Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol
Sugiyama, K.; Calzavarini, E.; Grossmann, S.; Lohse, Detlef
2007-01-01
We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number Ra up to 108 (for fixed temperature difference Î�
Invariant relations in Boussinesq-type equations
International Nuclear Information System (INIS)
Meletlidou, Efi; Pouget, Joeel; Maugin, Gerard; Aifantis, Elias
2004-01-01
A wide class of partial differential equations have at least three conservation laws that remain invariant for certain solutions of them and especially for solitary wave solutions. These conservation laws can be considered as the energy, pseudomomentum and mass integrals of these solutions. We investigate the invariant relation between the energy and the pseudomomentum for solitary waves in two Boussinesq-type equations that come from the theory of elasticity and lattice models
Numerical investigation of sixth order Boussinesq equation
Kolkovska, N.; Vucheva, V.
2017-10-01
We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.
Exact traveling wave solutions of the Boussinesq equation
International Nuclear Information System (INIS)
Ding Shuangshuang; Zhao Xiqiang
2006-01-01
The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained
Two dimensional generalizations of the Newcomb equation
International Nuclear Information System (INIS)
Dewar, R.L.; Pletzer, A.
1989-11-01
The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs
International Nuclear Information System (INIS)
Zhang Liang; Zhang Lifeng; Li Chongyin
2008-01-01
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions
problem for the damped Boussinesq equation
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Vladimir V. Varlamov
1997-01-01
Full Text Available For the damped Boussinesq equation utt−2butxx=−αuxxxx+uxx+β(u2xx,x∈(0,π,t>0;α,b=const>0,β=const∈R1, the second initial-boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long-time asymptotics is obtained in the explicit form and the question of the blow up of the solution in a certain case is examined. The possibility of passing to the limit b→+0 in the constructed solution is investigated.
An integrable semi-discretization of the Boussinesq equation
International Nuclear Information System (INIS)
Zhang, Yingnan; Tian, Lixin
2016-01-01
Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.
An integrable semi-discretization of the Boussinesq equation
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)
2016-10-23
Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.
Two-dimensional nonlinear equations of supersymmetric gauge theories
International Nuclear Information System (INIS)
Savel'ev, M.V.
1985-01-01
Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations
Solutions and Conservation Laws of a (2+1-Dimensional Boussinesq Equation
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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.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
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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.
Control Operator for the Two-Dimensional Energized Wave Equation
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Sunday Augustus REJU
2006-07-01
Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.
Analytic self-similar solutions of the Oberbeck–Boussinesq equations
International Nuclear Information System (INIS)
Barna, I.F.; Mátyás, L.
2015-01-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtonian–Navier–Stokes — with Boussinesq approximation — and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field shows a strongly damped single periodic oscillation which can mimic the appearance of Rayleigh–Bénard convection cells. Finally, it is discussed how our result may be related to nonlinear or chaotic dynamical regimes
On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation
Taskesen, Hatice; Polat, Necat; Ertaş, Abdulkadir
2012-01-01
We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity $\\gamma {|u|}^{p}$ and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.
Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form
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Reza Abazari
2013-01-01
Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.
Vorobev, Anatoliy
2010-11-01
We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
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Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid
2003-02-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
International Nuclear Information System (INIS)
Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid
2003-01-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method
Symmetries and conservation laws for a sixth-order Boussinesq equation
International Nuclear Information System (INIS)
Recio, E.; Gandarias, M.L.; Bruzón, M.S.
2016-01-01
This paper considers a generalization depending on an arbitrary function f(u) of a sixth-order Boussinesq equation which arises in shallow water waves theory. Interestingly, this equation admits a Hamiltonian formulation when written as a system. A classification of point symmetries and conservation laws in terms of the function f(u) is presented for both, the generalized Boussinesq equation and the equivalent Hamiltonian system.
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Sfahani, M. G.
2011-01-01
of time. The differential equations were solved using the method of Homotopy Perturbation. The simplicity and accuracy of the approximation are compared with “exact” solution and illustrated numerically and graphically. The results reveal that the HPM is very effective and simple and provides highly...... accurate solutions for nonlinear differential equations.......The phenomenon of stream–aquifer interaction was investigated via mathematical modeling using the Boussinesq equation. A new approximate solution of the one-dimensional Boussinesq equation is presented for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function...
A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
Sudao, Bilige; Wang, Xiaomin
2015-01-01
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
New application of Exp-function method for improved Boussinesq equation
Energy Technology Data Exchange (ETDEWEB)
Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Department of Physics, Faculty of Education for Girls, Science Departments, King Khalid University, Bisha (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com; Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College (Bisha), King Khalid University, Bisha, PO Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com; El-Basyony, S.T. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)
2007-10-01
The Exp-function method is used to obtain generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computation method, namely, the improved Boussinesq equation. The method is straightforward and concise, and its applications is promising for other nonlinear evolution equations in mathematical physics.
Finite element solution of two dimensional time dependent heat equation
International Nuclear Information System (INIS)
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling
DEFF Research Database (Denmark)
Banijamali, Babak
model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...
Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation
Zhao, Zhonglong; Han, Bo
2018-04-01
In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.
Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer
Verhoest, N.; Troch, P.A.
2000-01-01
Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer,
On Devising Boussinesq-type Equations with Bounded Eigenspectra: Two Horizontal Dimensions
DEFF Research Database (Denmark)
Eskilsson, Claes; Engsig-Karup, Allan Peter
2015-01-01
Boussinesq-type equations are used to describe the propagation and transformation of free-surface waves in the nearshore region. The nonlinear and dispersive performance of the equations are determined by tunable parameters. Recently the authors presented conditions on the free parameters under...... study and provide numerical experimentswhich confirms the theoretical results also is valid in two horizontal dimensions....
Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations
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Zhaohui Dai
2015-01-01
Full Text Available The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressure p in the homogeneous Besov space Ḃ∞,∞0.
A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji
2018-03-01
We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional extensions. The two dimensional lattice equation we present is linearizable in both directions, and has the Laurent and the coprimeness properties. Moreover, its reduction produces a generalized family of the Heideman-Hogan recurrence. Higher order examples of two dimensional linearizable lattice equations related to the Dana Scott recurrence are also discussed.
Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation
International Nuclear Information System (INIS)
Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng
2013-01-01
In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)
Blowup with vorticity control for a 2D model of the Boussinesq equations
Hoang, V.; Orcan-Ekmekci, B.; Radosz, M.; Yang, H.
2018-06-01
We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a vorticity stretching term and a non-local Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.
Auto-Baecklund Transformation and Analytic Solutions of (2+1)-Dimensional Boussinesq Equation
International Nuclear Information System (INIS)
Liu Guanting
2008-01-01
Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Baecklund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass wp function. Some of them are novel.
Exact periodic solutions of the sixth-order generalized Boussinesq equation
International Nuclear Information System (INIS)
Kamenov, O Y
2009-01-01
This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u tt = u xx + 3(u 2 ) xx + u xxxx + αu xxxxxx , α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.
International Nuclear Information System (INIS)
de Jong, G.
1975-01-01
With the aid of a two-dimensional integral equation formulation, the ground wave propagation of electromagnetic waves transmitted by a vertical electric dipole over an inhomogeneous flat earth is investigated. For the configuration in which a ground wave is propagating across an ''island'' on a flat earth, the modulus and argument of the attenuation function have been computed. The results for the two-dimensional treatment are significantly more accurate in detail than the calculations using a one-dimensional integral equation
On double reductions from symmetries and conservation laws for a damped Boussinesq equation
International Nuclear Information System (INIS)
Gandarias, M.L.; Rosa, M.
2016-01-01
In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. Some nontrivial conservation laws are derived by using the multipliers method. Taking into account the relationship between symmetries and conservation laws and applying the double reduction method, we obtain a direct reduction of order of the ordinary differential equations and in particular a kink solution.
Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations
Czech Academy of Sciences Publication Activity Database
Chiodaroli, E.; Michálek, Martin
2017-01-01
Roč. 353, č. 3 (2017), s. 1201-1216 ISSN 0010-3616 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Boussinesq equations * global weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.500, year: 2016 https://link.springer.com/article/10.1007%2Fs00220-017-2846-5
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
Application of the bifurcation method to the modified Boussinesq equation
Directory of Open Access Journals (Sweden)
Shaoyong Li
2014-08-01
Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers
Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru
2018-06-01
The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.
DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.
2008-01-01
equations in complex and curvilinear geometries which amends the application range of previous numerical models that have been based on structured Cartesian grids. The Boussinesq method provides the basis for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep...... waters within the breaking limit. To demonstrate the current applicability of the model both linear and mildly nonlinear test cases are considered in two horizontal dimensions where the water waves interact with bottom-mounted fully reflecting structures. It is established that, by simple symmetry...... considerations combined with a mirror principle, it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated...
Recognition of Equations Using a Two-Dimensional Stochastic Context-Free Grammar
Chou, Philip A.
1989-11-01
We propose using two-dimensional stochastic context-free grammars for image recognition, in a manner analogous to using hidden Markov models for speech recognition. The value of the approach is demonstrated in a system that recognizes printed, noisy equations. The system uses a two-dimensional probabilistic version of the Cocke-Younger-Kasami parsing algorithm to find the most likely parse of the observed image, and then traverses the corresponding parse tree in accordance with translation formats associated with each production rule, to produce eqn I troff commands for the imaged equation. In addition, it uses two-dimensional versions of the Inside/Outside and Baum re-estimation algorithms for learning the parameters of the grammar from a training set of examples. Parsing the image of a simple noisy equation currently takes about one second of cpu time on an Alliant FX/80.
Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations
Abdulwahhab, Muhammad Alim
2016-10-01
Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.
Exact periodic solutions of the sixth-order generalized Boussinesq equation
Energy Technology Data Exchange (ETDEWEB)
Kamenov, O Y [Department of Applied Mathematics and Informatics, Technical University of Sofia, PO Box 384, 1000 Sofia (Bulgaria)], E-mail: okam@abv.bg
2009-09-18
This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u{sub tt} = u{sub xx} + 3(u{sup 2}){sub xx} + u{sub xxxx} + {alpha}u{sub xxxxxx}, {alpha} in R, depending on the positive parameter {alpha}. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.
International Nuclear Information System (INIS)
Takeshi, Y.; Keisuke, K.
1983-01-01
The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method
International Nuclear Information System (INIS)
Sanchez, Richard.
1980-11-01
This work is divided into two parts: the first part deals with the solution of complex two-dimensional transport problems, the second one (note CEA-N-2166) treats the critically mixed methods of resolution. A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the interface current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding, and water, or homogenized structural material. The cells are divided into zones that are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is effected by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: CALLIOPE uses a cylindrical cell model and one or three terms for the flux expansion, and NAUSICAA uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes, one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark problems and by calculations performed in the APOLLO multigroup code [fr
Whitham modulation theory for the two-dimensional Benjamin-Ono equation.
Ablowitz, Mark; Biondini, Gino; Wang, Qiao
2017-09-01
Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.
Solution of the two- dimensional heat equation for a rectangular plate
Directory of Open Access Journals (Sweden)
Nurcan BAYKUŞ SAVAŞANERİL
2015-11-01
Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.
International Nuclear Information System (INIS)
Savel'ev, M.V.
1988-01-01
Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the corresponding class of the initial discrete system solutions is discussed. The latter takes place, in particular, for the kernel coinciding with the causal function
Stabilizing local boundary conditions for two-dimensional shallow water equations
Dia, Ben Mansour; Oppelstrup, Jesper
2018-01-01
In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary
Two-dimensional nonlinear string-type equations and their exact integration
International Nuclear Information System (INIS)
Leznov, A.N.; Saveliev, M.V.
1982-01-01
On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions
Solving the two-dimensional stationary transport equation with the aid of the nodal method
International Nuclear Information System (INIS)
Mesina, M.
1976-07-01
In this document the two-dimensional stationary transport equation for the geometry of a fuel assembly or for a system of square boxes has been formulated as an algebraic eigenvalue problem, and the solution was achieved with the computer code NODE 2 which was developed for this purpose. (orig.) [de
Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM
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Reza Abazari
2013-01-01
Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.
Directory of Open Access Journals (Sweden)
Musa Danjuma SHEHU
2008-06-01
Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
International Nuclear Information System (INIS)
Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.
2007-01-01
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple
Czech Academy of Sciences Publication Activity Database
Tichý, V.; Kuběna, Aleš Antonín; Skála, L.
2012-01-01
Roč. 90, č. 6 (2012), s. 503-513 ISSN 0008-4204 Institutional support: RVO:67985556 Keywords : Schroninger equation * partial differential equation * analytic solution * anharmonic oscilator * double-well Subject RIV: BE - Theoretical Physics Impact factor: 0.902, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kubena-analytic energies and wave functions of the two-dimensional schrodinger equation.pdf
Four-level conservative finite-difference schemes for Boussinesq paradigm equation
Kolkovska, N.
2013-10-01
In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.
On the Boussinesq-Burgers equations driven by dynamic boundary conditions
Zhu, Neng; Liu, Zhengrong; Zhao, Kun
2018-02-01
We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.
Global solutions in lower order Sobolev spaces for the generalized Boussinesq equation
Directory of Open Access Journals (Sweden)
Luiz G. Farah
2012-03-01
Full Text Available We show that the Cauchy problem for the defocusing generalized Boussinesq equation $$ u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u_{xx}=0, quad kgeq 1, $$ on the real line is globally well-posed in $H^s(mathbb{R}$ with s>1-(1/(3k. To do this, we use the I-method, introduced by Colliander, Keel, Staffilani, Takaoka and Tao [8,9], to define a modification of the energy functional that is almost conserved in time. Our result extends a previous result obtained by Farah and Linares [16] for the case k=1.
Family of two-dimensional Born-Infeld equations and a system of conservation laws
International Nuclear Information System (INIS)
Koiv, M.; Rosenhaus, V.
1979-01-01
Lower-order conserved quantities, the ''currents'', for two-dimensional Lorentz-invariant Born-Infeld equation are considered. The currents are divided into pairs, which contain a class (basic currents) leading to the family equations. The basic currents determine the transformations between the solutions of the Born-Infeld eqution family. The equations belonging to the family are fully hodograph-invariant, partly hodograph-invariant, and effectively linear, i.e. non-linear equations with linear image of hodograph transformation
International Nuclear Information System (INIS)
Sanchez, Richard.
1980-11-01
This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr
On integrability of a noncommutative q-difference two-dimensional Toda lattice equation
Energy Technology Data Exchange (ETDEWEB)
Li, C.X., E-mail: trisha_li2001@163.com [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Department of Mathematics, College of Charleston, Charleston, SC 29401 (United States); Nimmo, J.J.C., E-mail: jonathan.nimmo@glasgow.ac.uk [School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Shen, Shoufeng, E-mail: mathssf@zjut.edu.cn [Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023 (China)
2015-12-18
In our previous work (C.X. Li and J.J.C. Nimmo, 2009 [18]), we presented a generalized type of Darboux transformations in terms of a twisted derivation in a unified form. The twisted derivation includes ordinary derivatives, forward difference operators, super derivatives and q-difference operators as its special cases. This result not only enables one to recover the known Darboux transformations and quasideterminant solutions to the noncommutative KP equation, the non-Abelian two-dimensional Toda lattice equation, the non-Abelian Hirota–Miwa equation and the super KdV equation, but also inspires us to investigate quasideterminant solutions to q-difference soliton equations. In this paper, we first construct the bilinear Bäcklund transformations for the known bilinear q-difference two-dimensional Toda lattice equation (q-2DTL) and then derive a Lax pair whose compatibility gives a formally different nonlinear q-2DTL equation and finally obtain its quasideterminant solutions by iterating its Darboux transformations. - Highlights: • Examples are given to illustrate the extensive applications of twisted derivations. • Bilinear Bäcklund transformation is constructed for the known q-2DTL equation. • Lax pair is obtained for an equivalent q-2DTL equation. • Quasideterminant solutions are found for the nc q-2DTL equation.
International Nuclear Information System (INIS)
Chen, G.S.
1997-01-01
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)
International Nuclear Information System (INIS)
Tao Ganqiang; Yu Qing; Xiao Xiao
2011-01-01
Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)
Nodal DG-FEM solution of high-order Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan S.; Bingham, Harry B.
2006-01-01
We present a discontinuous Galerkin finite element method (DG-FEM) solution to a set of high-order Boussinesq-type equations for modelling highly nonlinear and dispersive water waves in one and two horizontal dimensions. The continuous equations are discretized using nodal polynomial basis...... functions of arbitrary order in space on each element of an unstructured computational domain. A fourth order explicit Runge-Kutta scheme is used to advance the solution in time. Methods for introducing artificial damping to control mild nonlinear instabilities are also discussed. The accuracy...... and convergence of the model with both h (grid size) and p (order) refinement are verified for the linearized equations, and calculations are provided for two nonlinear test cases in one horizontal dimension: harmonic generation over a submerged bar; and reflection of a steep solitary wave from a vertical wall...
Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation
International Nuclear Information System (INIS)
Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco
2002-01-01
In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Ishibashi, Hideo
1978-01-01
A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)
Methods for the solution of the two-dimensional radiation-transfer equation
International Nuclear Information System (INIS)
Weaver, R.; Mihalas, D.; Olson, G.
1982-01-01
We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich
2018-01-01
The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.
Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation
Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe
2018-04-01
In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.
Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation
International Nuclear Information System (INIS)
Shen Jianwei; Xu Wei; Lei Youming
2005-01-01
The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), u tt -u xx -a(u n ) xx +b(u m ) xxxx =0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1981-01-01
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1981-01-01
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)
Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method
International Nuclear Information System (INIS)
Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr
2008-01-01
Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code
Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method
International Nuclear Information System (INIS)
Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.
2010-01-01
The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.
Solution of Schroedinger Equation for Two-Dimensional Complex Quartic Potentials
International Nuclear Information System (INIS)
Singh, Ram Mehar; Chand, Fakir; Mishra, S. C.
2009-01-01
We investigate the quasi-exact solutions of the Schroedinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x 1 + ip 3 , y = x 2 + ip 4 , p x = p 1 + ix 3 , p y = p 2 + ix 4 . Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out. (general)
International Nuclear Information System (INIS)
Ravi Kanth, A.S.V.; Aruna, K.
2009-01-01
In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Stabilizing local boundary conditions for two-dimensional shallow water equations
Dia, Ben Mansour
2018-03-27
In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Sariaydin, Selin; Yildirim, Ahmet [Ege Univ., Dept. of Mathematics, Bornova-Izmir (Turkey)
2010-05-15
In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation u{sub tt} - u{sub xx} - u{sub yy} - (u{sup 2}){sub xx} - u{sub xxxx} = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation u{sub xt} - 6u{sub x}{sup 2} + 6uu{sub xx} - u{sub xxxx} - u{sub yy} - u{sub zz} = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically. (orig.)
Critical behavior in two-dimensional quantum gravity and equations of motion of the string
International Nuclear Information System (INIS)
Das, S.R.; Dhar, A.; Wadia, S.R.
1990-01-01
The authors show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. The authors discuss an example of such a trajectory in the space containing the c ≤ 1 minimal models. The authors also discuss the connection between this work and the recent attempts to construct non-pertubative string theories based on matrix models
RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry
International Nuclear Information System (INIS)
Valle, Edmundo del; Mund, Ernest H.
2004-01-01
This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature
Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations
Directory of Open Access Journals (Sweden)
Liping Gao
2017-01-01
Full Text Available In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...... of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped...... narrow spikes. The influence of the point impurities on this dynamics is also investigated....
Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions
International Nuclear Information System (INIS)
Ohtani, Nobuo
1976-01-01
A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)
Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary
Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing
2016-04-01
An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.
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Rahmatullah
2018-03-01
Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation
International Nuclear Information System (INIS)
Malescio, G.
1981-04-01
The two-dimensional Fokker-Planck equation describing the ion motion in a coherent lower hybrid wave above the stochasticity threshold is analytically solved. An expression is given for the steady state power dissipation
International Nuclear Information System (INIS)
Chen, G.S.; Yang, D.Y.
1998-01-01
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used: TFQMR (transpose free quasi-minimal residual algorithm) CGS (conjugate gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These subroutines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. The reasons to choose the generalized conjugate gradient methods are that the methods have better residual (equivalent to error) control procedures in the computation and have better convergent rate. The pointwise incomplete LU factorization ILU, modified pointwise incomplete LU factorization MILU, block incomplete factorization BILU and modified blockwise incomplete LU factorization MBILU are the preconditioning techniques used in the several testing problems. In Bi-CGSTAB, CGS, TFQMR and QMRCGSTAB method, we find that either CGS or Bi-CGSTAB method combined with preconditioner MBILU is the most efficient algorithm in these methods in the several testing problems. The numerical solution of flux by preconditioned CGS and Bi-CGSTAB methods has the same result as those from Cray computer, obtained by either the point successive relaxation method or the line successive relaxation method combined with Gaussian elimination
Charalampidis, E. G.; Kevrekidis, P. G.; Farrell, P. E.
2018-01-01
In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two-dimensional nonlinear Schrödinger equation with a parabolic trap and repulsive interactions. Despite the fact that this system has been studied extensively, we discover a wide variety of previously unknown branches of solutions. We analyze the stability of the newly discovered branches and discuss the bifurcations that relate them to known solutions both in the near linear (Cartesian, as well as polar) and in the highly nonlinear regimes. While deflated continuation is not guaranteed to compute the full bifurcation diagram, this analysis is a potent demonstration that the algorithm can discover new nonlinear states and provide insights into the energy landscape of complex high-dimensional Hamiltonian dynamical systems.
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Arnaldo Simal do Nascimento
1997-12-01
Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.
International Nuclear Information System (INIS)
Zhu Yonggui; Lu Chao
2007-01-01
In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(2n, 2n) equations: u tt + (u 2n ) xx + (u 2n ) xxxx 0 which exhibit compactons: solitons with compact support, are studied. New exact solitary solutions with compact support are found. The special case B(2, 2) is chosen to illustrate the concrete scheme of the decomposition method in B(2n, 2n) equations. General formulas for the solutions of B(2n, 2n) equations are established
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Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
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Zulfiqar Ali
2013-01-01
Full Text Available We find exact solutions of the Generalized Modified Boussinesq (GMB equation, the Kuromoto-Sivashinsky (KS equation the and, Camassa-Holm (CH equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.
Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation
Cardoso, Wesley B.; Salasnich, Luca; Malomed, Boris A.
2017-05-01
We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self-focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad stability areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie
2014-01-01
It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
Chen, Hao; Lv, Wen; Zhang, Tongtong
2018-05-01
We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.
International Nuclear Information System (INIS)
Polivanskij, V.P.
1989-01-01
The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs
International Nuclear Information System (INIS)
Yurov, A.V.; Yurova, A.A.
2006-01-01
The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru
Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation
Serdyukova, S I
2000-01-01
For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-k
Positioning in a flat two-dimensional space-time: The delay master equation
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [B. Coll, J. J. Ferrando, and J. A. Morales, Phys. Rev. D 73, 084017 (2006); ibid.74, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here, generic relativistic positioning systems in the Minkowski plane are studied. The information that can be obtained from the data received by a user of the positioning system is analyzed in detail. In particular, it is shown that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so-called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. These results are illustrated with the obtention of the dynamics of the emitters and of the user from specific sets of data received by the user.
Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa
2017-12-01
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.
General solution of the Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Sakaguchi, Hidetsugu; Ishibashi, Kazuya
2018-06-01
We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.
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Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
International Nuclear Information System (INIS)
Feng Zhaosheng
2003-01-01
In this paper, we study the two-dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analysing an equivalent two-dimensional autonomous system, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded travelling wave solution. Then by using a direct method, a travelling solitary wave solution to the 2D-BKdV equation is expressed explicitly, which appears to be more efficient than the existing methods proposed in the literature. At the end of the paper, the asymptotic behaviour of the proper solutions of the 2D-BKdV equation is established by applying the qualitative theory of differential equations
International Nuclear Information System (INIS)
Yomba, Emmanuel
2005-01-01
An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV-MKdV, Broer-Kaup-Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe
2015-06-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.
International Nuclear Information System (INIS)
Dubrovsky, V.G.; Formusatik, I.B.
2003-01-01
The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular
Solving the two-dimensional Schrödinger equation using basis ...
Indian Academy of Sciences (India)
Ihab H Naeim
2017-10-19
Oct 19, 2017 ... We shall study the case of a two-dimensional quantum system .... Solving (6) for ck,l is tantamount to pro- ... case, the final computational problem becomes quite ..... matrix approach fails in the case of two particles con-.
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e...
Yan, Zhen-Ya; Xie, Fu-Ding; Zhang, Hong-Qing
2001-07-01
Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of Ablowitz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation. The project supported by National Natural Science Foundation of China under Grant No. 19572022, the National Key Basic Research Development Project Program of China under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119
Akbar, M Ali; Hj Mohd Ali, Norhashidah
2014-01-01
The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.
Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-
2014-01-01
Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.
International Nuclear Information System (INIS)
Anderson, C.R.; Reider, M.B.
1994-01-01
The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown
International Nuclear Information System (INIS)
Sanchez, Richard
1977-01-01
A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the Interface Current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding and water, or homogenized structural material. The cells are divided into zones which are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is made by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: the first uses a cylindrical cell model and one or three terms for the flux expansion; the second uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark pr
Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar
2018-03-01
We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon
2017-09-01
Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
Directory of Open Access Journals (Sweden)
Mohammad Siddique
2010-08-01
Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
International Nuclear Information System (INIS)
Estevez, P G; Kuru, S; Negro, J; Nieto, L M
2006-01-01
The travelling wave solutions of the two-dimensional Korteweg-de Vries-Burgers and Kadomtsev-Petviashvili equations are studied from two complementary points of view. The first one is an adaptation of the factorization technique that provides particular as well as general solutions. The second one applies the Painleve analysis to both equations, throwing light on some aspects of the first method and giving an explanation to some restriction on the coefficients, as well as the relation between factorizations and integrals of motion
Galaktionov, Victor A.
2009-02-01
As a basic higher-order model, the fourth-order Boussinesq-type quasilinear wave equation (the QWE-4) \\[ \\begin{equation*}\\fl u_{tt} = -(|u|^n u)_{xxxx} \\tqs in\\ \\mathbb{R} \\times \\mathbb{R}_+, \\quad with\\ exponent\\ n > 0,\\end{equation*} \\] is considered. Self-similar blow-up solutions \\[ \\begin{eqnarray*}\\tqs\\tqs u_-(x,t)=g(z), \\quad\\, z=\\frac x{\\sqrt{T-t}},\\\\ where\\ g\\ solved\\ the\\ ODE\\ \\frac 14 g'' z^2 + \\frac 34 g'z = -(|g|^n g)^{(4)},\\end{eqnarray*} \\] are shown to exist that generate as t → T- discontinuous shock waves. The QWE-4 is also shown to admit a smooth (for t > 0) global 'fundamental solution' \\[ \\begin{eqnarray*}\\fl b_n(x,t)= t^{\\frac{2}{n+4}} F_n(y),\\ y = x/t^{\\frac{n+2}{n+4}},\\ such\\ that\\ b_{n}(x,0)= 0,\\ b_{nt}(x,0)= {\\delta}(x),\\end{eqnarray*} \\] i.e. having a measure as initial data. A 'homotopic' limit n → 0 is used to get b_0(x,t)= \\sqrt t \\, F_0(x/\\sqrt t) being the classic fundamental solution of the 1D linear beam equation \\[ \\begin{equation*}u_{tt} = -u_{xxxx} \\tqs in\\ \\mathbb{R} \\times \\mathbb{R}_+.\\end{equation*} \\
Passive tracer in a flow corresponding to two-dimensional stochastic Navier–Stokes equations
International Nuclear Information System (INIS)
Komorowski, Tomasz; Peszat, Szymon; Szarek, Tomasz
2013-01-01
In this paper we prove the law of large numbers and central limit theorem for trajectories of a particle carried by a two-dimensional Eulerian velocity field. The field is given by a solution of a stochastic Navier–Stokes system with non-degenerate noise. The spectral gap property, with respect to the Wasserstein metric, for such a system was shown in Hairer and Mattingly (2008 Ann. Probab. 36 2050–91). In this paper we show that a similar property holds for the environment process corresponding to the Lagrangian observations of the velocity. Consequently we conclude the law of large numbers and the central limit theorem for the tracer. The proof of the central limit theorem relies on the martingale approximation of the trajectory process. (paper)
International Nuclear Information System (INIS)
Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.
1990-01-01
Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs
Chen, Shanzhen; Jiang, Xiaoyun
2012-08-01
In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.
International Nuclear Information System (INIS)
Patra, A.; Saha Ray, S.
2014-01-01
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution
Guo, Yangyu; Wang, Moran
2017-10-01
The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.
A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study
International Nuclear Information System (INIS)
Angelo, P.M.; Riela, G.
1981-01-01
We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)
International Nuclear Information System (INIS)
Boiti, M.; Pempinelli, F.; Pogrebkov, A.K.; Polivanov, M.C.
1993-01-01
The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. The authors demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schroedinger equation as an example, it is shown that all types of solutions of the linear problem, as well as spectral data known in the literature, are given as specific values of this unique function - the resolvent function. A new form of the inverse problem is formulated. 7 refs
The Investigation of Solutions to the Coupled Schrödinger-Boussinesq Equations
Directory of Open Access Journals (Sweden)
Xin Huang
2013-01-01
equations. The hyperbolic function solutions, trigonometric function solutions, and rational function solutions to the equations are obtained. The decaying properties of several solutions are analyzed.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
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Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2015-10-15
Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.
MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1997-10-01
A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)
International Nuclear Information System (INIS)
Chen, G.S.; Christenson, J.M.
1985-01-01
In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program
International Nuclear Information System (INIS)
Lubuma, M.S.
1991-05-01
The non uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities. (author). 34 refs
International Nuclear Information System (INIS)
Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing
2005-01-01
A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion
Numerical methods to solve the two-dimensional heat conduction equation
International Nuclear Information System (INIS)
Santos, R.S. dos.
1981-09-01
A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt
Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.
Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano
2007-10-05
We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.
Tayebi, A.; Shekari, Y.; Heydari, M. H.
2017-07-01
Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.
Directory of Open Access Journals (Sweden)
Tor eNordam
2013-09-01
Full Text Available A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. Implementation and performance issues of the method, and various consistency checks of it, are presented and discussed. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization. As an illustration, we calculate the full angular distribution of the mean differential reflection coefficient for the scattering of p- or s-polarized light incident on two-dimensional dielectric or metallic randomly rough surfaces defined by (isotropic or anisotropic Gaussian and cylindrical power spectra. Simulation results obtained by the proposed method agree well with experimentally measured scattering data taken from similar well-characterized, rough metal samples, or to results obtained by other numerical methods.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-05-15
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.
Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R
2013-09-01
We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1986-01-01
In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)
International Nuclear Information System (INIS)
Inc, Mustafa
2007-01-01
In this Letter, a scheme is developed to study numerical doubly-periodic solutions of the (2+1)-dimensional Boussinesq equation with initial condition by the variational iteration method. As a result, the approximate and exact doubly-periodic solutions are obtained. For different modulus m, comparison between the approximate solution and the exact solution is made graphically, revealing that the variational iteration method is a powerful and effective tool to non-linear problems
Unstructured nodal DG-FEM solution of high-order Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2007-01-01
alternative to solving full three-dimensional wave problems by e.g. Navier-Stokes equations, which can capture all the important wave phenomena such as diffraction, refraction, nonlinear wave-wave interactions and interaction with structures. The main goal can be reached by using multi-domain methods...... a highly complex system of coupled equations which put any numerical method to the test. The main problems that need to be overcome to solve the equations are the treatment of strongly nonlinear convection-type terms and spatially varying coefficient terms; efficient and robust solution of the resultant...... equations. Remarkably, it is demonstrated that the linear eigenspectra of the linearized semi-discrete equation system is bounded and hence the stable time increment is not dictated by the spatial discretization. This is a favorable property for explicit time-integration schemes as the stable time increment...
Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi
2018-05-01
An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).
One- and two-dimensional search of an equation of state using a newly released 2DRoptimize package
Jamal, M.; Reshak, A. H.
2018-05-01
A new package called 2DRoptimize has been released for performing two-dimensional searches of the equation of state (EOS) for rhombohedral, tetragonal, and hexagonal compounds. The package is compatible and available with the WIEN2k package. The 2DRoptimize package performs a convenient volume and c/a structure optimization. First, the package finds the best value for c/a and the associated energy for each volume. In the second step, it calculates the EoS. The package then finds the equation of the c/a ratio vs. volume to calculate the c/a ratio at the optimized volume. In the last stage, by using the optimized volume and c/a ratio, the 2DRoptimize package calculates a and c lattice constants for tetragonal and hexagonal compounds, as well as the a lattice constant with the α angle for rhombohedral compounds. We tested our new package based on several hexagonal, tetragonal, and rhombohedral structures, and the 2D search results for the EOS showed that this method is more accurate than 1D search. Our results agreed very well with the experimental data and they were better than previous theoretical calculations.
Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng
2018-02-01
Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.
The application of Fast Fourier transforms to the primitive equations of Boussinesq convection
International Nuclear Information System (INIS)
Parrott, A.K.
1976-01-01
We have described a numerical scheme which is second-order in both space and time. The use of Fast Fourier Transform techniques for the solution of pressure equation guarantees accurate incompressibility at all time and enabled us to consider using iteration for part of this scheme. The iterations converge satisfactorily for values of the timestep of the order of one-half to one-quarter of the space step. Numerical calculations are being undertaken to clarify the range of Reynolds numbers and timestep over which the iteration converges. (orig.) [de
Directory of Open Access Journals (Sweden)
M. P. Markakis
2010-01-01
Full Text Available Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1 equations. Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.
Settle, Sean O.; Douglas, Craig C.; Kim, Imbunm; Sheen, Dongwoo
2013-01-01
- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-08-15
Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.
International Nuclear Information System (INIS)
Hoang-Do, Ngoc-Tram; Pham, Dang-Lan; Le, Van-Hoang
2013-01-01
Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity
International Nuclear Information System (INIS)
Zhang Guangjun; Xu Jianxue; Wang Jue; Yue Zhifeng; Zou Hailin
2009-01-01
In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.
International Nuclear Information System (INIS)
Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.
2010-01-01
We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.
Chudnovsky, D V
1978-09-01
For systems of nonlinear equations having the form [L(n) - ( partial differential/ partial differentialt), L(m) - ( partial differential/ partial differentialy)] = 0 the class of meromorphic solutions obtained from the linear equations [Formula: see text] is presented.
Moorthi, Shrinivas; Higgins, R. W.
1993-01-01
An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.
International Nuclear Information System (INIS)
Khisamutdinova, N A
2003-01-01
The behaviour as t→∞ of the solution of the mixed problem for the system of Navier-Stokes equations with a Dirichlet condition at the boundary is studied in an unbounded two-dimensional domain with several exits to infinity. A class of domains is distinguished in which an estimate characterizing the decay of solutions in terms of the geometry of the domain is proved for exponentially decreasing initial velocities. A similar estimate of the solution of the first mixed problem for the heat equation is sharp in a broad class of domains with several exits to infinity
Directory of Open Access Journals (Sweden)
Goncharova Olga
2016-01-01
Full Text Available Flows of a viscous incompressible liquid with a thermocapillary boundary are investigated numerically on the basis of the mathematical model that consists of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations, kinematic and dynamic conditions at the free boundary and of the slip boundary conditions at solid walls. We assume that the constant temperature is kept on the solid walls. On the thermocapillary gas-liquid interface the condition of the third order for temperature is imposed. The numerical algorithm based on a finite-difference scheme of the second order approximation on space and time has been constructed. The numerical experiments are performed for water under conditions of normal and low gravity for different friction coefficients and different values of the interphase heat transfer coefficient.
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...... losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials....
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe; Sarmiento, Adel; Cortes, Adriano Mauricio; Dalcin, Lisandro; Calo, Victor M.
2015-01-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow
International Nuclear Information System (INIS)
Rodriguez, B.D.A.; Vilhena, M.T.; Borges, V.; Hoff, G.
2008-01-01
In this paper we solve the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation for charged particles in a rectangular domain. To construct the solution we begin applying the P N approximation in the angular variable and the Laplace Transform in the x-variable, thus obtaining a first order linear differential equation in y-variable, which the solution is straightforward. The angular flux of electrons and the parameters of the medium are used for the calculation of the energy deposited by the secondary electrons generated by Compton Effect. The remaining effects will not be taken into account. The results will be presented under absorbed energy form in several points of interested. We present numerical simulations and comparisons with results obtained by using Geant4 (version 8) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the screened Rutherford differential scattering cross-section
International Nuclear Information System (INIS)
Rodriguez, Barbara D.A.; Tullio de Vilhena, Marco; Hoff, Gabriela
2008-01-01
In this paper we report a two-dimensional LTS N nodal solution for homogeneous and heterogeneous rectangular domains, assuming the Klein-Nishina scattering kernel and multigroup model. The main idea relies on the solution of the two one-dimensional S N equations resulting from transverse integration of the S N equations in the rectangular domain by the LTS N nodal method, considering the leakage angular fluxes approximated by exponential, which allow us to determine a closed-form solution for the photons transport equation. The angular flux and the parameters of the medium are used for the calculation of the absorbed energy in rectangular domains with different dimensions and compositions. The incoming photons will be tracked until their whole energy is deposited and/or they leave the domain of interest. In this study, the absorbed energy by Compton Effect will be considered. The remaining effects will not be taken into account. We present numerical simulations and comparisons with results obtained by using Geant4 (version 9.1) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the Klein-Nishina scattering kernel. (authors)
Energy Technology Data Exchange (ETDEWEB)
Yoon, E. S.; Chang, C. S., E-mail: cschang@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Korea Advanced Institute of Science and Technology, Yuseong-gu, DaeJeon 305-701 (Korea, Republic of)
2014-03-15
An approximate two-dimensional solver of the nonlinear Fokker-Planck-Landau collision operator has been developed using the assumption that the particle probability distribution function is independent of gyroangle in the limit of strong magnetic field. The isotropic one-dimensional scheme developed for nonlinear Fokker-Planck-Landau equation by Buet and Cordier [J. Comput. Phys. 179, 43 (2002)] and for linear Fokker-Planck-Landau equation by Chang and Cooper [J. Comput. Phys. 6, 1 (1970)] have been modified and extended to two-dimensional nonlinear equation. In addition, a method is suggested to apply the new velocity-grid based collision solver to Lagrangian particle-in-cell simulation by adjusting the weights of marker particles and is applied to a five dimensional particle-in-cell code to calculate the neoclassical ion thermal conductivity in a tokamak plasma. Error verifications show practical aspects of the present scheme for both grid-based and particle-based kinetic codes.
Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.
1992-11-01
The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.
Czech Academy of Sciences Publication Activity Database
Šremr, Jiří
2007-01-01
Roč. 132, č. 3 (2007), s. 263-295 ISSN 0862-7959 R&D Projects: GA ČR GP201/04/P183 Institutional research plan: CEZ:AV0Z10190503 Keywords : system of functional differential equations with monotone operators * initial value problem * unique solvability Subject RIV: BA - General Mathematics
Energy Technology Data Exchange (ETDEWEB)
Chafi, Fatima Zohra; Halle, Stephane [Mechanical engineering department, Ecole de technologie superieure, Quebec university, 1100 rue Notre-Dame Ouest, Montreal, Quebec H3C 1K3 (Canada)
2011-02-15
This paper presents the results of a study that consists of estimating the temperature distribution and air flow movement in a model room with a numerical model based on the Euler equations. Numerical results obtained for two scenarios of ventilation and heating are compared with the predictions of a Navier-Stokes model, as well as with experimental results. A comparison of the local thermal comfort indices PMV and PPD obtained experimentally and numerically is also presented. Results show that the Euler model is capable of properly estimating the temperature distribution, the air movement and the comfort indices in the room. Furthermore, the use of Euler equations allows a reduction of computational time in the order of 30% compared to the Navier-Stokes modeling. (author)
International Nuclear Information System (INIS)
Botelho, D.A.; Moreira, M.L.
1991-06-01
The Reynolds turbulent transport equations for an incompressible fluid are integrated on a bi-dimensional staggered grid, for velocity and pressure, using the SIMPLER method. With the resulting algebraic relations it was developed the TURBO program, which final objectives are the thermal stratification and natural convection analysis of nuclear reactor pools. This program was tested in problems applications with analytic or experimental solutions previously known. (author)
International Nuclear Information System (INIS)
Perez Guerrero, Jesus Salvador
1995-01-01
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author)
Energy Technology Data Exchange (ETDEWEB)
Djouder, M., E-mail: djouder-madjid@ummto.dz; Kermoun, F.; Mitiche, M. D.; Lamrous, O. [Laboratoire de Physique et Chimie Quantique, Université Mouloud Mammeri Tizi-Ouzou, BP 17 RP, 15000 Tizi-Ouzou (Algeria)
2016-01-15
Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere.
Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2
Directory of Open Access Journals (Sweden)
Stevo Stevic
2017-06-01
Full Text Available We prove that the following class of systems of difference equations is solvable in closed form: $$ z_{n+1}=\\alpha z_{n-1}^aw_n^b,\\quad w_{n+1}=\\beta w_{n-1}^cz_{n-1}^d,\\quad n\\in\\mathbb{N}_0, $$ where $a, b, c, d\\in\\mathbb{Z}$, $\\alpha, \\beta, z_{-1}, z_0, w_{-1}, w_0\\in\\mathbb{C}\\setminus\\{0\\}$. We present formulas for its solutions in all the cases. The most complex formulas are presented in terms of the zeros of three different associated polynomials to the systems corresponding to the cases a=0, c=0 and $abcd\
International Nuclear Information System (INIS)
Djouder, M.; Kermoun, F.; Mitiche, M. D.; Lamrous, O.
2016-01-01
Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere
Tay, Wei Choon; Tan, Eng Leong
2014-07-01
In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.
Settle, Sean O.
2013-01-01
The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.
Energy Technology Data Exchange (ETDEWEB)
Rodriguez, B.D.A., E-mail: barbararodriguez@furg.b [Universidade Federal do Rio Grande, Instituto de Matematica, Estatistica e Fisica, Rio Grande, RS (Brazil); Vilhena, M.T., E-mail: vilhena@mat.ufrgs.b [Universidade Federal do Rio Grande do Sul, Departamento de Matematica Pura e Aplicada, Porto Alegre, RS (Brazil); Hoff, G., E-mail: hoff@pucrs.b [Pontificia Universidade Catolica do Rio Grande do Sul, Faculdade de Fisica, Porto Alegre, RS (Brazil); Bodmann, B.E.J., E-mail: bardo.bodmann@ufrgs.b [Universidade Federal do Rio Grande do Sul, Departamento de Matematica Pura e Aplicada, Porto Alegre, RS (Brazil)
2011-01-15
In the present work we report on a closed-form solution for the two-dimensional Compton transport equation by the LTS{sub N} nodal method in the energy range of Compton effect. The solution is determined using the LTS{sub N} nodal approach for homogeneous and heterogeneous rectangular domains, assuming the Klein-Nishina scattering kernel and a multi-group model. The solution is obtained by two one-dimensional S{sub N} equation systems resulting from integrating out one of the orthogonal variables of the S{sub N} equations in the rectangular domain. The leakage angular fluxes are approximated by exponential forms, which allows to determine a closed-form solution for the photons transport equation. The angular flux and the parameters of the medium are used for the calculation of the absorbed energy in rectangular domains with different dimensions and compositions. In this study, only the absorbed energy by Compton effect is considered. We present numerical simulations and comparisons with results obtained by using the simulation platform GEANT4 (version 9.1) with its low energy libraries.
International Nuclear Information System (INIS)
Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang
2013-01-01
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schrödinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.
Energy Technology Data Exchange (ETDEWEB)
Wintermeyer, Niklas [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Winters, Andrew R., E-mail: awinters@math.uni-koeln.de [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Gassner, Gregor J. [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Kopriva, David A. [Department of Mathematics, The Florida State University, Tallahassee, FL 32306 (United States)
2017-07-01
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.
Energy Technology Data Exchange (ETDEWEB)
Rodriguez, B.D.A. [Universidade Federal Rio Grande do Sul, Programa de Pos-Graduacao em Engenharia Mecanica, Rua Portuguesa 218/304, 90650-12 Porto Alegre, RS (Brazil)], E-mail: barbara.arodriguez@gmail.com; Vilhena, M.T. [Universidade Federal Rio Grande do Sul, Departamento de Matematica Pura e Aplicada, Porto Alegre, RS (Brazil)], E-mail: vilhena@mat.ufrgs.br; Borges, V. [Universidade Federal Rio Grande do Sul, Programa de Pos-Graduacao em Engenharia Mecanica, Rua Portuguesa 218/304, 90650-12 Porto Alegre, RS (Brazil)], E-mail: borges@ufrgs.br; Hoff, G. [Pontificia Universidade Catolica do Rio Grande do Sul, Faculdade de Fisica, Porto Alegre, RS (Brazil)], E-mail: hoff@pucrs.br
2008-05-15
In this paper we solve the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation for charged particles in a rectangular domain. To construct the solution we begin applying the P{sub N} approximation in the angular variable and the Laplace Transform in the x-variable, thus obtaining a first order linear differential equation in y-variable, which the solution is straightforward. The angular flux of electrons and the parameters of the medium are used for the calculation of the energy deposited by the secondary electrons generated by Compton Effect. The remaining effects will not be taken into account. The results will be presented under absorbed energy form in several points of interested. We present numerical simulations and comparisons with results obtained by using Geant4 (version 8) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the screened Rutherford differential scattering cross-section.
Boussinesq Modeling of Wave Propagation and Runup over Fringing Coral Reefs, Model Evaluation Report
National Research Council Canada - National Science Library
Demirbilek, Zeki; Nwogu, Okey G
2007-01-01
This report describes evaluation of a two-dimensional Boussinesq-type wave model, BOUSS-2D, with data obtained from two laboratory experiments and two field studies at the islands of Guam and Hawaii...
Directory of Open Access Journals (Sweden)
Svetlana S. Vlasova
2016-09-01
Full Text Available The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in the two-dimensional layer with the square heating of a free surface in Stokes's approach is found. The linearization of the Oberbeck–Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.
International Nuclear Information System (INIS)
Anon.
1991-01-01
This chapter addresses the extension of previous work in one-dimensional (linear) error theory to two-dimensional error analysis. The topics of the chapter include the definition of two-dimensional error, the probability ellipse, the probability circle, elliptical (circular) error evaluation, the application to position accuracy, and the use of control systems (points) in measurements
Equilibrium: two-dimensional configurations
International Nuclear Information System (INIS)
Anon.
1987-01-01
In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
International Nuclear Information System (INIS)
Schroer, Bert; Freie Universitaet, Berlin
2005-02-01
It is not possible to compactly review the overwhelming literature on two-dimensional models in a meaningful way without a specific viewpoint; I have therefore tacitly added to the above title the words 'as theoretical laboratories for general quantum field theory'. I dedicate this contribution to the memory of J. A. Swieca with whom I have shared the passion of exploring 2-dimensional models for almost one decade. A shortened version of this article is intended as a contribution to the project 'Encyclopedia of mathematical physics' and comments, suggestions and critical remarks are welcome. (author)
Two-dimensional ferroelectrics
Energy Technology Data Exchange (ETDEWEB)
Blinov, L M; Fridkin, Vladimir M; Palto, Sergei P [A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russian Federaion (Russian Federation); Bune, A V; Dowben, P A; Ducharme, Stephen [Department of Physics and Astronomy, Behlen Laboratory of Physics, Center for Materials Research and Analysis, University of Nebraska-Linkoln, Linkoln, NE (United States)
2000-03-31
The investigation of the finite-size effect in ferroelectric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals had a diameter of {approx}200 A and the thinnest ferroelectric films were {approx}200 A thick, macroscopic sizes on an atomic scale. Langmuir-Blodgett deposition of films one monolayer at a time has produced high quality ferroelectric films as thin as 10 A, made from polyvinylidene fluoride and its copolymers. These ultrathin films permitted the ultimate investigation of finite-size effects on the atomic thickness scale. Langmuir-Blodgett films also revealed the fundamental two-dimensional character of ferroelectricity in these materials by demonstrating that there is no so-called critical thickness; films as thin as two monolayers (1 nm) are ferroelectric, with a transition temperature near that of the bulk material. The films exhibit all the main properties of ferroelectricity with a first-order ferroelectric-paraelectric phase transition: polarization hysteresis (switching); the jump in spontaneous polarization at the phase transition temperature; thermal hysteresis in the polarization; the increase in the transition temperature with applied field; double hysteresis above the phase transition temperature; and the existence of the ferroelectric critical point. The films also exhibit a new phase transition associated with the two-dimensional layers. (reviews of topical problems)
Two-dimensional capillary origami
Energy Technology Data Exchange (ETDEWEB)
Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Two-dimensional capillary origami
International Nuclear Information System (INIS)
Brubaker, N.D.; Lega, J.
2016-01-01
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Carling; Williams; Bowtell
1998-12-01
Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it, as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.
International Nuclear Information System (INIS)
Williams, M.M.R.; Hall, S.K.; Eaton, M.D.
2014-01-01
Highlights: • A rectangular reactor cell with an elliptical fuel element. • Solution of transport and diffusion equations by Fourier expansion. • Numerical examples showing convergence. • Two group cell problems. - Abstract: A method for solving the diffusion and transport equations in a rectangular lattice cell with an elliptical fuel element has been developed using a Fourier expansion of the neutron flux. The method is applied to a one group model with a source in the moderator. The cell flux is obtained and also the associated disadvantage factor. In addition to the one speed case, we also consider the two group equations in the cell which now become an eigenvalue problem for the lattice multiplication factor. The method of solution relies upon an efficient procedure to solve a large set of simultaneous linear equations and for this we use the IMSL library routines. Our method is compared with the results from a finite element code. The main drawback of the problem arises from the very large number of terms required in the Fourier series which taxes the storage and speed of the computer. Nevertheless, useful solutions are obtained in geometries that would normally require the use of finite element or analogous methods, for this reason the Fourier method is useful for comparison with that type of numerical approach. Extension of the method to more intricate fuel shapes, such as stars and cruciforms as well as superpositions of these, is possible
International Nuclear Information System (INIS)
Milioli, F.E.
1985-01-01
In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt
International Nuclear Information System (INIS)
Frank, T.D.
2011-01-01
We study the stability of solutions of a particular type of multistable selection equations proposed by Starke, Schanz and Haken in the case of an inhomogeneous spectrum of growth parameters. We determine how the stability of feasible solutions depends on the inhomogeneity of the spectrum. We show that the strength of the competitive interaction between feasible solutions can act as a control parameter that induces bifurcations reducing the degree of multistability. - Research highlights: → Feasible solutions can be stable in the case of inhomogeneous growth parameters. → Changing coupling strength can induce bifurcations of feasible solutions. → Optimal solutions are obtained when selected winnings are relatively large.
International Nuclear Information System (INIS)
Zayed, E.M.E.
2004-01-01
We study the influence of a finite container on an ideal gas using the wave equation approach. The asymptotic expansion of the trace of the wave kernel μ-circumflex(t)=Σ υ=1 ∞ exp(-itμ υ 1/2 ) for small vertical bar t vertical bar and i=√-1, where {μ ν } ν=1 ∞ are the eigenvalues of the negative Laplacian -Δ=-Σ k=1 2 (((∂)/(∂x k ))) 2 in the (x 1 ,x 2 )-plane, is studied for an annular vibrating membrane Ω in R 2 together with its smooth inner boundary ∂Ω 1 and its smooth outer boundary ∂Ω 2 , where a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Γ j (j=1,...,m) of ∂Ω 1 and on the piecewise smooth components Γ j (j=m+1,...,n) of ∂Ω 2 such that ∂Ω 1 =union j=1 m Γ j and ∂Ω 2 =union j=m+1 n Γ j is considered. The basic problem is to extract information on the geometry of the annular vibrating membrane Ω from complete knowledge of its eigenvalues using the wave equation approach by analyzing the asymptotic expansions of the spectral function μ-circumflex(t) for small vertical bar t vertical bar. Some applications of μ-circumflex(t) for an ideal gas enclosed in the general annular bounded domain Ω are given.
Analytical simulation of two dimensional advection dispersion ...
African Journals Online (AJOL)
The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would migrate ...
Analytical Simulation of Two Dimensional Advection Dispersion ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would ...
Two-Dimensional Motions of Rockets
Kang, Yoonhwan; Bae, Saebyok
2007-01-01
We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…
The Boussinesq Debate: Reversibility, Instability, and Free Will.
Michael Mueller, Thomas
2015-12-01
In 1877, a young mathematician named Joseph Boussinesq presented a mémoire to the Académie des sciences which demonstrated that some differential equations may have more than one solution. Boussinesq linked this fact to indeterminism and to a possible solution to the free will versus determinism debate. Boussinesq's main interest was to reconcile his philosophical and religious views with science by showing that matter and motion do not suffice to explain all there is in the world. His argument received mixed criticism that addressed both his philosophical views and the scientific content of his work, pointing to the physical "realisticness" of multiple solutions. While Boussinesq proved to be able to face the philosophical criticism, the scientific objections became a serious problem, thus slowly moving the focus of the debate from the philosophical plane to the scientific one. This change of perspective implied a wide discussion on topics such as instability, the sensitivity to initial conditions, and the conservation of energy. The Boussinesq debate is an example of a philosophically motivated debate that transforms into a scientific one, an example of the influence of philosophy on the development of science.
Mechanical Balance Laws for Boussinesq Models of Surface Water Waves
Ali, Alfatih; Kalisch, Henrik
2012-06-01
Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of these quantities are not known. This work presents a systematic derivation of mass, momentum and energy densities and fluxes associated with a general family of Boussinesq systems. The derivation is based on a reconstruction of the velocity field and the pressure in the fluid column below the free surface, and the derivation of differential balance equations which are of the same asymptotic validity as the evolution equations. It is shown that all these mechanical quantities can be expressed in terms of the principal dependent variables of the Boussinesq system: the surface excursion η and the horizontal velocity w at a given level in the fluid.
Equivalence of two-dimensional gravities
International Nuclear Information System (INIS)
Mohammedi, N.
1990-01-01
The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given
Lie algebra contractions on two-dimensional hyperboloid
International Nuclear Information System (INIS)
Pogosyan, G. S.; Yakhno, A.
2010-01-01
The Inoenue-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1 . The text was submitted by the authors in English.
Two-dimensional NMR spectrometry
International Nuclear Information System (INIS)
Farrar, T.C.
1987-01-01
This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) the authors discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gymnastics experiments that provide a capability for selective sensitivity enhancements. In this article and overview and some applications of two-dimensional NMR experiments are presented. These powerful experiments are important complements to the one-dimensional experiments. As in the more sophisticated one-dimensional experiments, the two-dimensional experiments involve three distinct time periods: a preparation period, t 0 ; an evolution period, t 1 ; and a detection period, t 2
Quasi-two-dimensional holography
International Nuclear Information System (INIS)
Kutzner, J.; Erhard, A.; Wuestenberg, H.; Zimpfer, J.
1980-01-01
The acoustical holography with numerical reconstruction by area scanning is memory- and time-intensive. With the experiences by the linear holography we tried to derive a scanning for the evaluating of the two-dimensional flaw-sizes. In most practical cases it is sufficient to determine the exact depth extension of a flaw, whereas the accuracy of the length extension is less critical. For this reason the applicability of the so-called quasi-two-dimensional holography is appropriate. The used sound field given by special probes is divergent in the inclined plane and light focussed in the perpendicular plane using cylindrical lenses. (orig.) [de
Multisoliton formula for completely integrable two-dimensional systems
International Nuclear Information System (INIS)
Chudnovsky, D.V.; Chudnovsky, G.V.
1979-01-01
For general two-dimensional completely integrable systems, the exact formulae for multisoliton type solutions are given. The formulae are obtained algebrically from solutions of two linear partial differential equations
Two-dimensional metamaterial optics
International Nuclear Information System (INIS)
Smolyaninov, I I
2010-01-01
While three-dimensional photonic metamaterials are difficult to fabricate, many new concepts and ideas in the metamaterial optics can be realized in two spatial dimensions using planar optics of surface plasmon polaritons. In this paper we review recent progress in this direction. Two-dimensional photonic crystals, hyperbolic metamaterials, and plasmonic focusing devices are demonstrated and used in novel microscopy and waveguiding schemes
Geometrical aspects of solvable two dimensional models
International Nuclear Information System (INIS)
Tanaka, K.
1989-01-01
It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e., when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra. 21 refs
Two-dimensional electroacoustic waves in silicene
Zhukov, Alexander V.; Bouffanais, Roland; Konobeeva, Natalia N.; Belonenko, Mikhail B.
2018-01-01
In this letter, we investigate the propagation of two-dimensional electromagnetic waves in a piezoelectric medium built upon silicene. Ultrashort optical pulses of Gaussian form are considered to probe this medium. On the basis of Maxwell's equations supplemented with the wave equation for the medium's displacement vector, we obtain the effective governing equation for the vector potential associated with the electromagnetic field, as well as the component of the displacement vector. The dependence of the pulse shape on the bandgap in silicene and the piezoelectric coefficient of the medium was analyzed, thereby revealing a nontrivial triadic interplay between the characteristics of the pulse dynamics, the electronic properties of silicene, and the electrically induced mechanical vibrations of the medium. In particular, we uncovered the possibility for an amplification of the pulse amplitude through the tuning of the piezoelectric coefficient. This property could potentially offer promising prospects for the development of amplification devices for the optoelectronics industry.
Two-dimensional flexible nanoelectronics
Akinwande, Deji; Petrone, Nicholas; Hone, James
2014-12-01
2014/2015 represents the tenth anniversary of modern graphene research. Over this decade, graphene has proven to be attractive for thin-film transistors owing to its remarkable electronic, optical, mechanical and thermal properties. Even its major drawback--zero bandgap--has resulted in something positive: a resurgence of interest in two-dimensional semiconductors, such as dichalcogenides and buckled nanomaterials with sizeable bandgaps. With the discovery of hexagonal boron nitride as an ideal dielectric, the materials are now in place to advance integrated flexible nanoelectronics, which uniquely take advantage of the unmatched portfolio of properties of two-dimensional crystals, beyond the capability of conventional thin films for ubiquitous flexible systems.
Two-dimensional topological photonics
Khanikaev, Alexander B.; Shvets, Gennady
2017-12-01
Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.
Two-dimensional thermofield bosonization
International Nuclear Information System (INIS)
Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.
2005-01-01
The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized
Optimized two-dimensional Sn transport (BISTRO)
International Nuclear Information System (INIS)
Palmiotti, G.; Salvatores, M.; Gho, C.
1990-01-01
This paper reports on an S n two-dimensional transport module developed for the French fast reactor code system CCRR to optimize algorithms in order to obtain the best performance in terms of computational time. A form of diffusion synthetic acceleration was adopted, and a special effort was made to solve the associated diffusion equation efficiently. The improvements in the algorithms, along with the use of an efficient programming language, led to a significant gain in computational time with respect to the DOT code
Two-dimensional heat flow apparatus
McDougall, Patrick; Ayars, Eric
2014-06-01
We have created an apparatus to quantitatively measure two-dimensional heat flow in a metal plate using a grid of temperature sensors read by a microcontroller. Real-time temperature data are collected from the microcontroller by a computer for comparison with a computational model of the heat equation. The microcontroller-based sensor array allows previously unavailable levels of precision at very low cost, and the combination of measurement and modeling makes for an excellent apparatus for the advanced undergraduate laboratory course.
Two-dimensional critical phenomena
International Nuclear Information System (INIS)
Saleur, H.
1987-09-01
Two dimensional critical systems are studied using transformation to free fields and conformal invariance methods. The relations between the two approaches are also studied. The analytical results obtained generally depend on universality hypotheses or on renormalization group trajectories which are not established rigorously, so numerical verifications, mainly using the transfer matrix approach, are presented. The exact determination of critical exponents; the partition functions of critical models on toruses; and results as the critical point is approached are discussed [fr
Two dimensional unstable scar statistics.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)
2006-12-01
This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
International Nuclear Information System (INIS)
Silagadze, Z.K.
2007-01-01
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well-known quantum mechanical tunneling property which enables small bodies to penetrate through narrow potential barriers. We merge this 'quantum' ideology with the philosophy of Particle Swarm Optimization to get the global optimization algorithm which can be called Quantum Swarm Optimization. The functionality of the newborn algorithm is tested on some benchmark optimization problems
Parallelization of elliptic solver for solving 1D Boussinesq model
Tarwidi, D.; Adytia, D.
2018-03-01
In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.
Two-dimensional transport of tokamak plasmas
International Nuclear Information System (INIS)
Hirshman, S.P.; Jardin, S.C.
1979-01-01
A reduced set of two-fluid transport equations is obtained from the conservation equations describing the time evolution of the differential particle number, entropy, and magnetic fluxes in an axisymmetric toroidal plasma with nested magnetic surfaces. Expanding in the small ratio of perpendicular to parallel mobilities and thermal conductivities yields as solubility constraints one-dimensional equations for the surface-averaged thermodynamic variables and magnetic fluxes. Since Ohm's law E +u x B =R', where R' accounts for any nonideal effects, only determines the particle flow relative to the diffusing magnetic surfaces, it is necessary to solve a single two-dimensional generalized differential equation, (partial/partialt) delpsi. (delp - J x B) =0, to find the absolute velocity of a magnetic surface enclosing a fixed toroidal flux. This equation is linear but nonstandard in that it involves flux surface averages of the unknown velocity. Specification of R' and the cross-field ion and electron heat fluxes provides a closed system of equations. A time-dependent coordinate transformation is used to describe the diffusion of plasma quantities through magnetic surfaces of changing shape
Two dimensional infinite conformal symmetry
International Nuclear Information System (INIS)
Mohanta, N.N.; Tripathy, K.C.
1993-01-01
The invariant discontinuous (discrete) conformal transformation groups, namely the Kleinian and Fuchsian groups Gamma (with an arbitrary signature) of H (the Poincare upper half-plane l) and the unit disc Delta are explicitly constructed from the fundamental domain D. The Riemann surface with signatures of Gamma and conformally invariant automorphic forms (functions) with Peterson scalar product are discussed. The functor, where the category of complex Hilbert spaces spanned by the space of cusp forms constitutes the two dimensional conformal field theory. (Author) 7 refs
Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
-dimensional separation space. Optimization of gradients in online RP×RP is more difficult than in normal HPLC as a result of the increased number of parameters and their influence on each other. Modeling the coverage of the compounds across the two-dimensional chromatogram as a result of a change in gradients could...... be used for optimization purposes, and reduce the time spend on optimization. In this thesis (chapter 6), and manuscript B, a measure of the coverage of the compounds in the twodimensional separation space is defined. It is then shown that this measure can be modeled for changes in the gradient in both...
Topological aspect of disclinations in two-dimensional crystals
International Nuclear Information System (INIS)
Wei-Kai, Qi; Tao, Zhu; Yong, Chen; Ji-Rong, Ren
2009-01-01
By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given. (the physics of elementary particles and fields)
Two dimensional solid state NMR
International Nuclear Information System (INIS)
Kentgens, A.P.M.
1987-01-01
This thesis illustrates, by discussing some existing and newly developed 2D solid state experiments, that two-dimensional NMR of solids is a useful and important extension of NMR techniques. Chapter 1 gives an overview of spin interactions and averaging techniques important in solid state NMR. As 2D NMR is already an established technique in solutions, only the basics of two dimensional NMR are presented in chapter 2, with an emphasis on the aspects important for solid spectra. The following chapters discuss the theoretical background and applications of specific 2D solid state experiments. An application of 2D-J resolved NMR, analogous to J-resolved spectroscopy in solutions, to natural rubber is given in chapter 3. In chapter 4 the anisotropic chemical shift is mapped out against the heteronuclear dipolar interaction to obtain information about the orientation of the shielding tensor in poly-(oxymethylene). Chapter 5 concentrates on the study of super-slow molecular motions in polymers using a variant of the 2D exchange experiment developed by us. Finally chapter 6 discusses a new experiment, 2D nutation NMR, which makes it possible to study the quadrupole interaction of half-integer spins. 230 refs.; 48 figs.; 8 tabs
Two-dimensional turbulent convection
Mazzino, Andrea
2017-11-01
We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].
Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...
Indian Academy of Sciences (India)
Aly R Seadawy
2017-09-13
Sep 13, 2017 ... We considered the two-dimensional DASWs in colli- sionless, unmagnetized cold plasma consisting of dust fluid, ions and electrons. The dynamics of DASWs is governed by the normalized fluid equations of nonlin- ear continuity (1), nonlinear motion of system (2) and. (3) and linear Poisson equation (4) as.
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Decoherence in two-dimensional quantum walks
International Nuclear Information System (INIS)
Oliveira, A. C.; Portugal, R.; Donangelo, R.
2006-01-01
We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk
Study of two-dimensional interchange turbulence
International Nuclear Information System (INIS)
Sugama, Hideo; Wakatani, Masahiro.
1990-04-01
An eddy viscosity model describing enstrophy transfer in two-dimensional turbulence is presented. This model is similar to that of Canuto et al. and provides an equation for the energy spectral function F(k) as a function of the energy input rate to the system per unit wavenumber, γ s (k). In the enstrophy-transfer inertial range, F(k)∝ k -3 is predicted by the model. The eddy viscosity model is applied to the interchange turbulence of a plasma in shearless magnetic field. Numerical simulation of the two-dimensional interchange turbulence demonstrates that the energy spectrum in the high wavenumber region is well described by this model. The turbulent transport driven by the interchange turbulence is expressed in terms of the Nusselt number Nu, the Rayleigh number Ra and Prantl number Pr in the same manner as that of thermal convection problem. When we use the linear growth rate for γ s (k), our theoretical model predicts that Nu ∝ (Ra·Pr) 1/2 for a constant background pressure gradient and Nu ∝ (Ra·Pr) 1/3 for a self-consistent background pressure profile with the stress-free slip boundary conditions. The latter agrees with our numerical result showing Nu ∝ Ra 1/3 . (author)
Two-dimensional motions of rockets
International Nuclear Information System (INIS)
Kang, Yoonhwan; Bae, Saebyok
2007-01-01
We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the descending parts of the trajectories tend to be gentler and straighter slopes than the ascending parts for relatively large launching angles due to the non-vanishing thrusts. We discuss the ranges, the maximum altitudes and the engine performances of the rockets. It seems that the exponential fuel exhaustion can be the most potent engine for the longest and highest flights
Two-Dimensional Homogeneous Fermi Gases
Hueck, Klaus; Luick, Niclas; Sobirey, Lennart; Siegl, Jonas; Lompe, Thomas; Moritz, Henning
2018-02-01
We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Second invariant for two-dimensional classical super systems
Indian Academy of Sciences (India)
Construction of superpotentials for two-dimensional classical super systems (for N. 2) is carried ... extensively used for the case of non-linear partial differential equation by various authors. [3,4–7,12 ..... found to be integrable just by accident.
Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Influence of Boussinesq coefficient on depth-averaged modelling of rapid flows
Yang, Fan; Liang, Dongfang; Xiao, Yang
2018-04-01
The traditional Alternating Direction Implicit (ADI) scheme has been proven to be incapable of modelling trans-critical flows. Its inherent lack of shock-capturing capability often results in spurious oscillations and computational instabilities. However, the ADI scheme is still widely adopted in flood modelling software, and various special treatments have been designed to stabilise the computation. Modification of the Boussinesq coefficient to adjust the amount of fluid inertia is a numerical treatment that allows the ADI scheme to be applicable to rapid flows. This study comprehensively examines the impact of this numerical treatment over a range of flow conditions. A shock-capturing TVD-MacCormack model is used to provide reference results. For unsteady flows over a frictionless bed, such as idealised dam-break floods, the results suggest that an increase in the value of the Boussinesq coefficient reduces the amplitude of the spurious oscillations. The opposite is observed for steady rapid flows over a frictional bed. Finally, a two-dimensional urban flooding phenomenon is presented, involving unsteady flow over a frictional bed. The results show that increasing the value of the Boussinesq coefficient can significantly reduce the numerical oscillations and reduce the predicted area of inundation. In order to stabilise the ADI computations, the Boussinesq coefficient could be judiciously raised or lowered depending on whether the rapid flow is steady or unsteady and whether the bed is frictional or frictionless. An increase in the Boussinesq coefficient generally leads to overprediction of the propagating speed of the flood wave over a frictionless bed, but the opposite is true when bed friction is significant.
GEPOIS: a two dimensional nonuniform mesh Poisson solver
International Nuclear Information System (INIS)
Quintenz, J.P.; Freeman, J.R.
1979-06-01
A computer code is described which solves Poisson's equation for the electric potential over a two dimensional cylindrical (r,z) nonuniform mesh which can contain internal electrodes. Poisson's equation is solved over a given region subject to a specified charge distribution with either Neumann or Dirichlet perimeter boundary conditions and with Dirichlet boundary conditions on internal surfaces. The static electric field is also computed over the region with special care given to normal electric field components at boundary surfaces
The Penalty Cost Functional for the Two-Dimensional
Directory of Open Access Journals (Sweden)
Victor Onomza WAZIRI
2006-07-01
Full Text Available This paper constructs the penalty cost functional for optimizing the two-dimensional control operator of the energized wave equation. In some multiplier methods such as the Lagrange multipliers and Pontrygean maximum principle, the cost of merging the constraint equation to the integral quadratic objective functional to obtain an unconstraint equation is normally guessed or obtained from the first partial derivatives of the unconstrained equation. The Extended Conjugate Gradient Method (ECGM necessitates that the penalty cost be sequentially obtained algebraically. The ECGM problem contains a functional which is completely given in terms of state and time spatial dependent variables.
Nonlinear excitations in two-dimensional molecular structures with impurities
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth
1995-01-01
We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....
International Nuclear Information System (INIS)
Chudnovsky, D.V.; Columbia Univ., New York; Chudnovsky, G.V.; Columbia Univ., New York
1980-01-01
General algebraic and analytic formalism for derivation and solution of general two dimensional field theory equations of Zakharov-Shabat-Mikhailov type is presented. The examples presented show that this class of equations covers most of the known two-dimensional completely integrable equations. Possible generalizations for four dimensional systems require detailed analysis of Baecklund transformation of these equations. Baecklund transformation is presented in the form of Riemann problem and one special case of dual symmetry is worked out. (orig.)
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Topology optimization of two-dimensional waveguides
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
Turbulent equipartitions in two dimensional drift convection
International Nuclear Information System (INIS)
Isichenko, M.B.; Yankov, V.V.
1995-01-01
Unlike the thermodynamic equipartition of energy in conservative systems, turbulent equipartitions (TEP) describe strongly non-equilibrium systems such as turbulent plasmas. In turbulent systems, energy is no longer a good invariant, but one can utilize the conservation of other quantities, such as adiabatic invariants, frozen-in magnetic flux, entropy, or combination thereof, in order to derive new, turbulent quasi-equilibria. These TEP equilibria assume various forms, but in general they sustain spatially inhomogeneous distributions of the usual thermodynamic quantities such as density or temperature. This mechanism explains the effects of particle and energy pinch in tokamaks. The analysis of the relaxed states caused by turbulent mixing is based on the existence of Lagrangian invariants (quantities constant along fluid-particle or other orbits). A turbulent equipartition corresponds to the spatially uniform distribution of relevant Lagrangian invariants. The existence of such turbulent equilibria is demonstrated in the simple model of two dimensional electrostatically turbulent plasma in an inhomogeneous magnetic field. The turbulence is prescribed, and the turbulent transport is assumed to be much stronger than the classical collisional transport. The simplicity of the model makes it possible to derive the equations describing the relaxation to the TEP state in several limits
Numerical resolution of the Navier-Stokes equations for a low Mach number by a spectral method
International Nuclear Information System (INIS)
Frohlich, Jochen
1990-01-01
The low Mach number approximation of the Navier-Stokes equations, also called isobar, is an approximation which is less restrictive than the one due to Boussinesq. It permits strong density variations while neglecting acoustic phenomena. We present a numerical method to solve these equations in the unsteady, two dimensional case with one direction of periodicity. The discretization uses a semi-implicit finite difference scheme in time and a Fourier-Chebycheff pseudo-spectral method in space. The solution of the equations of motion is based on an iterative algorithm of Uzawa type. In the Boussinesq limit we obtain a direct method. A first application is concerned with natural convection in the Rayleigh-Benard setting. We compare the results of the low Mach number equations with the ones in the Boussinesq case and consider the influence of variable fluid properties. A linear stability analysis based on a Chebychev-Tau method completes the study. The second application that we treat is a case of isobaric combustion in an open domain. We communicate results for the hydrodynamic Darrieus-Landau instability of a plane laminar flame front. [fr
Di Nucci, Carmine
2018-05-01
This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.
International Nuclear Information System (INIS)
Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra
2014-01-01
The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications
Energy Technology Data Exchange (ETDEWEB)
Chatterjee, Kausik, E-mail: kausik.chatterjee@aggiemail.usu.edu [Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341 (United States); Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322 (United States); Roadcap, John R., E-mail: john.roadcap@us.af.mil [Air Force Research Laboratory, Kirtland AFB, NM 87117 (United States); Singh, Surendra, E-mail: surendra-singh@utulsa.edu [Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104 (United States)
2014-11-01
The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.
Liao, Feng; Zhang, Luming; Wang, Shanshan
2018-02-01
In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.
Two dimensional analytical model for a reconfigurable field effect transistor
Ranjith, R.; Jayachandran, Remya; Suja, K. J.; Komaragiri, Rama S.
2018-02-01
This paper presents two-dimensional potential and current models for a reconfigurable field effect transistor (RFET). Two potential models which describe subthreshold and above-threshold channel potentials are developed by solving two-dimensional (2D) Poisson's equation. In the first potential model, 2D Poisson's equation is solved by considering constant/zero charge density in the channel region of the device to get the subthreshold potential characteristics. In the second model, accumulation charge density is considered to get above-threshold potential characteristics of the device. The proposed models are applicable for the device having lightly doped or intrinsic channel. While obtaining the mathematical model, whole body area is divided into two regions: gated region and un-gated region. The analytical models are compared with technology computer-aided design (TCAD) simulation results and are in complete agreement for different lengths of the gated regions as well as at various supply voltage levels.
Piezoelectricity in Two-Dimensional Materials
Wu, Tao; Zhang, Hua
2015-01-01
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards
Construction of two-dimensional quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Klimek, S.; Kondracki, W.
1987-12-01
We present a sketch of the construction of the functional measure for the SU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.
Development of Two-Dimensional NMR
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 11. Development of Two-Dimensional NMR: Strucure Determination of Biomolecules in Solution. Anil Kumar. General Article Volume 20 Issue 11 November 2015 pp 995-1002 ...
Phase transitions in two-dimensional systems
International Nuclear Information System (INIS)
Salinas, S.R.A.
1983-01-01
Some experiences are related using synchrotron radiation beams, to characterize solid-liquid (fusion) and commensurate solid-uncommensurate solid transitions in two-dimensional systems. Some ideas involved in the modern theories of two-dimensional fusion are shortly exposed. The systems treated consist of noble gases (Kr,Ar,Xe) adsorbed in the basal plane of graphite and thin films formed by some liquid crystal shells. (L.C.) [pt
Glowinski, R.; Dean, E.J.; Guidoboni, G.; Juárez, L.H.; Pan, T.-W.
2008-01-01
The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge--Ampère equation. The results of numerical ...
Two-dimensional heat conducting simulation of plasma armatures
International Nuclear Information System (INIS)
Huerta, M.A.; Boynton, G.
1991-01-01
This paper reports on our development of a two-dimensional MHD code to simulate internal motions in a railgun plasma armature. The authors use the equations of resistive MHD, with Ohmic heating, and radiation heat transport. The authors use a Flux Corrected Transport code to advance all quantities in time. Our runs show the development of complex flows, subsequent shedding of secondary arcs, and a drop in the acceleration of the armature
An energy principle for two-dimensional collisionless relativistic plasmas
International Nuclear Information System (INIS)
Otto, A.; Schindler, K.
1984-01-01
Using relativistic Vlasov theory an energy principle for two-dimensional plasmas is derived, which provides a sufficient and necessary criterion for the stability of relativistic plasma equilibria. This energy principle includes charge separating effects since the exact Poisson equation was taken into consideration. Applying the variational principle to the case of the relativistic plane plasma sheet, the same marginal wave length is found as in the non-relativistic case. (author)
Two-dimensional simulation of the MHD stability, (1)
International Nuclear Information System (INIS)
Kurita, Gen-ichi; Amano, Tsuneo.
1976-03-01
The two-dimensional computer code has been prepared to study MHD stability of an axisymmetric toroidal plasma with and without the surrounding vacuum region. It also includes the effect of magnetic surfaces with non-circular cross sections. The linearized equations of motion are solved as an initial value problem. The results by computer simulation are compared with those by the theory for the cylindrical plasma; they are in good agreement. (auth.)
Energy Technology Data Exchange (ETDEWEB)
Perez Guerrero, Jesus Salvador
1996-12-31
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.
Energy Technology Data Exchange (ETDEWEB)
Perez Guerrero, Jesus Salvador
1995-12-31
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.
On the confinement of a Dirac particle to a two-dimensional ring
International Nuclear Information System (INIS)
Bakke, K.; Furtado, C.
2012-01-01
In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring for systems described by the Dirac equation by introducing a new coupling into the Dirac equation. We show that the introduction of this new coupling into the Dirac equation yields a generalization of the two-dimensional quantum ring model proposed by Tan and Inkson [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635] for relativistic spin-half quantum particles. -- Highlights: ► Two-dimensional ring model for condensed matter systems described by the Dirac equation. ► Exact solutions of the Dirac equation. ► Persistent currents for Dirac-like systems confined to a two-dimensional quantum ring.
Two-dimensional nuclear magnetic resonance spectroscopy
International Nuclear Information System (INIS)
Bax, A.; Lerner, L.
1986-01-01
Great spectral simplification can be obtained by spreading the conventional one-dimensional nuclear magnetic resonance (NMR) spectrum in two independent frequency dimensions. This so-called two-dimensional NMR spectroscopy removes spectral overlap, facilitates spectral assignment, and provides a wealth of additional information. For example, conformational information related to interproton distances is available from resonance intensities in certain types of two-dimensional experiments. Another method generates 1 H NMR spectra of a preselected fragment of the molecule, suppressing resonances from other regions and greatly simplifying spectral appearance. Two-dimensional NMR spectroscopy can also be applied to the study of 13 C and 15 N, not only providing valuable connectivity information but also improving sensitivity of 13 C and 15 N detection by up to two orders of magnitude. 45 references, 10 figures
Two-dimensional x-ray diffraction
He, Bob B
2009-01-01
Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea
A Short Proof of the Large Time Energy Growth for the Boussinesq System
Brandolese, Lorenzo; Mouzouni, Charafeddine
2017-10-01
We give a direct proof of the fact that the L^p-norms of global solutions of the Boussinesq system in R^3 grow large as t→ ∞ for 1R+× R3. In particular, the kinetic energy blows up as \\Vert u(t)\\Vert _2^2˜ ct^{1/2} for large time. This contrasts with the case of the Navier-Stokes equations.
Wen, Baole; Chini, Gregory P.; Kerswell, Rich R.; Doering, Charles R.
2015-10-01
An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu˜PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L =2 √{2 },Nu≤0.106 Pr0Ra5/12 , which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.
Dynamics of vortex interactions in two-dimensional flows
DEFF Research Database (Denmark)
Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.
2002-01-01
The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...... a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 ... is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection...
Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases
Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.
2018-03-01
The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.
Directory of Open Access Journals (Sweden)
Roya Sattarzadeh
2018-01-01
Full Text Available Accurate measurement of Mitral Valve Area (MVA is essential to determining the Mitral Stenosis (MS severity and to achieving the best management strategies for this disease. The goal of the present study is to compare mitral valve area (MVA measurement by Continuity Equation (CE and Pressure Half-Time (PHT methods with that of 2D-Planimetry (PL in patients with moderate to severe mitral stenosis (MS. This comparison also was performed in subgroups of patients with significant Aortic Insufficiency (AI, Mitral Regurgitation (MR and Atrial Fibrillation (AF. We studied 70 patients with moderate to severe MS who were referred to echocardiography clinic. MVA was determined by PL, CE and PHT methods. The agreement and correlations between MVA’s obtained from various methods were determined by kappa index, Bland-Altman analysis, and linear regression analysis. The mean values for MVA calculated by CE was 0.81 cm (±0.27 and showed good correlation with those calculated by PL (0.95 cm, ±0.26 in whole population (r=0.771, P<0.001 and MR subgroup (r=0.763, P<0.001 and normal sinus rhythm and normal valve subgroups (r=0.858, P<0.001 and r=0.867, P<0.001, respectively. But CE methods didn’t show any correlation in AF and AI subgroups. MVA measured by PHT had a good correlation with that measured by PL in whole population (r=0.770, P<0.001 and also in NSR (r=0.814, P<0.001 and normal valve subgroup (r=0.781, P<0.001. Subgroup with significant AI and those with significant MR showed moderate correlation (r=0.625, P=0.017 and r=0.595, P=0.041, respectively. Bland Altman Analysis showed that CE would estimate MVA smaller in comparison with PL in the whole population and all subgroups and PHT would estimate MVA larger in comparison with PL in the whole population and all subgroups. The mean bias for CE and PHT are 0.14 cm and -0.06 cm respectively. In patients with moderate to severe mitral stenosis, in the absence of concomitant AF, AI or MR, the accuracy
Sums of two-dimensional spectral triples
DEFF Research Database (Denmark)
Christensen, Erik; Ivan, Cristina
2007-01-01
construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly...
Stability of two-dimensional vorticity filaments
International Nuclear Information System (INIS)
Elhmaidi, D.; Provenzale, A.; Lili, T.; Babiano, A.
2004-01-01
We discuss the results of a numerical study on the stability of two-dimensional vorticity filaments around a circular vortex. We illustrate how the stability of the filaments depends on the balance between the strain associated with the far field of the vortex and the local vorticity of the filament, and we discuss an empirical criterion for filament stability
Two-dimensional microstrip detector for neutrons
Energy Technology Data Exchange (ETDEWEB)
Oed, A [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.
Conformal invariance and two-dimensional physics
International Nuclear Information System (INIS)
Zuber, J.B.
1993-01-01
Actually, physicists and mathematicians are very interested in conformal invariance: geometric transformations which keep angles. This symmetry is very important for two-dimensional systems as phase transitions, string theory or node mathematics. In this article, the author presents the conformal invariance and explains its usefulness
Matching Two-dimensional Gel Electrophoresis' Spots
DEFF Research Database (Denmark)
Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza
2012-01-01
This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar...
Two-dimensional membranes in motion
Davidovikj, D.
2018-01-01
This thesis revolves around nanomechanical membranes made of suspended two - dimensional materials. Chapters 1-3 give an introduction to the field of 2D-based nanomechanical devices together with an overview of the underlying physics and the measurementtools used in subsequent chapters. The research
Extended Polymorphism of Two-Dimensional Material
Yoshida, Masaro; Ye, Jianting; Zhang, Yijin; Imai, Yasuhiko; Kimura, Shigeru; Fujiwara, Akihiko; Nishizaki, Terukazu; Kobayashi, Norio; Nakano, Masaki; Iwasa, Yoshihiro
When controlling electronic properties of bulk materials, we usually assume that the basic crystal structure is fixed. However, in two-dimensional (2D) materials, atomic structure or to functionalize their properties. Various polymorphs can exist in transition metal dichalcogenides (TMDCs) from
Piezoelectricity in Two-Dimensional Materials
Wu, Tao
2015-02-25
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.
Inverse problems for the Boussinesq system
International Nuclear Information System (INIS)
Fan, Jishan; Jiang, Yu; Nakamura, Gen
2009-01-01
We obtain two results on inverse problems for a 2D Boussinesq system. One is that we prove the Lipschitz stability for the inverse source problem of identifying a time-independent external force in the system with observation data in an arbitrary sub-domain over a time interval of the velocity and the data of velocity and temperature at a fixed positive time t 0 > 0 over the whole spatial domain. The other one is that we prove a conditional stability estimate for an inverse problem of identifying the two initial conditions with a single observation on a sub-domain
Two-dimensional confinement of heavy fermions
International Nuclear Information System (INIS)
Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito
2010-01-01
Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)
Two-dimensional sensitivity calculation code: SENSETWO
International Nuclear Information System (INIS)
Yamauchi, Michinori; Nakayama, Mitsuo; Minami, Kazuyoshi; Seki, Yasushi; Iida, Hiromasa.
1979-05-01
A SENSETWO code for the calculation of cross section sensitivities with a two-dimensional model has been developed, on the basis of first order perturbation theory. It uses forward neutron and/or gamma-ray fluxes and adjoint fluxes obtained by two-dimensional discrete ordinates code TWOTRAN-II. The data and informations of cross sections, geometry, nuclide density, response functions, etc. are transmitted to SENSETWO by the dump magnetic tape made in TWOTRAN calculations. The required input for SENSETWO calculations is thus very simple. The SENSETWO yields as printed output the cross section sensitivities for each coarse mesh zone and for each energy group, as well as the plotted output of sensitivity profiles specified by the input. A special feature of the code is that it also calculates the reaction rate with the response function used as the adjoint source in TWOTRAN adjoint calculation and the calculated forward flux from the TWOTRAN forward calculation. (author)
Two-dimensional ranking of Wikipedia articles
Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L.
2010-10-01
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.
Toward two-dimensional search engines
International Nuclear Information System (INIS)
Ermann, L; Shepelyansky, D L; Chepelianskii, A D
2012-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank–CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed. (paper)
Acoustic phonon emission by two dimensional plasmons
International Nuclear Information System (INIS)
Mishonov, T.M.
1990-06-01
Acoustic wave emission of the two dimensional plasmons in a semiconductor or superconductor microstructure is investigated by using the phenomenological deformation potential within the jellium model. The plasmons are excited by the external electromagnetic (e.m.) field. The power conversion coefficient of e.m. energy into acoustic wave energy is also estimated. It is shown, the coherent transformation has a sharp resonance at the plasmon frequency of the two dimensional electron gas (2DEG). The incoherent transformation of the e.m. energy is generated by ohmic dissipation of 2DEG. The method proposed for coherent phonon beam generation can be very effective for high mobility 2DEG and for thin superconducting layers if the plasmon frequency ω is smaller than the superconducting gap 2Δ. (author). 21 refs, 1 fig
Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver
Scott, Matthew T.; Mccune, James E.
1988-01-01
This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.
Inverse radiative transfer problems in two-dimensional heterogeneous media
International Nuclear Information System (INIS)
Tito, Mariella Janette Berrocal
2001-01-01
The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)
Magnus force in discrete and continuous two-dimensional superfluids
International Nuclear Information System (INIS)
Gecse, Z.; Khlebnikov, S.
2005-01-01
Motion of vortices in two-dimensional superfluids in the classical limit is studied by solving the Gross-Pitaevskii equation numerically on a uniform lattice. We find that, in the presence of a superflow directed along one of the main lattice periods, vortices move with the superflow on fine lattices but perpendicular to it on coarse ones. We interpret this result as a transition from the full Magnus force in a Galilean-invariant limit to vanishing effective Magnus force in a discrete system, in agreement with the existing experiments on vortex motion in Josephson junction arrays
Two-dimensional simulations of magnetically-driven instabilities
International Nuclear Information System (INIS)
Peterson, D.; Bowers, R.; Greene, A.E.; Brownell, J.
1986-01-01
A two-dimensional Eulerian MHD code is used to study the evolution of magnetically-driven instabilities in cylindrical geometry. The code incorporates an equation of state, resistivity, and radiative cooling model appropriate for an aluminum plasma. The simulations explore the effects of initial perturbations, electrical resistivity, and radiative cooling on the growth and saturation of the instabilities. Comparisons are made between the 2-D simulations, previous 1-D simulations, and results from the Pioneer experiments of the Los Alamos foil implosion program
Confined catalysis under two-dimensional materials
Li, Haobo; Xiao, Jianping; Fu, Qiang; Bao, Xinhe
2017-01-01
Small spaces in nanoreactors may have big implications in chemistry, because the chemical nature of molecules and reactions within the nanospaces can be changed significantly due to the nanoconfinement effect. Two-dimensional (2D) nanoreactor formed under 2D materials can provide a well-defined model system to explore the confined catalysis. We demonstrate a general tendency for weakened surface adsorption under the confinement of graphene overlayer, illustrating the feasible modulation of su...
Two-Dimensional Extreme Learning Machine
Directory of Open Access Journals (Sweden)
Bo Jia
2015-01-01
(BP networks. However, like many other methods, ELM is originally proposed to handle vector pattern while nonvector patterns in real applications need to be explored, such as image data. We propose the two-dimensional extreme learning machine (2DELM based on the very natural idea to deal with matrix data directly. Unlike original ELM which handles vectors, 2DELM take the matrices as input features without vectorization. Empirical studies on several real image datasets show the efficiency and effectiveness of the algorithm.
Superintegrability on the two dimensional hyperboloid
International Nuclear Information System (INIS)
Akopyan, E.; Pogosyan, G.S.; Kalnins, E.G.; Miller, W. Jr
1998-01-01
This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't been studied yet. An example of an interbasis expansion is given and the structure of the quadratic algebra generated by the integrals of motion is carried out
Two-dimensional Kagome photonic bandgap waveguide
DEFF Research Database (Denmark)
Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou
2000-01-01
The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....
Mechanical exfoliation of two-dimensional materials
Gao, Enlai; Lin, Shao-Zhen; Qin, Zhao; Buehler, Markus J.; Feng, Xi-Qiao; Xu, Zhiping
2018-06-01
Two-dimensional materials such as graphene and transition metal dichalcogenides have been identified and drawn much attention over the last few years for their unique structural and electronic properties. However, their rise begins only after these materials are successfully isolated from their layered assemblies or adhesive substrates into individual monolayers. Mechanical exfoliation and transfer are the most successful techniques to obtain high-quality single- or few-layer nanocrystals from their native multi-layer structures or their substrate for growth, which involves interfacial peeling and intralayer tearing processes that are controlled by material properties, geometry and the kinetics of exfoliation. This procedure is rationalized in this work through theoretical analysis and atomistic simulations. We propose a criterion to assess the feasibility for the exfoliation of two-dimensional sheets from an adhesive substrate without fracturing itself, and explore the effects of material and interface properties, as well as the geometrical, kinetic factors on the peeling behaviors and the torn morphology. This multi-scale approach elucidates the microscopic mechanism of the mechanical processes, offering predictive models and tools for the design of experimental procedures to obtain single- or few-layer two-dimensional materials and structures.
Propagation and quenching in a reactive Burgers–Boussinesq system
International Nuclear Information System (INIS)
Constantin, Peter; Ryzhik, Lenya; Roquejoffre, Jean-Michel; Vladimirova, Natalia
2008-01-01
We investigate the qualitative behaviour of solutions of a Burgers–Boussinesq system—a reaction–diffusion equation coupled via gravity to a Burgers equation—by a combination of numerical, asymptotic and mathematical techniques. Numerical simulations suggest that when the gravity ρ is small the solutions decompose into a travelling wave and an accelerated shock wave moving in opposite directions. There exists ρ cr1 so that, when ρ > ρ cr1 , this structure changes drastically, and the solutions become more complicated. The solutions are composed of three elementary pieces: a wave fan, a combustion travelling wave and an accelerating shock, the whole structure travelling in the same direction. There exists ρ cr2 so that when ρ > ρ cr2 , the wave fan catches up with the accelerating shock wave and the solution is quenched, no matter how large the support of the initial temperature. We prove that the three building blocks (wave fans, combustion travelling waves and shocks) exist and we construct asymptotic solutions made up of these three elementary pieces. We finally prove, in a mathematically rigorous way, a quenching result irrespective of the size of the region where the temperature was above ignition—a major difference from what happens in advection–reaction–diffusion equations where an incompressible flow is imposed
Vector (two-dimensional) magnetic phenomena
International Nuclear Information System (INIS)
Enokizono, Masato
2002-01-01
In this paper, some interesting phenomena were described from the viewpoint of two-dimensional magnetic property, which is reworded with the vector magnetic property. It shows imperfection of conventional magnetic property and some interested phenomena were discovered, too. We found magnetic materials had the strong nonlinearity both magnitude and spatial phase due to the relationship between the magnetic field strength H-vector and the magnetic flux density B-vector. Therefore, magnetic properties should be defined as the vector relationship. Furthermore, the new Barukhausen signal was observed under rotating flux. (Author)
Two-dimensional Semiconductor-Superconductor Hybrids
DEFF Research Database (Denmark)
Suominen, Henri Juhani
This thesis investigates hybrid two-dimensional semiconductor-superconductor (Sm-S) devices and presents a new material platform exhibiting intimate Sm-S coupling straight out of the box. Starting with the conventional approach, we investigate coupling superconductors to buried quantum well....... To overcome these issues we integrate the superconductor directly into the semiconducting material growth stack, depositing it in-situ in a molecular beam epitaxy system under high vacuum. We present a number of experiments on these hybrid heterostructures, demonstrating near unity interface transparency...
Binding energy of two-dimensional biexcitons
DEFF Research Database (Denmark)
Singh, Jai; Birkedal, Dan; Vadim, Lyssenko
1996-01-01
Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories....
Airy beams on two dimensional materials
Imran, Muhammad; Li, Rujiang; Jiang, Yuyu; Lin, Xiao; Zheng, Bin; Dehdashti, Shahram; Xu, Zhiwei; Wang, Huaping
2018-05-01
We propose that quasi-transverse-magnetic (quasi-TM) Airy beams can be supported on two dimensional (2D) materials. By taking graphene as a typical example, the solution of quasi-TM Airy beams is studied under the paraxial approximation. The analytical field intensity in a bilayer graphene-based planar plasmonic waveguide is confirmed by the simulation results. Due to the tunability of the chemical potential of graphene, the self-accelerating behavior of the quasi-TM Airy beam can be steered effectively. 2D materials thus provide a good platform to investigate the propagation of Airy beams.
Two-dimensional wave propagation in layered periodic media
Quezada de Luna, Manuel
2014-09-16
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using highorder homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coeffi cient equations.
Two-dimensional computer simulation of high intensity proton beams
Lapostolle, Pierre M
1972-01-01
A computer program has been developed which simulates the two- dimensional transverse behaviour of a proton beam in a focusing channel. The model is represented by an assembly of a few thousand 'superparticles' acted upon by their own self-consistent electric field and an external focusing force. The evolution of the system is computed stepwise in time by successively solving Poisson's equation and Newton's law of motion. Fast Fourier transform techniques are used for speed in the solution of Poisson's equation, while extensive area weighting is utilized for the accurate evaluation of electric field components. A computer experiment has been performed on the CERN CDC 6600 computer to study the nonlinear behaviour of an intense beam in phase space, showing under certain circumstances a filamentation due to space charge and an apparent emittance growth. (14 refs).
On the background independence of two-dimensional topological gravity
Imbimbo, Camillo
1995-04-01
We formulate two-dimensional topological gravity in a background covariant Lagrangian framework. We derive the Ward identities which characterize the dependence of physical correlators on the background world-sheet metric defining the gauge-slice. We point out the existence of an "anomaly" in Ward identitites involving correlators of observables with higher ghost number. This "anomaly" represents an obstruction for physical correlators to be globally defined forms on moduli space which could be integrated in a background independent way. Starting from the anomalous Ward identities, we derive "descent" equations whose solutions are cocycles of the Lie algebra of the diffeomorphism group with values in the space of local forms on the moduli space. We solve the descent equations and provide explicit formulas for the cocycles, which allow for the definition of background independent integrals of physical correlators on the moduli space.
Moderator feedback effects in two-dimensional nodal methods for pressurized water reactor analysis
International Nuclear Information System (INIS)
Downar, T.J.
1987-01-01
A method was developed for incorporating moderator feedback effects in two-dimensional nodal codes used for pressurized water reactor (PWR) neutronic analysis. Equations for the assembly average quality and density are developed in terms of the assembly power calculated in two dimensions. The method is validated with a Westinghouse PWR using the Electric Power Research Institute code SIMULATE-E. Results show a several percent improvement is achieved in the two-dimensional power distribution prediction compared to methods without moderator feedback
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
Two-Dimensional Theory of Scientific Representation
Directory of Open Access Journals (Sweden)
A Yaghmaie
2013-03-01
Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.
Newton-sor iterative method for solving the two-dimensional porous ...
African Journals Online (AJOL)
In this paper, we consider the application of the Newton-SOR iterative method in obtaining the approximate solution of the two-dimensional porous medium equation (2D PME). The nonlinear finite difference approximation equation to the 2D PME is derived by using the implicit finite difference scheme. The developed ...
Two-dimensional quantisation of the quasi-Landau hydrogenic spectrum
International Nuclear Information System (INIS)
Gallas, J.A.C.; O'Connell, R.F.
1982-01-01
Based on the two-dimensional WKB model, an equation is derived from which the non-relativistic quasi-Landau energy spectrum of hydrogen-like atoms may be easily obtained. In addition, the solution of radial equations in the WKB approximation and its relation with models recently used to fit experimental data are discussed. (author)
Statistical mechanics of two-dimensional and geophysical flows
International Nuclear Information System (INIS)
Bouchet, Freddy; Venaille, Antoine
2012-01-01
The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. After a brief presentation of the 2D Euler and quasi-geostrophic equations, the specificity of two-dimensional and geophysical turbulence is emphasized. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations and mean field approach) and thermodynamic concepts (ensemble inequivalence and negative heat capacity) are briefly explained and described. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations is provided. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equilibrium steady states. In this last case, forces and dissipation are in a statistical balance; fluxes of conserved quantity characterize the system and microcanonical or other equilibrium measures no longer describe the system.
Two-dimensional simulation of sintering process
International Nuclear Information System (INIS)
Vasconcelos, Vanderley de; Pinto, Lucio Carlos Martins; Vasconcelos, Wander L.
1996-01-01
The results of two-dimensional simulations are directly applied to systems in which one of the dimensions is much smaller than the others, and to sections of three dimensional models. Moreover, these simulations are the first step of the analysis of more complex three-dimensional systems. In this work, two basic features of the sintering process are studied: the types of particle size distributions related to the powder production processes and the evolution of geometric parameters of the resultant microstructures during the solid-state sintering. Random packing of equal spheres is considered in the sintering simulation. The packing algorithm does not take into account the interactive forces between the particles. The used sintering algorithm causes the densification of the particle set. (author)
Pressure of two-dimensional Yukawa liquids
International Nuclear Information System (INIS)
Feng, Yan; Wang, Lei; Tian, Wen-de; Goree, J; Liu, Bin
2016-01-01
A simple analytic expression for the pressure of a two-dimensional Yukawa liquid is found by fitting results from a molecular dynamics simulation. The results verify that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of the Wigner–Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytic expression, with its empirically determined coefficients, is plotted as isochores, or curves of constant area. These results should be applicable to monolayer dusty plasmas. (paper)
Two dimensional nanomaterials for flexible supercapacitors.
Peng, Xu; Peng, Lele; Wu, Changzheng; Xie, Yi
2014-05-21
Flexible supercapacitors, as one of most promising emerging energy storage devices, are of great interest owing to their high power density with great mechanical compliance, making them very suitable as power back-ups for future stretchable electronics. Two-dimensional (2D) nanomaterials, including the quasi-2D graphene and inorganic graphene-like materials (IGMs), have been greatly explored to providing huge potential for the development of flexible supercapacitors with higher electrochemical performance. This review article is devoted to recent progresses in engineering 2D nanomaterials for flexible supercapacitors, which survey the evolution of electrode materials, recent developments in 2D nanomaterials and their hybrid nanostructures with regulated electrical properties, and the new planar configurations of flexible supercapacitors. Furthermore, a brief discussion on future directions, challenges and opportunities in this fascinating area is also provided.
Two-dimensional materials for ultrafast lasers
International Nuclear Information System (INIS)
Wang Fengqiu
2017-01-01
As the fundamental optical properties and novel photophysics of graphene and related two-dimensional (2D) crystals are being extensively investigated and revealed, a range of potential applications in optical and optoelectronic devices have been proposed and demonstrated. Of the many possibilities, the use of 2D materials as broadband, cost-effective and versatile ultrafast optical switches (or saturable absorbers) for short-pulsed lasers constitutes a rapidly developing field with not only a good number of publications, but also a promising prospect for commercial exploitation. This review primarily focuses on the recent development of pulsed lasers based on several representative 2D materials. The comparative advantages of these materials are discussed, and challenges to practical exploitation, which represent good future directions of research, are laid out. (paper)
Two-dimensional phase fraction charts
International Nuclear Information System (INIS)
Morral, J.E.
1984-01-01
A phase fraction chart is a graphical representation of the amount of each phase present in a system as a function of temperature, composition or other variable. Examples are phase fraction versus temperature charts used to characterize specific alloys and as a teaching tool in elementary texts, and Schaeffler diagrams used to predict the amount of ferrite in stainless steel welds. Isothermal-transformation diagrams (TTT diagrams) are examples that give phase (or microconstituent) amount versus temperature and time. The purpose of this communication is to discuss the properties of two-dimensional phase fraction charts in more general terms than have been reported before. It is shown that they can represent multi-component, multiphase equilibria in a way which is easier to read and which contains more information than the isotherms and isopleths of multi-component phase diagrams
Two dimensional NMR studies of polysaccharides
International Nuclear Information System (INIS)
Byrd, R.A.; Egan, W.; Summers, M.F.
1987-01-01
Polysaccharides are very important components in the immune response system. Capsular polysaccharides and lipopolysaccharides occupy cell surface sites of bacteria, play key roles in recognition and some have been used to develop vaccines. Consequently, the ability to determine chemical structures of these systems is vital to an understanding of their immunogenic action. The authors have been utilizing recently developed two-dimensional homonuclear and heteronuclear correlation spectroscopy for unambiguous assignment and structure determination of a number of polysaccharides. In particular, the 1 H-detected heteronuclear correlation experiments are essential to the rapid and sensitive determination of these structures. Linkage sites are determined by independent polarization transfer experiments and multiple quantum correlation experiments. These methods permit the complete structure determination on very small amounts of the polysaccharides. They present the results of a number of structural determinations and discuss the limits of these experiments in terms of their applications to polysaccharides
Versatile two-dimensional transition metal dichalcogenides
DEFF Research Database (Denmark)
Canulescu, Stela; Affannoukoué, Kévin; Döbeli, Max
), a strategy for the fabrication of 2D heterostructures must be developed. Here we demonstrate a novel approach for the bottom-up synthesis of TMDC monolayers, namely Pulsed Laser Deposition (PLD) combined with a sulfur evaporation beam. PLD relies on the use of a pulsed laser (ns pulse duration) to induce...... material transfer from a solid source (such as a sintered target of MoS2) to a substrate (such as Si or sapphire). The deposition rate in PLD is typically much less than a monolayer per pulse, meaning that the number of MLs can be controlled by a careful selection of the number of laser pulses......Two-dimensional transition metal dichalcogenides (2D-TMDCs), such as MoS2, have emerged as a new class of semiconducting materials with distinct optical and electrical properties. The availability of 2D-TMDCs with distinct band gaps allows for unlimited combinations of TMDC monolayers (MLs...
Two-dimensional heterostructures for energy storage
Energy Technology Data Exchange (ETDEWEB)
Gogotsi, Yury G. [Drexel Univ., Philadelphia, PA (United States); Pomerantseva, Ekaterina [Drexel Univ., Philadelphia, PA (United States)
2017-06-12
Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. As a result, we also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
Energy Technology Data Exchange (ETDEWEB)
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1994-01-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation
Equivalency of two-dimensional algebras
International Nuclear Information System (INIS)
Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.
2011-01-01
Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)
On devising Boussinesq-type models with bounded eigenspectra: One horizontal dimension
DEFF Research Database (Denmark)
Eskilsson, Claes; Engsig-Karup, Allan Peter
2014-01-01
) are introduced. Using spectral element simulations of stream function waves it is illustrated that (i) the bounded equations capture the physics of the wave motion as well as the standard unbounded equations, and (ii) the bounded equations are computationally more efficient when explicit time-stepping schemes...... using a spectral element method of arbitrary spatial order p. It is shown that existing sets of parameters, found by optimising the linear dispersion relation, give rise to unbounded eigenspectra which govern stability. For explicit time-stepping schemes the global CFL time-step restriction typically...... requires Δt∝p−2. We derive and present conditions on the parameters under which implicitly-implicit Boussinesq-type equations will exhibit bounded eigenspectra. Two new bounded versions having comparable nonlinear and dispersive properties as the equations of Nwogu (1993) and Schäffer and Madsen (1995...
Two-dimensional steady unsaturated flow through embedded elliptical layers
Bakker, Mark; Nieber, John L.
2004-12-01
New analytic element solutions are presented for unsaturated, two-dimensional steady flow in vertical planes that include nonoverlapping impermeable elliptical layers and elliptical inhomogeneities. The hydraulic conductivity, which is represented by an exponential function of the pressure head, differs between the inside and outside of an elliptical inhomogeneity; both the saturated hydraulic conductivity and water retention parameters are allowed to differ between the inside and outside. The Richards equation is transformed, through the Kirchhoff transformation and a second standard transformation, into the modified Helmholtz equation. Analytic element solutions are obtained through separation of variables in elliptical coordinates. The resulting equations for the Kirchhoff potential consist of infinite sums of products of exponentials and modified Mathieu functions. In practical applications the series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately but up to machine accuracy, provided that enough terms are used. The pressure head, saturation, and flow may be computed analytically at any point in the vadose zone. Examples are given of the shadowing effect of an impermeable elliptical layer in a uniform flow field and funnel-type flow between two elliptical inhomogeneities. The presented solutions may be applied to study transport processes in vadose zones containing many impermeable elliptical layers or elliptical inhomogeneities.
Fractional calculus phenomenology in two-dimensional plasma models
Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill
2006-10-01
Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).
Dynamics of two-dimensional solitary vortices in a low-β plasma with convective motion
International Nuclear Information System (INIS)
Makino, Mitsuhiro; Kamimura, Tetsuo; Taniuti, Tosiya.
1980-12-01
Numerical studies of the Hasegawa-Mima equation, derived in the context of drift waves but equivalent to the quasigeostrophic vortex potential equation for Rossby waves, show the stable properties of solitary vortices which are two dimensional, localized, steady and translating solutions of this same equation. A solitary vortex can propagate only in the direction (x-direction) perpendicular to the density gradient. When this solitary vortex solution is inclined at some angle with respect to the x-axis, its propagation direction oscillates in the x and y plane. In two dimensional collisions, i.e. head-on collision and overtaking, solitary vortices interact two-dimensionally and recover their initial shapes at the end of both types of collisions. (author)
All or nothing: On the small fluctuations of two-dimensional string theoretic black holes
Energy Technology Data Exchange (ETDEWEB)
Gilbert, Gerald [Univ. of Maryland, College Park, MD (United States); Raiten, Eric [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
1992-10-01
A comprehensive analysis of small fluctuations about two-dimensional string-theoretic and string-inspired black holes is presented. It is shown with specific examples that two-dimensional black holes behave in a radically different way from all known black holes in four dimensions. For both the SL(2,R)/U(1) black hole and the two-dimensional black hole coupled to a massive dilaton with constant field strength, it is shown that there are a {\\it continuous infinity} of solutions to the linearized equations of motion, which are such that it is impossible to ascertain the classical linear response. It is further shown that the two-dimensional black hole coupled to a massive, linear dilaton admits {\\it no small fluctuations at all}. We discuss possible implications of our results for the Callan-Giddings-Harvey-Strominger black hole.
Thermoelectric transport in two-dimensional giant Rashba systems
Xiao, Cong; Li, Dingping; Ma, Zhongshui; Niu, Qian
Thermoelectric transport in strongly spin-orbit coupled two-dimensional Rashba systems is studied using the analytical solution of the linearized Boltzmann equation. To highlight the effects of inter-band scattering, we assume point-like potential impurities, and obtain the band-and energy-dependent transport relaxation times. Unconventional transport behaviors arise when the Fermi level lies near or below the band crossing point (BCP), such as the non-Drude electrical conducivity below the BCP, the failure of the standard Mott relation linking the Peltier coefficient to the electrical conductivity near the BCP, the enhancement of diffusion thermopower and figure of merit below the BCP, the zero-field Hall coefficient which is not inversely proportional to and not a monotonic function of the carrier density, the enhanced Nernst coefficient below the BCP, and the enhanced current-induced spin-polarization efficiency.
Two-dimensional divertor modeling and scaling laws
International Nuclear Information System (INIS)
Catto, P.J.; Connor, J.W.; Knoll, D.A.
1996-01-01
Two-dimensional numerical models of divertors contain large numbers of dimensionless parameters that must be varied to investigate all operating regimes of interest. To simplify the task and gain insight into divertor operation, we employ similarity techniques to investigate whether model systems of equations plus boundary conditions in the steady state admit scaling transformations that lead to useful divertor similarity scaling laws. A short mean free path neutral-plasma model of the divertor region below the x-point is adopted in which all perpendicular transport is due to the neutrals. We illustrate how the results can be used to benchmark large computer simulations by employing a modified version of UEDGE which contains a neutral fluid model. (orig.)
Cooperation in two-dimensional mixed-games
International Nuclear Information System (INIS)
Amaral, Marco A; Silva, Jafferson K L da; Wardil, Lucas
2015-01-01
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two individuals is uniformly drawn from a sample of two different games. Using the master equation approach we show that the random mixture of two games is equivalent to play the average game when (i) the strategies are statistically independent of the game distribution and (ii) the transition rates are linear functions of the payoffs. We also use Monte-Carlo simulations in a two-dimensional lattice and mean-field techniques to investigate the scenario when the two above conditions do not hold. We find that even outside of such conditions, several quantities characterizing the mixed-games are still the same as the ones obtained in the average game when the two games are not very different. (paper)
Two-dimensional strain gradient damage modeling: a variational approach
Placidi, Luca; Misra, Anil; Barchiesi, Emilio
2018-06-01
In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.
Surface Ship Shock Modeling and Simulation: Two-Dimensional Analysis
Directory of Open Access Journals (Sweden)
Young S. Shin
1998-01-01
Full Text Available The modeling and simulation of the response of a surface ship system to underwater explosion requires an understanding of many different subject areas. These include the process of underwater explosion events, shock wave propagation, explosion gas bubble behavior and bubble-pulse loading, bulk and local cavitation, free surface effect, fluid-structure interaction, and structural dynamics. This paper investigates the effects of fluid-structure interaction and cavitation on the response of a surface ship using USA-NASTRAN-CFA code. First, the one-dimensional Bleich-Sandler model is used to validate the approach, and second, the underwater shock response of a two-dimensional mid-section model of a surface ship is predicted with a surrounding fluid model using a constitutive equation of a bilinear fluid which does not allow transmission of negative pressures.
Charge ordering in two-dimensional ionic liquids
Perera, Aurélien; Urbic, Tomaz
2018-04-01
The structural properties of model two-dimensional (2D) ionic liquids are examined, with a particular focus on the charge ordering process, with the use of computer simulation and integral equation theories. The influence of the logarithmic form of the Coulomb interaction, versus that of a 3D screened interaction form, is analysed. Charge order is found to hold and to be analogous for both interaction models, despite their very different form. The influence of charge ordering in the low density regime is discussed in relation to well known properties of 2D Coulomb fluids, such as the Kosterlitz-Thouless transition and criticality. The present study suggests the existence of a stable thermodynamic labile cluster phase, implying the existence of a liquid-liquid "transition" above the liquid-gas binodal. The liquid-gas and Kosterlitz-Thouless transitions would then take place inside the predicted cluster phase.
Finite volume model for two-dimensional shallow environmental flow
Simoes, F.J.M.
2011-01-01
This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.
Quantum theory of two-dimensional generalized Toda lattice on bounded spatial interval
International Nuclear Information System (INIS)
Leznov, A.N.
1982-01-01
The quantization method of exactly solvable dynamical systems worked out in another paper is applied to a two-dimensional model described by the equations of generalized Toda lattice with a periodicity condition over spatial variable. The Heisenberg operators of the model are finite polynomials over the coupling constant g 2 , whose coefficients functionally depend on operators of noninteracting fields. The model has a direct relation with the string theories and reduces formally when L→infinity to two-dimensional quantum field theory described by the equations of generalized Toda lattice the formal solution of which has been found in Refs
Electronic Transport in Two-Dimensional Materials
Sangwan, Vinod K.; Hersam, Mark C.
2018-04-01
Two-dimensional (2D) materials have captured the attention of the scientific community due to the wide range of unique properties at nanometer-scale thicknesses. While significant exploratory research in 2D materials has been achieved, the understanding of 2D electronic transport and carrier dynamics remains in a nascent stage. Furthermore, because prior review articles have provided general overviews of 2D materials or specifically focused on charge transport in graphene, here we instead highlight charge transport mechanisms in post-graphene 2D materials, with particular emphasis on transition metal dichalcogenides and black phosphorus. For these systems, we delineate the intricacies of electronic transport, including band structure control with thickness and external fields, valley polarization, scattering mechanisms, electrical contacts, and doping. In addition, electronic interactions between 2D materials are considered in the form of van der Waals heterojunctions and composite films. This review concludes with a perspective on the most promising future directions in this fast-evolving field.
Stress distribution in two-dimensional silos
Blanco-Rodríguez, Rodolfo; Pérez-Ángel, Gabriel
2018-01-01
Simulations of a polydispersed two-dimensional silo were performed using molecular dynamics, with different numbers of grains reaching up to 64 000, verifying numerically the model derived by Janssen and also the main assumption that the walls carry part of the weight due to the static friction between grains with themselves and those with the silo's walls. We vary the friction coefficient, the radii dispersity, the silo width, and the size of grains. We find that the Janssen's model becomes less relevant as the the silo width increases since the behavior of the stresses becomes more hydrostatic. Likewise, we get the normal and tangential stress distribution on the walls evidencing the existence of points of maximum stress. We also obtained the stress matrix with which we observe zones of concentration of load, located always at a height around two thirds of the granular columns. Finally, we observe that the size of the grains affects the distribution of stresses, increasing the weight on the bottom and reducing the normal stress on the walls, as the grains are made smaller (for the same total mass of the granulate), giving again a more hydrostatic and therefore less Janssen-type behavior for the weight of the column.
Asymptotics for Two-dimensional Atoms
DEFF Research Database (Denmark)
Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip
2012-01-01
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....
Seismic isolation of two dimensional periodic foundations
International Nuclear Information System (INIS)
Yan, Y.; Mo, Y. L.; Laskar, A.; Cheng, Z.; Shi, Z.; Menq, F.; Tang, Y.
2014-01-01
Phononic crystal is now used to control acoustic waves. When the crystal goes to a larger scale, it is called periodic structure. The band gaps of the periodic structure can be reduced to range from 0.5 Hz to 50 Hz. Therefore, the periodic structure has potential applications in seismic wave reflection. In civil engineering, the periodic structure can be served as the foundation of upper structure. This type of foundation consisting of periodic structure is called periodic foundation. When the frequency of seismic waves falls into the band gaps of the periodic foundation, the seismic wave can be blocked. Field experiments of a scaled two dimensional (2D) periodic foundation with an upper structure were conducted to verify the band gap effects. Test results showed the 2D periodic foundation can effectively reduce the response of the upper structure for excitations with frequencies within the frequency band gaps. When the experimental and the finite element analysis results are compared, they agree well with each other, indicating that 2D periodic foundation is a feasible way of reducing seismic vibrations.
Two-dimensional topological photonic systems
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng
2017-09-01
The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.
Radiation effects on two-dimensional materials
Energy Technology Data Exchange (ETDEWEB)
Walker, R.C. II; Robinson, J.A. [Department of Materials Science, Penn State, University Park, PA (United States); Center for Two-Dimensional Layered Materials, Penn State, University Park, PA (United States); Shi, T. [Department of Mechanical and Nuclear Engineering, Penn State, University Park, PA (United States); Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States); Silva, E.C. [GlobalFoundries, Malta, NY (United States); Jovanovic, I. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States)
2016-12-15
The effects of electromagnetic and particle irradiation on two-dimensional materials (2DMs) are discussed in this review. Radiation creates defects that impact the structure and electronic performance of materials. Determining the impact of these defects is important for developing 2DM-based devices for use in high-radiation environments, such as space or nuclear reactors. As such, most experimental studies have been focused on determining total ionizing dose damage to 2DMs and devices. Total dose experiments using X-rays, gamma rays, electrons, protons, and heavy ions are summarized in this review. We briefly discuss the possibility of investigating single event effects in 2DMs based on initial ion beam irradiation experiments and the development of 2DM-based integrated circuits. Additionally, beneficial uses of irradiation such as ion implantation to dope materials or electron-beam and helium-beam etching to shape materials have begun to be used on 2DMs and are reviewed as well. For non-ionizing radiation, such as low-energy photons, we review the literature on 2DM-based photo-detection from terahertz to UV. The majority of photo-detecting devices operate in the visible and UV range, and for this reason they are the focus of this review. However, we review the progress in developing 2DMs for detecting infrared and terahertz radiation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Buckled two-dimensional Xene sheets.
Molle, Alessandro; Goldberger, Joshua; Houssa, Michel; Xu, Yong; Zhang, Shou-Cheng; Akinwande, Deji
2017-02-01
Silicene, germanene and stanene are part of a monoelemental class of two-dimensional (2D) crystals termed 2D-Xenes (X = Si, Ge, Sn and so on) which, together with their ligand-functionalized derivatives referred to as Xanes, are comprised of group IVA atoms arranged in a honeycomb lattice - similar to graphene but with varying degrees of buckling. Their electronic structure ranges from trivial insulators, to semiconductors with tunable gaps, to semi-metallic, depending on the substrate, chemical functionalization and strain. More than a dozen different topological insulator states are predicted to emerge, including the quantum spin Hall state at room temperature, which, if realized, would enable new classes of nanoelectronic and spintronic devices, such as the topological field-effect transistor. The electronic structure can be tuned, for example, by changing the group IVA element, the degree of spin-orbit coupling, the functionalization chemistry or the substrate, making the 2D-Xene systems promising multifunctional 2D materials for nanotechnology. This Perspective highlights the current state of the art and future opportunities in the manipulation and stability of these materials, their functions and applications, and novel device concepts.
Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems
Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya
2015-04-01
Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.
Two dimensional conformal supergravity and critical behavior
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Zadra, A.
1988-01-01
A recent construction of Z-D gravity is generalized to the supersymmetric case. Anomalous dimensions are found. A super Kac-Moody SL (Z,R) algebra is obtained as a starting point using the anomaly equation for the graviton/gravitino system. (authors) [pt
Two-dimensional model of coupled heat and moisture transport in frost-heaving soils
International Nuclear Information System (INIS)
Guymon, G.L.; Berg, R.L.; Hromadka, T.V.
1984-01-01
A two-dimensional model of coupled heat and moisture flow in frost-heaving soils is developed based upon well known equations of heat and moisture flow in soils. Numerical solution is by the nodal domain integration method which includes the integrated finite difference and the Galerkin finite element methods. Solution of the phase change process is approximated by an isothermal approach and phenomenological equations are assumed for processes occurring in freezing or thawing zones. The model has been verified against experimental one-dimensional freezing soil column data and experimental two-dimensional soil thawing tank data as well as two-dimensional soil seepage data. The model has been applied to several simple but useful field problems such as roadway embankment freezing and frost heaving
Two-dimensional vibrational-electronic spectroscopy
Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira
2015-10-01
Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([FeIII(CN)6]3- dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5FeIICNRuIII(NH3)5]- dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.
Two-dimensional silica opens new perspectives
Büchner, Christin; Heyde, Markus
2017-12-01
In recent years, silica films have emerged as a novel class of two-dimensional (2D) materials. Several groups succeeded in epitaxial growth of ultrathin SiO2 layers using different growth methods and various substrates. The structures consist of tetrahedral [SiO4] building blocks in two mirror symmetrical planes, connected via oxygen bridges. This arrangement is called a silica bilayer as it is the thinnest 2D arrangement with the stoichiometry SiO2 known today. With all bonds saturated within the nano-sheet, the interaction with the substrate is based on van der Waals forces. Complex ring networks are observed, including hexagonal honeycomb lattices, point defects and domain boundaries, as well as amorphous domains. The network structures are highly tuneable through variation of the substrate, deposition parameters, cooling procedure, introducing dopants or intercalating small species. The amorphous networks and structural defects were resolved with atomic resolution microscopy and modeled with density functional theory and molecular dynamics. Such data contribute to our understanding of the formation and characteristic motifs of glassy systems. Growth studies and doping with other chemical elements reveal ways to tune ring sizes and defects as well as chemical reactivities. The pristine films have been utilized as molecular sieves and for confining molecules in nanocatalysis. Post growth hydroxylation can be used to tweak the reactivity as well. The electronic properties of silica bilayers are favourable for using silica as insulators in 2D material stacks. Due to the fully saturated atomic structure, the bilayer interacts weakly with the substrate and can be described as quasi-freestanding. Recently, a mm-scale film transfer under structure retention has been demonstrated. The chemical and mechanical stability of silica bilayers is very promising for technological applications in 2D heterostacks. Due to the impact of this bilayer system for glass science
Two-dimensional vibrational-electronic spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira, E-mail: mkhalil@uw.edu [Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195 (United States)
2015-10-21
Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (ν{sub CN}) and either a ligand-to-metal charge transfer transition ([Fe{sup III}(CN){sub 6}]{sup 3−} dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN){sub 5}Fe{sup II}CNRu{sup III}(NH{sub 3}){sub 5}]{sup −} dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific ν{sub CN} modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a
A two-dimensional mathematical model of percutaneous drug absorption
Directory of Open Access Journals (Sweden)
Kubota K
2004-06-01
Full Text Available Abstract Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1 the flow rate of the drug, (2 the flux and the cumulative amount of drug eliminated into the receptor cell, (3 the steady-state value of the flux, (4 the time to reach the steady
Directory of Open Access Journals (Sweden)
Carlos A Bustamante Chaverra
2013-03-01
are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation diﬀerential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is veriﬁed by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme.
Stationary states of the two-dimensional nonlinear Schrödinger model with disorder
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth
1998-01-01
Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder...
Eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide
International Nuclear Information System (INIS)
Derguzov, V.I.
1986-01-01
One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide. One gives a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product. One defines the concept of the genus of the multipliers of a Hamiltonian equation, corresponding to the continuous spectrum of the optical waveguide
Quantum mechanical treatment of a constrained particle on two dimensional sphere
Energy Technology Data Exchange (ETDEWEB)
Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com; Panahi, H., E-mail: t-panahi@guilan.ac.ir
2016-12-15
In this work, we study the motion of a particle on two dimensional sphere. By writing the Schrodinger equation, we obtain the wave function and energy spectra for three dimensional harmonic oscillator potential plus trigonometric Rosen–Morse non-central potential. By letting three special cases for intertwining operator, we investigate the energy spectra and wave functions for Smorodinsky–Winternitz potential model.
Self-focusing instability of two-dimensional solitons and vortices
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Juul Rasmussen, J.
1995-01-01
The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl...
Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model
DEFF Research Database (Denmark)
Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth
2001-01-01
Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may...
Two-dimensional quantum electrodynamics as a model in the constructive quantum field theory
International Nuclear Information System (INIS)
Ito, K.R.
1976-01-01
We investigate two-dimensional quantum electrodynamics((QED) 2 ) type models on the basis of the Hamiltonian formalism of a vector field. The transformation into a sine-Gordon equation is clarified as a generalized mass-shift transformation through canonical linear transformations. (auth.)
International Nuclear Information System (INIS)
Shtromberger, N.L.
1989-01-01
To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs
LLUVIA-II: A program for two-dimensional, transient flow through partially saturated porous media
International Nuclear Information System (INIS)
Eaton, R.R.; Hopkins, P.L.
1992-08-01
LLUVIA-II is a program designed for the efficient solution of two- dimensional transient flow of liquid water through partially saturated, porous media. The code solves Richards equation using the method-of-lines procedure. This document describes the solution procedure employed, input data structure, output, and code verification
Particle simulation of a two-dimensional electrostatic plasma
International Nuclear Information System (INIS)
Patel, K.
1989-01-01
Computer simulation is a growing field of research and plasma physics is one of the important areas where it is being applied today. This report describes the particle method of simulating a two-dimensional electrostatic plasma. The methods used to discretise the plasma equations and integrate the equations of motion are outlined. The algorithm used in building a simulation program is described. The program is applied to simulating the Two-stream Instability occurring within an infinite plasma. The results of the simulation are presented. The growth rate of the instability as simulated is in excellent agreement with the growth rate as calculated using linear theory. Diagnostic techniques used in interpreting the data generated by the simulation program are discussed. A comparison of the computing environment of the ND and PC from a user's viewpoint is presented. It is observed that the PC is an acceptable computing tool for certain (non-trivial) physics problems, and that more extensive use of its computing power should be made. (author). 5 figs
TUTANK a two-dimensional neutron kinetics code
International Nuclear Information System (INIS)
Watts, M.G.; Halsall, M.J.; Fayers, F.J.
1975-04-01
TUTANK is a two-dimensional neutron kinetics code which treats two neutron energy groups and up to six groups of delayed neutron precursors. A 'theta differencing' method is used to integrate the time dependence of the equations. A position dependent exponential transformation on the time variable is available as an option, which in many circumstances can remove much of the time dependence, and thereby allow longer time steps to be taken. A further manipulation is made to separate the solutions of the neutron fluxes and the precursor concentrations. The spatial equations are based on standard diffusion theory, and their solution is obtained from alternating direction sweeps with a transverse buckling - the so-called ADI-B 2 method. Other features of the code include an elementary temperature feedback and heat removal treatment, automatic time step adjustment, a flexible method of specifying cross-section and heat transfer coefficient variations during a transient, and a restart facility which requires a minimal data specification. Full details of the code input are given. An example of the solution of a NEACRP benchmark for an LWR control rod withdrawal is given. (author)
Exactly integrable two-dimensional dynamical systems related with supersymmetric algebras
International Nuclear Information System (INIS)
Leznov, A.N.
1983-01-01
A wide class of exactly integrable dynamical systems in two-dimensional space related with superalgebras, which generalize supersymmetric Liouville equation, is constructed. The equations can be interpretated as nonlinearly interacting Bose and Fermi fields belonging within classical limit to even and odd parts of the Grassman space. Explicit expressions for the solutions of the constructed systems are obtained on the basis of standard perturbation theory
Two dimensional layered materials: First-principle investigation
Tang, Youjian
Two-dimensional layered materials have emerged as a fascinating research area due to their unique physical and chemical properties, which differ from those of their bulk counterparts. Some of these unique properties are due to carriers and transport being confined to 2 dimensions, some are due to lattice symmetry, and some arise from their large surface area, gateability, stackability, high mobility, spin transport, or optical accessibility. How to modify the electronic and magnetic properties of two-dimensional layered materials for desirable long-term applications or fundamental physics is the main focus of this thesis. We explored the methods of adsorption, intercalation, and doping as ways to modify two-dimensional layered materials, using density functional theory as the main computational methodology. Chapter 1 gives a brief review of density functional theory. Due to the difficulty of solving the many-particle Schrodinger equation, density functional theory was developed to find the ground-state properties of many-electron systems through an examination of their charge density, rather than their wavefunction. This method has great application throughout the chemical and material sciences, such as modeling nano-scale systems, analyzing electronic, mechanical, thermal, optical and magnetic properties, and predicting reaction mechanisms. Graphene and transition metal dichalcogenides are arguably the two most important two-dimensional layered materials in terms of the scope and interest of their physical properties. Thus they are the main focus of this thesis. In chapter 2, the structure and electronic properties of graphene and transition metal dichalcogenides are described. Alkali adsorption onto the surface of bulk graphite and metal intecalation into transition metal dichalcogenides -- two methods of modifying properties through the introduction of metallic atoms into layered systems -- are described in chapter 2. Chapter 3 presents a new method of tuning
Two dimensional MHD flows between porous boundaries
International Nuclear Information System (INIS)
Gratton, F.T.
1994-01-01
Similarity solutions of dissipative MHD equations representing conducting fluids injected through porous walls and flowing out in both directions from the center of the channel, are studied as a function of four non dimensional parameters, Reynolds number R e , magnetic Reynolds number R m , Alfvenic Mach number, M A , and pressure gradient coefficient, C. The effluence is restrained by an external magnetic field normal to the walls. When R m m >>1, the solution may model a collision of plasmas of astrophysical interest. In this case the magnetic field lines help to drive the outflow acting jointly with the pressure gradient. The law for C as a function of the other parameters is given for several asymptotic limits. (author). 3 refs, 6 figs
Geodesics on a hot plate: an example of a two-dimensional curved space
International Nuclear Information System (INIS)
Erkal, Cahit
2006-01-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion
Geodesics on a hot plate: an example of a two-dimensional curved space
Energy Technology Data Exchange (ETDEWEB)
Erkal, Cahit [Department of Geology, Geography, and Physics, University of Tennessee, Martin, TN 38238 (United States)
2006-07-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion.
Theory and application of the RAZOR two-dimensional continuous energy lattice physics code
International Nuclear Information System (INIS)
Zerkle, M.L.; Abu-Shumays, I.K.; Ott, M.W.; Winwood, J.P.
1997-01-01
The theory and application of the RAZOR two-dimensional, continuous energy lattice physics code are discussed. RAZOR solves the continuous energy neutron transport equation in one- and two-dimensional geometries, and calculates equivalent few-group diffusion theory constants that rigorously account for spatial and spectral self-shielding effects. A dual energy resolution slowing down algorithm is used to reduce computer memory and disk storage requirements for the slowing down calculation. Results are presented for a 2D BWR pin cell depletion benchmark problem
Two-dimensional theory of ionization waves in the contracted discharge of noble gases
International Nuclear Information System (INIS)
Golubovskij, Ju.B.; Kolobov, V.I.; Tsendin, L.D.
1985-01-01
The mechanism of instability generating ionization waves in contracted neon and argon discharges is connected to its two-dimensional structure. The two-dimensional perturbations of sausage-type may have the most increment. The numerical solution of the ambipolar diffusion equation and qualitative asymptotic solutions showed that the situation differs greatly from diffuse discharges at low pressure, where the waves of large wave number are instable. In the case discussed, there is a wave number interval of unstable waves. (D.Gy.)
Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)
Fan, Mark S.; Christou, Aris; Pecht, Michael G.
1992-01-01
Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.
Two-dimensional effects in the problem of tearing modes control by electron cyclotron current drive
International Nuclear Information System (INIS)
Comisso, L.; Lazzaro, E.
2010-01-01
The design of means to counteract robustly the classical and neoclassical tearing modes in a tokamak by localized injection of an external control current requires an ever growing understanding of the physical process, beyond the Rutherford-type zero-dimensional models. Here a set of extended magnetohydrodynamic nonlinear equations for four continuum fields is used to investigate the two-dimensional effects in the response of the reconnecting modes to specific inputs of the localized external current. New information is gained on the space- and time-dependent effects of the external action on the two-dimensional structure of magnetic islands, which is very important to formulate applicable control strategies.
On wave breaking for Boussinesq-type models
Kazolea, M.; Ricchiuto, M.
2018-03-01
We consider the issue of wave breaking closure for Boussinesq type models, and attempt at providing some more understanding of the sensitivity of some closure approaches to the numerical set-up, and in particular to mesh size. For relatively classical choices of weakly dispersive propagation models, we compare two closure strategies. The first is the hybrid method consisting in suppressing the dispersive terms in breaking regions, as initially suggested by Tonelli and Petti in 2009. The second is an eddy viscosity approach based on the solution of a a turbulent kinetic energy. The formulation follows early work by O. Nwogu in the 90's, and some more recent developments by Zhang and co-workers (Ocean Mod. 2014), adapting it to be consistent with the wave breaking detection used here. We perform a study of the behaviour of the two closures for different mesh sizes, with attention to the possibility of obtaining grid independent results. Based on a classical shallow water theory, we also suggest some monitors to quantify the different contributions to the dissipation mechanism, differentiating those associated to the scheme from those of the partial differential equation. These quantities are used to analyze the dynamics of dissipation in some classical benchmarks, and its dependence on the mesh size. Our main results show that numerical dissipation contributes very little to the the results obtained when using eddy viscosity method. This closure shows little sensitivity to the grid, and may lend itself to the development and use of non-dissipative/energy conserving numerical methods. The opposite is observed for the hybrid approach, for which numerical dissipation plays a key role, and unfortunately is sensitive to the size of the mesh. In particular, when working, the two approaches investigated provide results which are in the same ball range and which agree with what is usually reported in literature. With the hybrid method, however, the inception of instabilities
Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity
Czech Academy of Sciences Publication Activity Database
Consiglieri, L.; Nečasová, Šárka; Sokolowski, J.
2009-01-01
Roč. 38, č. 4 (2009), s. 1193-1215 ISSN 0324-8569 R&D Projects: GA ČR GA201/05/0005; GA ČR GA201/08/0012 Institutional research plan: CEZ:AV0Z10190503 Keywords : Maxwell-Boussinesq approximation Subject RIV: BA - General Mathematics Impact factor: 0.378, year: 2009
Variational Boussinesq model for simulation of coastal waves and tsunamis
Adytia, D.; Adytia, Didit; van Groesen, Embrecht W.C.; Tan, Soon Keat; Huang, Zhenhua
2009-01-01
In this paper we describe the basic ideas of a so-called Variational Boussinesq Model which is based on the Hamiltonian structure of gravity surface waves. By using a rather simple approach to prescribe the profile of vertical fluid potential in the expression for the kinetic energy, we obtain a set
Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy
Directory of Open Access Journals (Sweden)
Xiuzhi Xing
2014-01-01
Full Text Available Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.
Variational Boussinesq model for strongly nonlinear dispersive waves
Lawrence, C.; Adytia, D.; van Groesen, E.
2018-01-01
For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be
Beginning Introductory Physics with Two-Dimensional Motion
Huggins, Elisha
2009-01-01
During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…
Two-dimensional black holes and non-commutative spaces
International Nuclear Information System (INIS)
Sadeghi, J.
2008-01-01
We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon
Solution of the two-dimensional spectral factorization problem
Lawton, W. M.
1985-01-01
An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.
Two-dimensional Navier-Stokes turbulence in bounded domains
Clercx, H.J.H.; van Heijst, G.J.F.
In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the
Two-dimensional Navier-Stokes turbulence in bounded domains
Clercx, H.J.H.; Heijst, van G.J.F.
2009-01-01
In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the
Two Dimensional Heat Transfer around Penetrations in Multilayer Insulation
Johnson, Wesley L.; Kelly, Andrew O.; Jumper, Kevin M.
2012-01-01
The objective of this task was to quantify thermal losses involving integrating MLI into real life situations. Testing specifically focused on the effects of penetrations (including structural attachments, electrical conduit/feedthroughs, and fluid lines) through MLI. While there have been attempts at quantifying these losses both analytically and experimentally, none have included a thorough investigation of the methods and materials that could be used in such applications. To attempt to quantify the excess heat load coming into the system due to the integration losses, a calorimeter was designed to study two dimensional heat transfer through penetrated MLI. The test matrix was designed to take as many variables into account as was possible with the limited test duration and system size. The parameters varied were the attachment mechanism, the buffer material (for buffer attachment mechanisms only), the thickness of the buffer, and the penetration material. The work done under this task is an attempt to measure the parasitic heat loads and affected insulation areas produced by system integration, to model the parasitic loads, and from the model produce engineering equations to allow for the determination of parasitic heat loads in future applications. The methods of integration investigated were no integration, using a buffer to thermally isolate the strut from the MLI, and temperature matching the MLI on the strut. Several materials were investigated as a buffer material including aerogel blankets, aerogel bead packages, cryolite, and even an evacuated vacuum space (in essence a no buffer condition).
Stochastic aspects of two-dimensional vibration diagnostics
International Nuclear Information System (INIS)
Pazsit, I.; Antonopoulos-Domis, M.; Gloeckler, O.
1985-01-01
The aim of this paper is to investigate the stochastic features of two-dimensional lateral damped oscillations of PWR core internals, that are induced by random force components. It is also investigated how these vibrating components, or the forces giving rise to the vibrations could be diagnosed through the analysis of displacement or neutron noise signals. The approach pursued here is to select a realisation of the random force components, then the equations of the motion are integrated and the time history of displacement components is obtained. From here various statistical descriptors of the motion, such as trajectory pattern, spectra and PDF functions, etc. can be calculated. It was investigated how these statistical descriptors depend on the characteristics of the driving force for both stationary and non-stationary cases. A conclusion of possible diagnostical relevance is that, under certain circumstances, the PDF functions could be an indicator of whether a particular peak in the corresponding power spectra belongs to a resonance in system transfer or rather a resonance in the external driving force. (author)
Turbulence Statistics in a Two-Dimensional Vortex Condensate
Frishman, Anna; Herbert, Corentin
2018-05-01
Disentangling the evolution of a coherent mean-flow and turbulent fluctuations, interacting through the nonlinearity of the Navier-Stokes equations, is a central issue in fluid mechanics. It affects a wide range of flows, such as planetary atmospheres, plasmas, or wall-bounded flows, and hampers turbulence models. We consider the special case of a two-dimensional flow in a periodic box, for which the mean flow, a pair of box-size vortices called "condensate," emerges from turbulence. As was recently shown, a perturbative closure describes correctly the condensate when turbulence is excited at small scales. In this context, we obtain explicit results for the statistics of turbulence, encoded in the Reynolds stress tensor. We demonstrate that the two components of the Reynolds stress, the momentum flux and the turbulent energy, are determined by different mechanisms. It was suggested previously that the momentum flux is fixed by a balance between forcing and mean-flow advection: using unprecedently long numerical simulations, we provide the first direct evidence supporting this prediction. By contrast, combining analytical computations with numerical simulations, we show that the turbulent energy is determined only by mean-flow advection and obtain for the first time a formula describing its profile in the vortex.
Fluctuations and symmetries in two-dimensional active gels.
Sarkar, N; Basu, A
2011-04-01
Motivated by the unique physical properties of biological active matter, e.g., cytoskeletal dynamics in eukaryotic cells, we set up effective two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin active gels with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions (K. Kruse et al., Eur. Phys. J. E 16, 5 (2005); A. Basu et al., Eur. Phys. J. E 27, 149 (2008)) for thin active-gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the activity or nonequilibrium drive.
Finite-size scaling in two-dimensional superfluids
International Nuclear Information System (INIS)
Schultka, N.; Manousakis, E.
1994-01-01
Using the x-y model and a nonlocal updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two-dimensional superfluid on large-size square lattices LxL up to 400x400. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of L values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization-group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson renormalization group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments
Two-dimensional modeling of conduction-mode laser welding
International Nuclear Information System (INIS)
Russo, A.J.
1984-01-01
WELD2D is a two-dimensional finite difference computer program suitable for modeling the conduction-mode welding process when the molten weld pool motion can be neglected. The code is currently structured to treat butt-welded geometries in a plane normal to the beam motion so that dissimilar materials may be considered. The surface heat transfer models used in the code include a Gaussian beam or uniform laser source, and a free electron theory reflectance calculation. Temperature-dependent material parameters are used in the reflectance calculation. Measured cold reflection data are used to include surface roughness or oxide effects until melt occurs, after which the surface is assumed to be smooth and clean. Blackbody reradiation and a simple natural convection model are also included in the upper surface boundary condition. Either an implicit or explicit finite-difference representation of the heat conduction equation in an enthalpy form is solved at each time step. This enables phase transition energies to be easily and accurately incorporated into the formulation. Temperature-dependent 9second-order polynominal dependence) thermal conductivities are used in the conduction calculations. Constant values of specific heat are used for each material phase. At present, material properties for six metals are included in the code. These are: aluminium, nickel, steel, molybdenum, copper and silicon
Matrix method for two-dimensional waveguide mode solution
Sun, Baoguang; Cai, Congzhong; Venkatesh, Balajee Seshasayee
2018-05-01
In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a 'folded' plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.
Two dimensional magnetic field calculations for the SSC dipole magnets
International Nuclear Information System (INIS)
Krefta, M.P.; Pavlik, D.
1991-01-01
In this work two-dimensional methods are used to calculate the magnetic fields throughout the cross section of a SSC dipole magnet. Analytic techniques, which are based on closed form solutions to the defining field equations, are used to calculate the multipole content for any specified conductor positioning. The method is extended to investigate the effects of radial slots or keyways in the iron yoke. The multipole components of field, directly attributable to the slots or keyways, are examined as a function of size and location. It is shown that locating the slots or keyways at the magnet pole centers has a large effect on the multipole components; whereas, locating the keyways between the magnet poles has little effect on any of the multipoles. The investigation of nonlinear effects such as ferromagnetic saturation or superconductor magnetization relies on the use of numerical methods such as the finite element method. The errors associated with these codes are explained in terms of numerical round-off, spatial discretization error and the representation of distant boundaries. A method for increasing the accuracy of the multipole calculation from finite element solutions is set forth. It is shown that calculated multipole coefficients are sensitive to boundary conditions external to the cold mass during conditions of magnetic saturation
Stochastic aspects of two-dimensional vibration diagnostics
International Nuclear Information System (INIS)
Pazsit, I.; Antonopoulos-Domis, M.; Glockler, O.
1984-01-01
The aim of this paper is to investigate the stochastic features of two-dimensional lateral damped oscillations of PWR core internals that are induced by random force components. It is also investigated how these vibrating components, or the forces giving rise to the vibrations, could be diagnosed through the analysis of displacement or neutron noise signals. The approach pursued here is to select a realisation of the random force components, then the equations of the motion are integrated and the time history of displacement components is obtained. From here various statistical descriptors of the motion, such as trajectory pattern, spectra and PDF functions etc., can be calculated. It was investigated how these statistical descriptors depend on the characteristics of the driving force for both stationary and non-stationary cases. A conclusion of possible diagnostical relevance is that, under certain circumstances, the PDF functions could be an indicator of whether a particular peak in the corresponding power spectra belongs to a resonance in system transfer or rather a resonance in the external driving force
Stochastic aspects of two-dimensional vibration diagnostics
International Nuclear Information System (INIS)
Pazsit, I.; Gloeckler, O.
1984-01-01
The aim of this paper is to investigate the stochastic features of two-dimensional lateral damped oscillations of PWR core internals that are induced by random force components. It is also investigated how these vibrating components, or the forces giving rise to the vibrations, could be diagnosed through the analysis of displacement or neutron noise signals. The approach pursued here is to select a realisation of the random force components, then the equations of the motion ar integrated and the time history of displacement components is obtained. From here various statistical descriptors of the motion, such as trajectory pattern, spectra and PDF functions etc., can be calculated. It was investigated how these statistical descriptors depend on the characteristics of the driving force for both stationary and non-stationary cases. A conclusion of possible diagnostical relevance is that, under certain circumstances, the PDF functions could be an indicator of whether a particular peak in the corresponding power spectra belongs to a resonance in system transfer or rather a resonance in the external driving force. (author)
Almost two-dimensional treatment of drift wave turbulence
International Nuclear Information System (INIS)
Albert, J.M.; Similon, P.L.; Sudan, R.N.
1990-01-01
The approximation of two-dimensionality is studied and extended for electrostatic drift wave turbulence in a three-dimensional, magnetized plasma. It is argued on the basis of the direct interaction approximation that in the absence of parallel viscosity, purely 2-D solutions exist for which only modes with k parallel =0 are excited, but that the 2-D spectrum is unstable to perturbations at nonzero k parallel . A 1-D equation for the parallel profile g k perpendicular (k parallel ) of the saturated spectrum at steady state is derived and solved, allowing for parallel viscosity; the spectrum has finite width in k parallel , and hence finite parallel correlation length, as a result of nonlinear coupling. The enhanced energy dissipation rate, a 3-D effect, may be incorporated in the 2-D approximation by a suitable renormalization of the linear dissipation term. An algorithm is presented that reduces the 3-D problem to coupled 1- and 2-D problems. Numerical results from a 2-D spectral direct simulation, thus modified, are compared with the results from the corresponding 3-D (unmodified) simulation for a specific model of drift wave excitation. Damping at high k parallel is included. It is verified that the 1-D solution for g k perpendicular (k parallel ) accurately describes the shape and width of the 3-D spectrum, and that the modified 2-D simulation gives a good estimate of the 3-D energy saturation level and distribution E(k perpendicular )
Schimming, C. D.; Durian, D. J.
2017-09-01
For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called "border-blocking" models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux; however, this approximation dramatically fails in the wet or unjamming limit where the bubbles become close-packed spheres and coarsening proceeds even though there are no films. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We compute that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling by numerical solution of the diffusion equation. We similarly consider transport across inflated vertices and surface Plateau borders in quasi-two-dimensional foams. And we show how the d A /d t =K0(n -6 ) von Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scales. Finally, we use the modified von Neumann law to compute the growth rate of the average bubble area, which is not constant.
Two-dimensional topological field theories coupled to four-dimensional BF theory
International Nuclear Information System (INIS)
Montesinos, Merced; Perez, Alejandro
2008-01-01
Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level
The design of visible system of two-dimensional numerical simulation of radon-222 migration
International Nuclear Information System (INIS)
Zhang Xiongjie; Zhang Ye; Zhang Junkui; Tang Bin
2008-01-01
On the grounds of the radon transport equation in the even overburden layer, the value simulation equation using the two-dimensional finite difference method had been inferred, and the visible system of value simulation was proposed by programming with VB and Matlab. The mixed programming and the method of using repetitive process to solve difference equation were narrated in detail. Through this paper, a practical tool was offered to the researcher studying on the radon migration in the even overburden layer, and a more convenient developing way was explored for the researchers developing the relative system. (authors)
Diffraction of a plane wave on two-dimensional conductive structures and a surface wave
Davidovich, Mikhael V.
2018-04-01
We consider the structures type of two-dimensional electron gas in the form of a thin conductive, in particular, graphene films described by tensor conductivity, which are isolated or located on the dielectric layers. The dispersion equation for hybrid modes, as well as scattering parameters. We show that free wave (eigenwaves) problem follow from the problem of diffraction when linking the amplitude of the current of the linear equations are unsolvable, i.e., the determinant of this system is zero. As a particular case the dispersion equation follow from the conditions of matching (with zero reflection coefficient).
Optimizing separations in online comprehensive two-dimensional liquid chromatography.
Pirok, Bob W J; Gargano, Andrea F G; Schoenmakers, Peter J
2018-01-01
Online comprehensive two-dimensional liquid chromatography has become an attractive option for the analysis of complex nonvolatile samples found in various fields (e.g. environmental studies, food, life, and polymer sciences). Two-dimensional liquid chromatography complements the highly popular hyphenated systems that combine liquid chromatography with mass spectrometry. Two-dimensional liquid chromatography is also applied to the analysis of samples that are not compatible with mass spectrometry (e.g. high-molecular-weight polymers), providing important information on the distribution of the sample components along chemical dimensions (molecular weight, charge, lipophilicity, stereochemistry, etc.). Also, in comparison with conventional one-dimensional liquid chromatography, two-dimensional liquid chromatography provides a greater separation power (peak capacity). Because of the additional selectivity and higher peak capacity, the combination of two-dimensional liquid chromatography with mass spectrometry allows for simpler mixtures of compounds to be introduced in the ion source at any given time, improving quantitative analysis by reducing matrix effects. In this review, we summarize the rationale and principles of two-dimensional liquid chromatography experiments, describe advantages and disadvantages of combining different selectivities and discuss strategies to improve the quality of two-dimensional liquid chromatography separations. © 2017 The Authors. Journal of Separation Science published by WILEY-VCH Verlag GmbH & Co. KGaA.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
2014-10-07
The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.
Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres
Directory of Open Access Journals (Sweden)
J. Javier Brey
2017-02-01
Full Text Available The dynamics of a system of hard spheres enclosed between two parallel plates separated a distance smaller than two particle diameters is described at the level of kinetic theory. The interest focuses on the behavior of the quasi-two-dimensional fluid seen when looking at the system from above or below. In the first part, a collisional model for the effective two-dimensional dynamics is analyzed. Although it is able to describe quite well the homogeneous evolution observed in the experiments, it is shown that it fails to predict the existence of non-equilibrium phase transitions, and in particular, the bimodal regime exhibited by the real system. A critical revision analysis of the model is presented , and as a starting point to get a more accurate description, the Boltzmann equation for the quasi-two-dimensional gas has been derived. In the elastic case, the solutions of the equation verify an H-theorem implying a monotonic tendency to a non-uniform steady state. As an example of application of the kinetic equation, here the evolution equations for the vertical and horizontal temperatures of the system are derived in the homogeneous approximation, and the results compared with molecular dynamics simulation results.
International Nuclear Information System (INIS)
Mahmoud, K.S.; Szatmary, Z.
2005-01-01
An iterative method was developed for the numerical solution of the coupled two-dimensional time dependent multigroup diffusion equation and delayed precursor equations. Both forward (Explicit) and backward (Implicit) schemes were used. The second scheme was found to be numerically stable, while the first scheme requires that Δt -10 sec. for stability. An example is given for the second method. (authors)
Functional inks and printing of two-dimensional materials.
Hu, Guohua; Kang, Joohoon; Ng, Leonard W T; Zhu, Xiaoxi; Howe, Richard C T; Jones, Christopher G; Hersam, Mark C; Hasan, Tawfique
2018-05-08
Graphene and related two-dimensional materials provide an ideal platform for next generation disruptive technologies and applications. Exploiting these solution-processed two-dimensional materials in printing can accelerate this development by allowing additive patterning on both rigid and conformable substrates for flexible device design and large-scale, high-speed, cost-effective manufacturing. In this review, we summarise the current progress on ink formulation of two-dimensional materials and the printable applications enabled by them. We also present our perspectives on their research and technological future prospects.
Third sound in one and two dimensional modulated structures
International Nuclear Information System (INIS)
Komuro, T.; Kawashima, H., Shirahama, K.; Kono, K.
1996-01-01
An experimental technique is developed to study acoustic transmission in one and two dimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a two dimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimension. Nevertheless, the authors find that the transmission spectrum in the Penrose lattice, which is a two dimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained in terms of dynamical theory of diffraction
ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Directory of Open Access Journals (Sweden)
Nikola Stefanović
2007-06-01
Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.
Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations
International Nuclear Information System (INIS)
Agim, Y.Z.
1989-08-01
A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasi-linear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10 -10
Energy Spectra of Vortex Distributions in Two-Dimensional Quantum Turbulence
Directory of Open Access Journals (Sweden)
Ashton S. Bradley
2012-10-01
Full Text Available We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length ξ. We show that, for the divergence-free portion of the superfluid velocity field, the kinetic-energy spectrum over wave number k may be decomposed into an ultraviolet regime (k≫ξ^{-1} having a universal k^{-3} scaling arising from the vortex core structure, and an infrared regime (k≪ξ^{-1} with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent -1/3 for vortices of the same sign of circulation leads to an infrared kinetic-energy spectrum with a Kolmogorov k^{-5/3} power law, which is consistent with the existence of an inertial range. The presence of these k^{-3} and k^{-5/3} power laws, together with the constraint of continuity at the smallest configurational scale k≈ξ^{-1}, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous, compressible, two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic-energy distribution, once we introduce the concept of a clustered fraction consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.
A two-dimensional analytical model of laminar flame in lycopodium dust particles
Energy Technology Data Exchange (ETDEWEB)
Rahbari, Alireza [Shahid Rajaee Teacher Training University, Tehran (Iran, Islamic Republic of); Shakibi, Ashkan [Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Bidabadi, Mehdi [Combustion Research Laboratory, Narmak, Tehran (Iran, Islamic Republic of)
2015-09-15
A two-dimensional analytical model is presented to determine the flame speed and temperature distribution of micro-sized lycopodium dust particles. This model is based on the assumptions that the particle burning rate in the flame front is controlled by the process of oxygen diffusion and the flame structure consists of preheat, reaction and post flame zones. In the first step, the energy conservation equations for fuel-lean condition are expressed in two dimensions, and then these differential equations are solved using the required boundary condition and matching the temperature and heat flux at the interfacial boundaries. Consequently, the obtained flame temperature and flame speed distributions in terms of different particle diameters and equivalence ratio for lean mixture are compared with the corresponding experimental data for lycopodium dust particles. Consequently, it is shown that this two-dimensional model demonstrates better agreement with the experimental results compared to the previous models.
Kinetics of two-dimensional electron plasma, interacting with fluctuating potential
International Nuclear Information System (INIS)
Boiko, I.I.; Sirenko, Y.M.
1990-01-01
In this paper, from the first principles, after the fashion of Klimontovich, the authors derive quantum kinetic equation for electron gas, inhomogeneous in z-direction and homogeneous in XY-plane. Special attention is given to the systems with quasi-two-dimensional electron gas (2 DEG), which are widely explored now. Both interaction between the particles of 2 DEG (in general, of several sorts), and interaction with an external system (phonons, impurities, after change carries etc.) are considered. General theory is used to obtain energy and momentum balance equations and relaxation frequencies for 2 DEG in the basis of plane waves. The case of crossed electric and magnetic fields is also treated. As an illustration the problems of 2 DEG scattering on semibounded three-dimensional electron gas and on two-dimensional hole gas are considered; transverse conductivity of nondegenerate 2 DEG, scattered by impurities in ultraquantum magnetic field, is calculated
A two-dimensional analytical model of laminar flame in lycopodium dust particles
International Nuclear Information System (INIS)
Rahbari, Alireza; Shakibi, Ashkan; Bidabadi, Mehdi
2015-01-01
A two-dimensional analytical model is presented to determine the flame speed and temperature distribution of micro-sized lycopodium dust particles. This model is based on the assumptions that the particle burning rate in the flame front is controlled by the process of oxygen diffusion and the flame structure consists of preheat, reaction and post flame zones. In the first step, the energy conservation equations for fuel-lean condition are expressed in two dimensions, and then these differential equations are solved using the required boundary condition and matching the temperature and heat flux at the interfacial boundaries. Consequently, the obtained flame temperature and flame speed distributions in terms of different particle diameters and equivalence ratio for lean mixture are compared with the corresponding experimental data for lycopodium dust particles. Consequently, it is shown that this two-dimensional model demonstrates better agreement with the experimental results compared to the previous models.
Two-dimensional electronic femtosecond stimulated Raman spectroscopy
Directory of Open Access Journals (Sweden)
Ogilvie J.P.
2013-03-01
Full Text Available We report two-dimensional electronic spectroscopy with a femtosecond stimulated Raman scattering probe. The method reveals correlations between excitation energy and excited state vibrational structure following photoexcitation. We demonstrate the method in rhodamine 6G.
Micromachined two dimensional resistor arrays for determination of gas parameters
van Baar, J.J.J.; Verwey, Willem B.; Dijkstra, Mindert; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; Krijnen, Gijsbertus J.M.; Elwenspoek, Michael Curt
A resistive sensor array is presented for two dimensional temperature distribution measurements in a micromachined flow channel. This allows simultaneous measurement of flow velocity and fluid parameters, like thermal conductivity, diffusion coefficient and viscosity. More general advantages of
Generalized similarity method in unsteady two-dimensional MHD ...
African Journals Online (AJOL)
user
International Journal of Engineering, Science and Technology. Vol. 1, No. 1, 2009 ... temperature two-dimensional MHD laminar boundary layer of incompressible fluid. ...... Φ η is Blasius solution for stationary boundary layer on the plate,. ( ). 0.
Structures of two-dimensional three-body systems
International Nuclear Information System (INIS)
Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.
1996-01-01
Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)
Study on two-dimensional induced signal readout of MRPC
International Nuclear Information System (INIS)
Wu Yucheng; Yue Qian; Li Yuanjing; Ye Jin; Cheng Jianping; Wang Yi; Li Jin
2012-01-01
A kind of two-dimensional readout electrode structure for the induced signal readout of MRPC has been studied in both simulation and experiments. Several MRPC prototypes are produced and a series of test experiments have been done to compare with the result of simulation, in order to verify the simulation model. The experiment results are in good agreement with those of simulation. This method will be used to design the two-dimensional signal readout mode of MRPC in the future work.
Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers
2016-06-15
AFRL-AFOSR-JP-TR-2016-0071 Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers Cheolmin Park YONSEI UNIVERSITY...Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4054 5c. PROGRAM ELEMENT...prospects for a variety of emerging applications in a broad range of fields, such as electronics, energy conversion and storage, catalysis and polymer
Magnetoresistance of a two-dimensional electron gas in a random magnetic field
DEFF Research Database (Denmark)
Smith, Anders; Taboryski, Rafael Jozef; Hansen, Luise Theil
1994-01-01
We report magnetoresistance measurements on a two-dimensional electron gas made from a high-mobility GaAs/AlxGa1-xAs heterostructure, where the externally applied magnetic field was expelled from regions of the semiconductor by means of superconducting lead grains randomly distributed on the surf...... on the surface of the sample. A theoretical explanation in excellent agreement with the experiment is given within the framework of the semiclassical Boltzmann equation. © 1994 The American Physical Society...
Energy of N two-dimensional bosons with zero-range interactions
Bazak, B.; Petrov, D. S.
2018-02-01
We derive an integral equation describing N two-dimensional bosons with zero-range interactions and solve it for the ground state energy B N by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling B N ∝ 8.567 N predicted by Hammer and Son (2004 Phys. Rev. Lett. 93 250408) in the large-N limit.
Magnetic Field Effect on Ultrashort Two-dimensional Optical Pulse Propagation in Silicon Nanotubes
Konobeeva, N. N.; Evdokimov, R. A.; Belonenko, M. B.
2018-05-01
The paper deals with the magnetic field effect which provides a stable propagation of ultrashort pulses in silicon nanotubes from the viewpoint of their waveform. The equation is derived for the electromagnetic field observed in silicon nanotubes with a glance to the magnetic field for two-dimensional optical pulses. The analysis is given to the dependence between the waveform of ultrashort optical pulses and the magnetic flux passing through the cross-sectional area of the nanotube.
International Nuclear Information System (INIS)
Moura, A.R.; Pereira, A.R.; Moura-Melo, W.A.; Pires, A.S.T.
2008-01-01
We develop an effective theory to study the skyrmion dynamics in the presence of a hole (removed spins from the lattice) in Neel ordered two-dimensional antiferromagnets with arbitrary spin value S. The general equation of motion for the 'mass center' of this structure is obtained. The frequency of small amplitude oscillations of pinned skyrmions around the defect center is calculated. It is proportional to the hole size and inversely proportional to the square of the skyrmion size
International Nuclear Information System (INIS)
Hou Jingmin; Lu Qingqing
2009-01-01
We study the energy spectrum of ultracold fermionic atoms on the two-dimensional triangular optical lattice subjected to a perpendicular effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations and numerically solve them, then we obtain the Hofstadter's butterfly-like energy spectrum, which has a novel fractal structure. The observability of the Hofstadter's butterfly spectrum is also discussed
International Nuclear Information System (INIS)
Mori, N.; Kobayashi, K.
1996-01-01
A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)
The theory of critical phenomena in two-dimensional systems
International Nuclear Information System (INIS)
Olvera de la C, M.
1981-01-01
An exposition of the theory of critical phenomena in two-dimensional physical systems is presented. The first six chapters deal with the mean field theory of critical phenomena, scale invariance of the thermodynamic functions, Kadanoff's spin block construction, Wilson's renormalization group treatment of critical phenomena in configuration space, and the two-dimensional Ising model on a triangular lattice. The second part of this work is made of four chapters devoted to the application of the ideas expounded in the first part to the discussion of critical phenomena in superfluid films, two-dimensional crystals and the two-dimensional XY model of magnetic systems. Chapters seven to ten are devoted to the following subjects: analysis of long range order in one, two, and three-dimensional physical systems. Topological defects in the XY model, in superfluid films and in two-dimensional crystals. The Thouless-Kosterlitz iterated mean field theory of the dipole gas. The renormalization group treatment of the XY model, superfluid films and two-dimensional crystal. (author)
Two-dimensional multifractal cross-correlation analysis
International Nuclear Information System (INIS)
Xi, Caiping; Zhang, Shuning; Xiong, Gang; Zhao, Huichang; Yang, Yonghong
2017-01-01
Highlights: • We study the mathematical models of 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Present the definition of the two-dimensional N 2 -partitioned multiplicative cascading process. • Do the comparative analysis of 2D-MC by 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Provide a reference on the choice and parameter settings of these methods in practice. - Abstract: There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.
Two-Dimensional Materials for Sensing: Graphene and Beyond
Directory of Open Access Journals (Sweden)
Seba Sara Varghese
2015-09-01
Full Text Available Two-dimensional materials have attracted great scientific attention due to their unusual and fascinating properties for use in electronics, spintronics, photovoltaics, medicine, composites, etc. Graphene, transition metal dichalcogenides such as MoS2, phosphorene, etc., which belong to the family of two-dimensional materials, have shown great promise for gas sensing applications due to their high surface-to-volume ratio, low noise and sensitivity of electronic properties to the changes in the surroundings. Two-dimensional nanostructured semiconducting metal oxide based gas sensors have also been recognized as successful gas detection devices. This review aims to provide the latest advancements in the field of gas sensors based on various two-dimensional materials with the main focus on sensor performance metrics such as sensitivity, specificity, detection limit, response time, and reversibility. Both experimental and theoretical studies on the gas sensing properties of graphene and other two-dimensional materials beyond graphene are also discussed. The article concludes with the current challenges and future prospects for two-dimensional materials in gas sensor applications.
Earth's core convection: Boussinesq approximation or incompressible approach?
Czech Academy of Sciences Publication Activity Database
Anufriev, A. P.; Hejda, Pavel
2010-01-01
Roč. 104, č. 1 (2010), s. 65-83 ISSN 0309-1929 R&D Projects: GA AV ČR IAA300120704 Grant - others:INTAS(XE) 03-51-5807 Institutional research plan: CEZ:AV0Z30120515 Keywords : geodynamic models * core convection * Boussinesq approximation Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.831, year: 2010
International Nuclear Information System (INIS)
Maruno, Ken-ichi; Biondini, Gino
2004-01-01
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)
International Nuclear Information System (INIS)
Boukadida, T.
1988-01-01
The compatibility between accuracy and stability of the quasilinear equations is studied. Three stuations are analyzed: the discontinuous P-1 approximation of the first order quasilinear equation, the two dimensional version of the Lax-Friedrichs scheme and the coupling of modes in a plasma. For the one dimensional case, the proposed scheme matches the available data. In the two dimensional case, tests to show the explosion condition are performed. This investigation can be applied in laser-matter interactions, nonlinear optics and in many fields of physics [fr
Two-dimensional spatial structure of the dissipative trapped-electron mode
International Nuclear Information System (INIS)
Rewoldt, G.; Tang, W.M.; Frieman, E.A.
1976-09-01
This paper deals with the complete two-dimensional structure of the dissipative trapped-electron mode over its full width, which may extend over several mode-rational surfaces. The complete integro-differential equation is studied in the limit k/sub r/rho/sub i/ less than 1, where rho/sub i/ is the ion gyroradius, and k/sub r/, the radial wavenumber, is regarded as a differential operator. This is converted into a matrix equation which is then solved by standard numerical methods
Mixed finite element simulations in two-dimensional groundwater flow problems
International Nuclear Information System (INIS)
Kimura, Hideo
1989-01-01
A computer code of groundwater flow in two-dimensional porous media based on the mixed finite element method was developed for accurate approximations of Darcy velocities in safety evaluation of radioactive waste disposal. The mixed finite element procedure solves for both the Darcy velocities and pressure heads simultaneously in the Darcy equation and continuity equation. Numerical results of a single well pumping at a constant rate in a uniform flow field showed that the mixed finite element method gives more accurate Darcy velocities nearly 50 % on average error than standard finite element method. (author)
Traditional Semiconductors in the Two-Dimensional Limit.
Lucking, Michael C; Xie, Weiyu; Choe, Duk-Hyun; West, Damien; Lu, Toh-Ming; Zhang, S B
2018-02-23
Interest in two-dimensional materials has exploded in recent years. Not only are they studied due to their novel electronic properties, such as the emergent Dirac fermion in graphene, but also as a new paradigm in which stacking layers of distinct two-dimensional materials may enable different functionality or devices. Here, through first-principles theory, we reveal a large new class of two-dimensional materials which are derived from traditional III-V, II-VI, and I-VII semiconductors. It is found that in the ultrathin limit the great majority of traditional binary semiconductors studied (a series of 28 semiconductors) are not only kinetically stable in a two-dimensional double layer honeycomb structure, but more energetically stable than the truncated wurtzite or zinc-blende structures associated with three dimensional bulk. These findings both greatly increase the landscape of two-dimensional materials and also demonstrate that in the double layer honeycomb form, even ordinary semiconductors, such as GaAs, can exhibit exotic topological properties.
Two-dimensional analytic weighting functions for limb scattering
Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.
2017-10-01
Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.
Rogue waves in the multicomponent Mel'nikov system and multicomponent Schrödinger-Boussinesq system
Sun, Baonan; Lian, Zhan
2018-02-01
By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel'nikov equation and the multicomponent Schrödinger-Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel'nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constant background with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line rogue waves. Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger-Boussinesq system are generated.
Dynamical class of a two-dimensional plasmonic Dirac system.
Silva, Érica de Mello
2015-10-01
A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.
Velocity and Dispersion for a Two-Dimensional Random Walk
International Nuclear Information System (INIS)
Li Jinghui
2009-01-01
In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem. (general)
Rabinskiy, L. N.; Zhavoronok, S. I.
2018-04-01
The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is
Two-dimensional electron flow in pulsed power transmission lines and plasma opening switches
International Nuclear Information System (INIS)
Church, B.W.; Longcope, D.W.; Ng, C.K.; Sudan, R.N.
1991-01-01
The operation of magnetically insulated transmission lines (MITL) and the interruption of current in a plasma opening switch (POS) are determined by the physics of the electrons emitted by the cathode surface. A mathematical model describes the self-consistent two-dimensional flow of an electron fluid. A finite element code, FERUS, has been developed to solve the two equations which describe Poisson's and Ampere's law in two dimensions. The solutions from this code are obtained for parameters where the electron orbits are considerably modified by the self-magnetic field of the current. Next, the self-insulated electron flow in a MITL with a step change in cross-section is studied using a conventional two-dimensional fully electromagnetic particle-in-cell code, MASK. The equations governing two-dimensional quasi-static electron flow are solved numerically by a third technique which is suitable for predicting current interruption in a POS. The object of the study is to determine the critical load impedance, Z CL , required for current interruption for a given applied voltage, cathode voltage and plasma length. (author). 9 refs, 5 figs
Rezaei, M. P.; Zamanian, M.
2017-01-01
In this paper, the influences of nonideal boundary conditions (due to flexibility) on the primary resonant behavior of a piezoelectrically actuated microbeam have been studied, for the first time. The structure has been assumed to treat as an Euler-Bernoulli beam, considering the effects of geometric nonlinearity. In this work, the general nonideal supports have been modeled as a the combination of horizontal, vertical and rotational springs, simultaneously. Allocating particular values to the stiffness of these springs provides the mathematical models for the majority of boundary conditions. This consideration leads to use a two-dimensional analysis of the multiple scales method instead of previous works' method (one-dimensional analysis). If one neglects the nonideal effects, then this paper would be an effort to solve the two-dimensional equations of motion without a need of a combination of these equations using the shortening or stretching effect. Letting the nonideal effects equal to zero and comparing their results with the results of previous approaches have been demonstrated the accuracy of the two-dimensional solutions. The results have been identified the unique effects of constraining and stiffening of boundaries in horizontal, vertical and rotational directions. This means that it is inaccurate to suppose the nonideality of supports only in one or two of these directions like as previous works. The findings are of vital importance as a better prediction of the frequency response for the nonideal supports. Furthermore, the main findings of this effort can help to choose appropriate boundary conditions for desired systems.
Spin dynamics in a two-dimensional quantum gas
DEFF Research Database (Denmark)
Pedersen, Poul Lindholm; Gajdacz, Miroslav; Deuretzbacher, Frank
2014-01-01
We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimp......We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions...
Pair Interaction of Dislocations in Two-Dimensional Crystals
Eisenmann, C.; Gasser, U.; Keim, P.; Maret, G.; von Grünberg, H. H.
2005-10-01
The pair interaction between crystal dislocations is systematically explored by analyzing particle trajectories of two-dimensional colloidal crystals measured by video microscopy. The resulting pair energies are compared to Monte Carlo data and to predictions derived from the standard Hamiltonian of the elastic theory of dislocations. Good agreement is found with respect to the distance and temperature dependence of the interaction potential, but not regarding the angle dependence where discrete lattice effects become important. Our results on the whole confirm that the dislocation Hamiltonian allows a quantitative understanding of the formation and interaction energies of dislocations in two-dimensional crystals.
Two dimensional nonlinear spectral estimation techniques for breast cancer localization
International Nuclear Information System (INIS)
Stathaki, P.T.; Constantinides, A.G.
1994-01-01
In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging
Densis. Densimetric representation of two-dimensional matrices
International Nuclear Information System (INIS)
Los Arcos Merino, J.M.
1978-01-01
Densis is a Fortran V program which allows off-line control of a Calcomp digital plotter, to represent a two-dimensional matrix of numerical elements in the form of a variable shading intensity map in two colours. Each matrix element is associated to a square of a grid which is traced over by lines whose number is a function of the element value according to a selected scale. Program features, subroutine structure and running instructions, are described. Some typical results, for gamma-gamma coincidence experimental data and a sampled two-dimensional function, are indicated. (author)
Two-dimensional QCD in the Coulomb gauge
International Nuclear Information System (INIS)
Kalashnikova, Yu.S.; Nefed'ev, A.V.
2002-01-01
Various aspects of the 't Hooft model for two-dimensional QCD in the limit of infinite number of colours in the Coulomb gauge are discussed. The properties of mesonic excitations are studied, with special emphasis on the pion. Attention is paid to the dual role of the pion. which, while a genuine qq-bar state, is a Goldstone boson of two-dimensional QCD as well. In particular, the validity of the soft-pion theorems is demonstrated. It is shown that the Coulomb gauge is the most suitable choice for the study of hadronic observables involving pions [ru
Quantum Communication Through a Two-Dimensional Spin Network
International Nuclear Information System (INIS)
Wang Zhaoming; Gu Yongjian
2012-01-01
We investigate the state or entanglement transfer through a two-dimensional spin network. We show that for state transfer, better fidelity can be gained along the diagonal direction but for entanglement transfer, when the initial entanglement is created along the boundary, the concurrence is more inclined to propagate along the boundary. This behavior is produced by quantum mechanical interference and the communication quality depends on the precise size of the network. For some number of sites, the fidelity in a two-dimensional channel is higher than one-dimensional case. This is an important result for realizing quantum communication through high dimension spin chain networks.
Critical Behaviour of a Two-Dimensional Random Antiferromagnet
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Birgeneau, R. J.; Guggenheim, H. J.
1976-01-01
A neutron scattering study of the order parameter, correlation length and staggered susceptibility of the two-dimensional random antiferromagnet Rb2Mn0.5Ni0.5F4 is reported. The system is found to exhibit a well-defined phase transition with critical exponents identical to those of the isomorphou...... pure materials K2NiF4 and K2MnF4. Thus, in these systems, which have the asymptotic critical behaviour of the two-dimensional Ising model, randomness has no measurable effect on the phase-transition behaviour....
Two dimensional nonlinear spectral estimation techniques for breast cancer localization
Energy Technology Data Exchange (ETDEWEB)
Stathaki, P T; Constantinides, A G [Signal Processing Section, Department of Electrical and Electronic Engineering, Imperial College, Exhibition Road, London SW7 2BT, UK (United Kingdom)
1994-12-31
In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging. 7 refs, 2 figs.
Chaotic dynamics in two-dimensional noninvertible maps
Mira, Christian; Cathala, Jean-Claude; Gardini, Laura
1996-01-01
This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this resea
Chiral anomaly, fermionic determinant and two dimensional models
International Nuclear Information System (INIS)
Rego Monteiro, M.A. do.
1985-01-01
The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt
The simulation of two-dimensional migration patterns - a novel approach
Energy Technology Data Exchange (ETDEWEB)
Villar, Heldio Pereira [Universidade de Pernambuco, Recife, PE (Brazil). Escola Politecnica]|[Centro Regional de Ciencias Nucleares, Recife, PE (Brazil)
1997-12-31
A novel approach to the problem of simulation of two-dimensional migration of solutes in saturated soils is presented. In this approach, the two-dimensional advection-dispersion equation is solved by finite-differences in a stepwise fashion, by employing the one-dimensional solution first in the direction of flow and then perpendicularly, using the same time increment in both cases. As the results of this numerical model were to be verified against experimental results obtained by radioactive tracer experiments, an attenuation factor, to account for the contribution of the gamma rays emitted by the whole plume of tracer to the readings of the adopted radiation detectors, was introduced into the model. The comparison between experimental and simulated concentration contours showed good agreement, thus establishing the feasibility of the approach proposed herein. (author) 6 refs., 6 figs.
A Novel Machine Learning Strategy Based on Two-Dimensional Numerical Models in Financial Engineering
Directory of Open Access Journals (Sweden)
Qingzhen Xu
2013-01-01
Full Text Available Machine learning is the most commonly used technique to address larger and more complex tasks by analyzing the most relevant information already present in databases. In order to better predict the future trend of the index, this paper proposes a two-dimensional numerical model for machine learning to simulate major U.S. stock market index and uses a nonlinear implicit finite-difference method to find numerical solutions of the two-dimensional simulation model. The proposed machine learning method uses partial differential equations to predict the stock market and can be extensively used to accelerate large-scale data processing on the history database. The experimental results show that the proposed algorithm reduces the prediction error and improves forecasting precision.
Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data
Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.
2017-10-01
The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.
A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern
Prybytak, Dzmitry; Zima, Piotr
2017-12-01
The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.
The simulation of two-dimensional migration patterns - a novel approach
International Nuclear Information System (INIS)
Villar, Heldio Pereira
1997-01-01
A novel approach to the problem of simulation of two-dimensional migration of solutes in saturated soils is presented. In this approach, the two-dimensional advection-dispersion equation is solved by finite-differences in a stepwise fashion, by employing the one-dimensional solution first in the direction of flow and then perpendicularly, using the same time increment in both cases. As the results of this numerical model were to be verified against experimental results obtained by radioactive tracer experiments, an attenuation factor, to account for the contribution of the gamma rays emitted by the whole plume of tracer to the readings of the adopted radiation detectors, was introduced into the model. The comparison between experimental and simulated concentration contours showed good agreement, thus establishing the feasibility of the approach proposed herein. (author)
Non-perturbative effects in two-dimensional lattice O(N) models
International Nuclear Information System (INIS)
Ogilvie, M.C.; Maryland Univ., College Park
1981-01-01
Non-abelian analogues of Kosterlitz-Thouless vortices may have important effects in two-dimensional lattice spin systems with O(N) symmetries. Renormalization group equations which include these effects are developed in two ways. The first set of equations extends the renormalization group equations of Kosterlitz to 0(N) spin systems, in a form suggested by Cardy and Hamber. The second is derived from a Villain-type 0(N) model using Migdal's recursion relations. Using these equations, the part played by topological excitations int he crossover from weak to strong coupling behavior is studied. Another effect which influences crossover behavior is also discussed; irrelevant operators which occur naturally in lattice theories can make important contributions to the renormalization group flow in the crossover region. When combined with conventional perturbative results, these two effects may explain the observed crossover behavior of these models. (orig.)
Singular solitons and other solutions to a couple of nonlinear wave equations
International Nuclear Information System (INIS)
Inc Mustafa; Ulutaş Esma; Biswas Anjan
2013-01-01
This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method
Directory of Open Access Journals (Sweden)
Isaac Lare Animasaun
2016-06-01
Full Text Available The problem of unsteady convective with thermophoresis, chemical reaction and radiative heat transfer in a micropolar fluid flow past a vertical porous surface moving through binary mixture considering temperature dependent dynamic viscosity and constant vortex viscosity has been investigated theoretically. For proper and correct analysis of fluid flow along vertical surface with a temperature lesser than that of the free stream, Boussinesq approximation and temperature dependent viscosity model were modified and incorporated into the governing equations. The governing equations are converted to systems of ordinary differential equations by applying suitable similarity transformations and solved numerically using fourth-order Runge–Kutta method along with shooting technique. The results of the numerical solution are presented graphically and in tabular forms for different values of parameters. Velocity profile increases with temperature dependent variable fluid viscosity parameter. Increase of suction parameter corresponds to an increase in both temperature and concentration within the thin boundary layer.
Vectorized Matlab Codes for Linear Two-Dimensional Elasticity
Directory of Open Access Journals (Sweden)
Jonas Koko
2007-01-01
Full Text Available A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.
Level crossings in complex two-dimensional potentials
Indian Academy of Sciences (India)
Two-dimensional P T -symmetric quantum-mechanical systems with the complex cubic potential 12 = 2 + 2 + 2 and the complex Hénon–Heiles potential HH = 2 + 2 + (2 − 3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both ...
Zero sound in a two-dimensional dipolar Fermi gas
Lu, Z.K.; Matveenko, S.I.; Shlyapnikov, G.V.
2013-01-01
We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both
Interior design of a two-dimensional semiclassical black hole
Levanony, Dana; Ori, Amos
2009-10-01
We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. Two kinds of spacelike singularities are found inside the black hole, and their structure is investigated. We also study the evolution of spacetime from the horizon to the singularity.
On final states of two-dimensional decaying turbulence
Yin, Z.
2004-01-01
Numerical and analytical studies of final states of two-dimensional (2D) decaying turbulence are carried out. The first part of this work is trying to give a definition for final states of 2D decaying turbulence. The functional relation of ¿-¿, which is frequently adopted as the characterization of
Vibrations of thin piezoelectric shallow shells: Two-dimensional ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
In this paper we consider the eigenvalue problem for piezoelectric shallow shells and we show that, as the thickness of the shell goes to zero, the eigensolutions of the three-dimensional piezoelectric shells converge to the eigensolutions of a two- dimensional eigenvalue problem. Keywords. Vibrations; piezoelectricity ...
Inter-layer Cooper pairing of two-dimensional electrons
International Nuclear Information System (INIS)
Inoue, Masahiro; Takemori, Tadashi; Yoshizaki, Ryozo; Sakudo, Tunetaro; Ohtaka, Kazuo
1987-01-01
The authors point out the possibility that the high transition temperatures of the recently discovered oxide superconductors are dominantly caused by the inter-layer Cooper pairing of two-dimensional electrons that are coupled through the exchange of three-dimensional phonons. (author)
Two-dimensional generalized harmonic oscillators and their Darboux partners
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2011-01-01
We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (paper)
First principles calculation of two dimensional antimony and antimony arsenide
Energy Technology Data Exchange (ETDEWEB)
Pillai, Sharad Babu, E-mail: sbpillai001@gmail.com; Narayan, Som; Jha, Prafulla K. [Department. of Physics, Faculty of Science, The M. S. University of Baroda, Vadodara-390002 (India); Dabhi, Shweta D. [Department of Physics, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar-364001 (India)
2016-05-23
This work focuses on the strain dependence of the electronic properties of two dimensional antimony (Sb) material and its alloy with As (SbAs) using density functional theory based first principles calculations. Both systems show indirect bandgap semiconducting character which can be transformed into a direct bandgap material with the application of relatively small strain.
Two-dimensional models in statistical mechanics and field theory
International Nuclear Information System (INIS)
Koberle, R.
1980-01-01
Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt
Theory of the one- and two-dimensional electron gas
International Nuclear Information System (INIS)
Emery, V.J.
1987-01-01
Two topics are discussed: (1) the competition between 2k/sub F/ and 4k/sub F/ charge state waves in a one-dimensional electron gas and (2) a two-dimensional model of high T/sub c/ superconductivity in the oxides
Two-dimensional turbulent flows on a bounded domain
Kramer, W.
2006-01-01
Large-scale flows in the oceans and the atmosphere reveal strong similarities with purely two-dimensional flows. One of the most typical features is the cascade of energy from smaller flow scales towards larger scales. This is opposed to three-dimensional turbulence where larger flow structures
Exterior calculus and two-dimensional supersymmetric models
International Nuclear Information System (INIS)
Sciuto, S.
1980-01-01
An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.)
Quantitative optical mapping of two-dimensional materials
DEFF Research Database (Denmark)
Jessen, Bjarke S.; Whelan, Patrick R.; Mackenzie, David M. A.
2018-01-01
The pace of two-dimensional materials (2DM) research has been greatly accelerated by the ability to identify exfoliated thicknesses down to a monolayer from their optical contrast. Since this process requires time-consuming and error-prone manual assignment to avoid false-positives from image...
Temperature maxima in stable two-dimensional shock waves
International Nuclear Information System (INIS)
Kum, O.; Hoover, W.G.; Hoover, C.G.
1997-01-01
We use molecular dynamics to study the structure of moderately strong shock waves in dense two-dimensional fluids, using Lucy pair potential. The stationary profiles show relatively broad temperature maxima, for both the longitudinal and the average kinetic temperatures, just as does Mott-Smith model for strong shock waves in dilute three-dimensional gases. copyright 1997 The American Physical Society
Two-dimensional molecular line transfer for a cometary coma
Szutowicz, S.
2017-09-01
In the proposed axisymmetric model of the cometary coma the gas density profile is described by an angular density function. Three methods for treating two-dimensional radiative transfer are compared: the Large Velocity Gradient (LVG) (the Sobolev method), Accelerated Lambda Iteration (ALI) and accelerated Monte Carlo (MC).
Sub-Nanometer Channels Embedded in Two-Dimensional Materials
Han, Yimo; Li, Ming-yang; Jung, Gang-Seob; Marsalis, Mark A.; Qin, Zhao; Buehler, Markus J.; Li, Lain-Jong; Muller, David A.
2017-01-01
Two-dimensional (2D) materials are among the most promising candidates for next-generation electronics due to their atomic thinness, allowing for flexible transparent electronics and ultimate length scaling1. Thus far, atomically-thin p-n junctions2
Complex dynamical invariants for two-dimensional complex potentials
Indian Academy of Sciences (India)
Abstract. Complex dynamical invariants are searched out for two-dimensional complex poten- tials using rationalization method within the framework of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. It is found that the cubic oscillator and shifted harmonic oscillator ...
Coherent Electron Focussing in a Two-Dimensional Electron Gas.
Houten, H. van; Wees, B.J. van; Mooij, J.E.; Beenakker, C.W.J.; Williamson, J.G.; Foxon, C.T.
1988-01-01
The first experimental realization of ballistic point contacts in a two-dimensional electron gas for the study of transverse electron focussing by a magnetic field is reported. Multiple peaks associated with skipping orbits of electrons reflected specularly by the channel boundary are observed. At
Two-dimensional ion effects in relativistic diodes
International Nuclear Information System (INIS)
Poukey, J.W.
1975-01-01
In relativistic diodes, ions are emitted from the anode plasma. The effects and properties of these ions are studied via a two-dimensional particle simulation code. The space charge of these ions enhances the electron emission, and this additional current (including that of the ions, themselves) aids in obtaining superpinched electron beams for use in pellet fusion studies. (U.S.)
Bounds on the capacity of constrained two-dimensional codes
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
2000-01-01
Bounds on the capacity of constrained two-dimensional (2-D) codes are presented. The bounds of Calkin and Wilf apply to first-order symmetric constraints. The bounds are generalized in a weaker form to higher order and nonsymmetric constraints. Results are given for constraints specified by run-l...
Interior design of a two-dimensional semiclassical black hole
International Nuclear Information System (INIS)
Levanony, Dana; Ori, Amos
2009-01-01
We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. Two kinds of spacelike singularities are found inside the black hole, and their structure is investigated. We also study the evolution of spacetime from the horizon to the singularity.
Two-dimensional profiling of Xanthomonas campestris pv. viticola ...
African Journals Online (AJOL)
However, the analysis of the 2D-PAGE gel images revealed a larger number of spots in the lysis method when compared to the others. Taking ... Keywords: Bacterial canker, Vitis vinifera, proteomics, sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE), two-dimensional gel electrophoresis (2D-PAGE).
Image Making in Two Dimensional Art; Experiences with Straw and ...
African Journals Online (AJOL)
Image making in art is professionally referred to as bust in Sculpture andPortraiture in Painting. ... havebeen used to achieve these forms of art; like clay cement, marble, stone,different metals and, fibre glass in the three dimensional form; We also have Pencil, Charcoal Pastel and, Acrylic oil-paint in two dimensional form.
Image Making in Two Dimensional Art; Experiences with Straw and ...
African Journals Online (AJOL)
Image making in art is professionally referred to as bust in Sculpture andPortraiture in Painting. It is an art form executed in three dimensional (3D)and two dimensional (2D) formats respectively. Uncountable materials havebeen used to achieve these forms of art; like clay cement, marble, stone,different metals and, fibre ...
Mass relations for two-dimensional classical configurations
International Nuclear Information System (INIS)
Tataru-Mihai, P.
1980-01-01
Using the two-dimensional sigma-nonlinear models as a framework mass relations for classical configurations of instanton/soliton type are derived. Our results suggest an interesting differential-geometric interpretation of the mass of a classical configuration in terms of the topological characteristics of an associated manifold. (orig.)
Seismically constrained two-dimensional crustal thermal structure of ...
Indian Academy of Sciences (India)
The temperature field within the crust is closely related to tectonic history as well as many other geological processes inside the earth. Therefore, knowledge of the crustal thermal structure of a region is of great importance for its tectonophysical studies. This work deals with the two-dimensional thermal modelling to ...
Waiting Time Dynamics in Two-Dimensional Infrared Spectroscopy
Jansen, Thomas L. C.; Knoester, Jasper
We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example,
Two-dimensional NMR studies of allyl palladium complexes of ...
Indian Academy of Sciences (India)
Administrator
h3-Allyl complexes are intermediates in organic synthetic reactions such as allylic alkylation and amination. There is growing interest in understanding the structures of chiral h3-allyl intermediates as this would help to unravel the mechanism of enantioselective C–C bond forming reactions. Two-dimensional NMR study is a.
Two-dimensional position sensitive Si(Li) detector
International Nuclear Information System (INIS)
Walton, J.T.; Hubbard, G.S.; Haller, E.E.; Sommer, H.A.
1978-11-01
Circular, large-area two-dimensional Si(Li) position sensitive detectors have been fabricated. The detectors employ a thin lithium-diffused n + resisitive layer for one contact and a boron implanted p + resistive layer for the second contact. A position resolution of the order of 100 μm is indicated
A TWO-DIMENSIONAL POSITION SENSITIVE SI(LI) DETECTOR
Energy Technology Data Exchange (ETDEWEB)
Walton, Jack T.; Hubbard, G. Scott; Haller, Eugene E.; Sommer, Heinrich A.
1978-11-01
Circular, large-area two-dimensional Si(Li) position sensitive detectors have been fabricated. The detectors employ a thin lithium-diffused n{sup +} resistive layer for one contact and a boron implanted p{sup +} resistive layer for the second contact. A position resolution of the order of 100 {micro}m is indicated.
Solar Internal Rotation and Dynamo Waves: A Two Dimensional ...
Indian Academy of Sciences (India)
tribpo
Solar Internal Rotation and Dynamo Waves: A Two Dimensional. Asymptotic Solution in the Convection Zone ... We calculate here a spatial 2 D structure of the mean magnetic field, adopting real profiles of the solar internal ... of the asymptotic solution in low (middle) and high (right panel) latitudes. field is shifted towards the ...
Linkage analysis by two-dimensional DNA typing
te Meerman, G J; Mullaart, E; Meulen ,van der Martin; den Daas, J H; Morolli, B; Uitterlinden, A G; Vijg, J
1993-01-01
In two-dimensional (2-D) DNA typing, genomic DNA fragments are separated, first according to size by electrophoresis in a neutral polyacrylamide gel and second according to sequence by denaturing gradient gel electrophoresis, followed by hybridization analysis using micro- and minisatellite core
Proximity Induced Superconducting Properties in One and Two Dimensional Semiconductors
DEFF Research Database (Denmark)
Kjærgaard, Morten
This report is concerned with the properties of one and two dimensional semiconducting materials when brought into contact with a superconductor. Experimentally we study the 2D electron gas in an InGaAs/InAs heterostructure with aluminum grown in situ on the surface, and theoretically we show tha...
Two-Dimensional Charge Transport in Disordered Organic Semiconductors
Brondijk, J. J.; Roelofs, W. S. C.; Mathijssen, S. G. J.; Shehu, A.; Cramer, T.; Biscarini, F.; Blom, P. W. M.; de Leeuw, D. M.
2012-01-01
We analyze the effect of carrier confinement on the charge-transport properties of organic field-effect transistors. Confinement is achieved experimentally by the use of semiconductors of which the active layer is only one molecule thick. The two-dimensional confinement of charge carriers provides
Noninteracting beams of ballistic two-dimensional electrons
International Nuclear Information System (INIS)
Spector, J.; Stormer, H.L.; Baldwin, K.W.; Pfeiffer, L.N.; West, K.W.
1991-01-01
We demonstrate that two beams of two-dimensional ballistic electrons in a GaAs-AlGaAs heterostructure can penetrate each other with negligible mutual interaction analogous to the penetration of two optical beams. This allows electrical signal channels to intersect in the same plane with negligible crosstalk between the channels
Two-dimensional dissipation in third sound resonance
International Nuclear Information System (INIS)
Buck, A.L.; Mochel, J.M.; Illinois Univ., Urbana
1981-01-01
The first determination of non-linear superflow dissipation in a truly two-dimensional helium film is reported. Superfluid velocities were measured using third sound resonance on a closed superfluid film. The predicted power law dissipation function, with exponent of approximately eight, is observed at three temperatures in a film of 0.58 mobile superfluid layers. (orig.)
Graphene: a promising two-dimensional support for heterogeneous catalysts
Directory of Open Access Journals (Sweden)
Xiaobin eFan
2015-01-01
Full Text Available Graphene has many advantages that make it an attractive two-dimensional (2D support for heterogeneous catalysts. It not only allows the high loading of targeted catalytic species, but also facilitates the mass transfer during the reaction processes. These advantages, along with its unique physical and chemical properties, endow graphene great potential as catalyst support in heterogeneous catalysis.
Two-dimensional interpolation with experimental data smoothing
International Nuclear Information System (INIS)
Trejbal, Z.
1989-01-01
A method of two-dimensional interpolation with smoothing of time statistically deflected points is developed for processing of magnetic field measurements at the U-120M field measurements at the U-120M cyclotron. Mathematical statement of initial requirements and the final result of relevant algebraic transformations are given. 3 refs
Tunneling between parallel two-dimensional electron liquids
Czech Academy of Sciences Publication Activity Database
Jungwirth, Tomáš; MacDonald, A. H.
361/362, - (1996), s. 167-170 ISSN 0039-6028. [International Conference on the Electronic Properties of Two Dimensional Systems /11./. Nottingham, 07.08.1995-11.08.1995] R&D Projects: GA ČR GA202/94/1278 Grant - others:INT(XX) 9106888 Impact factor: 2.783, year: 1996
Influence of index contrast in two dimensional photonic crystal lasers
DEFF Research Database (Denmark)
Jørgensen, Mette Marie; Petersen, Sidsel Rübner; Christiansen, Mads Brøkner
2010-01-01
The influence of index contrast variations for obtaining single-mode operation and low threshold in dye doped polymer two dimensional photonic crystal (PhC) lasers is investigated. We consider lasers made from Pyrromethene 597 doped Ormocore imprinted with a rectangular lattice PhC having a cavity...
Two-Dimensional Tellurene as Excellent Thermoelectric Material
Sharma, Sitansh; Singh, Nirpendra; Schwingenschlö gl, Udo
2018-01-01
We study the thermoelectric properties of two-dimensional tellurene by first-principles calculations and semiclassical Boltzmann transport theory. The HSE06 hybrid functional results in a moderate direct band gap of 1.48 eV at the Γ point. A high
Analysis of Two-Dimensional Electrophoresis Gel Images
DEFF Research Database (Denmark)
Pedersen, Lars
2002-01-01
This thesis describes and proposes solutions to some of the currently most important problems in pattern recognition and image analysis of two-dimensional gel electrophoresis (2DGE) images. 2DGE is the leading technique to separate individual proteins in biological samples with many biological...
Patched Green's function techniques for two-dimensional systems
DEFF Research Database (Denmark)
Settnes, Mikkel; Power, Stephen; Lin, Jun
2015-01-01
We present a numerically efficient technique to evaluate the Green's function for extended two-dimensional systems without relying on periodic boundary conditions. Different regions of interest, or “patches,” are connected using self-energy terms which encode the information of the extended parts...
Nonlinear dynamic characterization of two-dimensional materials
Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.
2017-01-01
Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's
Transient two-dimensional flow in porous media
International Nuclear Information System (INIS)
Sharpe, L. Jr.
1979-01-01
The transient flow of an isothermal ideal gas from the cavity formed by an underground nuclear explosion is investigated. A two-dimensional finite element method is used in analyzing the gas flow. Numerical results of the pressure distribution are obtained for both the stemming column and the surrounding porous media
Two-dimensional QCD as a model for strong interaction
International Nuclear Information System (INIS)
Ellis, J.
1977-01-01
After an introduction to the formalism of two-dimensional QCD, its applications to various strong interaction processes are reviewed. Among the topics discussed are spectroscopy, deep inelastic cross-sections, ''hard'' processes involving hadrons, ''Regge'' behaviour, the existence of the Pomeron, and inclusive hadron cross-sections. Attempts are made to abstracts features useful for four-dimensional QCD phenomenology. (author)
Two-dimensional gel electrophoresis analysis of different parts of ...
African Journals Online (AJOL)
Two-dimensional gel electrophoresis analysis of different parts of Panax quinquefolius L. root. ... From these results it was concluded that proteomic analysis method was an effective way to identify the different parts of quinquefolius L. root. These findings may contribute to further understanding of the physiological ...
Two-dimensional optimization of free-electron-laser designs
Prosnitz, D.; Haas, R.A.
1982-05-04
Off-axis, two-dimensional designs for free electron lasers are described that maintain correspondence of a light beam with a synchronous electron at an optimal transverse radius r > 0 to achieve increased beam trapping efficiency and enhanced laser beam wavefront control so as to decrease optical beam diffraction and other deleterious effects.
Kubo conductivity of a strongly magnetized two-dimensional plasma.
Montgomery, D.; Tappert, F.
1971-01-01
The Kubo formula is used to evaluate the bulk electrical conductivity of a two-dimensional guiding-center plasma in a strong dc magnetic field. The particles interact only electrostatically. An ?anomalous' electrical conductivity is derived for this system, which parallels a recent result of Taylor and McNamara for the coefficient of spatial diffusion.
Bayesian approach for peak detection in two-dimensional chromatography
Vivó-Truyols, G.
2012-01-01
A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual
Equilibrium spherically curved two-dimensional Lennard-Jones systems
Voogd, J.M.; Sloot, P.M.A.; van Dantzig, R.
2005-01-01
To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For many N-values (N < 800) equilibrium configu- rations are traced
Giant 1/f noise in two-dimensional polycrystalline media
International Nuclear Information System (INIS)
Snarskii, A.; Bezsudnov, I.
2008-01-01
The behaviour of excess (1/f noise) in two-dimensional polycrystalline media is investigated. On the base of current trap model, it is shown that there exists a certain anisotropy value of conductivity tensor for polycrystalline media when the amplitude of 1/f noise becomes giant
An analytical approach for a nodal scheme of two-dimensional neutron transport problems
International Nuclear Information System (INIS)
Barichello, L.B.; Cabrera, L.C.; Prolo Filho, J.F.
2011-01-01
Research highlights: → Nodal equations for a two-dimensional neutron transport problem. → Analytical Discrete Ordinates Method. → Numerical results compared with the literature. - Abstract: In this work, a solution for a two-dimensional neutron transport problem, in cartesian geometry, is proposed, on the basis of nodal schemes. In this context, one-dimensional equations are generated by an integration process of the multidimensional problem. Here, the integration is performed for the whole domain such that no iterative procedure between nodes is needed. The ADO method is used to develop analytical discrete ordinates solution for the one-dimensional integrated equations, such that final solutions are analytical in terms of the spatial variables. The ADO approach along with a level symmetric quadrature scheme, lead to a significant order reduction of the associated eigenvalues problems. Relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed, in nodal schemes, auxiliary equations. Numerical results are presented and compared with test problems.
Non-Oberbeck-Boussinesq Effects in Gaseous Rayleigh-Bénard Convection
Ahlers, Günter; Fontenele Araujo Junior, F.; Funfschilling, Denis; Grossmann, Siegfried; Lohse, Detlef
2007-01-01
Non-Oberbeck-Boussinesq (NOB) effects are measured experimentally and calculated theoretically for strongly turbulent Rayleigh-Be´nard convection of ethane gas under pressure where the material properties strongly depend on the temperature. Relative to the Oberbeck-Boussinesq case we find a decrease
The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure
International Nuclear Information System (INIS)
Si-Xing, Tao; Tie-Cheng, Xia
2010-01-01
Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super-Hamiltonian structure is obtained by making use of super-trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville. (general)