4 - x) (x = 0.825) binary compound has been determined in the superspace. The compound crystallizes in the orthorhombic superspace group Cmcm(α00)0s0 with a = 2.7680 (6), b = 4.7942 (6), c = 4.3864 (9) Å, modulation wavevector: q ≃ 4/7a*. The structure is a derivative from the hexagonal close packing. The cubo-octahedron as a coordination polyhedron (c.n. = 12) is typical for all atoms. Bonding between atoms is explored by means of the TB-LMTO-ASA program package. The absence of strong interatomic interactions in LiZn(4 - x) is the main reason for the possible structure transformations.

  16. Dynamics Calculation of Spoke

    Institute of Scientific and Technical Information of China (English)

    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

  17. Haida Numbers and Calculation.

    Science.gov (United States)

    Cogo, Robert

    Experienced traders in furs, blankets, and other goods, the Haidas of the 1700's had a well-developed decimal system for counting and calculating. Their units of linear measure included the foot, yard, and fathom, or six feet. This booklet lists the numbers from 1 to 20 in English and Haida; explains the Haida use of ten, hundred, and thousand…

  18. Curvature calculations with GEOCALC

    Energy Technology Data Exchange (ETDEWEB)

    Moussiaux, A.; Tombal, P.

    1987-04-01

    A new method for calculating the curvature tensor has been recently proposed by D. Hestenes. This method is a particular application of geometric calculus, which has been implemented in an algebraic programming language on the form of a package called GEOCALC. They show how to apply this package to the Schwarzchild case and they discuss the different results.

  19. Daylight calculations in practice

    DEFF Research Database (Denmark)

    Iversen, Anne; Roy, Nicolas; Hvass, Mette;

    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...

  20. Radioprotection calculations for MEGAPIE.

    Science.gov (United States)

    Zanini, L

    2005-01-01

    The MEGAwatt PIlot Experiment (MEGAPIE) liquid lead-bismuth spallation neutron source will commence operation in 2006 at the SINQ facility of the Paul Scherrer Institut. Such an innovative system presents radioprotection concerns peculiar to a liquid spallation target. Several radioprotection issues have been addressed and studied by means of the Monte Carlo transport code, FLUKA. The dose rates in the room above the target, where personnel access may be needed at times, from the activated lead-bismuth and from the volatile species produced were calculated. Results indicate that the dose rate level is of the order of 40 mSv h(-1) 2 h after shutdown, but it can be reduced below the mSv h(-1) level with slight modifications to the shielding. Neutron spectra and dose rates from neutron transport, of interest for possible damage to radiation sensitive components, have also been calculated.

  1. PIC: Protein Interactions Calculator.

    Science.gov (United States)

    Tina, K G; Bhadra, R; Srinivasan, N

    2007-07-01

    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 bonds, interactions between hydrophobic residues, ionic interactions, hydrogen bonds, aromatic-aromatic interactions, aromatic-sulphur interactions and cation-pi interactions within a protein or between proteins in a complex. Interactions are calculated on the basis of standard, published criteria. The identified interactions between residues can be visualized using a RasMol and Jmol interface. The advantage with PIC server is the easy availability of inter-residue interaction calculations in a single site. It also determines the accessible surface area and residue-depth, which is the distance of a residue from the surface of the protein. User can also recognize specific kind of interactions, such as apolar-apolar residue interactions or ionic interactions, that are formed between buried or exposed residues or near the surface or deep inside.

  2. Zero Temperature Hope Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Rozsnyai, B F

    2002-07-26

    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

  3. Linewidth calculations and simulations

    CERN Document Server

    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.

  4. Acute calculous cholecystitis

    OpenAIRE

    Angarita, Fernando A.; University Health Network; Acuña, Sergio A.; Mount Sinai Hospital; Jimenez, Carolina; University of Toronto; Garay, Javier; Pontificia Universidad Javeriana; Gömez, David; University of Toronto; Domínguez, Luis Carlos; Pontificia Universidad Javeriana

    2010-01-01

    Acute calculous cholecystitis is the most important cause of cholecystectomies worldwide. We review the physiopathology of the inflammatory process in this organ secondary to biliary tract obstruction, as well as its clinical manifestations, workup, and the treatment it requires. La colecistitis calculosa aguda es la causa más importante de colecistectomías en el mundo. En esta revisión de tema se resume la fisiopatología del proceso inflamatorio de la vesículabiliar secundaria a la obstru...

  5. Calculations in furnace technology

    CERN Document Server

    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

  6. Traveling Wave Solutions for Fifth Order (1+1-Dimensional Kaup-Keperschmidt Equation with the Help of Exp(-Phi-Expansion Method

    Directory of Open Access Journals (Sweden)

    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

  7. OECD Maximum Residue Limit Calculator

    Science.gov (United States)

    With the goal of harmonizing the calculation of maximum residue limits (MRLs) across the Organisation for Economic Cooperation and Development, the OECD has developed an MRL Calculator. View the calculator.

  8. Calculating Speed of Sound

    Science.gov (United States)

    Bhatnagar, Shalabh

    2017-01-01

    Sound is an emerging source of renewable energy but it has some limitations. The main limitation is, the amount of energy that can be extracted from sound is very less and that is because of the velocity of the sound. The velocity of sound changes as per medium. If we could increase the velocity of the sound in a medium we would be probably able to extract more amount of energy from sound and will be able to transfer it at a higher rate. To increase the velocity of sound we should know the speed of sound. If we go by the theory of classic mechanics speed is the distance travelled by a particle divided by time whereas velocity is the displacement of particle divided by time. The speed of sound in dry air at 20 °C (68 °F) is considered to be 343.2 meters per second and it won't be wrong in saying that 342.2 meters is the velocity of sound not the speed as it's the displacement of the sound not the total distance sound wave covered. Sound travels in the form of mechanical wave, so while calculating the speed of sound the whole path of wave should be considered not just the distance traveled by sound. In this paper I would like to focus on calculating the actual speed of sound wave which can help us to extract more energy and make sound travel with faster velocity.

  9. Multilayer optical calculations

    CERN Document Server

    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 ...

  10. Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Broer-Kaup-Kupershmidt system in the shallow water of uniform depth

    Science.gov (United States)

    Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Mao, Bing-Qing

    2017-03-01

    Under investigation in this paper is a (2+1)-dimensional Broer-Kaup-Kupershmidt system for the nonlinear and dispersive long gravity waves on two horizontal directions in the shallow water of uniform depth. Bilinear forms, Bäcklund transformation and Lax pair are derived based on the Bell polynomials and symbolic computation. One- and two-soliton solutions with a real function ϕ(y) are constructed via the Hirota method, where y is the scaled space coordinate. Propagation and interaction of the solitons are illustrated graphically: (i) ϕ(y) affects the shape of the solitons. (ii) Interaction of the solitons including the elastic and inelastic interactions are discussed. When the solitons' interaction is elastic, the amplitude, velocity and shape of the soliton remain invariant after the interaction except for a phase shift, and the smaller-amplitude soliton has a larger phase shift. (iii) Height of the water surface above a horizontal bottom can be a bell-shaped soliton or an upside-down bell-shaped soliton under certain conditions, while horizontal velocity of the water wave always keeps bell-shaped.

  11. Probing the equation of state in Au+Au at 11 GeV/nucleon with (3+1)-dimensional hydrodynamics

    Science.gov (United States)

    Arbex, N.; Ornik, U.; Plümer, M.; Weiner, R. M.

    1997-02-01

    The effect of (i) the phase transition between a quark gluon plasma (QGP) and a hadron gas and (ii) the number of resonance degrees of freedom in the hadronic phase on the single inclusive distributions of 16 different types of produced hadrons for Au+Au collisions at the Brookhaven Alternating Gradient Synchroton (AGS) energies is studied. We have used an exact numerical solution of the relativistic hydrodynamical equations without free parameters which, because of its (3+1)-dimensional character, constitutes a considerable improvement over the classical Landau solution. We assume chemical equilibration and we use two different equations of state (EOS): one describing a phase transition from QGP to the hadronic phase and two versions of a purely hadronic EOS; we find that the first one gives an overall better description of the Au+Au experimental data at AGS energies. We reproduce and analyze measured meson and proton spectra and also make predictions for antiprotons, deltas, antideltas, and hyperons. The low mt enhancement in π- spectra is explained by baryon number conservation and strangeness equilibration. The sensitivity of various production channels to the EOS is analyzed.

  12. Some Interaction Solutions of a Reduced Generalised (3+1)-Dimensional Shallow Water Wave Equation for Lump Solutions and a Pair of Resonance Solitons

    Science.gov (United States)

    Wang, Yao; Chen, Mei-Dan; Li, Xian; Li, Biao

    2017-05-01

    Through Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.

  13. Soliton-like, periodic wave and rational solutions for a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid

    Science.gov (United States)

    Jia, Shu-Liang; Gao, Yi-Tian; Hu, Lei; Huang, Qian-Min; Hu, Wen-Qiang

    2017-02-01

    Under investigation in this paper is a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid. With the aid of the bilinear form, Nth-order soliton-like solutions are obtained via the Pffafian method, rational solutions are derived with the ansätz method and periodic wave solutions are constructed via the Riemann theta function. The analytic solutions obtained via the Pffafian method are similar to the kink solitons, while, the interaction regions with little peaks are different from those of the usual kink solitons. The rational solutions which have one upper lump and one down deep hole are the bright-dark solitary wave solutions. For the rational solutions which combine the kink solitary wave with breather-like wave, asymptotic behaviors show that the breather-like wave disappears with the evolution of t. Relations between the one-soliton solutions and one-periodic wave solutions are analysed, which exhibit the asymptotic behaviors of the periodic waves.

  14. Molecular Dynamics Calculations

    Science.gov (United States)

    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

  15. Impact cratering calculations

    Science.gov (United States)

    Ahrens, Thomas J.; Okeefe, J. D.; Smither, C.; Takata, T.

    1991-01-01

    In the course of carrying out finite difference calculations, it was discovered that for large craters, a previously unrecognized type of crater (diameter) growth occurred which was called lip wave propagation. This type of growth is illustrated for an impact of a 1000 km (2a) silicate bolide at 12 km/sec (U) onto a silicate half-space at earth gravity (1 g). The von Misses crustal strength is 2.4 kbar. The motion at the crater lip associated with this wave type phenomena is up, outward, and then down, similar to the particle motion of a surface wave. It is shown that the crater diameter has grown d/a of approximately 25 to d/a of approximately 4 via lip propagation from Ut/a = 5.56 to 17.0 during the time when rebound occurs. A new code is being used to study partitioning of energy and momentum and cratering efficiency with self gravity for finite-sized objects rather than the previously discussed planetary half-space problems. These are important and fundamental subjects which can be addressed with smoothed particle hydrodynamic (SPH) codes. The SPH method was used to model various problems in astrophysics and planetary physics. The initial work demonstrates that the energy budget for normal and oblique impacts are distinctly different than earlier calculations for silicate projectile impact on a silicate half space. Motivated by the first striking radar images of Venus obtained by Magellan, the effect of the atmosphere on impact cratering was studied. In order the further quantify the processes of meteor break-up and trajectory scattering upon break-up, the reentry physics of meteors striking Venus' atmosphere versus that of the Earth were studied.

  16. MBPT calculations with ABINIT

    Science.gov (United States)

    Giantomassi, Matteo; Huhs, Georg; Waroquiers, David; Gonze, Xavier

    2014-03-01

    Many-Body Perturbation Theory (MBPT) defines a rigorous framework for the description of excited-state properties based on the Green's function formalism. Within MBPT, one can calculate charged excitations using e.g. Hedin's GW approximation for the electron self-energy. In the same framework, neutral excitations are also well described through the solution of the Bethe-Salpeter equation (BSE). In this talk, we report on the recent developments concerning the parallelization of the MBPT algorithms available in the ABINIT code (www.abinit.org). In particular, we discuss how to improve the parallel efficiency thanks to a hybrid version that employs MPI for the coarse-grained parallelization and OpenMP (a de facto standard for parallel programming on shared memory architectures) for the fine-grained parallelization of the most CPU-intensive parts. Benchmark results obtained with the new implementation are discussed. Finally, we present results for the GW corrections of amorphous SiO2 in the presence of defects and the BSE absorption spectrum. This work has been supported by the Prace project (PaRtnership for Advanced Computing in Europe, http://www.prace-ri.eu).

  17. The rating reliability calculator

    Directory of Open Access Journals (Sweden)

    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.

  18. Classification of (2+1)-dimensional topological order and symmetry-protected topological order for bosonic and fermionic systems with on-site symmetries

    Science.gov (United States)

    Lan, Tian; Kong, Liang; Wen, Xiao-Gang

    2017-06-01

    In 2+1-dimensional space-time, gapped quantum states are always gapped quantum liquids (GQL) which include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQLs for both bosonic and fermionic systems: 2+1D bosonic/fermionic GQLs with finite on-site symmetry are classified by nondegenerate unitary braided fusion categories over a symmetric fusion category (SFC) E , abbreviated as UMTC/E, together with their modular extensions and total chiral central charges. In our classification, SFC E describes the symmetry, which is Rep(G ) for bosonic symmetry G , or sRep(Gf) for fermionic symmetry Gf. As a special case of the above result, we find that the modular extensions of Rep(G ) classify the 2+1D bosonic SPT states of symmetry G , while the c =0 modular extensions of sRep(Gf) classify the 2+1D fermionic SPT states of symmetry Gf. Many fermionic SPT states are studied based on the constructions from free-fermion models. But free-fermion constructions cannot produce all fermionic SPT states. Our classification does not have such a drawback. We show that, for interacting 2+1D fermionic systems, there are exactly 16 superconducting phases with no symmetry and no fractional excitations (up to E8 bosonic quantum Hall states). Also, there are exactly 8 Z2×Z2f -SPT phases, 2 Z8f-SPT phases, and so on. Besides, we show that two topological orders with identical bulk excitations and central charge always differ by the stacking of the SPT states of the same symmetry.

  19. Integral method for the calculation of Hawking radiation in dispersive media. II. Asymmetric asymptotics.

    Science.gov (United States)

    Robertson, Scott

    2014-11-01

    Analog gravity experiments make feasible the realization of black hole space-times in a laboratory setting and the observational verification of Hawking radiation. Since such analog systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary 1+1-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalized to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.

  20. New Arsenic Cross Section Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Kawano, Toshihiko [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-03-04

    This report presents calculations for the new arsenic cross section. Cross sections for 73,74,75 As above the resonance range were calculated with a newly developed Hauser-Feshbach code, CoH3.

  1. Cosmological Calculations on the GPU

    CERN Document Server

    Bard, Deborah; Allen, Mark T; Yepremyan, Hasmik; Kratochvil, Jan M

    2012-01-01

    Cosmological measurements require the calculation of nontrivial quantities over large datasets. The next generation of survey telescopes (such as DES, PanSTARRS, and LSST) will yield measurements of billions of galaxies. The scale of these datasets, and the nature of the calculations involved, make cosmological calculations ideal models for implementation on graphics processing units (GPUs). We consider two cosmological calculations, the two-point angular correlation function and the aperture mass statistic, and aim to improve the calculation time by constructing code for calculating them on the GPU. Using CUDA, we implement the two algorithms on the GPU and compare the calculation speeds to comparable code run on the CPU. We obtain a code speed-up of between 10 - 180x faster, compared to performing the same calculation on the CPU. The code has been made publicly available.

  2. Application of a 1-Dimensional Viscoelastic Bending Beam Model to the Buoyant Terminus of Lake-Calving Mendenhall Glacier, Southeast Alaska

    Science.gov (United States)

    Boyce, E.; Motyka, R. J.; Bueler, E.

    2005-12-01

    Mendenhall Glacier is a lake-calving glacier in southeastern Alaska that is experiencing substantial thinning and increasingly rapid recession. The recent retreat of the terminus has been controlled mainly by calving dynamics, and therefore may not be directly driven by climatic trends. Lake-terminating glaciers form a population distinct from both tidewater glaciers and polar ice tongues, with some similarities to both groups. Unlike polar ice tongues, it is generally thought that temperate tidewater glaciers are unable to maintain a floating front. Studies of Mendenhall Glacier and other temperate lake-calving glaciers suggest that partial terminus floatation may not be uncommon, and may play a role in calving. At Mendenhall, we observed upward displacement of the calving front during a two-year period, which culminated in large-scale calving and terminus collapse during summer 2004. Rapid thinning and simultaneous retreat into a deeper basin led to floatation conditions along approximately 50 % of the calving front. This unstable terminus geometry lasted for ~ 2 years. We used a simple 1-dimensional model to investigate the transient response of a floating glacier tongue to buoyant forcing. The basic equations we used to model a viscoelastic bending beam of ice were developed by Reeh et al. (2003) We solve the model numerically using a Chebyshev spectral method. Rather than look at deflections along a transverse profile, we apply the appropriate boundary conditions for a grounding line and floating front. The model results may be compared to the measured glacier upwarping. Temperatures in Mendenhall Lake adjacent to the calving face show a cooling trend (4 to 2 °C) over the summer melt season and a stable thermal stratification, suggesting little or no convection along the calving front. Although melting of a submerged ice cliff may be an important mechanism for ice loss at tidewater glaciers, lack of convection and low water temperatures indicate it is much

  3. One-dimensional linear calculation of the heat flux from infrared and thermocouple measurements at Jet tokamak; Calcul 1D lineaire du flux de chaleur par inversion des mesures de temperatures infrarouges et des thermocouples du Tokamak Jet

    Energy Technology Data Exchange (ETDEWEB)

    Poyet, M

    2005-07-01

    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.)

  4. Equilibrium calculations of firework mixtures

    Energy Technology Data Exchange (ETDEWEB)

    Hobbs, M.L. [Sandia National Labs., Albuquerque, NM (United States); Tanaka, Katsumi; Iida, Mitsuaki; Matsunaga, Takehiro [National Inst. of Materials and Chemical Research, Tsukuba, Ibaraki (Japan)

    1994-12-31

    Thermochemical equilibrium calculations have been used to calculate detonation conditions for typical firework components including three report charges, two display charges, and black powder which is used as a fuse or launch charge. Calculations were performed with a modified version of the TIGER code which allows calculations with 900 gaseous and 600 condensed product species at high pressure. The detonation calculations presented in this paper are thought to be the first report on the theoretical study of firework detonation. Measured velocities for two report charges are available and compare favorably to predicted detonation velocities. However, the measured velocities may not be true detonation velocities. Fast deflagration rather than an ideal detonation occurs when reactants contain significant amounts of slow reacting constituents such as aluminum or titanium. Despite such uncertainties in reacting pyrotechnics, the detonation calculations do show the complex nature of condensed phase formation at elevated pressures and give an upper bound for measured velocities.

  5. Global nuclear-structure calculations

    Energy Technology Data Exchange (ETDEWEB)

    Moeller, P.; Nix, J.R.

    1990-04-20

    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 {epsilon}{sub 2} and {epsilon}{sub 4} 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 {Beta}-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.

  6. CALCULATION OF LASER CUTTING COSTS

    Directory of Open Access Journals (Sweden)

    Bogdan Nedic

    2016-09-01

    Full Text Available The paper presents description methods of metal cutting and calculation of treatment costs based on model that is developed on Faculty of mechanical engineering in Kragujevac. Based on systematization and analysis of large number of calculation models of cutting with unconventional methods, mathematical model is derived, which is used for creating a software for calculation costs of metal cutting. Software solution enables resolving the problem of calculating the cost of laser cutting, comparison' of costs made by other unconventional methods and provides documentation that consists of reports on estimated costs.

  7. Calculation of Spectra of Solids:

    DEFF Research Database (Denmark)

    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 condu...

  8. Calculator. Owning a Small Business.

    Science.gov (United States)

    Parma City School District, OH.

    Seven activities are presented in this student workbook designed for an exploration of small business ownership and the use of the calculator in this career. Included are simulated situations in which students must use a calculator to compute property taxes; estimate payroll taxes and franchise taxes; compute pricing, approximate salaries,…

  9. Calculating charged defects using CRYSTAL

    Science.gov (United States)

    Bailey, Christine L.; Liborio, Leandro; Mallia, Giuseppe; Tomić, Stanko; Harrison, Nicholas M.

    2010-07-01

    The methodology for the calculation of charged defects using the CRYSTAL program is discussed. Two example calculations are used to illustrate the methodology: He+ ions in a vacuum and two intrinsic charged defects, Cu vacancies and Ga substitution for Cu, in the chalcopyrite CuGaS2.

  10. Economic calculation in socialist countries

    NARCIS (Netherlands)

    Ellman, M.; Durlauf, S.N.; Blume, L.E.

    2008-01-01

    In the 1930s, when the classical socialist system emerged, economic decisions were based not on detailed and precise economic methods of calculation but on rough and ready political methods. An important method of economic calculation - particularly in the post-Stalin period - was that of

  11. Closure and Sealing Design Calculation

    Energy Technology Data Exchange (ETDEWEB)

    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

  12. Practical astronomy with your calculator

    CERN Document Server

    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

  13. The Collective Practice of Calculation

    DEFF Research Database (Denmark)

    Schrøder, Ida

    on the idea that professions are hybrids by introducing the notion of qualculation as an entry point to investigate decision-making in child protection work as an extreme case of calculating on the basis of other elements than quantitative numbers. The analysis reveals that it takes both calculation...... and judgement to reach decisions to invest in social services. The line is not drawn between the two, but between the material arrangements that make decisions possible. This implies that the insisting on qualitatively based decisions gives the professionals agency to collectively engage in practical...... arrangements that affords calculations of both qualitative measures of the individual case and distant accounting numbers....

  14. Transfer Area Mechanical Handling Calculation

    Energy Technology Data Exchange (ETDEWEB)

    B. Dianda

    2004-06-23

    This calculation is intended to support the License Application (LA) submittal of December 2004, in accordance with the directive given by DOE correspondence received on the 27th of January 2004 entitled: ''Authorization for Bechtel SAX Company L.L. C. to Include a Bare Fuel Handling Facility and Increased Aging Capacity in the License Application, Contract Number DE-AC28-01R W12101'' (Arthur, W.J., I11 2004). This correspondence was appended by further Correspondence received on the 19th of February 2004 entitled: ''Technical Direction to Bechtel SAIC Company L.L. C. for Surface Facility Improvements, Contract Number DE-AC28-OIRW12101; TDL No. 04-024'' (BSC 2004a). These documents give the authorization for a Fuel Handling Facility to be included in the baseline. The purpose of this calculation is to establish preliminary bounding equipment envelopes and weights for the Fuel Handling Facility (FHF) transfer areas equipment. This calculation provides preliminary information only to support development of facility layouts and preliminary load calculations. The limitations of this preliminary calculation lie within the assumptions of section 5 , as this calculation is part of an evolutionary design process. It is intended that this calculation is superseded as the design advances to reflect information necessary to support License Application. The design choices outlined within this calculation represent a demonstration of feasibility and may or may not be included in the completed design. This calculation provides preliminary weight, dimensional envelope, and equipment position in building for the purposes of defining interface variables. This calculation identifies and sizes major equipment and assemblies that dictate overall equipment dimensions and facility interfaces. Sizing of components is based on the selection of commercially available products, where applicable. This is not a specific recommendation for the future use

  15. Calculation of Rydberg interaction potentials

    Science.gov (United States)

    Weber, Sebastian; Tresp, Christoph; Menke, Henri; Urvoy, Alban; Firstenberg, Ofer; Büchler, Hans Peter; Hofferberth, Sebastian

    2017-07-01

    The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be fine-tuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipole-dipole interaction term are no longer sufficient. In this tutorial, we review all relevant aspects of the full calculation of Rydberg interaction potentials. We discuss the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments and the inclusion of electromagnetic fields with arbitrary direction. We focus specifically on symmetry arguments and selection rules, which greatly reduce the size of the Hamiltonian matrix, enabling the direct diagonalization of the Hamiltonian up to higher multipole orders on a desktop computer. Finally, we present example calculations showing the relevance of the full interaction calculation to current experiments. Our software for calculating Rydberg potentials including all features discussed in this tutorial is available as open source.

  16. A Romberg Integral Spreadsheet Calculator

    Directory of Open Access Journals (Sweden)

    Kim Gaik Tay

    2015-04-01

    Full Text Available Motivated by the work of Richardson’s extrapolation spreadsheet calculator up to level 4 to approximate definite differentiation, we have developed a Romberg integral spreadsheet calculator to approximate definite integral. The main feature of this version of spreadsheet calculator is a friendly graphical user interface developed to capture the needed information to solve the integral by Romberg method. Users simply need to enter the variable in the integral, function to be integrated, lower and upper limits of the integral, select the desired accuracy of computation, select the exact function if it exists and lastly click the Compute button which is associated with VBA programming written to compute Romberg integral table. The full solution of the Romberg integral table up to any level can be obtained quickly and easily using this method. The attached spreadsheet calculator together with this paper helps educators to prepare their marking scheme easily and assist students in checking their answers instead of reconstructing the answers from scratch. A summative evaluation of this Romberg Spreadsheet Calculator has been conducted by involving 36 students as sample. The data was collected using questionnaire. The findings showed that the majority of the students agreed that the Romberg Spreadsheet Calculator provides a structured learning environment that allows learners to be guided through a step-by-step solution.

  17. SIMULATE-4 pin power calculations

    Energy Technology Data Exchange (ETDEWEB)

    Bahadir, T. [Studsvik Scandpower, Inc., 1087 Beacon St., Newton, MA 02459 (United States); Lindahl, S. Oe [Studsvik Scandpower AB, Hantverkargatan 2A, SE-722 12 Vasteraas (Sweden)

    2006-07-01

    A new pin power reconstruction module has been implemented in Studsvik Scandpower's next generation nodal code, SIMULATE-4. Heterogeneous pin powers are calculated by modulating multi-group pin powers from the sub-mesh solver of SIMULATE-4 with pin form factors from single-assembly CASMO-5 lattice calculations. The multi-group pin power model captures instantaneous spectral effects, and actinide tracking on the assembly sub-mesh describes exposure-induced pin power variations. Model details and verification tests against high order multi-assembly transport methods are presented. The accuracy of the new methods is also demonstrated by comparing SIMULATE-4 calculations with measured critical experiment pin powers. (authors)

  18. Insertion device calculations with mathematica

    Energy Technology Data Exchange (ETDEWEB)

    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.

  19. MFTF-B performance calculations

    Energy Technology Data Exchange (ETDEWEB)

    Thomassen, K.I.; Jong, R.A.

    1982-12-06

    In this report we document the operating scenario models and calculations as they exist and comment on those aspects of the models where performance is sensitive to the assumptions that are made. We also focus on areas where improvements need to be made in the mathematical descriptions of phenomena, work which is in progress. To illustrate the process of calculating performance, and to be very specific in our documentation, part 2 of this report contains the complete equations and sequence of calculations used to determine parameters for the MARS mode of operation in MFTF-B. Values for all variables for a particular set of input parameters are also given there. The point design so described is typical, but should be viewed as a snapshot in time of our ongoing estimations and predictions of performance.

  20. (2+1)-维反对称Nizhnik-Novikov-Veselov方程的Bcklund变换和局域相干结构%Backlund Transformation and Localized Coherent Structure for the(2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov Equation

    Institute of Scientific and Technical Information of China (English)

    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.

  1. Molecular calculations with B functions

    CERN Document Server

    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.

  2. Friction and wear calculation methods

    CERN Document Server

    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

  3. Multifragmentation calculated with relativistic forces

    CERN Document Server

    Feldmeier, H; Papp, G

    1995-01-01

    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 depe ndence 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. PACS: 25.70Mn, 25.75.+r

  4. Methods for Melting Temperature Calculation

    Science.gov (United States)

    Hong, Qi-Jun

    Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly. We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments. We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which

  5. Theoretical Calculation of MMF's Bandwidth

    Institute of Scientific and Technical Information of China (English)

    LI Xiao-fu; JIANG De-sheng; YU Hai-hu

    2004-01-01

    The difference between over-filled launch bandwidth (OFL BW) and restricted mode launch bandwidth (RML BW) is described. A theoretical model is founded to calculate the OFL BW of grade index multimode fiber (GI-MMF),and the result is useful to guide the modification of the manufacturing method.

  6. Data Acquisition and Flux Calculations

    DEFF Research Database (Denmark)

    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....

  7. Calculations for cosmic axion detection

    Science.gov (United States)

    Krauss, L.; Moody, J.; Wilczek, F.; Morris, D. E.

    1985-01-01

    Calculations are presented, using properly nomalized couplings and masses for Dine-Fischler-Srednicki axions, of power rates and signal temperatures for axion-photon conversion in microwave cavities. The importance of the galactic-halo axion line shape is emphasized. Spin-coupled detection as an alternative to magnetic-field-coupled detection is mentioned.

  8. ITER Port Interspace Pressure Calculations

    Energy Technology Data Exchange (ETDEWEB)

    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.

  9. Affect and Graphing Calculator Use

    Science.gov (United States)

    McCulloch, Allison W.

    2011-01-01

    This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…

  10. Ab Initio Calculations of Oxosulfatovanadates

    DEFF Research Database (Denmark)

    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...

  11. Dead reckoning calculating without instruments

    CERN Document Server

    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

  12. The Dental Trauma Internet Calculator

    DEFF Research Database (Denmark)

    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 pro...... were based on the tooth’s root development stage and other risk factors at the time of the injury. Conclusions This article explains the data base, the functionality and the statistical approach of the Internet risk calculator....... injuries: concussion, sub-luxation, extrusion, lateral luxation, intrusion, avulsion, crown fractures without luxation, root fractures and avulsion. The prognoses for pulp necrosis, pulp canal obliteration, infection related root resorption, ankylosis, surface resorption, marginal bone loss and tooth loss...

  13. CONTRIBUTION FOR MINING ATMOSPHERE CALCULATION

    Directory of Open Access Journals (Sweden)

    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.

  14. Archimedes' calculations of square roots

    CERN Document Server

    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.

  15. Parallel plasma fluid turbulence calculations

    Energy Technology Data Exchange (ETDEWEB)

    Leboeuf, J.N.; Carreras, B.A.; Charlton, L.A.; Drake, J.B.; Lynch, V.E.; Newman, D.E.; Sidikman, K.L.; Spong, D.A.

    1994-12-31

    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.

  16. AGING FACILITY CRITICALITY SAFETY CALCULATIONS

    Energy Technology Data Exchange (ETDEWEB)

    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

  17. Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms

    CERN Document Server

    Ablinger, Jakob; Raab, Clemens; Schneider, Carsten; Wißbrock, Fabian

    2014-01-01

    We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\\tau =2$ 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 $\\sim 30$ square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for $N \\in...

  18. Calculation of gas turbine characteristic

    Science.gov (United States)

    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.

  19. Semiclassical calculation of decay rates

    CERN Document Server

    Bessa, A; Fraga, E S

    2008-01-01

    Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around them, provide non-perturbative information about the theory. In this work, we discuss the calculation of the one-loop effective action from the semiclasssical viewpoint. We intend to use this formalism to obtain an accurate expression for the decay rate of non-static metastable states.

  20. Digital calculations of engine cycles

    CERN Document Server

    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

  1. Yet another partial wave calculator

    Energy Technology Data Exchange (ETDEWEB)

    Greenwald, Daniel; Rauch, Johannes [TUM, Munich (Germany)

    2016-07-01

    We will present a new C++ library for partial wave analysis: YAP - yet another partial wave calculator. YAP is intended for amplitude analyses of the decays of spin-0 heavy mesons (principally B and D) to multiple (3, 4, etc.) pseudoscalar mesons but is not hard coded for such situations and is flexible enough to handle other decay scenarios. The library allows for both model dependent and model independent analysis methods. We introduce the software, and demonstrate examples for generating Monte Carlo data efficiently, and for analyzing data (both with the aid of the Bayesian Analysis Toolkit).

  2. Rate calculation with colored noise

    CERN Document Server

    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.

  3. Electronics reliability calculation and design

    CERN Document Server

    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

  4. Band calculation of lonsdaleite Ge

    Science.gov (United States)

    Chen, Pin-Shiang; Fan, Sheng-Ting; Lan, Huang-Siang; Liu, Chee Wee

    2017-01-01

    The band structure of Ge in the lonsdaleite phase is calculated using first principles. Lonsdaleite Ge has a direct band gap at the Γ point. For the conduction band, the Γ valley is anisotropic with the low transverse effective mass on the hexagonal plane and the large longitudinal effective mass along the c axis. For the valence band, both heavy-hole and light-hole effective masses are anisotropic at the Γ point. The in-plane electron effective mass also becomes anisotropic under uniaxial tensile strain. The strain response of the heavy-hole mass is opposite to the light hole.

  5. Calculational Tool for Skin Contamination Dose Assessment

    CERN Document Server

    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.

  6. NATIONAL STORMWATER CALCULATOR USER'S GUIDE ...

    Science.gov (United States)

    The National Stormwater Calculator is a simple to use tool for computing small site hydrology for any location within the US. It estimates the amount of stormwater runoff generated from a site under different development and control scenarios over a long term period of historical rainfall. The analysis takes into account local soil conditions, slope, land cover and meteorology. Different types of low impact development (LID) practices (also known as green infrastructure) can be employed to help capture and retain rainfall on-site. Future climate change scenarios taken from internationally recognized climate change projections can also be considered. The calculator provides planning level estimates of capital and maintenance costs which will allow planners and managers to evaluate and compare effectiveness and costs of LID controls.The calculator’s primary focus is informing site developers and property owners on how well they can meet a desired stormwater retention target. It can be used to answer such questions as:• What is the largest daily rainfall amount that can be captured by a site in either its pre-development, current, or post-development condition?• To what degree will storms of different magnitudes be captured on site?• What mix of LID controls can be deployed to meet a given stormwater retention target?• How well will LID controls perform under future meteorological projections made by global climate change models?• What are the relativ

  7. Flow Field Calculations for Afterburner

    Institute of Scientific and Technical Information of China (English)

    ZhaoJianxing; LiuQuanzhong; 等

    1995-01-01

    In this paper a calculation procedure for simulating the coimbustion flow in the afterburner with the heat shield,flame stabilizer and the contracting nozzle is described and evaluated by comparison with experimental data.The modified two-equation κ-ε model is employed to consider the turbulence effects,and the κ-ε-g turbulent combustion model is used to determine the reaction rate.To take into accunt the influence of heat radiation on gas temperature distribution,heat flux model is applied to predictions of heat flux distributions,The solution domain spanned the entire region between centerline and afterburner wall ,with the heat shield represented as a blockage to the mesh.The enthalpy equation and wall boundary of the heat shield require special handling for two passages in the afterburner,In order to make the computer program suitable to engineering applications,a subregional scheme is developed for calculating flow fields of complex geometries.The computational grids employed are 100×100 and 333×100(non-uniformly distributed).The numerical results are compared with experimental data,Agreement between predictions and measurements shows that the numerical method and the computational program used in the study are fairly reasonable and appopriate for primary design of the afterburner.

  8. Dissecting Reactor Antineutrino Flux Calculations

    Science.gov (United States)

    Sonzogni, A. A.; McCutchan, E. A.; Hayes, A. C.

    2017-09-01

    Current predictions for the antineutrino yield and spectra from a nuclear reactor rely on the experimental electron spectra from 235U, 239Pu, 241Pu and a numerical method to convert these aggregate electron spectra into their corresponding antineutrino ones. In the present work we investigate quantitatively some of the basic assumptions and approximations used in the conversion method, studying first the compatibility between two recent approaches for calculating electron and antineutrino spectra. We then explore different possibilities for the disagreement between the measured Daya Bay and the Huber-Mueller antineutrino spectra, including the 238U contribution as well as the effective charge and the allowed shape assumption used in the conversion method. We observe that including a shape correction of about +6 % MeV-1 in conversion calculations can better describe the Daya Bay spectrum. Because of a lack of experimental data, this correction cannot be ruled out, concluding that in order to confirm the existence of the reactor neutrino anomaly, or even quantify it, precisely measured electron spectra for about 50 relevant fission products are needed. With the advent of new rare ion facilities, the measurement of shape factors for these nuclides, for many of which precise beta intensity data from TAGS experiments already exist, would be highly desirable.

  9. Calculation of sound propagation in fibrous materials

    DEFF Research Database (Denmark)

    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....

  10. Painless causality in defect calculations

    CERN Document Server

    Cheung, C; Cheung, Charlotte; Magueijo, Joao

    1997-01-01

    Topological defects must respect causality, a statement leading to restrictive constraints on the power spectrum of the total cosmological perturbations they induce. Causality constraints have for long been known to require the presence of an under-density in the surrounding matter compensating the defect network on large scales. This so-called compensation can never be neglected and significantly complicates calculations in defect scenarios, eg. computing cosmic microwave background fluctuations. A quick and dirty way to implement the compensation are the so-called compensation fudge factors. Here we derive the complete photon-baryon-CDM backreaction effects in defect scenarios. The fudge factor comes out as an algebraic identity and so we drop the negative qualifier ``fudge''. The compensation scale is computed and physically interpreted. Secondary backreaction effects exist, and neglecting them constitutes the well-defined approximation scheme within which one should consider compensation factor calculatio...

  11. Dyscalculia and the Calculating Brain.

    Science.gov (United States)

    Rapin, Isabelle

    2016-08-01

    Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals.

  12. A Note on 3 + 1 Dimensionality

    CERN Document Server

    Sidharth, B G

    2000-01-01

    Recent work by Castro, Granik and El Naschie has given a rationale for the three dimensionality of our physical space within the framework of cantorian fractal space time using similar ideas of quantized fractal space time and noncommutativity. We also deduce the same result. Interestingly this is also seen to provide a rationale for an unproven conjecture of Poincare.

  13. CONDOR-CITVAP-MCNP calculation line description

    Energy Technology Data Exchange (ETDEWEB)

    Villarino, Eduardo Anibal [INVAP S.E., San Carlos de Bariloche (Argentina)

    2002-07-01

    A general description of the CONDOR-CITVAP-MCNP calculation line is given. This calculation line starts at cross section library and allows burnup dependent detailed calculation using MCNP. This calculation line is divided in two main methodologies: CONDOR-CITVAP that allows the 3-Dimensional core burnup calculation and MCNP that performs detailed transport calculations, both methodologies are coupled using the NDDUMP code. A short description of the used codes are given: CONDOR code performs the cell calculation, generating burnup dependent macroscopic cross section and burnup dependent numerical densities per material. CITVAP codes perform the burnup dependent core calculation, including the fuel management and calculates the burnup distribution per material. NDDUMP code generates materials burnup dependent numerical densities to be used by MCNP code. This paper presents a detailed description of the CONDOR-CITVAP-MCNP calculation line and a numerical comparison of the proposed methodology. (author)

  14. Factors affecting calculation of L

    Science.gov (United States)

    Ciotola, Mark P.

    2001-08-01

    A detectable extraterrestrial civilization can be modeled as a series of successive regimes over time each of which is detectable for a certain proportion of its lifecycle. This methodology can be utilized to produce an estimate for L. Potential components of L include quantity of fossil fuel reserves, solar energy potential, quantity of regimes over time, lifecycle patterns of regimes, proportion of lifecycle regime is actually detectable, and downtime between regimes. Relationships between these components provide a means of calculating the lifetime of communicative species in a detectable state, L. An example of how these factors interact is provided, utilizing values that are reasonable given known astronomical data for components such as solar energy potential while existing knowledge about the terrestrial case is used as a baseline for other components including fossil fuel reserves, quantity of regimes over time, and lifecycle patterns of regimes, proportion of lifecycle regime is actually detectable, and gaps of time between regimes due to recovery from catastrophic war or resource exhaustion. A range of values is calculated for L when parameters are established for each component so as to determine the lowest and highest values of L. roadmap for SETI research at the SETI Institute for the next few decades. Three different approaches were identified. 1) Continue the radio search: build an affordable array incorporating consumer market technologies, expand the search frequency, and increase the target list to 100,000 stars. This array will also serve as a technology demonstration and enable the international radio astronomy community to realize an array that is a hundred times larger and capable (among other things) of searching a million stars. 2) Begin searches for very fast optical pulses from a million stars. 3) As Moore's Law delivers increased computational capacity, build an omni-directional sky survey array capable of detecting strong, transient

  15. Thermodynamic Calculations for Complex Chemical Mixtures

    Science.gov (United States)

    Mcbride, B. J.

    1986-01-01

    General computer program, CECTRP, developed for calculation of thermodynamic properties of complex mixtures with option to calculate transport properties of these mixtures. Free-energy minimization technique used in equilibrium calculation. Rigorous equations used in transport calculations. Program calculates equilibrium compositions and corresponding thermodynamic and transport properties of mixtures. CECTRP accommodates up to 24 reactants, 20 elements, and 600 products, 400 of which are condensed. Written in FORTRAN IV for any large computer system.

  16. Selfconsistent calculations for hyperdeformed nuclei

    Energy Technology Data Exchange (ETDEWEB)

    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.

  17. RTU Comparison Calculator Enhancement Plan

    Energy Technology Data Exchange (ETDEWEB)

    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.

  18. RTU Comparison Calculator Enhancement Plan

    Energy Technology Data Exchange (ETDEWEB)

    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.

  19. RTU Comparison Calculator Enhancement Plan

    Energy Technology Data Exchange (ETDEWEB)

    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.

  20. Explosion Calculations of SN1087

    Science.gov (United States)

    Wooden, Diane H.; Morrison, David (Technical Monitor)

    1994-01-01

    Explosion calculations of SNT1987A generate pictures of Rayleigh-Taylor fingers of radioactive Ni-56 which are boosted to velocities of several thousand km/s. From the KAO observations of the mid-IR iron lines, a picture of the iron in the ejecta emerges which is consistent with the "frothy iron fingers" having expanded to fill about 50% of the metal-rich volume of the ejecta. The ratio of the nickel line intensities yields a high ionization fraction of greater than or equal to 0.9 in the volume associated with the iron-group elements at day 415, before dust condenses in the ejecta. From the KAO observations of the dust's thermal emission, it is deduced that when the grains condense their infrared radiation is trapped, their apparent opacity is gray, and they have a surface area filling factor of about 50%. The dust emission from SN1987A is featureless: no 9.7 micrometer silicate feature, nor PAH features, nor dust emission features of any kind are seen at any time. The total dust opacity increases with time even though the surface area filling factor and the dust/gas ratio remain constant. This suggests that the dust forms along coherent structures which can maintain their radial line-of-sight opacities, i.e., along fat fingers. The coincidence of the filling factor of the dust and the filling factor of the iron strongly suggests that the dust condenses within the iron, and therefore the dust is iron-rich. It only takes approximately 4 x 10(exp -4) solar mass of dust for the ejecta to be optically thick out to approximately 100 micrometers; a lower limit of 4 x 10(exp -4) solar mass of condensed grains exists in the metal-rich volume, but much more dust could be present. The episode of dust formation started at about 530 days and proceeded rapidly, so that by 600 days 45% of the bolometric luminosity was being emitted in the IR; by 775 days, 86% of the bolometric luminosity was being reradiated by the dust. Measurements of the bolometric luminosity of SN1987A from

  1. CHP Energy and Emissions Savings Calculator

    Science.gov (United States)

    Download the CHP Emissions Calculator, a tool that calculates the difference between the anticipated carbon dioxide, methane, nitrous oxide, sulfur dioxide, and nitrogen oxide emissions from a CHP system to those of a separate heat and power system.

  2. Dynamics Calculation of Travel Wave Tube

    Institute of Scientific and Technical Information of China (English)

    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

  3. A New Approach for Calculating Vacuum Susceptibility

    Institute of Scientific and Technical Information of China (English)

    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.

  4. 76 FR 71431 - Civil Penalty Calculation Methodology

    Science.gov (United States)

    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... methodology for calculation of certain civil penalties. To induce compliance with federal regulations,...

  5. Pressure Vessel Calculations for VVER-440 Reactors

    Science.gov (United States)

    Hordósy, G.; Hegyi, Gy.; Keresztúri, A.; Maráczy, Cs.; Temesvári, E.; Vértes, P.; Zsolnay, É.

    2003-06-01

    Monte Carlo calculations were performed for a selected cycle of the Paks NPP Unit II to test a computational model. In the model the source term was calculated by the core design code KARATE and the neutron transport calculations were performed by the MCNP. Different forms of the source specification were examined. The calculated results were compared with measurements and in most cases fairly good agreement was found.

  6. Mathematical Creative Activity and the Graphic Calculator

    Science.gov (United States)

    Duda, Janina

    2011-01-01

    Teaching mathematics using graphic calculators has been an issue of didactic discussions for years. Finding ways in which graphic calculators can enrich the development process of creative activity in mathematically gifted students between the ages of 16-17 is the focus of this article. Research was conducted using graphic calculators with…

  7. 47 CFR 1.1623 - Probability calculation.

    Science.gov (United States)

    2010-10-01

    ... 47 Telecommunication 1 2010-10-01 2010-10-01 false Probability calculation. 1.1623 Section 1.1623... Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall be computed to no less than three significant digits. Probabilities will be truncated to the number of...

  8. Status Report of NNLO QCD Calculations

    CERN Document Server

    Klasen, M

    2005-01-01

    We review recent progress in next-to-next-to-leading order (NNLO) perturbative QCD calculations with special emphasis on results ready for phenomenological applications. Important examples are new results on structure functions and jet or Higgs boson production. In addition, we describe new calculational techniques based on twistors and their potential for efficient calculations of multiparticle amplitudes.

  9. A general formalism for phase space calculations

    Science.gov (United States)

    Norbury, John W.; Deutchman, Philip A.; Townsend, Lawrence W.; Cucinotta, Francis A.

    1988-01-01

    General formulas for calculating the interactions of galactic cosmic rays with target nuclei are presented. Methods for calculating the appropriate normalization volume elements and phase space factors are presented. Particular emphasis is placed on obtaining correct phase space factors for 2-, and 3-body final states. Calculations for both Lorentz-invariant and noninvariant phase space are presented.

  10. Decimals, Denominators, Demons, Calculators, and Connections

    Science.gov (United States)

    Sparrow, Len; Swan, Paul

    2005-01-01

    The authors provide activities for overcoming some fraction misconceptions using calculators specially designed for learners in primary years. The writers advocate use of the calculator as a way to engage children in thinking about mathematics. By engaging with a calculator as part of mathematics learning, children are learning about and using the…

  11. Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

    Energy Technology Data Exchange (ETDEWEB)

    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.

  12. Microscopic Calculations of 240Pu Fission

    Energy Technology Data Exchange (ETDEWEB)

    Younes, W; Gogny, D

    2007-09-11

    Hartree-Fock-Bogoliubov calculations have been performed with the Gogny finite-range effective interaction for {sup 240}Pu out to scission, using a new code developed at LLNL. A first set of calculations was performed with constrained quadrupole moment along the path of most probable fission, assuming axial symmetry but allowing for the spontaneous breaking of reflection symmetry of the nucleus. At a quadrupole moment of 345 b, the nucleus was found to spontaneously scission into two fragments. A second set of calculations, with all nuclear moments up to hexadecapole constrained, was performed to approach the scission configuration in a controlled manner. Calculated energies, moments, and representative plots of the total nuclear density are shown. The present calculations serve as a proof-of-principle, a blueprint, and starting-point solutions for a planned series of more comprehensive calculations to map out a large set of scission configurations, and the associated fission-fragment properties.

  13. Status of lattice field theory calculations

    Energy Technology Data Exchange (ETDEWEB)

    Sharpe, S.R.

    1990-01-01

    This report briefly discusses the following topics: overview of all present calculation; reliability criteria for quenched calculation; quenched versus full QCD, and difficulties facing full QCD; results for the quenched pion wavefunction''; results for the quenched hadron spectrum; results for quenched B{sub K}; A new method for calculating the surface tension; the non-pertubative upper bound on the Higgs mass; and toward the TERAFLOP machine.

  14. Calculation of the Moments of Polygons.

    Science.gov (United States)

    1987-06-01

    2.1) VowUK-1N0+IDIO TUUNTKPlNO.YKNO C Calculate AREA YKXK-YKPIND*IKNO-YKNO*XKP1NO AIKA-hEEA4YKXX C Calculate ACEIT ACENT (1)- ACEIT ( 1) VSUNI4TKIK... ACEIT (2) -ACENT(2) .VSUNYKXK C Calculate SECHON 3ECNON (1) -SCNON( 1) TKXK*(XX~PIdO*VSUNXKKO**2) SECNO(2) -SEn N(2) .yrf* (XKP114*YKP1MO.XKO*YXO+VB1hi

  15. Axial force calculation of passive magnetic bearing

    National Research Council Canada - National Science Library

    Vučković Ana N; Raičević Nebojša B; Ilić Saša S; Aleksić Slavoljub R; Perić Mirjana T

    2014-01-01

    .... Configuration like this one resembles the one passive magnetic bearing has. Force calculation is performed using semi analytical approach based on fictitious magnetization charges and discretization technique...

  16. Pile Load Capacity – Calculation Methods

    Directory of Open Access Journals (Sweden)

    Wrana Bogumił

    2015-12-01

    Full Text Available The article is a review of the current problems of the foundation pile capacity calculations. The article considers the main principles of pile capacity calculations presented in Eurocode 7 and other methods with adequate explanations. Two main methods are presented: α – method used to calculate the short-term load capacity of piles in cohesive soils and β – method used to calculate the long-term load capacity of piles in both cohesive and cohesionless soils. Moreover, methods based on cone CPTu result are presented as well as the pile capacity problem based on static tests.

  17. MATNORM: Calculating NORM using composition matrices

    Science.gov (United States)

    Pruseth, Kamal L.

    2009-09-01

    This paper discusses the implementation of an entirely new set of formulas to calculate the CIPW norm. MATNORM does not involve any sophisticated programming skill and has been developed using Microsoft Excel spreadsheet formulas. These formulas are easy to understand and a mere knowledge of the if-then-else construct in MS-Excel is sufficient to implement the whole calculation scheme outlined below. The sequence of calculation used here differs from that of the standard CIPW norm calculation, but the results are very similar. The use of MS-Excel macro programming and other high-level programming languages has been deliberately avoided for simplicity.

  18. Surface Tension Calculation of Undercooled Alloys

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (xNi=0.42) and Ni-Fe (xNi=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys.

  19. Modern Feynman Diagrammatic One-Loop Calculations

    CERN Document Server

    Reiter, Thomas; Greiner, Nicolas; Guffanti, Alberto; Guillet, Jean-Philippe; Heinrich, Gudrun; Karg, Stefan; Kauer, Nikolas; Kleinschmidt, Tobias; Koch-Janusz, Maciej; Luisoni, Gionata; Mastrolia, Pierpaolo; Ossola, Giovanni; Pilon, Eric; Rodgers, Mark; Tramontano, Francesco; Wigmore, Ioan

    2010-01-01

    In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\\to b\\bar{b}b\\bar{b}+X$.

  20. Calculating Electromagnetic Fields Of A Loop Antenna

    Science.gov (United States)

    Schieffer, Mitchell B.

    1987-01-01

    Approximate field values computed rapidly. MODEL computer program developed to calculate electromagnetic field values of large loop antenna at all distances to observation point. Antenna assumed to be in x-y plane with center at origin of coordinate system. Calculates field values in both rectangular and spherical components. Also solves for wave impedance. Written in MicroSoft FORTRAN 77.

  1. 46 CFR 154.520 - Piping calculations.

    Science.gov (United States)

    2010-10-01

    ... 46 Shipping 5 2010-10-01 2010-10-01 false Piping calculations. 154.520 Section 154.520 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Process Piping Systems § 154.520 Piping calculations. A piping system must be designed to meet...

  2. SGEMP Analysis using the Programmable Calculator.

    Science.gov (United States)

    1980-08-30

    step represents a single key stroke on the calculator such as a multiply or storage operation.) Calculator memory can he partitioned variably between...is (in M KS units): Em = / Fmr 0 v1 E , (A-18) where F is a dimensionless number that is a function of the emission spectrum and angular distribution

  3. 10 CFR 766.102 - Calculation methodology.

    Science.gov (United States)

    2010-01-01

    ... 10 Energy 4 2010-01-01 2010-01-01 false Calculation methodology. 766.102 Section 766.102 Energy DEPARTMENT OF ENERGY URANIUM ENRICHMENT DECONTAMINATION AND DECOMMISSIONING FUND; PROCEDURES FOR SPECIAL ASSESSMENT OF DOMESTIC UTILITIES Procedures for Special Assessment § 766.102 Calculation methodology. (a...

  4. 40 CFR 1065.850 - Calculations.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Calculations. 1065.850 Section 1065.850 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR POLLUTION CONTROLS ENGINE-TESTING PROCEDURES Testing With Oxygenated Fuels § 1065.850 Calculations. Use the...

  5. Calculated optical absorption of different perovskite phases

    DEFF Research Database (Denmark)

    Castelli, Ivano Eligio; Thygesen, Kristian Sommer; Jacobsen, Karsten Wedel

    2015-01-01

    We present calculations of the optical properties of a set of around 80 oxides, oxynitrides, and organometal halide cubic and layered perovskites (Ruddlesden-Popper and Dion-Jacobson phases) with a bandgap in the visible part of the solar spectrum. The calculations show that for different classes...

  6. Teaching Discrete Mathematics with Graphing Calculators.

    Science.gov (United States)

    Masat, Francis E.

    Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…

  7. Using Calculators in Mathematics 12. Student Text.

    Science.gov (United States)

    Rising, Gerald R.; And Others

    This student textbook is designed to incorporate programable calculators in grade 12 mathematics. The seven chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Sequences, Series, and Limits; (3) Iteration, Mathematical Induction, and the Binomial Theorem; (4) Applications of the Fundamental Counting Principle; (5)…

  8. Calculation reliability in vehicle accident reconstruction.

    Science.gov (United States)

    Wach, Wojciech

    2016-06-01

    The reconstruction of vehicle accidents is subject to assessment in terms of the reliability of a specific system of engineering and technical operations. In the article [26] a formalized concept of the reliability of vehicle accident reconstruction, defined using Bayesian networks, was proposed. The current article is focused on the calculation reliability since that is the most objective section of this model. It is shown that calculation reliability in accident reconstruction is not another form of calculation uncertainty. The calculation reliability is made dependent on modeling reliability, adequacy of the model and relative uncertainty of calculation. All the terms are defined. An example is presented concerning the analytical determination of the collision location of two vehicles on the road in the absence of evidential traces. It has been proved that the reliability of this kind of calculations generally does not exceed 0.65, despite the fact that the calculation uncertainty itself can reach only 0.05. In this example special attention is paid to the analysis of modeling reliability and calculation uncertainty using sensitivity coefficients and weighted relative uncertainty.

  9. Calculated Atomic Volumes of the Actinide Metals

    DEFF Research Database (Denmark)

    Skriver, H.; Andersen, O. K.; Johansson, B.

    1979-01-01

    The equilibrium atomic volume is calculated for the actinide metals. It is possible to account for the localization of the 5f electrons taking place in americium.......The equilibrium atomic volume is calculated for the actinide metals. It is possible to account for the localization of the 5f electrons taking place in americium....

  10. Calculation of cohesive energy of actinide metals

    Institute of Scientific and Technical Information of China (English)

    钱存富; 陈秀芳; 余瑞璜; 耿平; 段占强

    1997-01-01

    According to empirical electron theory of solids and molecules (EET), an equation for calculating the cohesive energy of actinide metals is given, the cohesive energy of 9 actinide metals with known crystal structure is calculated, which is identical with the experimental values on the whole, and the cohesive energy of 6 actinide metals with unknown crystal structure is forecast.

  11. Atomic Structure Calculations for Neutral Oxygen

    OpenAIRE

    Norah Alonizan; Rabia Qindeel; Nabil Ben Nessib

    2016-01-01

    Energy levels and oscillator strengths for neutral oxygen have been calculated using the Cowan (CW), SUPERSTRUCTURE (SS), and AUTOSTRUCTURE (AS) atomic structure codes. The results obtained with these atomic codes have been compared with MCHF calculations and experimental values from the National Institute of Standards and Technology (NIST) database.

  12. Calculating "g" from Acoustic Doppler Data

    Science.gov (United States)

    Torres, Sebastian; Gonzalez-Espada, Wilson J.

    2006-01-01

    Traditionally, the Doppler effect for sound is introduced in high school and college physics courses. Students calculate the perceived frequency for several scenarios relating a stationary or moving observer and a stationary or moving sound source. These calculations assume a constant velocity of the observer and/or source. Although seldom…

  13. Calculation of Temperature Rise in Calorimetry.

    Science.gov (United States)

    Canagaratna, Sebastian G.; Witt, Jerry

    1988-01-01

    Gives a simple but fuller account of the basis for accurately calculating temperature rise in calorimetry. Points out some misconceptions regarding these calculations. Describes two basic methods, the extrapolation to zero time and the equal area method. Discusses the theoretical basis of each and their underlying assumptions. (CW)

  14. New tool for standardized collector performance calculations

    DEFF Research Database (Denmark)

    Perers, Bengt; Kovacs, Peter; Olsson, Marcus;

    2011-01-01

    A new tool for standardized calculation of solar collector performance has been developed in cooperation between SP Technical Research Institute Sweden, DTU Denmark and SERC Dalarna University. The tool is designed to calculate the annual performance for a number of representative cities in Europe...

  15. Efficient Calculation of Earth Penetrating Projectile Trajectories

    Science.gov (United States)

    2006-09-01

    CALCULATION OF EARTH PENETRATING PROJECTILE TRAJECTORIES by Daniel F . Youch September 2006 Thesis Advisor: Joshua Gordis... Daniel F . Youch 5. FUNDING NUMBERS 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Postgraduate School Monterey, CA 93943-5000 8. PERFORMING...EFFICIENT CALCULATION OF EARTH PENETRATING PROJECTILE TRAJECTORIES Daniel F . Youch Lieutenant Commander, United States Navy B.S., Temple

  16. Calculation of LDL apoB

    NARCIS (Netherlands)

    Sniderman, A.D.; Tremblay, A.J.; Graaf, J. de; Couture, P.

    2014-01-01

    OBJECTIVES: This study tests the validity of the Hattori formula to calculate LDL apoB based on plasma lipids and total apoB. METHODS: In 2178 patients in a tertiary care lipid clinic, LDL apoB calculated as suggested by Hattori et al. was compared to directly measured LDL apoB isolated by ultracent

  17. Data base to compare calculations and observations

    Energy Technology Data Exchange (ETDEWEB)

    Tichler, J.L.

    1985-01-01

    Meteorological and climatological data bases were compared with known tritium release points and diffusion calculations to determine if calculated concentrations could replace measure concentrations at the monitoring stations. Daily tritium concentrations were monitored at 8 stations and 16 possible receptors. Automated data retrieval strategies are listed. (PSB)

  18. Heat Calculation of Borehole Heat Exchangers

    Directory of Open Access Journals (Sweden)

    S. Filatov

    2013-01-01

    Full Text Available The paper considers a heat calculation method of borehole heat exchangers (BHE which can be used for designing and optimization of their design values and included in a comprehensive mathematical model of heat supply system with a heat pump based on utilization of low-grade heat from the ground.The developed method of calculation is based on the reduction of the problem general solution pertaining to heat transfer in BHE with due account of heat transfer between top-down and bottom-up flows of heat carrier to the solution for a boundary condition of one kind on the borehole wall. Used the a method of electrothermal analogy has been used for a calculation of the thermal resistance and  the required shape factors for calculation of  a borehole filler thermal resistance have been obtained numerically. The paper presents results of heat calculation of various BHE designs in accordance with the proposed method.

  19. Development of Fast running DNBR Calculation Code

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Hyuk; Seo, K. W.; Kim, S. J.; Hwang, D. H. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2010-10-15

    SMART core adopted a core protection(SCOPS) and a supervising system(SCOMS) to satisfy the SAFDL for AOO and normal operation. Generally, the criteria is limited to the DNBR limit so that the DNBR calculation module is required in the protection and the supervising system of core. There are CPU time limit and calculation robustness as some requirements of the DNBR calculation module in SCOPS and SCOMS caused by hardware limitations. The non-iterative few channel methods are needed to satisfy the requirements. Non-iterative numerical method is similar to the CETOP algorithm originated from ref. 1. The method is known as the non-iterative prediction and correction method. An optimum number of channels for core lumping model is selected as 4- channel which is same channel number of CETOP model. A compensation model of lumped channel is needed to ensure that the 4-channel thermal hydraulic field is nearly equivalent to that field of 1/8-core model that is calculated by MATRA-S. The code called FAST that is fast running DNBR calculation is developed to satisfy the requirements of CPU time and calculation robustness. Present paper is described of characteristics and calculation results of developed FAST code

  20. Validation of fluorescence transition probability calculations

    CERN Document Server

    Pia, M G; Sudhaka, Manju

    2009-01-01

    A systematic and quantitative validation of the K and L shell X-ray transition probability calculations according to different theoretical methods has been performed against experimental data. This study is relevant to the optimization of data libraries used by software systems, namely Monte Carlo codes, dealing with X-ray fluorescence. The results support the adoption of transition probabilities calculated according to the Hartree-Fock approach, which manifest better agreement with experimental measurements than calculations based on the Hartree-Slater method.