Spacetime Singularities in (2+1)-Dimensional Quantum Gravity
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.
Spacetime singularities in (2 + 1)-dimensional quantum gravity
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.
Teleparallel equivalent theory of (1+ 1)-dimensional gravity
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.
New Interaction Solutions of (3+1-Dimensional KP and (2+1-Dimensional Boussinesq Equations
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.
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.
Rainich conditions in (2 + 1)-dimensional gravity
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.
Connectivity of Random 1-Dimensional Networks
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...
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.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Exploration of Similarity Renormalization Group Generators in 1-Dimensional Potentials
Heinz, Matthias
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.
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.
Kink manifolds in (1+1)-dimensional scalar field theory
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)
High energy scattering in (2+1)-dimensional QCD A dipole picture
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.
Upon Generating (2+1)-dimensional Dynamical Systems
Zhang, Yufeng; Bai, Yang; Wu, Lixin
2016-06-01
Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.
Md Nur Alam; M Ali Akbar; M Fazlul Hoque
2014-09-01
In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown that the new approach of generalized (′/)-expansion method is a straightforward and effective mathematical tool for solving nonlinear evolution equations in applied mathematics, mathematical physics and engineering. Moreover, this procedure reduces the large volume of calculations.
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.
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.
Rainich Conditions in (2+1)-Dimensional Gravity
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.
Exact solutions of (3 + 1)-dimensional stochastic Burgers equation
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.
Ruppeiner Geometry of (2 + 1)-Dimensional Spinning Dilaton Black Hole*
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.
Exact interior solutions in 2 + 1-dimensional spacetime
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.)
Causality in 1+1-dimensional Yukawa model-II
Asrarul Haque; Satish D Joglekar
2013-10-01
The limits → large, $M →$ large with ($g^{3}/M$) = const. of the 1+1-dimensional Yukawa model are discussed. The conclusion of the results on bound states of the Yukawa model in this limit (obtained in arXiv:0908.4510v3 [hep-th]) is taken into account. It is found that model reduces to an effective non-local 3 theory in this limit. Causality violation also is observed in this limit.
Integrable lattice hierarchies associated with two new (2+1)-dimensional discrete spectral problems
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.
Lump Solution of (2+1)-Dimensional Boussinesq Equation
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
(2+1)-Dimensional Gravity in Weyl Integrable Spacetime
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.
1+1 dimensional compactifications of string theory.
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.
Quench Dynamics in Confined 1+1-Dimensional Systems
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.
Generalized (2+1) dimensional black hole by Noether symmetry
Darabi, F. [Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM), Maragha (Iran, Islamic Republic of); Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Atazadeh, K.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of)
2013-12-15
We use the Noether symmetry approach to find f(R) theory of (2+1) dimensional gravity and (2+1) dimensional black hole solution consistent with this f(R) gravity and the associated symmetry. We obtain f(R)=D{sub 1} R(n/n+1)(R/K){sup 1/n} + D{sub 2}R + D{sub 3}, where the constant term D{sub 3} plays no dynamical role. Then, we find general spherically symmetric solution for this f(R) gravity which is potentially capable of being as a black hole. Moreover, in the special case D{sub 1} = 0, D{sub 2} = 1, namely f(R) = R + D{sub 3}, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D{sub 3} and represents symmetry of the action under the transformation R {yields}R' = R + D{sub 3} along the killing vector {partial_derivative}{sub R}. The ordinary BTZ black hole is obtained as the special case where D{sub 3} is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q=0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy-Verlinde formula. (orig.)
Topology and incompleteness for 2+1-dimensional cosmological spacetimes
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.
Tipping Points in 1-Dimensional Schelling Models with Switching Agents
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.
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.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R.; Nicolini, Piero
2011-08-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length θ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Aspects of noncommutative (1+1)-dimensional black holes
Mureika, Jonas R
2011-01-01
We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\\sqrt{\\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass $M$, cosmological constant $\\Lambda$, etc...), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.
Entanglement and majorization in (1+1)-dimensional quantum systems
Orus, R
2005-01-01
Motivated by the idea of entanglement loss along Renormalization Group flows, analytical majorization relations are proven for the ground state of (1+1)-dimensional conformal field theories. For any of these theories, majorization is proven to hold in the spectrum of the reduced density matrices in a bipartite system when changing the size L of one of the subsystems. Continuous majorization along uniparametric flows is also proven as long as part of the conformal structure is preserved under the deformation and some monotonicity conditions hold as well. As particular examples of our derivations, we study the cases of the XX, Heisenberg and XY quantum spin chains. Our results provide in a rigorous way explicit proves for all the majorization conjectures raised by Latorre, Lutken, Rico, Vidal and Kitaev in previous papers on quantum spin chains.
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.
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).
Quantum cosmology in (1 +1 )-dimensional Hořava-Lifshitz theory of gravity
Pitelli, J. P. M.
2016-05-01
In a recent paper [Phys. Rev. D 92, 084012 (2015)], the author studied the classical (1 +1 )-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in the Hořava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will take one step further in the understanding of (1 +1 )-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with the equation of state (EoS) p =w ρ . The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schrödinger equation for the wave function of the universe has the following properties: for w =1 (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for w ≠1 , a characteristic inverse square potential appears in addition to a regular polynomial that depends on the EoS. Explicit solutions for a few cases of interest will be found and the expectation value of the scale factor will be calculated. As in usual quantum cosmology, it will be shown that the quantum theory smooths out the big-bang singularity, but the classical behavior of the universe is recovered in the low-energy limit.
A (2+1)-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings
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.
Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model
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.
Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model
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 $D$.
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.
Solutions and Conservation Laws of a (2+1-Dimensional Boussinesq Equation
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.
Study of (2+1)-Dimensional Higher-Order Broer-Kaup System
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.
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.
(1 + 1) dimensional hydrodynamics for high-energy heavy-ion collisions
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.
N-Soliton Solutions of (2+1)-Dimensional Non-isospectral AKNS System
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.
NEW EXPLICIT SOLUTIONS TO THE (2+1)-DIMENSIONAL BROER-KAUP EQUATIONS
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.
Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations
Guo, Xiu-Rong
2016-06-01
We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58
Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation
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.
Abundant Multisoliton Structure of the (3+1)-Dimensional Nizhnik-Novikov-Veselov Equation
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.
(2+1-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves
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.
Horizons in 2+1-dimensional collapse of particles
Dieter Brill; Puneet Khetarpal; Vijay Kaul
2007-07-01
A simple, geometrical construction is given for three-dimensional spacetimes with negative cosmological constant that contain two particles colliding head-on. Depending on parameters like particle masses and distance, the combined geometry will be that of a particle, or of a black hole. In the black hole case the horizon is calculated. It is found that the horizon typically starts at a point and spreads into a closed curve with corners, which propagate along spacelike caustics and disappear as the horizon passes the particles.
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...
Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge
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 ...
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Construction of Perturbatively Correct Light Front Hamiltonian for (2+1)-Dimensional Gauge Theory
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.
Exact Solutions of the (3+1)-Dimensional KP and KdV-Type Equations
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.
Determinant Solutions to a (3+1)-Dimensional Generalized KP Equation with Variable Coefficients
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.
Feedback Equivalence of 1-dimensional Control Systems of the 1-st Order
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.
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
ZHANG Jie-Fang
2001-01-01
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
Integrability and Solutions of the (2 + 1)-dimensional Hunter-Saxton Equation
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
Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes
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...
Lie symmetry group of (2+1-dimensional Jaulent-Miodek equation
Ma Hong-Cai
2014-01-01
Full Text Available In this paper, we consider a system of (2+1-dimensional non-linear model by using auxiliary equation method and Clarkson-Kruskal direct method which is very important in fluid and physics. We construct some new exact solutions of (2+1-dimensional non-linear models with the aid of symbolic computation which can illustrate some actions in fluid in the future.
Series of (2+1)-dimensional stable self-dual interacting conformal field theories
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.
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.
The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach
Lu, W F
1999-01-01
The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum in the field system is asymmetrical, which verifies an earlier conjecture. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for some portion of the aforementioned region. Besides, the masses of one particle and tow-particle bound state upon the symmetric vacuum are also calculated, and the resultant masses agree with the recent second-order results of fermion-mass perturbation for the massive Schwinger model.
Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry
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.)
Bulk-boundary correspondence in (3+1)-dimensional topological phases
Chen, Xiao; Tiwari, Apoorv; Ryu, Shinsei
2016-07-01
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level K , and its generalization. In particular, we put these theories on a flat (2+1)-dimensional torus T3 parameterized by its modular parameters, and compute the partition functions obeying various twisted boundary conditions. We show the partition functions are transformed into each other under S L (3 ,Z ) modular transformations, and furthermore establish the bulk-boundary correspondence in (3+1) dimensions by matching the modular S and T matrices computed from the boundary field theories with those computed in the bulk. We also propose the three-loop braiding statistics can be studied by constructing the modular S and T matrices from an appropriate boundary field theory.
Multisoliton Solutions of the (2+1)-Dimensional KdV Equation
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.``
Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation
Zhengde Dai; Chuanjian Wang; Jun Liu
2014-10-01
A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.
Compacton, Peakon, and Foldon Structures in the (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation
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.
Symmetry Reductions of (2 + 1-Dimensional CDGKS Equation and Its Reduced Lax Pairs
Na Lv
2014-01-01
Full Text Available With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.
Chaos and Fractals in a (2+1)-Dimensional Soliton System
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.
Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation
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.
A note on the Painleve analysis of a (2 + 1) dimensional Camassa-Holm equation
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.
Annihilation Solitons and Chaotic Solitons for the (2+1)-Dimensional Breaking Soliton System
无
2007-01-01
By means of an improved mapping method and a variable separation method, a scries of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
New Exact Solutions and Localized Structures for (3+1)-Dimensional Burgers System
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.
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.
Methods of numerical analysis of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics
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.
Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
Jean-Michel CORON; Jesús Ildefonso D（I）AZ; Abdelmalek DRICI; Tommaso MINGAZZINI
2013-01-01
The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control.They assume that the internal control is only time dependent.The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.
Conservation laws for two (2 + 1)-dimensional differential-difference systems
Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080 (China) and Graduate School of the Chinese Academy of Sciences, Beijing (China)]. E-mail: gfyu@lsec.cc.ac.cn; Tam, H.-W. [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China)]. E-mail: tam@comp.hkbu.edu.hk
2006-10-15
Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced.
New and More General Rational Formal Solutions to (2+1)-Dimensional Toda System
无
2007-01-01
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to (2+1)-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
New Exact Solutions of the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces
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.
New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations
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.
Periodic Homoclinic Wave of (1+1)-Dimensional Long-Short Wave Equation
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.
A new method to the(2+1)-dimensional modified KP equation
无
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.
The exact solutions to (2+1)-dimensional nonlinear Schrǒdinger equation
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.
New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients
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.
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.
Variable Separation Solutions for the (2+1)-Dimensional Burgers Equation
唐晓艳; 楼森岳
2003-01-01
Considering that the multi-linear variable separation approach has been proved to be very useful to solve many (2+1)-dimensional integrable systems, we obtain the variable separation solutions of the Burgers equation with arbitrary number of variable separated functions. The Y-shaped soliton fusion phenomenon is revealed.
Exact Solutions of Some (1+1)-Dimensional Nonlinear Evolution Equations
无
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.
Localized Excitations in a Sixth-Order (1+1)-Dimensional Nonlinear Evolution Equation
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.
Study on (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation by Using Extended Mapping Approach
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.
Symmetry Analysis of (2+1)-Dimensional Nonlinear Klein-Gordon Equations
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.
Abundant new travelling wave solutions for the (2 + 1)-dimensional Sine-Gordon equation
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.
Folded localized excitations in the (2+1)-dimensional modified dispersive water-wave system
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.
Nonpropagating Solitons in (2+1)-Dimensional Dispersive Long-Water Wave System
FANG Jian-Ping; ZHENG Chun-Long; LIU Qing
2005-01-01
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
Peakon Excitations and Fractal Dromions for General (2+1)-Dimensional Korteweg de Vries System
无
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.
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.
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).
(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material
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.
Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations
Liu, Han-Ze; Xin, Xiang-Peng
2016-08-01
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. Supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009, and the doctorial foundation of Liaocheng University under Grant No. 31805
New Similarity Reduction Solutions for the (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation
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.
Fission and Fusion of Solitons for the (1+1)-Dimensional Kupershmidt Equation
YING Jin-Ping
2001-01-01
By means of the heat conduction equation and the standard truncated Painlevé expansion, the (1+1) dimensional Kupershmidt equation is solved. Some significant exact multi-soliton solutions are given. Especially; for the interaction of the multi-solitons of the Kupershmidt equation, we find that a single (resonant) kink or bell soliton may be fissioned to several kink or bell solitons. Inversely, several kink or bell solitons may also be fused to one kink or bell soliton.
Painlevé Analysis and Some Solutions of(2+1)-Dimensional Generalized Burgers Equations
HONG Ke-Zhu; WU B-in; CHEN Xian-Feng
2003-01-01
Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e') analysis,the most generalized Painlev(e') integrable(2+1)-dimensional integrable Burgers systems are obtained.Some exact solutions of the generalized Burgers system are obtained via variable separation approach.
Pair production of Dirac particles in a d+1-dimensional noncommutative space-time
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.
A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
Hongli An
2012-08-01
Full Text Available A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when γ=2 to a nonlinear dynamical subsystem with underlying integrable Hamiltonian-Ermakov structure. Exact solutions of the magnetogasdynamic system are thereby obtained which describe a rotating elliptic plasma cylinder. The semi-axes of the elliptical cross-section, remarkably, satisfy a Ermakov-Ray-Reid system.
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time
Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)
2014-11-15
This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
Non-completely elastic interactions in a (2+1)-dimensional dispersive long wave equation
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.
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.
Interaction between compacton an danticompacton,peakon and antipeakon in(2+1)-dimensional spaces
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.
Symmetry Analysis and Exact Solutions of (2+1)-Dimensional Sawada-Kotera Equation
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.
New Types of Travelling Wave Solutions From (2+1)-Dimensional Davey-Stewartson Equation
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.
A study of geodesic motion in a (2+1)-dimensional charged BTZ black hole
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.
(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator
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.``
Extended Complex tanh-Function Method and Exact Solutions to (2+1)-Dimensional Hirota Equation
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.
The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations
M Matinfar; M Eslami; S Roshandel
2015-10-01
In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.
New Exact Solutions to (2+1)-Dimensional Variable Coefficients Broer-Kaup Equations
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.
The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation
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.
Quasi-periodic and Non-periodic Waves in (2+1)-Dimensional Nonlinear Systems
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.
Rich Localized Coherent Structures of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation
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.
Doubly Periodic Propagating Wave for (2+1)-Dimensional Breaking Soliton Equation
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.
Interactions Among Peakons,Dromions,and Compactons for a (2+1)-Dimensional Soliton System
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.
Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation
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.
New Complexiton Solutions of (1+1)-Dimensional Dispersive Long Wave Equation
无
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.
New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations
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.
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.
Embed-Solitons and Their Evolutional Behaviors of (3+1)-Dimensional Burgers System
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.
Relaxation of 2+1 dimensional classical O(2) symmetric scalar fields
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.
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.
Searching for the (3+1)-Dimensional Painlevé Integrable Model and its Solitary Wave Solution
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.
A Bilinear B(a)cklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation
WU Jian-Ping
2008-01-01
@@ Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation.As an application, soliton solution and stationary rational solution for the (3+1)-dimensional soliton equation are presented.
Critical behavior of (2 +1 )-dimensional QED: 1 /Nf corrections in the Landau gauge
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
Periodic Semifolded Solitary Waves for (2+1)-Dimensional Variable Coefficient Broer-Kaup System
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.
Embedded-Soliton and Complex Wave Excitations of (3+1)-Dimensional Burgers System
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.
Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
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.
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.
Holographic conductivity of 1+1 dimensional systems in soft wall model
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.
Lorentz contraction of bound states in 1+1 dimensional gauge theory
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.
Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation
Huang Wen-Hua
2009-01-01
A general solution,including three arbitrary functions,is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method.Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution,special types of periodic folded waves are derived.In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions of the periodic folded waves and the degenerated single folded solitary waves axe investigated graphically and found to be completely elastic.
Lump Solutions for the (3+1)-Dimensional Kadomtsev-Petviashvili Equation
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.
APPLICATION OF EXP-FUNCTION METHOD TO THE (2+1-DIMENSIONAL CALOGERO BOGOYAVLANSKII SCHIFF EQUATION
Z. AYATI
2009-07-01
Full Text Available In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1 -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving Calogero Bogoyavlanskii Schiff equation.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
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.
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.
Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
Gecim, Ganim
2016-01-01
In this paper, we study early-time inflation and late-time acceleration of the universe in the presence of non-minimal coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background by using the Noether symmetry approach. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with the results obtained in the context of the 3+1 dimensional teleparallel gravity under Noether symmetry approach, and we see that the two models have similar physically results about the inflation of the universe.
Dirac Field as a Source of the Inflation in 2+1 Dimensional Teleparallel Gravity
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.
Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation
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.
LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS
张解放; 刘宇陆
2002-01-01
By using the extended homogeneous balance method, the localized coherentstructures are studied. A nonlinear transformation was first established, and then thelinearization form was obtained based on the extended homogeneous balance method for thehigher order ( 2 + 1 ) -dimensional Broer-Kaup equations. Starting from this linearizationform equation, a variable separation solution with the entrance of some arbitrary functionsand some arbitrary parameters was constructed. The quite rich localized coherent structureswere revealed. This method, which can be generalized to other (2 + 1 )-dimensionalnonlinear evolution equation, is simple and powerful.
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.
Symmetry Groups and Exact Solutions of New (4+1)-Dimensional Fokas Equation
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.
Canonical Formulation of A Bosonic Matter Field in 1+1 Dimensional Curved Space
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.
A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation
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.
Interaction Solutions for (1+1)-Dimensional Higher-Order Broer—Kaup System
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
Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials
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.
Exact periodic waves and their interactions for the (2+1)-dimensional KdV equation
Yan-Ze Peng
2005-08-01
By means of the singular manifold method we obtain a general solution involving three arbitrary functions for the (2+1)-dimensional KdV equation. Diverse periodic wave solutions may be produced by appropriately selecting these arbitrary functions as the Jacobi elliptic functions. The interaction properties of the periodic waves are investigated numerically and found to be nonelastic. The long wave limit yields some new types of solitary wave solutions. Especially the dromion and the solitoff solutions obtained in this paper possess new types of solution structures which are quite different from the basic dromion and solitoff ones reported previously in the literature.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
Complexiton solutions of the (2+1)-dimensional dispersive long wave equation
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.
Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation
ZHANG JieFang
2002-01-01
This article is concerned with the extended homogeneous balance method for studying thc abundantlocalized solution structures in the (2-k1)-dimensional dispersive long-wave equations uty + xx + (u2)xy/2 = 0, ηt +(u + u + uxy)x = 0. Starting from the homogeneous balance method, we find that the richness of the localized coherentstructures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selectionsof the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers,instantons and ring solitons.
Thermodynamics of (d+1)-dimensional NUT-charged AdS spacetimes
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.
Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes
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...
Quantum Cosmology in $(1+1)$-dimensional Ho\\v{r}ava-Lifshitz theory of gravity
Pitelli, J P M
2016-01-01
In a recent paper [Phys. Rev. D 92:084012, 2015], the author studied the classical $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in Ho\\v{r}ava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will give one step further in the understanding of (1+1)-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with equation of state (EoS) $p=w\\rho$. The fluid will be introduced in the model via Schutz formalism and Dirac's algorithm will be used for quantization. It will be shown that the Schr\\"odinger equation for the wave function of the universe has the following properties: for $w=1$ (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for $w\
Some New Exact Solutions to the Dispersive Long-Wave Equation in(2+1)-Dimensional Spaces
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.
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.
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.
Casimir interaction between spheres in $\\boldsymbol{(D+1)}$-dimensional Minkowski spacetime
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...
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
Noether Gauge Symmetry of Dirac Field in (2 + 1-Dimensional Gravity
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.
Bellucci, S; Bragança, E; Saharian, A A
2016-01-01
We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even funct...
Chiral density wave versus pion condensation in the 1+1 dimensional NJL model
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.
Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation
ZHANG SHENG; TIAN CHI; QIAN WEI-YI
2016-06-01
The (4+1)-dimensional Fokas equation is derived in the process of extending the integrable Kadomtsev–Petviashvili and Davey–Stewartson equations to higher-dimensional nonlinear wave equations. This equation is under investigation in this paper. Hirota’s bilinear method is, for the first time, used to solve such a higher-dimensional equation. In order to bilinearize the Fokas equation, some appropriate transformations are adopted. As a result, single-soliton solution,double-soliton solution and three-soliton solution are obtained. A new uniform formula of n-soliton solution is derived from this. It is shown that the transformations adopted in this work play a key role in converting the Fokas equation into Hirota’s bilinear form.
BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term
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.
Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness
Ammon, A; Jansen, K; Leövey, H; Volmer, J
2016-01-01
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that our new method leads to orders of magnitude reduced errors also in other regions of parameter space.
An Eternal Time Machine in 2+1 Dimensional anti-de Sitter Space
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.
Localized structures for (2+1)-dimensional Boiti–Leon–Pempinelli equation
Gui Mu; Zhengde Dai; Zhanhui Zhao
2013-09-01
It is shown that Painlevé integrability of (2+1)-dimensional Boiti–Leon–Pempinelli equation is easy to be verified using the standard Weiss–Tabor–Carnevale (WTC) approach after introducing the Kruskal’s simplification. Furthermore, by employing a singular manifold method based on Painlevé truncation, variable separation solutions are obtained explicitly in terms of two arbitrary functions. The two arbitrary functions provide us a way to study some interesting localized structures. The choice of rational functions leads to the rogue wave structure of Boiti–Leon–Pempinelli equation. In addition, for the other choices, it is observed that two solitons may evolve into breather after interaction. Also, the interaction between two kink compactons is investigated.
Regularization strategy for an inverse problem for a 1 + 1 dimensional wave equation
Korpela, Jussi; Lassas, Matti; Oksanen, Lauri
2016-06-01
An inverse boundary value problem for a 1 + 1 dimensional wave equation with a wave speed c(x) is considered. We give a regularization strategy for inverting the map { A } :c\\mapsto {{Λ }}, where Λ is the hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed c. That is, we consider the case when we are given a perturbation of the Neumann-to-Dirichlet map \\tilde{{{Λ }}}={{Λ }}+{ E }, where { E } corresponds to the measurement errors, and reconstruct an approximative wave speed \\tilde{c}. We emphasize that \\tilde{{{Λ }}} may not be in the range of the map { A }. We show that the reconstructed wave speed \\tilde{c} satisfies \\parallel \\tilde{c}-c\\parallel ≤slant C\\parallel { E }{\\parallel }1/54. Our regularization strategy is based on a new formula to compute c from Λ.
Critical behavior of (2 +1 )-dimensional QED: 1 /Nf corrections in an arbitrary nonlocal gauge
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 .
A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
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.
Analytical, 1-Dimensional Impedance Model of a Composite Solid Oxide Fuel Cell Cathode
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....
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...
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.
A model of random center vortex lines in continuous 2+1-dimensional space-time
Altarawneh, Derar; Höllwieser, Roman
2016-01-01
A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining ph...
Smooth and sharp creation of a pointlike source for a $(3+1)$-dimensional quantum field
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...
Model of random center vortex lines in continuous 2 +1 -dimensional spacetime
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.
Vacuum energy is non-positive for (2+1)-dimensional holographic CFTs
Hickling, Andrew
2015-01-01
We consider a (2+1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial vacuum energy at zero temperature due to the Casimir effect. We assume a thermal state has an AdS/CFT dual description as a static smooth solution to gravity with a negative cosmological constant, which ends only on the conformal boundary or horizons. A bulk geometric argument then provides an upper bound on the ratio of CFT free energy to temperature. Considering the zero temperature limit of this bound implies the vacuum energy of the CFT is non-positive. Furthermore the vacuum energy must be negative unless the boundary metric is locally conformal to a product of time with a constant curvature space. We emphasise the argument does not require the zero temperature bulk geometry to be smooth, but only that singularities are `good' so are hidden by horizons at finite temperature.
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.
An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its solutions
Hu Xingbiao [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Li Chunxia [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Nimmo, Jonathan J C [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China)
2005-01-07
A symmetric (2+1)-dimensional Lotka-Volterra equation is proposed. By means of a dependent variable transformation, the equation is firstly transformed into multilinear form and further decoupled into bilinear form by introducing auxiliary independent variables. A bilinear Baecklund transformation is found and then the corresponding Lax pair is derived. Explicit solutions expressed in terms of pfaffian solutions of the bilinear form of the symmetric (2+1)-dimensional Lotka-Volterra equation are given. As a special case of the pfaffian solutions, we obtain soliton solutions and dromions.
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.
SRD 166 MEMS Calculator (Web, free access) This MEMS Calculator determines the following thin film properties from data taken with an optical interferometer or comparable instrument: a) residual strain from fixed-fixed beams, b) strain gradient from cantilevers, c) step heights or thicknesses from step-height test structures, and d) in-plane lengths or deflections. Then, residual stress and stress gradient calculations can be made after an optical vibrometer or comparable instrument is used to obtain Young's modulus from resonating cantilevers or fixed-fixed beams. In addition, wafer bond strength is determined from micro-chevron test structures using a material test machine.
Magnetic catalysis effect in the (2+1-dimensional Gross–Neveu model with Zeeman interaction
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.
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.)
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.
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.
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.
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.
A Series of Exact Solutions for a New (2+1)-Dimensional Calogero KdV Equation
无
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.
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.
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.
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.
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.
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.
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.
A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions
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
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.
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.
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.
无
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.
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.
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.
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.
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.
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.
无
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.
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.
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.
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.
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.
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.
Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation
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.
Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in (1+1)-Dimensional Spacetime
HE Xiao-Kai; LIU Wen-Biao; QIU Wei-Gang
2009-01-01
The Casimir energy of maesive scalar field with hybrid (Dirichlet-Neumann) boundary condition is calcu-lated. In order to regularize the model, the typical methods named as mode summation method and Green's function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field's mass. When the field is massless, the result is consistent with previous literatures.
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...
Thermodynamics of hot quantum scalar field in a (D+1) dimensional curved spacetime
C., W A Rojas
2016-01-01
We use the brick wall model to calculate the free energy of quantum scalar field in a curved spacetime (D +1) dimensions. We find the thermodynamics properties of quantum scalar field in several scenaries: Minkowski spacetime, Schwarzschild spacetime and BTZ spacetime. For the cases analysed, the thermodynamical properties of quantum scalar field is exactly with the reported. It was found that the entropy of the gas is proportional to the horizon area in a gravity field strong, which is consistent with the holographic principle.
Massive vector bosons tunnelled from the (2+1)-dimensional black holes
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.
Statistical Entropy and Superradiance in 2+1 Dimensional Acoustic Black Holes
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.
The 4-Body Problem in a (1+1)-Dimensional Self-Gravitating System
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.
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.
Cloud of strings as source in 2 + 1-dimensional f(R) = R{sup n} gravity
Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2016-02-15
We present three parameters exact solutions with possible black holes in 2 + 1-dimensional f(R) = R{sup n} modified gravity coupled minimally to a cloud of strings. These three parameters are n, the coupling constant of the cloud of strings ξ, and an integration constant C. Although in general one has to consider each set of parameters separately, for n an even integer greater than one we give a unified picture providing black holes. For n ≥ 1 we analyze a null/timelike geodesic within the context of particle confinement. (orig.)
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.
Storage and retrieval of (3+1)-dimensional weak-light bullets and vortices in a coherent atomic gas
Chen, Zhiming; Li, Hui-jun; Hang, Chao; Huang, Guoxiang
2016-01-01
A robust light storage and retrieval (LSR) in high dimensions is highly desirable for light and quantum information processing. However, most schemes on LSR realized up to now encounter problems due to not only dissipation, but also dispersion and diffraction, which make LSR with a very low fidelity. Here we propose a scheme to achieve a robust storage and retrieval of weak nonlinear high-dimensional light pulses in a coherent atomic gas via electromagnetically induced transparency. We show that it is available to produce stable (3+1)-dimensional light bullets and vortices, which have very attractive physical property and are suitable to obtain a robust LSR in high dimensions.
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.
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).
$Q-\\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
Ma, Yu-Bo; Cao, Shuo
2016-01-01
In order to achieve a deeper understanding of gravity theories, it is important to further investigate the thermodynamic properties of black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose $T,Q,\\Phi$ as the state parameters and study the phase equilibrium problem of general $(n+1)$-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide theoretical foundation for studying the phase transition and phase structure of black hole systems.
Local scale-invariance of the 2 + 1 dimensional Kardar–Parisi–Zhang model
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.
Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
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.
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.
A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System
无
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.
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.
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.
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.
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.
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.
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
Thermodynamics of (2 +1 )-dimensional charged black holes with power-law Maxwell field
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.
无
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Q-Φ criticality in the extended phase space of (n+1)-dimensional RN-AdS black holes
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.
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.
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.
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.
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.
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.
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.
Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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,...
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.
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.
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.
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.
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.
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.
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.
Geochemical Calculations Using Spreadsheets.
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)
Autistic Savant Calendar Calculators.
Patti, Paul J.
This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…
Lakshminarayana, S.
://www10.org/cdrom/ papers/317/node9.html), Back propagation and regression advan- tages in neural networks are also used for better ranking models for a Web page. One level and two levels of Reputation Calculations for a page rank found that the duality... and identifying the topics will be a short come (http://www9.org/w9cdrom/368/368.html). Experiments found that search engine access less than 16% of information available over the net (http://www.math.tau.ac.il/~fiat/ smarty.ps). In addition a polysemy...
How Do Calculators Calculate Trigonometric Functions?
Underwood, Jeremy M.; Edwards, Bruce H.
How does your calculator quickly produce values of trigonometric functions? You might be surprised to learn that it does not use series or polynomial approximations, but rather the so-called CORDIC method. This paper will focus on the geometry of the CORDIC method, as originally developed by Volder in 1959. This algorithm is a wonderful…
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.
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.)
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.
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.
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.
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.
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.
Electrical installation calculations advanced
Kitcher, Christopher
2013-01-01
All the essential calculations required for advanced electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practiceA step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3For apprentices and electrical installatio
Electrical installation calculations basic
Kitcher, Christopher
2013-01-01
All the essential calculations required for basic electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practice. A step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3Fo
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...
Radar Signature Calculation Facility
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...
Electronics Environmental Benefits Calculator
U.S. Environmental Protection Agency — The Electronics Environmental Benefits Calculator (EEBC) was developed to assist organizations in estimating the environmental benefits of greening their purchase,...
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.
Baryons and Low-Density Baryonic Matter in 1+1 Dimensional Large N_c QCD with Heavy Quarks
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...
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.
Calculators and Polynomial Evaluation.
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.…
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.
Tensor RG calculations and quantum simulations near criticality
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.
Interval arithmetic in calculations
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.
Unit Cost Compendium Calculations
U.S. Environmental Protection Agency — The Unit Cost Compendium (UCC) Calculations raw data set was designed to provide for greater accuracy and consistency in the use of unit costs across the USEPA...
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...
EFFECTIVE DISCHARGE CALCULATION GUIDE
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.
Magnetic Field Grid Calculator
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...
Current interruption transients calculation
Peelo, David F
2014-01-01
Provides an original, detailed and practical description of current interruption transients, origins, and the circuits involved, and how they can be calculated Current Interruption Transients Calculationis a comprehensive resource for the understanding, calculation and analysis of the transient recovery voltages (TRVs) and related re-ignition or re-striking transients associated with fault current interruption and the switching of inductive and capacitive load currents in circuits. This book provides an original, detailed and practical description of current interruption transients, origins,
Source and replica calculations
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.
Scientific calculating peripheral
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.
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.
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.
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.
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.
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
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.
LiZn(4 - x) (x = 0.825) as a (3 + 1)-dimensional modulated derivative of hexagonal close packing.
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.
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.
INVAP's Nuclear Calculation System
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.
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...
OFTIFEL PERSONALIZED NUTRITIONAL CALCULATOR
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.
Spin Resonance Strength Calculations
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.
Spin resonance strength calculations
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.
Curvature calculations with GEOCALC
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.
Haida Numbers and Calculation.
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…
Daylight calculations in practice
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...
无
2011-01-01
Compared with ellipse cavity, the spoke cavity has many advantages, especially for the low and medium beam energy. It will be used in the superconductor accelerator popular in the future. Based on the spoke cavity, we design and calculate an accelerator
Radioprotection calculations for MEGAPIE.
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.
PIC: Protein Interactions Calculator.
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.
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
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.
Probing the equation of state in Au+Au at 11 GeV/nucleon with (3+1)-dimensional hydrodynamics
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.
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.
Calculations in furnace technology
Davies, Clive; Hopkins, DW; Owen, WS
2013-01-01
Calculations in Furnace Technology presents the theoretical and practical aspects of furnace technology. This book provides information pertinent to the development, application, and efficiency of furnace technology. Organized into eight chapters, this book begins with an overview of the exothermic reactions that occur when carbon, hydrogen, and sulfur are burned to release the energy available in the fuel. This text then evaluates the efficiencies to measure the quantity of fuel used, of flue gases leaving the plant, of air entering, and the heat lost to the surroundings. Other chapters consi
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...
Zero Temperature Hope Calculations
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
Linewidth calculations and simulations
Strandberg, Ingrid
2016-01-01
We are currently developing a new technique to further enhance the sensitivity of collinear laser spectroscopy in order to study the most exotic nuclides available at radioactive ion beam facilities, such as ISOLDE at CERN. The overall goal is to evaluate the feasibility of the new method. This report will focus on the determination of the expected linewidth (hence resolution) of this approach. Different effects which could lead to a broadening of the linewidth, e.g. the ions' energy spread and their trajectories inside the trap, are studied with theoretical calculations as well as simulations.
Lopez, Cesar
2015-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. This book is designed for use as a scientific/business calculator so that you can get numerical solutions to problems involving a wide array of mathematics using MATLAB. Just look up the function y
Multilayer optical calculations
Byrnes, Steven J
2016-01-01
When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain aspects of it are difficult to find explicitly and consistently worked out in the literature. Here, we derive the formulas underlying the transfer-matrix method of calculating the optical properties of these stacks, including oblique-angle incidence, absorption-vs-position profiles, and ellipsometry parameters. We discuss and explain some strange consequences of the formulas in the situation where the incident and/or final (semi-infinite) medium are absorptive, such as calculating $T>1$ in the absence of gain. We also discuss some implementation details like complex-plane branch cuts. Finally, we derive modified formulas for including one or more "incoherent" layers, i.e. very thick layers in which interference can be neglected. This document was written in conjunction with ...
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.
Molecular Dynamics Calculations
1996-01-01
The development of thermodynamics and statistical mechanics is very important in the history of physics, and it underlines the difficulty in dealing with systems involving many bodies, even if those bodies are identical. Macroscopic systems of atoms typically contain so many particles that it would be virtually impossible to follow the behavior of all of the particles involved. Therefore, the behavior of a complete system can only be described or predicted in statistical ways. Under a grant to the NASA Lewis Research Center, scientists at the Case Western Reserve University have been examining the use of modern computing techniques that may be able to investigate and find the behavior of complete systems that have a large number of particles by tracking each particle individually. This is the study of molecular dynamics. In contrast to Monte Carlo techniques, which incorporate uncertainty from the outset, molecular dynamics calculations are fully deterministic. Although it is still impossible to track, even on high-speed computers, each particle in a system of a trillion trillion particles, it has been found that such systems can be well simulated by calculating the trajectories of a few thousand particles. Modern computers and efficient computing strategies have been used to calculate the behavior of a few physical systems and are now being employed to study important problems such as supersonic flows in the laboratory and in space. In particular, an animated video (available in mpeg format--4.4 MB) was produced by Dr. M.J. Woo, now a National Research Council fellow at Lewis, and the G-VIS laboratory at Lewis. This video shows the behavior of supersonic shocks produced by pistons in enclosed cylinders by following exactly the behavior of thousands of particles. The major assumptions made were that the particles involved were hard spheres and that all collisions with the walls and with other particles were fully elastic. The animated video was voted one of two
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.
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).
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.
The rating reliability calculator
Solomon David J
2004-04-01
Full Text Available Abstract Background Rating scales form an important means of gathering evaluation data. Since important decisions are often based on these evaluations, determining the reliability of rating data can be critical. Most commonly used methods of estimating reliability require a complete set of ratings i.e. every subject being rated must be rated by each judge. Over fifty years ago Ebel described an algorithm for estimating the reliability of ratings based on incomplete data. While his article has been widely cited over the years, software based on the algorithm is not readily available. This paper describes an easy-to-use Web-based utility for estimating the reliability of ratings based on incomplete data using Ebel's algorithm. Methods The program is available public use on our server and the source code is freely available under GNU General Public License. The utility is written in PHP, a common open source imbedded scripting language. The rating data can be entered in a convenient format on the user's personal computer that the program will upload to the server for calculating the reliability and other statistics describing the ratings. Results When the program is run it displays the reliability, number of subject rated, harmonic mean number of judges rating each subject, the mean and standard deviation of the averaged ratings per subject. The program also displays the mean, standard deviation and number of ratings for each subject rated. Additionally the program will estimate the reliability of an average of a number of ratings for each subject via the Spearman-Brown prophecy formula. Conclusion This simple web-based program provides a convenient means of estimating the reliability of rating data without the need to conduct special studies in order to provide complete rating data. I would welcome other researchers revising and enhancing the program.
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.)
Cosmological Calculations on the GPU
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.
New Arsenic Cross Section Calculations
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.
Global nuclear-structure calculations
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.
Equilibrium calculations of firework mixtures
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.
CALCULATION OF LASER CUTTING COSTS
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.
Calculator. Owning a Small Business.
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,…
Calculation of Spectra of Solids:
Lindgård, Per-Anker
1975-01-01
The Gilat-Raubenheimer method simplified to tetrahedron division is used to calculate the real and imaginary part of the dynamical response function for electrons. A frequency expansion for the real part is discussed. The Lindhard function is calculated as a test for numerical accuracy. The condu...
Closure and Sealing Design Calculation
T. Lahnalampi; J. Case
2005-08-26
The purpose of the ''Closure and Sealing Design Calculation'' is to illustrate closure and sealing methods for sealing shafts, ramps, and identify boreholes that require sealing in order to limit the potential of water infiltration. In addition, this calculation will provide a description of the magma that can reduce the consequences of an igneous event intersecting the repository. This calculation will also include a listing of the project requirements related to closure and sealing. The scope of this calculation is to: summarize applicable project requirements and codes relating to backfilling nonemplacement openings, removal of uncommitted materials from the subsurface, installation of drip shields, and erecting monuments; compile an inventory of boreholes that are found in the area of the subsurface repository; describe the magma bulkhead feature and location; and include figures for the proposed shaft and ramp seals. The objective of this calculation is to: categorize the boreholes for sealing by depth and proximity to the subsurface repository; develop drawing figures which show the location and geometry for the magma bulkhead; include the shaft seal figures and a proposed construction sequence; and include the ramp seal figure and a proposed construction sequence. The intent of this closure and sealing calculation is to support the License Application by providing a description of the closure and sealing methods for the Safety Analysis Report. The closure and sealing calculation will also provide input for Post Closure Activities by describing the location of the magma bulkhead. This calculation is limited to describing the final configuration of the sealing and backfill systems for the underground area. The methods and procedures used to place the backfill and remove uncommitted materials (such as concrete) from the repository and detailed design of the magma bulkhead will be the subject of separate analyses or calculations. Post
Practical astronomy with your calculator
Duffett-Smith, Peter
1989-01-01
Practical Astronomy with your Calculator, first published in 1979, has enjoyed immense success. The author's clear and easy to follow routines enable you to solve a variety of practical and recreational problems in astronomy using a scientific calculator. Mathematical complexity is kept firmly in the background, leaving just the elements necessary for swiftly making calculations. The major topics are: time, coordinate systems, the Sun, the planetary system, binary stars, the Moon, and eclipses. In the third edition there are entirely new sections on generalised coordinate transformations, nutr
Transfer Area Mechanical Handling Calculation
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
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.
MFTF-B performance calculations
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.
Insertion device calculations with mathematica
Carr, R. [Stanford Synchrotron Radiation Lab., CA (United States); Lidia, S. [Univ. of California, Davis, CA (United States)
1995-02-01
The design of accelerator insertion devices such as wigglers and undulators has usually been aided by numerical modeling on digital computers, using code in high level languages like Fortran. In the present era, there are higher level programming environments like IDL{reg_sign}, MatLab{reg_sign}, and Mathematica{reg_sign} in which these calculations may be performed by writing much less code, and in which standard mathematical techniques are very easily used. The authors present a suite of standard insertion device modeling routines in Mathematica to illustrate the new techniques. These routines include a simple way to generate magnetic fields using blocks of CSEM materials, trajectory solutions from the Lorentz force equations for given magnetic fields, Bessel function calculations of radiation for wigglers and undulators and general radiation calculations for undulators.
The Collective Practice of Calculation
Schrøder, Ida
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......The calculation of costs plays an increasingly large role in the decision-making processes of public sector human service organizations. This has brought scholars of management accounting to investigate the relationship between caring professions and demands to make economic entities of the service...... 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...
Friction and wear calculation methods
Kragelsky, I V; Kombalov, V S
1981-01-01
Friction and Wear: Calculation Methods provides an introduction to the main theories of a new branch of mechanics known as """"contact interaction of solids in relative motion."""" This branch is closely bound up with other sciences, especially physics and chemistry. The book analyzes the nature of friction and wear, and some theoretical relationships that link the characteristics of the processes and the properties of the contacting bodies essential for practical application of the theories in calculating friction forces and wear values. The effect of the environment on friction and wear is a
Multifragmentation calculated with relativistic forces
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
Molecular calculations with B functions
Steinborn, E O; Ema, I; López, R; Ramírez, G
1998-01-01
A program for molecular calculations with B functions is reported and its performance is analyzed. All the one- and two-center integrals, and the three-center nuclear attraction integrals are computed by direct procedures, using previously developed algorithms. The three- and four-center electron repulsion integrals are computed by means of Gaussian expansions of the B functions. A new procedure for obtaining these expansions is also reported. Some results on full molecular calculations are included to show the capabilities of the program and the quality of the B functions to represent the electronic functions in molecules.
Methods for Melting Temperature Calculation
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
Ab Initio Calculations of Oxosulfatovanadates
Frøberg, Torben; Johansen, Helge
1996-01-01
Restricted Hartree-Fock and multi-configurational self-consistent-field calculations together with secondorder perturbation theory have been used to study the geometry, the electron density, and the electronicspectrum of (VO2SO4)-. A bidentate sulphate attachment to vanadium was found to be stable...
Dead reckoning calculating without instruments
Doerfler, Ronald W
1993-01-01
No author has gone as far as Doerfler in covering methods of mental calculation beyond simple arithmetic. Even if you have no interest in competing with computers you'll learn a great deal about number theory and the art of efficient computer programming. -Martin Gardner
ITER Port Interspace Pressure Calculations
Carbajo, Juan J [ORNL; Van Hove, Walter A [ORNL
2016-01-01
The ITER Vacuum Vessel (VV) is equipped with 54 access ports. Each of these ports has an opening in the bioshield that communicates with a dedicated port cell. During Tokamak operation, the bioshield opening must be closed with a concrete plug to shield the radiation coming from the plasma. This port plug separates the port cell into a Port Interspace (between VV closure lid and Port Plug) on the inner side and the Port Cell on the outer side. This paper presents calculations of pressures and temperatures in the ITER (Ref. 1) Port Interspace after a double-ended guillotine break (DEGB) of a pipe of the Tokamak Cooling Water System (TCWS) with high temperature water. It is assumed that this DEGB occurs during the worst possible conditions, which are during water baking operation, with water at a temperature of 523 K (250 C) and at a pressure of 4.4 MPa. These conditions are more severe than during normal Tokamak operation, with the water at 398 K (125 C) and 2 MPa. Two computer codes are employed in these calculations: RELAP5-3D Version 4.2.1 (Ref. 2) to calculate the blowdown releases from the pipe break, and MELCOR, Version 1.8.6 (Ref. 3) to calculate the pressures and temperatures in the Port Interspace. A sensitivity study has been performed to optimize some flow areas.
Calculations for cosmic axion detection
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.
Theoretical Calculation of MMF's Bandwidth
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.
Data Acquisition and Flux Calculations
Rebmann, C.; Kolle, O; Heinesch, B;
2012-01-01
In this chapter, the basic theory and the procedures used to obtain turbulent fluxes of energy, mass, and momentum with the eddy covariance technique will be detailed. This includes a description of data acquisition, pretreatment of high-frequency data and flux calculation....
CONTRIBUTION FOR MINING ATMOSPHERE CALCULATION
Franica Trojanović
1989-12-01
Full Text Available Humid air is an unavoidable feature of mining atmosphere, which plays a significant role in defining the climate conditions as well as permitted circumstances for normal mining work. Saturated humid air prevents heat conduction from the human body by means of evaporation. Consequently, it is of primary interest in the mining practice to establish the relative air humidity either by means of direct or indirect methods. Percentage of water in the surrounding air may be determined in various procedures including tables, diagrams or particular calculations, where each technique has its specific advantages and disadvantages. Classical calculation is done according to Sprung's formula, in which case partial steam pressure should also be taken from the steam table. The new method without the use of diagram or tables, established on the functional relation of pressure and temperature on saturated line, is presented here for the first time (the paper is published in Croatian.
Archimedes' calculations of square roots
Davies, E B
2011-01-01
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide internal evidence that he probably used an interpolation technique. The conclusions are relevant to the precise calculations by which he obtained upper and lower bounds on pi.
Parallel plasma fluid turbulence calculations
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.
Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
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...
AGING FACILITY CRITICALITY SAFETY CALCULATIONS
C.E. Sanders
2004-09-10
The purpose of this design calculation is to revise and update the previous criticality calculation for the Aging Facility (documented in BSC 2004a). This design calculation will also demonstrate and ensure that the storage and aging operations to be performed in the Aging Facility meet the criticality safety design criteria in the ''Project Design Criteria Document'' (Doraswamy 2004, Section 4.9.2.2), and the functional nuclear criticality safety requirement described in the ''SNF Aging System Description Document'' (BSC [Bechtel SAIC Company] 2004f, p. 3-12). The scope of this design calculation covers the systems and processes for aging commercial spent nuclear fuel (SNF) and staging Department of Energy (DOE) SNF/High-Level Waste (HLW) prior to its placement in the final waste package (WP) (BSC 2004f, p. 1-1). Aging commercial SNF is a thermal management strategy, while staging DOE SNF/HLW will make loading of WPs more efficient (note that aging DOE SNF/HLW is not needed since these wastes are not expected to exceed the thermal limits form emplacement) (BSC 2004f, p. 1-2). The description of the changes in this revised document is as follows: (1) Include DOE SNF/HLW in addition to commercial SNF per the current ''SNF Aging System Description Document'' (BSC 2004f). (2) Update the evaluation of Category 1 and 2 event sequences for the Aging Facility as identified in the ''Categorization of Event Sequences for License Application'' (BSC 2004c, Section 7). (3) Further evaluate the design and criticality controls required for a storage/aging cask, referred to as MGR Site-specific Cask (MSC), to accommodate commercial fuel outside the content specification in the Certificate of Compliance for the existing NRC-certified storage casks. In addition, evaluate the design required for the MSC that will accommodate DOE SNF/HLW. This design calculation will achieve the objective of providing the
Calculation of gas turbine characteristic
Mamaev, B. I.; Murashko, V. L.
2016-04-01
The reasons and regularities of vapor flow and turbine parameter variation depending on the total pressure drop rate π* and rotor rotation frequency n are studied, as exemplified by a two-stage compressor turbine of a power-generating gas turbine installation. The turbine characteristic is calculated in a wide range of mode parameters using the method in which analytical dependences provide high accuracy for the calculated flow output angle and different types of gas dynamic losses are determined with account of the influence of blade row geometry, blade surface roughness, angles, compressibility, Reynolds number, and flow turbulence. The method provides satisfactory agreement of results of calculation and turbine testing. In the design mode, the operation conditions for the blade rows are favorable, the flow output velocities are close to the optimal ones, the angles of incidence are small, and the flow "choking" modes (with respect to consumption) in the rows are absent. High performance and a nearly axial flow behind the turbine are obtained. Reduction of the rotor rotation frequency and variation of the pressure drop change the flow parameters, the parameters of the stages and the turbine, as well as the form of the characteristic. In particular, for decreased n, nonmonotonic variation of the second stage reactivity with increasing π* is observed. It is demonstrated that the turbine characteristic is mainly determined by the influence of the angles of incidence and the velocity at the output of the rows on the losses and the flow output angle. The account of the growing flow output angle due to the positive angle of incidence for decreased rotation frequencies results in a considerable change of the characteristic: poorer performance, redistribution of the pressure drop at the stages, and change of reactivities, growth of the turbine capacity, and change of the angle and flow velocity behind the turbine.
Rate calculation with colored noise
Bartsch, Thomas; Benito, R M; Borondo, F
2016-01-01
The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a new method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.
Electronics reliability calculation and design
Dummer, Geoffrey W A; Hiller, N
1966-01-01
Electronics Reliability-Calculation and Design provides an introduction to the fundamental concepts of reliability. The increasing complexity of electronic equipment has made problems in designing and manufacturing a reliable product more and more difficult. Specific techniques have been developed that enable designers to integrate reliability into their products, and reliability has become a science in its own right. The book begins with a discussion of basic mathematical and statistical concepts, including arithmetic mean, frequency distribution, median and mode, scatter or dispersion of mea
Band calculation of lonsdaleite Ge
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.
Semiclassical calculation of decay rates
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.
Digital calculations of engine cycles
Starkman, E S; Taylor, C Fayette
1964-01-01
Digital Calculations of Engine Cycles is a collection of seven papers which were presented before technical meetings of the Society of Automotive Engineers during 1962 and 1963. The papers cover the spectrum of the subject of engine cycle events, ranging from an examination of composition and properties of the working fluid to simulation of the pressure-time events in the combustion chamber. The volume has been organized to present the material in a logical sequence. The first two chapters are concerned with the equilibrium states of the working fluid. These include the concentrations of var
The Dental Trauma Internet Calculator
Gerds, Thomas Alexander; Lauridsen, Eva Fejerskov; Christensen, Søren Steno Ahrensburg
2012-01-01
Background/Aim Prediction tools are increasingly used to inform patients about the future dental health outcome. Advanced statistical methods are required to arrive at unbiased predictions based on follow-up studies. Material and Methods The Internet risk calculator at the Dental Trauma Guide...... provides prognoses for teeth with traumatic injuries based on the Copenhagen trauma database: http://www.dentaltraumaguide.org The database includes 2191 traumatized permanent teeth from 1282 patients that were treated at the dental trauma unit at the University Hospital in Copenhagen (Denmark...
Calculational Tool for Skin Contamination Dose Assessment
Hill, R L
2002-01-01
Spreadsheet calculational tool was developed to automate the calculations preformed for dose assessment of skin contamination. This document reports on the design and testing of the spreadsheet calculational tool.
Calculation of sound propagation in fibrous materials
Tarnow, Viggo
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....
Flow Field Calculations for Afterburner
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.
47 CFR 1.1623 - Probability calculation.
2010-10-01
... Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall be... determine their new intermediate probabilities. (g) Multiply each applicant's probability pursuant...
A Note on 3 + 1 Dimensionality
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.
Painless causality in defect calculations
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...
Dyscalculia and the Calculating Brain.
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.
Factors affecting calculation of L
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
RTU Comparison Calculator Enhancement Plan
Miller, James D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Wang, Weimin [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Katipamula, Srinivas [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2015-07-01
Over the past two years, Department of Energy’s Building Technologies Office (BTO) has been investigating ways to increase the operating efficiency of the packaged rooftop units (RTUs) in the field. First, by issuing a challenge to the RTU manufactures to increase the integrated energy efficiency ratio (IEER) by 60% over the existing ASHRAE 90.1-2010 standard. Second, by evaluating the performance of an advanced RTU controller that reduces the energy consumption by over 40%. BTO has previously also funded development of a RTU comparison calculator (RTUCC). RTUCC is a web-based tool that provides the user a way to compare energy and cost savings for two units with different efficiencies. However, the RTUCC currently cannot compare savings associated with either the RTU Challenge unit or the advanced RTU controls retrofit. Therefore, BTO has asked PNNL to enhance the tool so building owners can compare energy and savings associated with this new class of products. This document provides the details of the enhancements that are required to support estimating energy savings from use of RTU challenge units or advanced controls on existing RTUs.
Selfconsistent calculations for hyperdeformed nuclei
Molique, H.; Dobaczewski, J.; Dudek, J.; Luo, W.D. [Universite Louis Pasteur, Strasbourg (France)
1996-12-31
Properties of the hyperdeformed nuclei in the A {approximately} 170 mass range are re-examined using the self-consistent Hartree-Fock method with the SOP parametrization. A comparison with the previous predictions that were based on a non-selfconsistent approach is made. The existence of the {open_quotes}hyper-deformed shell closures{close_quotes} at the proton and neutron numbers Z=70 and N=100 and their very weak dependence on the rotational frequency is suggested; the corresponding single-particle energy gaps are predicted to play a role similar to that of the Z=66 and N=86 gaps in the super-deformed nuclei of the A {approximately} 150 mass range. Selfconsistent calculations suggest also that the A {approximately} 170 hyperdeformed structures have neglegible mass asymmetry in their shapes. Very importantly for the experimental studies, both the fission barriers and the {open_quotes}inner{close_quotes} barriers (that separate the hyperdeformed structures from those with smaller deformations) are predicted to be relatively high, up to the factor of {approximately}2 higher than the corresponding ones in the {sup 152}Dy superdeformed nucleus used as a reference.
RTU Comparison Calculator Enhancement Plan
Miller, James D.; Wang, Weimin; Katipamula, Srinivas
2014-03-31
Over the past two years, Department of Energy’s Building Technologies Office (BTO) has been investigating ways to increase the operating efficiency of the packaged rooftop units (RTUs) in the field. First, by issuing a challenge to the RTU manufactures to increase the integrated energy efficiency ratio (IEER) by 60% over the existing ASHRAE 90.1-2010 standard. Second, by evaluating the performance of an advanced RTU controller that reduces the energy consumption by over 40%. BTO has previously also funded development of a RTU comparison calculator (RTUCC). RTUCC is a web-based tool that provides the user a way to compare energy and cost savings for two units with different efficiencies. However, the RTUCC currently cannot compare savings associated with either the RTU Challenge unit or the advanced RTU controls retrofit. Therefore, BTO has asked PNNL to enhance the tool so building owners can compare energy and savings associated with this new class of products. This document provides the details of the enhancements that are required to support estimating energy savings from use of RTU challenge units or advanced controls on existing RTUs.
Explosion Calculations of SN1087
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
A New Approach for Calculating Vacuum Susceptibility
宗红石; 平加伦; 顾建中
2004-01-01
Based on the Dyson-Schwinger approach, we propose a new method for calculating vacuum susceptibilities. As an example, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is presented.
Dynamics Calculation of Travel Wave Tube
无
2011-01-01
During the dynamics calculating of the travel tube, we must obtain the field map in the tube. The field map can be affected by not only the beam loading, but also the attenuation coefficient. The calculation of the attenuation coefficient
Pressure Vessel Calculations for VVER-440 Reactors
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.
A general formalism for phase space calculations
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.
Status Report of NNLO QCD Calculations
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.
Mathematical Creative Activity and the Graphic Calculator
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…
Decimals, Denominators, Demons, Calculators, and Connections
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…
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC)
2014-02-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a{sup N}, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Microscopic Calculations of 240Pu Fission
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.
Calculation of the Moments of Polygons.
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
Surface Tension Calculation of Undercooled Alloys
无
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.
The conundrum of calculating carbon footprints
Strobel, Bjarne W.; Erichsen, Anders Christian; Gausset, Quentin
2016-01-01
A pre-condition for reducing global warming is to minimise the emission of greenhouse gasses (GHGs). A common approach to informing people about the link between behaviour and climate change rests on developing GHG calculators that quantify the ‘carbon footprint’ of a product, a sector or an actor....... There is, however, an abundance of GHG calculators that rely on very different premises and give very different estimates of carbon footprints. In this chapter, we compare and analyse the main principles of calculating carbon footprints, and discuss how calculators can inform (or misinform) people who wish...
MATNORM: Calculating NORM using composition matrices
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.
Pile Load Capacity – Calculation Methods
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.
Atomic Structure Calculations for Neutral Oxygen
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.
10 CFR 766.102 - Calculation methodology.
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....
Calculation of cohesive energy of actinide metals
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.
Calculation reliability in vehicle accident reconstruction.
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.
Calculating "g" from Acoustic Doppler Data
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…
Efficient Calculation of Earth Penetrating Projectile Trajectories
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
Direct calculation of wind turbine tip loss
Wood, D.H.; Okulov, Valery; Bhattacharjee, D.
2016-01-01
. We develop three methods for the direct calculation of the tip loss. The first is the computationally expensive calculation of the velocities induced by the helicoidal wake which requires the evaluation of infinite sums of products of Bessel functions. The second uses the asymptotic evaluation...
Calculating Electromagnetic Fields Of A Loop Antenna
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.
New tool for standardized collector performance calculations
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...
Calculation of Temperature Rise in Calorimetry.
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)
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
Investment Return Calculations and Senior School Mathematics
Fitzherbert, Richard M.; Pitt, David G. W.
2010-01-01
The methods for calculating returns on investments are taught to undergraduate level business students. In this paper, the authors demonstrate how such calculations are within the scope of senior school students of mathematics. In providing this demonstration the authors hope to give teachers and students alike an illustration of the power and the…
40 CFR 1065.850 - Calculations.
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...
Teaching Discrete Mathematics with Graphing Calculators.
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…
Using Calculators in Mathematics 12. Student Text.
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)…
46 CFR 154.520 - Piping calculations.
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...
Data base to compare calculations and observations
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)
76 FR 71431 - Civil Penalty Calculation Methodology
2011-11-17
... Uniform Fine Assessment (UFA) algorithm, which FMCSA currently uses for calculation of civil penalties. UFA takes into account the statutory penalty factors under 49 U.S.C. 521(b)(2)(D). The evaluation will... will impose a minimum civil penalty that is calculated by UFA. In many cases involving small...
Heat Calculation of Borehole Heat Exchangers
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.
Spreadsheet Based Scaling Calculations and Membrane Performance
Wolfe, T D; Bourcier, W L; Speth, T F
2000-12-28
Many membrane element manufacturers provide a computer program to aid buyers in the use of their elements. However, to date there are few examples of fully integrated public domain software available for calculating reverse osmosis and nanofiltration system performance. The Total Flux and Scaling Program (TFSP), written for Excel 97 and above, provides designers and operators new tools to predict membrane system performance, including scaling and fouling parameters, for a wide variety of membrane system configurations and feedwaters. The TFSP development was funded under EPA contract 9C-R193-NTSX. It is freely downloadable at www.reverseosmosis.com/download/TFSP.zip. TFSP includes detailed calculations of reverse osmosis and nanofiltration system performance. Of special significance, the program provides scaling calculations for mineral species not normally addressed in commercial programs, including aluminum, iron, and phosphate species. In addition, ASTM calculations for common species such as calcium sulfate (CaSO{sub 4}{times}2H{sub 2}O), BaSO{sub 4}, SrSO{sub 4}, SiO{sub 2}, and LSI are also provided. Scaling calculations in commercial membrane design programs are normally limited to the common minerals and typically follow basic ASTM methods, which are for the most part graphical approaches adapted to curves. In TFSP, the scaling calculations for the less common minerals use subsets of the USGS PHREEQE and WATEQ4F databases and use the same general calculational approach as PHREEQE and WATEQ4F. The activities of ion complexes are calculated iteratively. Complexes that are unlikely to form in significant concentration were eliminated to simplify the calculations. The calculation provides the distribution of ions and ion complexes that is used to calculate an effective ion product ''Q.'' The effective ion product is then compared to temperature adjusted solubility products (Ksp's) of solids in order to calculate a Saturation Index (SI
Ti-84 Plus graphing calculator for dummies
McCalla
2013-01-01
Get up-to-speed on the functionality of your TI-84 Plus calculator Completely revised to cover the latest updates to the TI-84 Plus calculators, this bestselling guide will help you become the most savvy TI-84 Plus user in the classroom! Exploring the standard device, the updated device with USB plug and upgraded memory (the TI-84 Plus Silver Edition), and the upcoming color screen device, this book provides you with clear, understandable coverage of the TI-84's updated operating system. Details the new apps that are available for download to the calculator via the USB cabl
Energy of plate tectonics calculation and projection
N. H. Swedan
2013-02-01
Full Text Available Mathematics and observations suggest that the energy of the geological activities resulting from plate tectonics is equal to the latent heat of melting, calculated at mantle's pressure, of the new ocean crust created at midocean ridges following sea floor spreading. This energy varies with the temperature of ocean floor, which is correlated with surface temperature. The objective of this manuscript is to calculate the force that drives plate tectonics, estimate the energy released, verify the calculations based on experiments and observations, and project the increase of geological activities with surface temperature rise caused by climate change.
Assessment of seismic margin calculation methods
Kennedy, R.P.; Murray, R.C.; Ravindra, M.K.; Reed, J.W.; Stevenson, J.D.
1989-03-01
Seismic margin review of nuclear power plants requires that the High Confidence of Low Probability of Failure (HCLPF) capacity be calculated for certain components. The candidate methods for calculating the HCLPF capacity as recommended by the Expert Panel on Quantification of Seismic Margins are the Conservative Deterministic Failure Margin (CDFM) method and the Fragility Analysis (FA) method. The present study evaluated these two methods using some representative components in order to provide further guidance in conducting seismic margin reviews. It is concluded that either of the two methods could be used for calculating HCLPF capacities. 21 refs., 9 figs., 6 tabs.
Program Calculates Current Densities Of Electronic Designs
Cox, Brian
1996-01-01
PDENSITY computer program calculates current densities for use in calculating power densities of electronic designs. Reads parts-list file for given design, file containing current required for each part, and file containing size of each part. For each part in design, program calculates current density in units of milliamperes per square inch. Written by use of AWK utility for Sun4-series computers running SunOS 4.x and IBM PC-series and compatible computers running MS-DOS. Sun version of program (NPO-19588). PC version of program (NPO-19171).
Hamming generalized corrector for reactivity calculation
Suescun-Diaz, Daniel; Ibarguen-Gonzalez, Maria C.; Figueroa-Jimenez, Jorge H. [Pontificia Universidad Javeriana Cali, Cali (Colombia). Dept. de Ciencias Naturales y Matematicas
2014-06-15
This work presents the Hamming method generalized corrector for numerically resolving the differential equation of delayed neutron precursor concentration from the point kinetics equations for reactivity calculation, without using the nuclear power history or the Laplace transform. A study was carried out of several correctors with their respective modifiers with different time step calculations, to offer stability and greater precision. Better results are obtained for some correctors than with other existing methods. Reactivity can be calculated with precision of the order h{sup 5}, where h is the time step. (orig.)
Pressure vessel calculations for VVER-440 reactors.
Hordósy, G; Hegyi, Gy; Keresztúri, A; Maráczy, Cs; Temesvári, E; Vértes, P; Zsolnay, E
2005-01-01
For the determination of the fast neutron load of the reactor pressure vessel a mixed calculational procedure was developed. The procedure was applied to the Unit II of Paks NPP, Hungary. The neutron source on the outer surfaces of the reactor was determined by a core design code, and the neutron transport calculations outside the core were performed by the Monte Carlo code MCNP. The reaction rate in the activation detectors at surveillance positions and at the cavity were calculated and compared with measurements. In most cases, fairly good agreement was found.
The WFIRST Galaxy Survey Exposure Time Calculator
Hirata, Christopher M.; Gehrels, Neil; Kneib, Jean-Paul; Kruk, Jeffrey; Rhodes, Jason; Wang, Yun; Zoubian, Julien
2013-01-01
This document describes the exposure time calculator for the Wide-Field Infrared Survey Telescope (WFIRST) high-latitude survey. The calculator works in both imaging and spectroscopic modes. In addition to the standard ETC functions (e.g. background and SN determination), the calculator integrates over the galaxy population and forecasts the density and redshift distribution of galaxy shapes usable for weak lensing (in imaging mode) and the detected emission lines (in spectroscopic mode). The source code is made available for public use.
Temperature calculation in fire safety engineering
Wickström, Ulf
2016-01-01
This book provides a consistent scientific background to engineering calculation methods applicable to analyses of materials reaction-to-fire, as well as fire resistance of structures. Several new and unique formulas and diagrams which facilitate calculations are presented. It focuses on problems involving high temperature conditions and, in particular, defines boundary conditions in a suitable way for calculations. A large portion of the book is devoted to boundary conditions and measurements of thermal exposure by radiation and convection. The concepts and theories of adiabatic surface temperature and measurements of temperature with plate thermometers are thoroughly explained. Also presented is a renewed method for modeling compartment fires, with the resulting simple and accurate prediction tools for both pre- and post-flashover fires. The final chapters deal with temperature calculations in steel, concrete and timber structures exposed to standard time-temperature fire curves. Useful temperature calculat...
Measured and Calculated Volumes of Wetland Depressions
U.S. Environmental Protection Agency — Measured and calculated volumes of wetland depressions This dataset is associated with the following publication: Wu, Q., and C. Lane. Delineation and quantification...
Spectra: Time series power spectrum calculator
Gallardo, Tabaré
2017-01-01
Spectra calculates the power spectrum of a time series equally spaced or not based on the Spectral Correlation Coefficient (Ferraz-Mello 1981, Astron. Journal 86 (4), 619). It is very efficient for detection of low frequencies.
Large Numbers and Calculators: A Classroom Activity.
Arcavi, Abraham; Hadas, Nurit
1989-01-01
Described is an activity demonstrating how a scientific calculator can be used in a mathematics classroom to introduce new content while studying a conventional topic. Examples of reading and writing large numbers, and reading hidden results are provided. (YP)
Fair and Reasonable Rate Calculation Data -
Department of Transportation — This dataset provides guidelines for calculating the fair and reasonable rates for U.S. flag vessels carrying preference cargoes subject to regulations contained at...
Quantum Monte Carlo Calculations of Light Nuclei
Pieper, Steven C
2007-01-01
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
Multigrid Methods in Electronic Structure Calculations
Briggs, E L; Bernholc, J
1996-01-01
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all length scales, thereby permitting efficient calculations for ill-conditioned systems with long length scales or high energy cut-offs. We discuss specific implementations of multigrid and real-space algorithms for electronic structure calculations, including an efficient multigrid-accelerated solver for Kohn-Sham equations, compact yet accurate discretization schemes for the Kohn-Sham and Poisson equations, optimized pseudo\\-potentials for real-space calculations, efficacious computation of ionic forces, and a complex-wavefunction implementation for arbitrary sampling of the Brillioun zone. A particular strength of a real-space multigrid approach is its ready adaptability to massively parallel computer architectures, and we present an implementation for the Cray-T3D with essen...
46 CFR 170.090 - Calculations.
2010-10-01
... necessary to compute and plot any of the following curves as part of the calculations required in this subchapter, these plots must also be submitted: (1) Righting arm or moment curves. (2) Heeling arm or...
Representation and calculation of economic uncertainties
Schjær-Jacobsen, Hans
2002-01-01
Management and decision making when certain information is available may be a matter of rationally choosing the optimal alternative by calculation of the utility function. When only uncertain information is available (which is most often the case) decision-making calls for more complex methods...... of representation and calculation and the basis for choosing the optimal alternative may become obscured by uncertainties of the utility function. In practice, several sources of uncertainties of the required information impede optimal decision making in the classical sense. In order to be able to better handle...... to uncertain economic numbers are discussed. When solving economic models for decision-making purposes calculation of uncertain functions will have to be carried out in addition to the basic arithmetical operations. This is a challenging numerical problem since improper methods of calculation may introduce...
Note about socio-economic calculations
Landex, Alex; Andersen, Jonas Lohmann Elkjær; Salling, Kim Bang
2006-01-01
these effects must be described qualitatively. This note describes the socio-economic evaluation based on market prices and not factor prices which has been the tradition in Denmark till now. This is due to the recommendation from the Ministry of Transport to start using calculations based on market prices......This note gives a short introduction of how to make socio-economic evaluations in connection with the teaching at the Centre for Traffic and Transport (CTT). It is not a manual for making socio-economic calculations in transport infrastructure projects – in this context we refer to the guidelines...... for socio-economic calculations within the transportation area (Ministry of Traffic, 2003). The note also explains the theory of socio-economic calculations – reference is here made to ”Road Infrastructure Planning – a Decision-oriented approach” (Leleur, 2000). Socio-economic evaluations of infrastructure...
Obliged to Calculate: "My School", Markets, and Equipping Parents for Calculativeness
Gobby, Brad
2016-01-01
This paper argues neoliberal programs of government in education are equipping parents for calculativeness. Regimes of testing and the publication of these results and other organizational data are contributing to a public economy of numbers that increasingly oblige citizens to calculate. Using the notions of calculative and market devices, this…
A revised calculational model for fission
Atchison, F.
1998-09-01
A semi-empirical parametrization has been developed to calculate the fission contribution to evaporative de-excitation of nuclei with a very wide range of charge, mass and excitation-energy and also the nuclear states of the scission products. The calculational model reproduces measured values (cross-sections, mass distributions, etc.) for a wide range of fissioning systems: Nuclei from Ta to Cf, interactions involving nucleons up to medium energy and light ions. (author)
A Java Interface for Roche Lobe Calculations
Leahy, D. A.; Leahy, J. C.
2015-09-01
A JAVA interface for calculating various properties of the Roche lobe has been created. The geometry of the Roche lobe is important for studying interacting binary stars, particularly those with compact objects which have a companion which fills the Roche lobe. There is no known analytic solution to the Roche lobe problem. Here the geometry of the Roche lobe is calculated numerically to high accuracy and made available to the user for arbitrary input mass ratio, q.
Realistic level density calculation for heavy nuclei
Cerf, N. [Institut de Physique Nucleaire, Orsay (France); Pichon, B. [Observatoire de Paris, Meudon (France); Rayet, M.; Arnould, M. [Institut d`Astronomie et d`Astrophysique, Bruxelles (Belgium)
1994-12-31
A microscopic calculation of the level density is performed, based on a combinatorial evaluation using a realistic single-particle level scheme. This calculation relies on a fast Monte Carlo algorithm, allowing to consider heavy nuclei (i.e., large shell model spaces) which could not be treated previously in combinatorial approaches. An exhaustive comparison of the predicted neutron s-wave resonance spacings with experimental data for a wide range of nuclei is presented.
Flow calculation of a bulb turbine
Goede, E.; Pestalozzi, J.
1987-01-01
In recent years remarkable progress has been made in the field of theoretical flow calculation. Studying the relevant literature one might receive the impression that most problems have been solved. But probing more deeply into details one becomes aware that by no means all questions are answered. The report tries to point out what may be expected of the quasi-three-dimensional flow calculation method employed and - much more important - what it must not be expected to accomplish. (orig.)
Green's function calculations of light nuclei
Sun, ZhongHao; Wu, Qiang; Xu, FuRong
2016-09-01
The influence of short-range correlations in nuclei was investigated with realistic nuclear force. The nucleon-nucleon interaction was renormalized with V lowk technique and applied to the Green's function calculations. The Dyson equation was reformulated with algebraic diagrammatic constructions. We also analyzed the binding energy of 4He, calculated with chiral potential and CD-Bonn potential. The properties of Green's function with realistic nuclear forces are also discussed.
Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution
Fog, Agner
2008-01-01
distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems....... is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...
Users enlist consultants to calculate costs, savings
1982-05-24
Consultants who calculate payback provide expertise and a second opinion to back up energy managers' proposals. They can lower the costs of an energy-management investment by making complex comparisons of systems and recommending the best system for a specific application. Examples of payback calculations include simple payback for a school system, a university, and a Disneyland hotel, as well as internal rate of return for a corporate office building and a chain of clothing stores. (DCK)
DOWNSCALE APPLICATION OF BOILER THERMAL CALCULATION APPROACH
Zelený, Zbynĕk; Hrdlička, Jan
2016-01-01
Commonly used thermal calculation methods are intended primarily for large scale boilers. Hot water small scale boilers, which are commonly used for home heating have many specifics, that distinguish them from large scale boilers especially steam boilers. This paper is focused on application of thermal calculation procedure that is designed for large scale boilers, on a small scale boiler for biomass combustion of load capacity 25 kW. Special issue solved here is influence of formation of dep...
Reciprocity Theorems for Ab Initio Force Calculations
Wei, C; Mele, E J; Rappe, A M; Lewis, Steven P.; Rappe, Andrew M.
1996-01-01
We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.
R-matrix calculation for photoionization
无
2000-01-01
We have employed the R-matrix method to calculate differe ntial cross sections for photoionization of helium leaving helium ion in an exci ted state for incident photon energy between the N=2 and N=3 thresholds (69～73 eV) of He+ ion. Differential cross sections for photoionization in the N=2 level at emission angle 0° are provide. Our results are in good agreem ent with available experimental data and theoretical calculations.
Efficient Finite Element Calculation of Nγ
Clausen, Johan; Damkilde, Lars; Krabbenhøft, K.
2007-01-01
This paper deals with the computational aspects of the Mohr-Coulomb material model, in particular the calculation of the bearing capacity factor Nγfor a strip and a circular footing.......This paper deals with the computational aspects of the Mohr-Coulomb material model, in particular the calculation of the bearing capacity factor Nγfor a strip and a circular footing....
Computerized calculation of material balances in carbonization
Chistyakov, A.M.
1980-09-01
Charge formulations and carbonisation schedules are described by empirical formulae used to calculate the yield of coking products. An algorithm is proposed for calculating the material balance, and associated computer program. The program can be written in conventional languages, e.g. Fortran, Algol etc. The information obtained can be used for on-line assessment of the effects of charge composition and properties on the coke and by-products yields, as well as the effects of the carbonisation conditions.
Calculating Cumulative Binomial-Distribution Probabilities
Scheuer, Ernest M.; Bowerman, Paul N.
1989-01-01
Cumulative-binomial computer program, CUMBIN, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), used independently of one another. Reliabilities and availabilities of k-out-of-n systems analyzed. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Used for calculations of reliability and availability. Program written in C.
PROSPECTS OF MANAGEMENT ACCOUNTING AND COST CALCULATION
Marian ŢAICU
2014-11-01
Full Text Available Progress in improving production technology requires appropriate measures to achieve an efficient management of costs. This raises the need for continuous improvement of management accounting and cost calculation. Accounting information in general, and management accounting information in particular, have gained importance in the current economic conditions, which are characterized by risk and uncertainty. The future development of management accounting and cost calculation is essential to meet the information needs of management.
Linear Response Calculations of Spin Fluctuations
Savrasov, S. Y.
1998-09-01
A variational formulation of the time-dependent linear response based on the Sternheimer method is developed in order to make practical ab initio calculations of dynamical spin susceptibilities of solids. Using gradient density functional and a muffin-tin-orbital representation, the efficiency of the approach is demonstrated by applications to selected magnetic and strongly paramagnetic metals. The results are found to be consistent with experiment and are compared with previous theoretical calculations.
Environmental flow allocation and statistics calculator
Konrad, Christopher P.
2011-01-01
The Environmental Flow Allocation and Statistics Calculator (EFASC) is a computer program that calculates hydrologic statistics based on a time series of daily streamflow values. EFASC will calculate statistics for daily streamflow in an input file or will generate synthetic daily flow series from an input file based on rules for allocating and protecting streamflow and then calculate statistics for the synthetic time series. The program reads dates and daily streamflow values from input files. The program writes statistics out to a series of worksheets and text files. Multiple sites can be processed in series as one run. EFASC is written in MicrosoftRegistered Visual BasicCopyright for Applications and implemented as a macro in MicrosoftOffice Excel 2007Registered. EFASC is intended as a research tool for users familiar with computer programming. The code for EFASC is provided so that it can be modified for specific applications. All users should review how output statistics are calculated and recognize that the algorithms may not comply with conventions used to calculate streamflow statistics published by the U.S. Geological Survey.
Good Practices in Free-energy Calculations
Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christopher
2013-01-01
As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.
Paramedics’ Ability to Perform Drug Calculations
Eastwood, Kathyrn J
2009-11-01
Full Text Available Background: The ability to perform drug calculations accurately is imperative to patient safety. Research into paramedics’ drug calculation abilities was first published in 2000 and for nurses’ abilities the research dates back to the late 1930s. Yet, there have been no studies investigating an undergraduate paramedic student’s ability to perform drug or basic mathematical calculations. The objective of this study was to review the literature and determine the ability of undergraduate and qualified paramedics to perform drug calculations.Methods: A search of the prehospital-related electronic databases was undertaken using the Ovid and EMBASE systems available through the Monash University Library. Databases searched included the Cochrane Central Register of Controlled Trials (CENTRAL, MEDLINE, CINAHL, JSTOR, EMBASE and Google Scholar, from their beginning until the end of August 2009. We reviewed references from articles retrieved.Results: The electronic database search located 1,154 articles for review. Six additional articles were identified from reference lists of retrieved articles. Of these, 59 were considered relevant. After reviewing the 59 articles only three met the inclusion criteria. All articles noted some level of mathematical deficiencies amongst their subjects.Conclusions: This study identified only three articles. Results from these limited studies indicate a significant lack of mathematical proficiency amongst the paramedics sampled. A need exists to identify if undergraduate paramedic students are capable of performing the required drug calculations in a non-clinical setting.[WestJEM. 2009;10:240-243.
Comparison of Polar Cap (PC) index calculations.
Stauning, P.
2012-04-01
The Polar Cap (PC) index introduced by Troshichev and Andrezen (1985) is derived from polar magnetic variations and is mainly a measure of the intensity of the transpolar ionospheric currents. These currents relate to the polar cap antisunward ionospheric plasma convection driven by the dawn-dusk electric field, which in turn is generated by the interaction of the solar wind with the Earth's magnetosphere. Coefficients to calculate PCN and PCS index values from polar magnetic variations recorded at Thule and Vostok, respectively, have been derived by several different procedures in the past. The first published set of coefficients for Thule was derived by Vennerstrøm, 1991 and is still in use for calculations of PCN index values by DTU Space. Errors in the program used to calculate index values were corrected in 1999 and again in 2001. In 2005 DMI adopted a unified procedure proposed by Troshichev for calculations of the PCN index. Thus there exists 4 different series of PCN index values. Similarly, at AARI three different sets of coefficients have been used to calculate PCS indices in the past. The presentation discusses the principal differences between the various PC index procedures and provides comparisons between index values derived from the same magnetic data sets using the different procedures. Examples from published papers are examined to illustrate the differences.
Accurate free energy calculation along optimized paths.
Chen, Changjun; Xiao, Yi
2010-05-01
The path-based methods of free energy calculation, such as thermodynamic integration and free energy perturbation, are simple in theory, but difficult in practice because in most cases smooth paths do not exist, especially for large molecules. In this article, we present a novel method to build the transition path of a peptide. We use harmonic potentials to restrain its nonhydrogen atom dihedrals in the initial state and set the equilibrium angles of the potentials as those in the final state. Through a series of steps of geometrical optimization, we can construct a smooth and short path from the initial state to the final state. This path can be used to calculate free energy difference. To validate this method, we apply it to a small 10-ALA peptide and find that the calculated free energy changes in helix-helix and helix-hairpin transitions are both self-convergent and cross-convergent. We also calculate the free energy differences between different stable states of beta-hairpin trpzip2, and the results show that this method is more efficient than the conventional molecular dynamics method in accurate free energy calculation.
Perturbation calculation of thermodynamic density of states.
Brown, G; Schulthess, T C; Nicholson, D M; Eisenbach, M; Stocks, G M
2011-12-01
The density of states g (ε) is frequently used to calculate the temperature-dependent properties of a thermodynamic system. Here a derivation is given for calculating the warped density of states g*(ε) resulting from the addition of a perturbation. The method is validated for a classical Heisenberg model of bcc Fe and the errors in the free energy are shown to be second order in the perturbation. Taking the perturbation to be the difference between a first-principles quantum-mechanical energy and a corresponding classical energy, this method can significantly reduce the computational effort required to calculate g(ε) for quantum systems using the Wang-Landau approach.
Using Inverted Indices for Accelerating LINGO Calculations
Kristensen, Thomas Greve; Nielsen, Jesper; Pedersen, Christian Nørgaard Storm
2011-01-01
The ever growing size of chemical data bases calls for the development of novel methods for representing and comparing molecules. One such method called LINGO is based on fragmenting the SMILES string representation of molecules. Comparison of molecules can then be performed by calculating...... the Tanimoto coefficient which is called the LINGOsim when used on LINGO multisets. This paper introduces a verbose representation for storing LINGO multisets which makes it possible to transform them into sparse fingerprints such that fingerprint data structures and algorithms can be used to accelerate...... queries. The previous best method for rapidly calculating the LINGOsim similarity matrix required specialised hardware to yield a significant speedup over existing methods. By representing LINGO multisets in the verbose representation and using inverted indices it is possible to calculate LINGOsim...
Using inverted indices for accelerating LINGO calculations.
Kristensen, Thomas G; Nielsen, Jesper; Pedersen, Christian N S
2011-03-28
The ever growing size of chemical databases calls for the development of novel methods for representing and comparing molecules. One such method called LINGO is based on fragmenting the SMILES string representation of molecules. Comparison of molecules can then be performed by calculating the Tanimoto coefficient, which is called LINGOsim when used on LINGO multisets. This paper introduces a verbose representation for storing LINGO multisets, which makes it possible to transform them into sparse fingerprints such that fingerprint data structures and algorithms can be used to accelerate queries. The previous best method for rapidly calculating the LINGOsim similarity matrix required specialized hardware to yield a significant speedup over existing methods. By representing LINGO multisets in the verbose representation and using inverted indices, it is possible to calculate LINGOsim similarity matrices roughly 2.6 times faster than existing methods without relying on specialized hardware.
Automated one-loop calculations with GOSAM
Cullen, Gavin [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Greiner, Nicolas [Illinois Univ., Urbana-Champaign, IL (United States). Dept. of Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany); Heinrich, Gudrun; Reiter, Thomas [Max-Planck-Institut fuer Physik, Muenchen (Germany); Luisoni, Gionata [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; Mastrolia, Pierpaolo [Max-Planck-Institut fuer Physik, Muenchen (Germany); Padua Univ. (Italy). Dipt. di Fisica; Ossola, Giovanni [New York City Univ., NY (United States). New York City College of Technology; New York City Univ., NY (United States). The Graduate School and University Center; Tramontano, Francesco [European Organization for Nuclear Research (CERN), Geneva (Switzerland)
2011-11-15
We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the loop. (orig.)
Benchmarking calculations of excitonic couplings between bacteriochlorophylls
Kenny, Elise P
2015-01-01
Excitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated couplings. Because quantum-chemical corrections are smaller than 20% in most biologically relevant cases, their considerable computational cost is rarely justified. We therefore recommend the electrostatic TrEsp method across the entire range of molecular separations and orientations because its cost is minimal and it generally agrees with quantum-chemical calculations to better than the geometric uncertainty. We also caution ...
Detailed Burnup Calculations for Research Reactors
Leszczynski, F. [Centro Atomico Bariloche (CNEA), 8400 S. C. de Bariloche (Argentina)
2011-07-01
A general method (RRMCQ) has been developed by introducing a microscopic burn up scheme which uses the Monte Carlo calculated spatial power distribution of a research reactor core and a depletion code for burn up calculations, as a basis for solving nuclide material balance equations for each spatial region in which the system is divided. Continuous energy dependent cross-section libraries and full 3D geometry of the system is input for the calculations. The resulting predictions for the system at successive burn up time steps are thus based on a calculation route where both geometry and cross-sections are accurately represented, without geometry simplifications and with continuous energy data. The main advantage of this method over the classical deterministic methods currently used is that RRMCQ System is a direct 3D method without the limitations and errors introduced on the homogenization of geometry and condensation of energy of deterministic methods. The Monte Carlo and burn up codes adopted until now are the widely used MCNP5 and ORIGEN2 codes, but other codes can be used also. For using this method, there is a need of a well-known set of nuclear data for isotopes involved in burn up chains, including burnable poisons, fission products and actinides. For fixing the data to be included on this set, a study of the present status of nuclear data is performed, as part of the development of RRMCQ method. This study begins with a review of the available cross-section data of isotopes involved in burn up chains for research nuclear reactors. The main data needs for burn up calculations are neutron cross-sections, decay constants, branching ratios, fission energy and yields. The present work includes results of selected experimental benchmarks and conclusions about the sensitivity of different sets of cross-section data for burn up calculations, using some of the main available evaluated nuclear data files. Basically, the RRMCQ detailed burn up method includes four
Dose calculations for intakes of ore dust
O`Brien, R.S
1998-08-01
This report describes a methodology for calculating the committed effective dose for mixtures of radionuclides, such as those which occur in natural radioactive ores and dusts. The formulae are derived from first principles, with the use of reasonable assumptions concerning the nature and behaviour of the radionuclide mixtures. The calculations are complicated because these `ores` contain a range of particle sizes, have different degrees of solubility in blood and other body fluids, and also have different biokinetic clearance characteristics from the organs and tissues in the body. The naturally occurring radionuclides also tend to occur in series, i.e. one is produced by the radioactive decay of another `parent` radionuclide. The formulae derived here can be used, in conjunction with a model such as LUDEP, for calculating total dose resulting from inhalation and/or ingestion of a mixture of radionuclides, and also for deriving annual limits on intake and derived air concentrations for these mixtures. 15 refs., 14 tabs., 3 figs.
Numerical inductance calculations based on first principles.
Shatz, Lisa F; Christensen, Craig W
2014-01-01
A method of calculating inductances based on first principles is presented, which has the advantage over the more popular simulators in that fundamental formulas are explicitly used so that a deeper understanding of the inductance calculation is obtained with no need for explicit discretization of the inductor. It also has the advantage over the traditional method of formulas or table lookups in that it can be used for a wider range of configurations. It relies on the use of fast computers with a sophisticated mathematical computing language such as Mathematica to perform the required integration numerically so that the researcher can focus on the physics of the inductance calculation and not on the numerical integration.
Challenges in Large Scale Quantum Mechanical Calculations
Ratcliff, Laura E; Huhs, Georg; Deutsch, Thierry; Masella, Michel; Genovese, Luigi
2016-01-01
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.
Cosmology calculations almost without general relativity
Jordan, T F
2003-01-01
The Friedmann equation can be derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that govern the expansion of the universe. Descriptions and explanations of radiation pressure and vacuum pressure are added to complete a basic kit of cosmology tools. It provides a basis for teaching cosmology to undergraduates in a way that quickly equips them to do basic calculations. This is demonstrated with calculations involving: characteristics of the expansion for densities dominated by radiation, matter, or vacuum; the closeness of the density to the critical density; how much vacuum energy compared to matter energy is needed to make the expansion accelerate; and how little is needed to make it stop. Travel time and luninosity distance are calculated in terms of the redshift and the densities of matter and vacuum energy, using a scaled Friedmann equation with the...
Parallel scalability of Hartree–Fock calculations
Chow, Edmond, E-mail: echow@cc.gatech.edu; Liu, Xing [School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0765 (United States); Smelyanskiy, Mikhail; Hammond, Jeff R. [Parallel Computing Lab, Intel Corporation, Santa Clara, California 95054-1549 (United States)
2015-03-14
Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree–Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.
Lagrange interpolation for the radiation shielding calculation
Isozumi, Y; Miyatake, H; Kato, T; Tosaki, M
2002-01-01
Basing on some formulas of Lagrange interpolation derived in this paper, a computer program for table calculations has been prepared. Main features of the program are as follows; 1) maximum degree of polynomial in Lagrange interpolation is 10, 2) tables with both one variable and two variables can be applied, 3) logarithmic transformations of function and/or variable values can be included and 4) tables with discontinuities and cusps can be applied. The program has been carefully tested by using the data tables in the manual of shielding calculation for radiation facilities. For all available tables in the manual, calculations with the program have been reasonably performed under conditions of 1) logarithmic transformation of both function and variable values and 2) degree 4 or 5 of the polynomial.
eQuilibrator--the biochemical thermodynamics calculator.
Flamholz, Avi; Noor, Elad; Bar-Even, Arren; Milo, Ron
2012-01-01
The laws of thermodynamics constrain the action of biochemical systems. However, thermodynamic data on biochemical compounds can be difficult to find and is cumbersome to perform calculations with manually. Even simple thermodynamic questions like 'how much Gibbs energy is released by ATP hydrolysis at pH 5?' are complicated excessively by the search for accurate data. To address this problem, eQuilibrator couples a comprehensive and accurate database of thermodynamic properties of biochemical compounds and reactions with a simple and powerful online search and calculation interface. The web interface to eQuilibrator (http://equilibrator.weizmann.ac.il) enables easy calculation of Gibbs energies of compounds and reactions given arbitrary pH, ionic strength and metabolite concentrations. The eQuilibrator code is open-source and all thermodynamic source data are freely downloadable in standard formats. Here we describe the database characteristics and implementation and demonstrate its use.
Daylight calculations using constant luminance curves
Betman, E. [CRICYT, Mendoza (Argentina). Laboratorio de Ambiente Humano y Vivienda
2005-02-01
This paper presents a simple method to manually estimate daylight availability and to make daylight calculations using constant luminance curves calculated with local illuminance and irradiance data and the all-weather model for sky luminance distribution developed in the Atmospheric Science Research Center of the University of New York (ARSC) by Richard Perez et al. Work with constant luminance curves has the advantage that daylight calculations include the problem's directionality and preserve the information of the luminous climate of the place. This permits accurate knowledge of the resource and a strong basis to establish conclusions concerning topics related to the energy efficiency and comfort in buildings. The characteristics of the proposed method are compared with the method that uses the daylight factor. (author)
Calculation of Radiation Damage in SLAC Targets
Wirth, B D; Monasterio, P; Stein, W
2008-04-03
Ti-6Al-4V alloys are being considered as a positron producing target in the Next Linear Collider, with an incident photon beam and operating temperatures between room temperature and 300 C. Calculations of displacement damage in Ti-6Al-4V alloys have been performed by combining high-energy particle FLUKA simulations with SPECTER calculations of the displacement cross section from the resulting energy-dependent neutron flux plus the displacements calculated from the Lindhard model from the resulting energy-dependent ion flux. The radiation damage calculations have investigated two cases, namely the damage produced in a Ti-6Al-4V SLAC positron target where the irradiation source is a photon beam with energies between 5 and 11 MeV. As well, the radiation damage dose in displacements per atom, dpa, has been calculated for a mono-energetic 196 MeV proton irradiation experiment performed at Brookhaven National Laboratory (BLIP experiment). The calculated damage rate is 0.8 dpa/year for the Ti-6Al-4V SLAC photon irradiation target, and a total damage exposure of 0.06 dpa in the BLIP irradiation experiment. In both cases, the displacements are predominantly ({approx}80%) produced by recoiling ions (atomic nuclei) from photo-nuclear collisions or proton-nuclear collisions, respectively. Approximately 25% of the displacement damage results from the neutrons in both cases. Irradiation effects studies in titanium alloys have shown substantial increases in the yield and ultimate strength of up to 500 MPa and a corresponding decrease in uniform ductility for neutron and high energy proton irradiation at temperatures between 40 and 300 C. Although the data is limited, there is an indication that the strength increases will saturate by doses on the order of a few dpa. Microstructural investigations indicate that the dominant features responsible for the strength increases were dense precipitation of a {beta} (body-centered cubic) phase precipitate along with a high number density
Precise calculations of the deuteron quadrupole moment
Gross, Franz L. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-06-01
Recently, two calculations of the deuteron quadrupole moment have have given predictions that agree with the measured value to within 1%, resolving a long-standing discrepancy. One of these uses the covariant spectator theory (CST) and the other chiral effective field theory (cEFT). In this talk I will first briefly review the foundations and history of the CST, and then compare these two calculations with emphasis on how the same physical processes are being described using very different language. The comparison of the two methods gives new insights into the dynamics of the low energy NN interaction.
Local orbitals in electron scattering calculations*
Winstead, Carl L.; McKoy, Vincent
2016-05-01
We examine the use of local orbitals to improve the scaling of calculations that incorporate target polarization in a description of low-energy electron-molecule scattering. After discussing the improved scaling that results, we consider the results of a test calculation that treats scattering from a two-molecule system using both local and delocalized orbitals. Initial results are promising. Contribution to the Topical Issue "Advances in Positron and Electron Scattering", edited by Paulo Limao-Vieira, Gustavo Garcia, E. Krishnakumar, James Sullivan, Hajime Tanuma and Zoran Petrovic.
Numerical calculation of impurity charge state distributions
Crume, E. C.; Arnurius, D. E.
1977-09-01
The numerical calculation of impurity charge state distributions using the computer program IMPDYN is discussed. The time-dependent corona atomic physics model used in the calculations is reviewed, and general and specific treatments of electron impact ionization and recombination are referenced. The complete program and two examples relating to tokamak plasmas are given on a microfiche so that a user may verify that his version of the program is working properly. In the discussion of the examples, the corona steady-state approximation is shown to have significant defects when the plasma environment, particularly the electron temperature, is changing rapidly.
The new pooled cohort equations risk calculator
Preiss, David; Kristensen, Søren L
2015-01-01
total cardiovascular risk score. During development of joint guidelines released in 2013 by the American College of Cardiology (ACC) and American Heart Association (AHA), the decision was taken to develop a new risk score. This resulted in the ACC/AHA Pooled Cohort Equations Risk Calculator. This risk...... disease and any measure of social deprivation. An early criticism of the Pooled Cohort Equations Risk Calculator has been its alleged overestimation of ASCVD risk which, if confirmed in the general population, is likely to result in statin therapy being prescribed to many individuals at lower risk than...
Idiot savant calendrical calculators: maths or memory?
O'Connor, N; Hermelin, B
1984-11-01
Eight idiot savant calendrical calculators were tested on dates in the years 1963, 1973, 1983, 1986 and 1993. The study was carried out in 1983. Speeds of correct response were minimal in 1983 and increased markedly into the past and the future. The response time increase was matched by an increase in errors. Speeds of response were uncorrelated with measured IQ, but the numbers were insufficient to justify any inference in terms of IQ-independence. Results are interpreted as showing that memory alone is inadequate to explain the calendrical calculating performance of the idiot savant subjects.
Calculated Electron Fluxes at Airplane Altitudes
Schaefer, R K; Stanev, T
1993-01-01
A precision measurement of atmospheric electron fluxes has been performed on a Japanese commercial airliner (Enomoto, {\\it et al.}, 1991). We have performed a monte carlo calculation of the cosmic ray secondary electron fluxes expected in this experiment. The monte carlo uses the hadronic portion of our neutrino flux cascade program combined with the electromagnetic cascade portion of the CERN library program GEANT. Our results give good agreement with the data, provided we boost the overall normalization of the primary cosmic ray flux by 12\\% over the normalization used in the neutrino flux calculation.
Program Calculates Power Demands Of Electronic Designs
Cox, Brian
1995-01-01
CURRENT computer program calculates power requirements of electronic designs. For given design, CURRENT reads in applicable parts-list file and file containing current required for each part. Program also calculates power required for circuit at supply potentials of 5.5, 5.0, and 4.5 volts. Written by use of AWK utility for Sun4-series computers running SunOS 4.x and IBM PC-series and compatible computers running MS-DOS. Sun version of program (NPO-19590). PC version of program (NPO-19111).
Calculated optical absorption of different perovskite phases
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...... of perovskites the solar light absorption efficiency varies greatly depending not only on bandgap size and character (direct/indirect) but also on the dipole matrix elements. The oxides exhibit generally a fairly weak absorption efficiency due to indirect bandgaps while the most efficient absorbers are found...... in the classes of oxynitride and organometal halide perovskites with strong direct transitions....
Relaxation Method For Calculating Quantum Entanglement
Tucci, R R
2001-01-01
In a previous paper, we showed how entanglement of formation can be defined as a minimum of the quantum conditional mutual information (a.k.a. quantum conditional information transmission). In classical information theory, the Arimoto-Blahut method is one of the preferred methods for calculating extrema of mutual information. We present a new method akin to the Arimoto-Blahut method for calculating entanglement of formation. We also present several examples computed with a computer program called Causa Comun that implements the ideas of this paper.
DFT calculations with the exact functional
Burke, Kieron
2014-03-01
I will discuss several works in which we calculate the exact exchange-correlation functional of density functional theory, mostly using the density-matrix renormalization group method invented by Steve White, our collaborator. We demonstrate that a Mott-Hubard insulator is a band metal. We also perform Kohn-Sham DFT calculations with the exact functional and prove that a simple algoritm always converges. But we find convergence becomes harder as correlations get stronger. An example from transport through molecular wires may also be discussed. Work supported by DOE grant DE-SC008696.
Calculating reliability measures for ordinal data.
Gamsu, C V
1986-11-01
Establishing the reliability of measures taken by judges is important in both clinical and research work. Calculating the statistic of choice, the kappa coefficient, unfortunately is not a particularly quick and simple procedure. Two much-needed practical tools have been developed to overcome these difficulties: a comprehensive and easily understood guide to the manual calculation of the most complex form of the kappa coefficient, weighted kappa for ordinal data, has been written; and a computer program to run under CP/M, PC-DOS and MS-DOS has been developed. With simple modification the program will also run on a Sinclair Spectrum home computer.
Improving on calculation of martensitic phenomenological theory
无
2003-01-01
Exemplified by the martensitic transformation from DO3 to 18R in Cu-14.2Al-4.3Ni alloy and according to the principle that invariant-habit-plane can be obtained by self-accommodation between variants with twin relationships, and on the basis of displacement vector, volume fractions of two variants with twin relationships in martensitic transformation, habit-plane indexes, and orientation relationships between martensite and austenite after phase transformation can be calculated. Because no additional rotation matrixes are needed to be considered and mirror symmetric operations are used, the calculation process is simple and the results are accurate.
Transmission pipeline calculations and simulations manual
Menon, E Shashi
2014-01-01
Transmission Pipeline Calculations and Simulations Manual is a valuable time- and money-saving tool to quickly pinpoint the essential formulae, equations, and calculations needed for transmission pipeline routing and construction decisions. The manual's three-part treatment starts with gas and petroleum data tables, followed by self-contained chapters concerning applications. Case studies at the end of each chapter provide practical experience for problem solving. Topics in this book include pressure and temperature profile of natural gas pipelines, how to size pipelines for specified f
Pumping slots: Coupling impedance calculations and estimates
Kurennoy, S.
1993-08-01
Coupling impedances of small pumping holes in vacuum-chamber walls have been calculated at low frequencies, i.e., for wavelengths large compared to a typical hole size, in terms of electric and magnetic polarizabilities of the hole. The polarizabilities can be found by solving and electro- or magnetostatic problem and are known analytically for the case of the elliptic shape of the hole in a thin wall. The present paper studies the case of pumping slots. Using results of numerical calculations and analytical approximations of polarizabilities, we give formulae for practically important estimates of slot contribution to low-frequency coupling impedances.
Necessity of Exact Calculation for Transition Probability
LIU Fu-Sui; CHEN Wan-Fang
2003-01-01
This paper shows that exact calculation for transition probability can make some systems deviate fromFermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate inducedby phonons for deuteron in Pd-D system with the many-body electron screening, proposed by Ichimaru, can explainthe experimental fact observed in Pd-D system, and predicts that perfection and low-dimension of Pd lattice are veryimportant for the phonon-induced hopping rate enhancement in Pd-D system.
Calculation of U-value for Concrete Element
Rose, Jørgen
1997-01-01
This report is a U-value calculation of a typical concrete element used in industrial buildings.The calculations are performed using a 2-dimensional finite difference calculation programme.......This report is a U-value calculation of a typical concrete element used in industrial buildings.The calculations are performed using a 2-dimensional finite difference calculation programme....
无
2002-01-01
The improved form of calculation formula for the activities of the components in binary liquids and solid alloys has been derived based on the free volume theory considering excess entropy and Miedema's model for calculating the formation heat of binary alloys. A calculation method of excess thermodynamic functions for binary alloys, the formulas of integral molar excess properties and partial molar excess properties for solid ordered or disordered binary alloys have been developed. The calculated results are in good agreement with the experimental values.
Engineering calculations in radiative heat transfer
Gray, W A; Hopkins, D W
1974-01-01
Engineering Calculations in Radiative Heat Transfer is a six-chapter book that first explains the basic principles of thermal radiation and direct radiative transfer. Total exchange of radiation within an enclosure containing an absorbing or non-absorbing medium is then described. Subsequent chapters detail the radiative heat transfer applications and measurement of radiation and temperature.
Net analyte signal calculation for multivariate calibration
Ferre, J.; Faber, N.M.
2003-01-01
A unifying framework for calibration and prediction in multivariate calibration is shown based on the concept of the net analyte signal (NAS). From this perspective, the calibration step can be regarded as the calculation of a net sensitivity vector, whose length is the amount of net signal when the