Two-dimensional analytical solution for nodal calculation of nuclear reactors
International Nuclear Information System (INIS)
Silva, Adilson C.; Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2017-01-01
Highlights: • A proposal for a coarse mesh nodal method is presented. • The proposal uses the analytical solution of the two-dimensional neutrons diffusion equation. • The solution is performed homogeneous nodes with dimensions of the fuel assembly. • The solution uses four average fluxes on the node surfaces as boundary conditions. • The results show good accuracy and efficiency. - Abstract: In this paper, the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G). The spatial domain of reactor core is divided into a set of nodes with uniform nuclear parameters. To determine iteratively the multiplication factor and the neutron flux in the reactor we combine the analytical solution of the neutron diffusion equation with an iterative method known as power method. The analytical solution for different types of regions that compose the reactor is obtained, such as fuel and reflector regions. Four average fluxes in the node surfaces are used as boundary conditions for analytical solution. Discontinuity factors on the node surfaces derived from the homogenization process are applied to maintain averages reaction rates and the net current in the fuel assembly (FA). To validate the results obtained by the analytical solution a relative power density distribution in the FAs is determined from the neutron flux distribution and compared with the reference values. The results show good accuracy and efficiency.
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)
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
International Nuclear Information System (INIS)
Marshall, H.; Sahraoui, M.; Kaviany, M.
1994-01-01
The Kuwabara solution for creeping fluid flow through periodic arrangement of cylinders is widely used in analytic and numerical studies of fibrous filters. Numerical solutions have shown that the Kuwabara solution has systematic errors, and when used for the particle trajectories in filters it results in some error in the predicted filter efficiency. The numerical solutions, although accurate, preclude further analytic treatments, and are not as compact and convenient to use as the Kuwabara solution. By reexamining the outer boundary conditions of the Kuwabara solution, a correction term to the Kuwabara solution has been derived to obtain an extended solution that is more accurate and improves prediction of the filter efficiency. By comparison with the numerical solutions, it is shown that the Kuwabara solution is the high porosity asymptote, and that the extended solution has an improved porosity dependence. A rectification is explained that can make particle collection less efficient for periodic, in-line arrangements of fibers with particle diffusion or body force. This rectification also results in the alignment of particles with inertia (i.e., high Stokes number particles)
Directory of Open Access Journals (Sweden)
Yang Shen
Full Text Available China is a country with vast territory, but economic development and population growth have reduced the usable land resources in recent years. Therefore, reclamation by pumping and filling is carried out in eastern coastal regions of China in order to meet the needs of urbanization. However, large areas of reclaimed land need rapid drainage consolidation treatment. Based on past researches on how to improve the treatment efficiency of soft clay using vacuum preloading combined with electro-osmosis, a two-dimensional drainage plane model was proposed according to the Terzaghi and Esrig consolidation theory. However, the analytical solution using two-dimensional plane model was never involved. Current analytical solutions can't have a thorough theoretical analysis of practical engineering and give relevant guidance. Considering the smearing effect and the rectangle arrangement pattern, an analytical solution is derived to describe the behavior of pore-water and the consolidation process by using EKG (electro-kinetic geo synthetics materials. The functions of EKG materials include drainage, electric conduction and corrosion resistance. Comparison with test results is carried out to verify the analytical solution. It is found that the measured value is larger than the applied vacuum degree because of the stacking effect of the vacuum preloading and electro-osmosis. The trends of the mean measured value and the mean analytical value processes are comparable. Therefore, the consolidation model can accurately assess the change in pore-water pressure and the consolidation process during vacuum preloading combined with electro-osmosis.
Qiu, Chenchen; Li, Yande
2017-01-01
China is a country with vast territory, but economic development and population growth have reduced the usable land resources in recent years. Therefore, reclamation by pumping and filling is carried out in eastern coastal regions of China in order to meet the needs of urbanization. However, large areas of reclaimed land need rapid drainage consolidation treatment. Based on past researches on how to improve the treatment efficiency of soft clay using vacuum preloading combined with electro-osmosis, a two-dimensional drainage plane model was proposed according to the Terzaghi and Esrig consolidation theory. However, the analytical solution using two-dimensional plane model was never involved. Current analytical solutions can’t have a thorough theoretical analysis of practical engineering and give relevant guidance. Considering the smearing effect and the rectangle arrangement pattern, an analytical solution is derived to describe the behavior of pore-water and the consolidation process by using EKG (electro-kinetic geo synthetics) materials. The functions of EKG materials include drainage, electric conduction and corrosion resistance. Comparison with test results is carried out to verify the analytical solution. It is found that the measured value is larger than the applied vacuum degree because of the stacking effect of the vacuum preloading and electro-osmosis. The trends of the mean measured value and the mean analytical value processes are comparable. Therefore, the consolidation model can accurately assess the change in pore-water pressure and the consolidation process during vacuum preloading combined with electro-osmosis. PMID:28771496
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
2008-01-01
Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.
Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films
Perazzo, Carlos Alberto; Mac Intyre, J. R.; Gomba, J. M.
2017-12-01
By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.
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.
Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder
Directory of Open Access Journals (Sweden)
Morteza Eskandari-Ghadi
2013-12-01
Full Text Available An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements.
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 ...
International Nuclear Information System (INIS)
Markos, P; Schweitzer, L; Weyrauch, M
2004-01-01
In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announced an analytical solution of the two-dimensional Anderson localization problem via the calculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalized states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy of using a generalized Lyapunov exponent for studying Anderson localization. (comment)
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.
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
Sarmah, Ratan; Tiwari, Shubham
2018-03-01
An analytical solution is developed for predicting two-dimensional transient seepage into ditch drainage network receiving water from a non-uniform steady ponding field from the surface of the soil under the influence of source/sink in the flow domain. The flow domain is assumed to be saturated, homogeneous and anisotropic in nature and have finite extends in horizontal and vertical directions. The drains are assumed to be standing vertical and penetrating up to impervious layer. The water levels in the drains are unequal and invariant with time. The flow field is also assumed to be under the continuous influence of time-space dependent arbitrary source/sink term. The correctness of the proposed model is checked by developing a numerical code and also with the existing analytical solution for the simplified case. The study highlights the significance of source/sink influence in the subsurface flow. With the imposition of the source and sink term in the flow domain, the pathline and travel time of water particles started deviating from their original position and above that the side and top discharge to the drains were also observed to have a strong influence of the source/sink terms. The travel time and pathline of water particles are also observed to have a dependency on the height of water in the ditches and on the location of source/sink activation area.
International Nuclear Information System (INIS)
Filho, J. F. P.; Barichello, L. B.
2013-01-01
In this work, an analytical discrete ordinates method is used to solve a nodal formulation of a neutron transport problem in x, y-geometry. The proposed approach leads to an important reduction in the order of the associated eigenvalue systems, when combined with the classical level symmetric quadrature scheme. Auxiliary equations are proposed, as usually required for nodal methods, to express the unknown fluxes at the boundary introduced as additional unknowns in the integrated equations. Numerical results, for the problem defined by a two-dimensional region with a spatially constant and isotropically emitting source, are presented and compared with those available in the literature. (authors)
Khan, Farman U; Qamar, Shamsul
2017-05-01
A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
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.
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.
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.
International Nuclear Information System (INIS)
Shan, C.; Javandel, I.
1996-05-01
Analytical solutions are developed for modeling solute transport in a vertical section of a homogeneous aquifer. Part 1 of the series presents a simplified analytical solution for cases in which a constant-concentration source is located at the top (or the bottom) of the aquifer. The following transport mechanisms have been considered: advection (in the horizontal direction), transverse dispersion (in the vertical direction), adsorption, and biodegradation. In the simplified solution, however, longitudinal dispersion is assumed to be relatively insignificant with respect to advection, and has been neglected. Example calculations are given to show the movement of the contamination front, the development of concentration profiles, the mass transfer rate, and an application to determine the vertical dispersivity. The analytical solution developed in this study can be a useful tool in designing an appropriate monitoring system and an effective groundwater remediation 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
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.
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.
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 analytical model of a proton exchange membrane fuel cell
International Nuclear Information System (INIS)
Liu, Jia Xing; Guo, Hang; Ye, Fang; Ma, Chong Fang
2017-01-01
In this study, a two-dimensional full cell analytical model of a proton exchange membrane fuel cell is developed. The analytical model describes electrochemical reactions on the anode and cathode catalyst layer, reactants diffusion in the gas diffusion layer, and gases flow in the gas channel, etc. The analytical solution is derived according to the basic physical equations. The performance predicted by the model is in good agreement with the experimental data. The results show that the polarization mainly occurs in the cathode side of the proton exchange membrane fuel cell. The anodic overpotential cannot be neglected. The hydrogen and oxygen concentrations decrease along the channel flow direction. The hydrogen and oxygen concentrations in the catalyst layer decrease with the current density. As predicted by the model, concentration polarization mainly occurs in the cathode side. - Highlights: • A 2D full cell analytical model of a proton exchange membrane fuel cell is developed. • The analytical solution is deduced according to the basic equations. • The anode overpotential is not so small that it cannot be neglected. • Species concentration distributions in the fuel cell is obtained and analyzed.
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)
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.
A two-dimensional, semi-analytic expansion method for nodal calculations
International Nuclear Information System (INIS)
Palmtag, S.P.
1995-08-01
Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure
Two-dimensional semi-analytic nodal method for multigroup pin power reconstruction
International Nuclear Information System (INIS)
Seung Gyou, Baek; Han Gyu, Joo; Un Chul, Lee
2007-01-01
A pin power reconstruction method applicable to multigroup problems involving square fuel assemblies is presented. The method is based on a two-dimensional semi-analytic nodal solution which consists of eight exponential terms and 13 polynomial terms. The 13 polynomial terms represent the particular solution obtained under the condition of a 2-dimensional 13 term source expansion. In order to achieve better approximation of the source distribution, the least square fitting method is employed. The 8 exponential terms represent a part of the analytically obtained homogeneous solution and the 8 coefficients are determined by imposing constraints on the 4 surface average currents and 4 corner point fluxes. The surface average currents determined from a transverse-integrated nodal solution are used directly whereas the corner point fluxes are determined during the course of the reconstruction by employing an iterative scheme that would realize the corner point balance condition. The outgoing current based corner point flux determination scheme is newly introduced. The accuracy of the proposed method is demonstrated with the L336C5 benchmark problem. (authors)
International Nuclear Information System (INIS)
Hagel, J.; Moshammer, H.
1988-01-01
In this paper the authors study the on- momentum nonlinear equations of motion for the coupled transverse motion of a single charged particle in a storage ring. The authors seek for the maximum initial linear amplitudes in the two transverse directions x and y which lead to bounded particle motion as t tends to infinity. Although the authors restrict themselves to sextupole fields in this paper, the authors may easily extend the method to any order multipole. The aim of this work is to derive an analytic approximate expression for the dynamical aperture. The authors approach the solutions of x and y by use of a classical secular perturbation theory. Every coefficient of the perturbation series can be expressed as an analytic function of all the lower order coefficients. Although perturbation theory if it is evaluated to certain specific order leads only to an approximation in terms of bounded (trigonometric) functions the authors may derive information about the stability limit by considering the convergency radius of the general perturbation. This is done in the present paper by deriving an approximate analytic expression for the n-th order perturbation contribution of the whole series using only results up to second order. The actual calculations have been performed for the fully two dimensional case but for simplicity the authors shall explain only the one dimensional case of the pure horizontal motion
New analytical treatment for a kind of two dimensional integrals in ion-atom collisions
International Nuclear Information System (INIS)
Yang Qifeng; Kuang Yurang
1994-01-01
A kind of two-dimensional integrals, separated from two-center matrix elements in ion-atom collisions, is analytically integrated by introducing the Laplace transform into the integrals and expressed by the modified Bessel functions. The traditional Feynman transform is very complicated for this kind of more general integrals related to the excited state capture
Directory of Open Access Journals (Sweden)
Djordjevich Alexandar
2017-12-01
Full Text Available The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity. Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.
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)
Chuang, Mo-Hsiung; Hung, Chi-Tung; -Yen Lin, Wen; Ma, Kuo-chen
2017-04-01
In recent years, cities and industries in the vicinity of the estuarine region have developed rapidly, resulting in a sharp increase in the population concerned. The increasing demand for human activities, agriculture irrigation, and aquaculture relies on massive pumping of water in estuarine area. Since the 1950s, numerous studies have focused on the effects of tidal fluctuations on groundwater flow in the estuarine area. Tide-induced head fluctuation in a two-dimensional estuarine aquifer system is complicated and rather important in dealing with many groundwater management or remediation problems. The conceptual model of the aquifer system considered is multi-layered with estuarine bank and the leaky aquifer extend finite distance under the estuary. The solution of the model describing the groundwater head distribution in such an estuarine aquifer system and subject to the tidal fluctuation effects from estuarine river is developed based on the method of separation of variables along with river boundary. The solutions by Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour. Res. 1997; 33:1429-35) as well as Tang and Jiao (Tang Z. and J. J. Jiao, A two-dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water, Hydrological Processes, 2001; 15: 573-585) can be shown to be special cases of the present solution. On the basis of the analytical solution, the groundwater head distribution in response to estuarine boundary is examined and the influences of leakage, hydraulic parameters, and loading effect on the groundwater head fluctuation due to tide are investigated and discussed. KEYWORDS: analytical model, estuarine river, groundwater fluctuation, leaky aquifer.
An accurate two-dimensional LBIC solution for bipolar transistors
Benarab, A.; Baudrand, H.; Lescure, M.; Boucher, J.
1988-05-01
A complete solution of the diffusion problem of carriers generated by a located light beam in the emitter and base region of a bipolar structure is presented. Green's function method and moment method are used to solve the 2-D diffusion equation in these regions. From the Green's functions solution of these equations, the light beam induced currents (LBIC) in the different junctions of the structure due to an extended generation represented by a rectangular light spot; are thus decided. The equations of these currents depend both on the parameters which characterise the structure, surface states, dimensions of the emitter and the base region, and the characteristics of the light spot, that is to say, the width and the wavelength. Curves illustrating the variation of the various LBIC in the base region junctions as a function of the impact point of the light beam ( x0) for different values of these parameters are discussed. In particular, the study of the base-emitter currents when the light beam is swept right across the sample illustrates clearly a good geometrical definition of the emitter region up to base end of the emitter-base space-charge areas and a "whirl" lateral diffusion beneath this region, (i.e. the diffusion of the generated carriers near the surface towards the horizontal base-emitter junction and those created beneath this junction towards the lateral (B-E) junctions).
Analytic theory for the selection of a two-dimensional needle crystal at arbitrary Peclet number
Tanveer, S.
1989-01-01
An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.
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.
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.
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.
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...
Exact Solution of the Two-Dimensional Problem on an Impact Ideal-Liquid Jet
Belik, V. D.
2018-05-01
The two-dimensional problem on the collision of a potential ideal-liquid jet, outflowing from a reservoir through a nozzle, with an infinite plane obstacle was considered for the case where the distance between the nozzle exit section and the obstacle is finite. An exact solution of this problem has been found using methods of the complex-variable function theory. Simple analytical expressions for the complex velocity of the liquid, its flow rate, and the force of action of the jet on the obstacle have been obtained. The velocity distributions of the liquid at the nozzle exit section, in the region of spreading of the jet, and at the obstacle have been constructed for different distances between the nozzle exit section and the obstacle. Analytical expressions for the thickness of the boundary layer and the Nusselt number at the point of stagnation of the jet have been obtained. A number of distributions of the local friction coefficient and the Nusselt number of the indicated jet are presented.
Two-dimensional threshold voltage analytical model of DMG strained-silicon-on-insulator MOSFETs
International Nuclear Information System (INIS)
Li Jin; Liu Hongxia; Li Bin; Cao Lei; Yuan Bo
2010-01-01
For the first time, a simple and accurate two-dimensional analytical model for the surface potential variation along the channel in fully depleted dual-material gate strained-Si-on-insulator (DMG SSOI) MOSFETs is developed. We investigate the improved short channel effect (SCE), hot carrier effect (HCE), drain-induced barrier-lowering (DIBL) and carrier transport efficiency for the novel structure MOSFET. The analytical model takes into account the effects of different metal gate lengths, work functions, the drain bias and Ge mole fraction in the relaxed SiGe buffer. The surface potential in the channel region exhibits a step potential, which can suppress SCE, HCE and DIBL. Also, strained-Si and SOI structure can improve the carrier transport efficiency, with strained-Si being particularly effective. Further, the threshold voltage model correctly predicts a 'rollup' in threshold voltage with decreasing channel length ratios or Ge mole fraction in the relaxed SiGe buffer. The validity of the two-dimensional analytical model is verified using numerical simulations. (semiconductor devices)
Solution-Based Processing and Applications of Two-Dimensional Heterostructures
Hersam, Mark
Two-dimensional materials have emerged as promising candidates for next-generation electronics and optoelectronics, but advances in scalable nanomanufacturing are required to exploit this potential in real-world technology. This talk will explore methods for improving the uniformity of solution-processed two-dimensional materials with an eye toward realizing dispersions and inks that can be deposited into large-area thin-films. In particular, density gradient ultracentrifugation allows the solution-based isolation of graphene, boron nitride, montmorillonite, and transition metal dichalcogenides (e.g., MoS2, WS2, ReS2, MoSe2, WSe2) with homogeneous thickness down to the atomically thin limit. Similarly, two-dimensional black phosphorus is isolated in organic solvents or deoxygenated aqueous surfactant solutions with the resulting phosphorene nanosheets showing field-effect transistor mobilities and on/off ratios that are comparable to micromechanically exfoliated flakes. By adding cellulosic polymer stabilizers to these dispersions, the rheological properties can be tuned by orders of magnitude, thereby enabling two-dimensional material inks that are compatible with a range of additive manufacturing methods including inkjet, gravure, screen, and 3D printing. The resulting solution-processed two-dimensional heterostructures show promise in several device applications including photodiodes, anti-ambipolar transistors, gate-tunable memristors, and heterojunction photovoltaics.
Perturbation theory and coupling constant analyticity in two-dimensional field theories
International Nuclear Information System (INIS)
Simon, B.
1973-01-01
Conjectural material and results over a year old are presented in the discussion of perturbation theory and coupling constant analyticity in two-dimensional field theories. General properties of perturbation series are discussed rather than questions of field theory. The question is interesting for two reasons: First, one would like to understand why perturbation theory is such a good guide (to show that perturbation theory determines the theory in some way). Secondly, one hopes to prove that some or all of the theories are nontrivial. (U.S.)
Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field
International Nuclear Information System (INIS)
Hoang, Ngoc-Tram D.; Nguyen, Duy-Anh P.; Hoang, Van-Hung; Le, Van-Hoang
2016-01-01
Explicit expressions are given for analytically describing the dependence of the energy of a two-dimensional exciton on magnetic field intensity. These expressions are highly accurate with the precision of up to three decimal places for the whole range of the magnetic field intensity. The results are shown for the ground state and some excited states; moreover, we have all formulae to obtain similar expressions of any excited state. Analysis of numerical results shows that the precision of three decimal places is maintained for the excited states with the principal quantum number of up to n=100.
Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field
Energy Technology Data Exchange (ETDEWEB)
Hoang, Ngoc-Tram D. [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Nguyen, Duy-Anh P. [Department of Natural Science, Thu Dau Mot University, 6, Tran Van On Street, Thu Dau Mot City, Binh Duong Province (Viet Nam); Hoang, Van-Hung [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: levanhoang@tdt.edu.vn [Atomic Molecular and Optical Physics Research Group, Ton Duc Thang University, 19 Nguyen Huu Tho Street, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Faculty of Applied Sciences, Ton Duc Thang University, 19 Nguyen Huu Tho Street, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam)
2016-08-15
Explicit expressions are given for analytically describing the dependence of the energy of a two-dimensional exciton on magnetic field intensity. These expressions are highly accurate with the precision of up to three decimal places for the whole range of the magnetic field intensity. The results are shown for the ground state and some excited states; moreover, we have all formulae to obtain similar expressions of any excited state. Analysis of numerical results shows that the precision of three decimal places is maintained for the excited states with the principal quantum number of up to n=100.
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
Two numerical methods for the solution of two-dimensional eddy current problems
International Nuclear Information System (INIS)
Biddlecombe, C.S.
1978-07-01
A general method for the solution of eddy current problems in two dimensions - one component of current density and two of magnetic field, is reported. After examining analytical methods two numerical methods are presented. Both solve the two dimensional, low frequency limit of Maxwell's equations for transient eddy currents in conducting material, which may be permeable, in the presence of other non-conducting permeable material. Both solutions are expressed in terms of the magnetic vector potential. The first is an integral equation method, using zero order elements in the discretisation of the unknown source regions. The other is a differential equation method, using a first order finite element mesh, and the Galerkin weighted residual procedure. The resulting equations are solved as initial-value problems. Results from programs based on each method are presented showing the power and limitations of the methods and the range of problems solvable. The methods are compared and recommendations are made for choosing between them. Suggestions are made for improving both methods, involving boundary integral techniques. (author)
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 compact breather-like solutions of two-dimensional Fermi-Pasta-Ulam lattice
International Nuclear Information System (INIS)
Sarkar, Ranja; Dey, Bishwajyoti
2006-01-01
We demonstrate that two-dimensional Fermi-Pasta-Ulam lattice support exact discrete compact breather-like solutions. We also find exact compact breather solutions of the same lattice in presence of long-range interaction with r -s dependence on the distance in the continuum limit. The usefulness of these solutions for energy localization and transport in various physical systems are discussed. (letter to the editor)
Energy Technology Data Exchange (ETDEWEB)
Basso Barichello, Liliane; Dias da Cunha, Rudnei [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst. de Matematica; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2015-05-15
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps
International Nuclear Information System (INIS)
Méndez-Bermúdez, J.A.; Oliveira, Juliano A. de; Leonel, Edson D.
2016-01-01
The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.
Analytic structure and power series expansion of the Jost function for the two-dimensional problem
International Nuclear Information System (INIS)
Rakityansky, S A; Elander, N
2012-01-01
For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. (paper)
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)
Eliezer, S.; Loeb, A.
1985-08-01
A simple model in two dimensions is developed and solved analytically taking into account the electric and magnetic fields in laser procuded plasmas. The electric potential in this model is described by a nonlinear differential equation. The stationary solution of this model is consistent for -0.1 less than or equal to psi 6 v/cm]/[B/MGauss] approx. 1
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.)
Non-Schwinger solution of the two-dimensional massless spinor electrodynamics
International Nuclear Information System (INIS)
Mikhov, S.G.
1981-01-01
In the present paper a regularization procedure is formulated for the current in the two-dimensional massless spinor electrodynamics that is both gauge and γ 5 -gauge invariant. This gives rise to an operator solution of the model that does not involve a massive photon. The latter solution is studied in some detail, and it is shown that although a charge operator exists, it does not define the electric charge of the spinor field. This can be a manifestation of the charge screening mechanism that is present in the Schwinger model [ru
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
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
International Nuclear Information System (INIS)
Chan, T.; Nakka, B.W.
1994-12-01
A two-dimensional analytical well model has been developed to describe steady groundwater flow in an idealized, confined aquifer intersected by a withdrawal well. The aquifer comprises a low-dipping fracture zone. The model is useful for making simple quantitative estimates of the transport of contaminants along groundwater pathways in the fracture zone to the well from an underground source that intercepts the fracture zone. This report documents the mathematical development of the analytical well model. It outlines the assumptions and method used to derive an exact analytical solution, which is verified by two other methods. It presents expressions for calculating quantities such as streamlines (groundwater flow paths), fractional volumetric flow rates, contaminant concentration in well water and minimum convective travel time to the well. In addition, this report presents the results of applying the analytical model to a site-specific conceptual model of the Whiteshell Research Area in southeastern Manitoba, Canada. This hydrogeological model includes the presence of a 20-m-thick, low-dipping (18 deg) fracture zone (LD1) that intercepts the horizon of a hypothetical disposal vault located at a depth of 500 m. A withdrawal well intercepts LD1 between the vault level and the ground surface. Predictions based on parameters and boundary conditions specific to LD1 are presented graphically. The analytical model has specific applications in the SYVAC geosphere model (GEONET) to calculate the fraction of a plume of contaminants moving up the fracture zone that is captured by the well, and to describe the drawdown in the hydraulic head in the fracture zone caused by the withdrawal well. (author). 16 refs., 6 tabs., 35 figs
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)
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
Energy Technology Data Exchange (ETDEWEB)
Zhu, Jian; Kang, Joohoon; Kang, Junmo; Jariwala, Deep; Wood, Joshua D.; Seo, Jung-Woo T.; Chen, Kan-Sheng; Marks, Tobin J.; Hersam, Mark C.
2015-10-14
Gate dielectrics directly affect the mobility, hysteresis, power consumption, and other critical device metrics in high-performance nanoelectronics. With atomically flat and dangling bond-free surfaces, hexagonal boron nitride (h-BN) has emerged as an ideal dielectric for graphene and related two-dimensional semiconductors. While high-quality, atomically thin h-BN has been realized via micromechanical cleavage and chemical vapor deposition, existing liquid exfoliation methods lack sufficient control over h-BN thickness and large-area film quality, thus limiting its use in solution-processed electronics. Here, we employ isopycnic density gradient ultracentrifugation for the preparation of monodisperse, thickness-sorted h-BN inks, which are subsequently layer-by-layer assembled into ultrathin dielectrics with low leakage currents of 3 × 10–9 A/cm2 at 2 MV/cm and high capacitances of 245 nF/cm2. The resulting solution-processed h-BN dielectric films enable the fabrication of graphene field-effect transistors with negligible hysteresis and high mobilities up to 7100 cm2 V–1 s–1 at room temperature. These h-BN inks can also be used as coatings on conventional dielectrics to minimize the effects of underlying traps, resulting in improvements in overall device performance. Overall, this approach for producing and assembling h-BN dielectric inks holds significant promise for translating the superlative performance of two-dimensional heterostructure devices to large-area, solution-processed nanoelectronics.
Cross Validation Through Two-Dimensional Solution Surface for Cost-Sensitive SVM.
Gu, Bin; Sheng, Victor S; Tay, Keng Yeow; Romano, Walter; Li, Shuo
2017-06-01
Model selection plays an important role in cost-sensitive SVM (CS-SVM). It has been proven that the global minimum cross validation (CV) error can be efficiently computed based on the solution path for one parameter learning problems. However, it is a challenge to obtain the global minimum CV error for CS-SVM based on one-dimensional solution path and traditional grid search, because CS-SVM is with two regularization parameters. In this paper, we propose a solution and error surfaces based CV approach (CV-SES). More specifically, we first compute a two-dimensional solution surface for CS-SVM based on a bi-parameter space partition algorithm, which can fit solutions of CS-SVM for all values of both regularization parameters. Then, we compute a two-dimensional validation error surface for each CV fold, which can fit validation errors of CS-SVM for all values of both regularization parameters. Finally, we obtain the CV error surface by superposing K validation error surfaces, which can find the global minimum CV error of CS-SVM. Experiments are conducted on seven datasets for cost sensitive learning and on four datasets for imbalanced learning. Experimental results not only show that our proposed CV-SES has a better generalization ability than CS-SVM with various hybrids between grid search and solution path methods, and than recent proposed cost-sensitive hinge loss SVM with three-dimensional grid search, but also show that CV-SES uses less running time.
Claessens, H.A.; Lammerts van Bueren, L.G.D.
1987-01-01
Smoke aerosol from stoves consists of a wide variety of chemical substances of which a number have toxic properties. To study the impact of aerosol emissions on health and environment reliable analytical procedures must be available for these samples. An off-line two-dimensional HPLC method is
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)
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
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
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.
International Nuclear Information System (INIS)
Lubuma, M.S.
1991-05-01
The applicability of the Neumann indirect method of potentials to the Dirichlet and Neumann problems for the two-dimensional Stokes operator on a non smooth boundary Γ is subject to two kinds of sufficient and/or necessary conditions on Γ. The first one, occurring in electrostatic, is equivalent to the boundedness on C(Γ) of the velocity double layer potential W as well as to the existence of jump relations of potentials. The second condition, which forces Γ to be a simple rectifiable curve and which, compared to the Laplacian, is a stronger restriction on the corners of Γ, states that the Fredholm radius of W is greater than 2. Under these conditions, the Radon boundary integral equations defined by the above mentioned jump relations are solvable by the Fredholm theory; the double (for Dirichlet) and the single (for Neumann) layer potentials corresponding to their solutions are classical solutions of the Stokes problems. (author). 48 refs
International Nuclear Information System (INIS)
Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.
1990-01-01
A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems
Energy Technology Data Exchange (ETDEWEB)
Liu, L.H. [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001 (China)]. E-mail: lhliu@hit.edu.cn
2006-11-15
In graded index media, the ray goes along a curved path determined by Fermat principle. Generally, the curved ray trajectory in graded index media is a complex implicit function, and the curved ray tracing is very difficult and complex. Only for some special refractive index distributions, the curved ray trajectory can be expressed as a simple explicit function. Two important examples are the layered and the radial graded index distributions. In this paper, the radiative heat transfer problems in two-dimensional square semitransparent with layered and radial graded index distributions are analyzed. After deduction of the ray trajectory, the radiative heat transfer problems are solved by using the Monte Carlo curved ray-tracing method. Some numerical solutions of dimensionless net radiative heat flux and medium temperature are tabulated as the benchmark solutions for the future development of approximation techniques for multi-dimensional radiative heat transfer in graded index media.
Equidistance of the complex two-dimensional anharmonic oscillator spectrum: the exact solution
International Nuclear Information System (INIS)
Cannata, F; Ioffe, M V; Nishnianidze, D N
2012-01-01
We study a class of quantum two-dimensional models with complex potentials of a specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to the conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must also include the corresponding associated functions. In the specific case of anharmonic second plus fourth-order interaction, expressions for the wavefunctions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wavefunctions is given. (paper)
International Nuclear Information System (INIS)
Li Cong; Zhuang Yi-Qi; Zhang Li; Jin Gang
2014-01-01
A two-dimensional analytical subthreshold behavior model for junctionless dual-material cylindrical surrounding-gate (JLDMCSG) metal-oxide-semiconductor field-effect transistors (MOSFETs) is proposed. It is derived by solving the two-dimensional Poisson's equation in two continuous cylindrical regions with any simplifying assumption. Using this analytical model, the subthreshold characteristics of JLDMCSG MOSFETs are investigated in terms of channel electrostatic potential, horizontal electric field, and subthreshold current. Compared to junctionless single-material cylindrical surrounding-gate MOSFETs, JLDMCSG MOSFETs can effectively suppress short-channel effects and simultaneously improve carrier transport efficiency. It is found that the subthreshold current of JLDMCSG MOSFETs can be significantly reduced by adopting both a thin oxide and thin silicon channel. The accuracy of the analytical model is verified by its good agreement with the three-dimensional numerical simulator ISE TCAD
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
Directory of Open Access Journals (Sweden)
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.
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
Novel solution conformation of DNA observed in d(GAATTCGAATTC) by two-dimensional NMR spectroscopy
International Nuclear Information System (INIS)
Chary, K.V.R.; Hosur, R.V.; Govil, G.; Zu-kun, T.; Miles, H.T.
1987-01-01
Resonance assignments of nonexchangeable base and sugar protons of the self-complementary dodecanucleotide d(GAATTCGAATTC) have been obtained by using the two-dimensional Fourier transform NMR methods correlated spectroscopy and nuclear Overhauser effect spectroscopy. Conformational details about the sugar pucker, the glycosidic dihedral angle, and the overall secondary structure of the molecule has been derived from the relative intensities of cross peaks in the two-dimensional NMR spectra in aqueous solution. It is observed that d(GAATTCGAATTC) assumes a novel double-helical structure. The solution conformations of the two complementary strands are identical, unlike those observed in a related sequence in the solid state. Most of the five-membered sugar rings adopt an unusual O1'-endo geometry. All the glycosidic dihedral angles are in the anti domain. The AATT segments A2-T5 and A8-T11 show better stacking compared to the rest of the molecule. These features fit into a right-handed DNA model for the above two segments, with the sugar geometries different from the conventional ones. There are important structural variations in the central TCG portion, which is known to show preferences for DNase I activity, and between G1-A2 and G7-A8, which are cleavage points in the EcoRI recognition sequence. The sugar puckers for G1 and G7 are significantly different from the rest of the molecule. Further, in the three segments mentioned above, the sugar phosphate geometry is such that the distances between protons on adjacent nucleotides are much larger than those expected for a right-handed DNA. The authors suggest that such crevices in the DNA structure may act as hot points in initiation of protein recognition
Energy Technology Data Exchange (ETDEWEB)
Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione
1997-10-01
Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.
Solution structures of α-conotoxin G1 determined by two-dimensional NMR spectroscopy
International Nuclear Information System (INIS)
Pardi, A.; Galdes, A.; Florance, J.; Maniconte, D.
1989-01-01
Two-dimensional NMR data have been used to generate solution structures of α-conotoxin G1, a potent peptide antagonist of the acetylcholine receptor. Structural information was obtained in the form of proton-proton internuclear distance constraints, and initial structures were produced with a distance geometry algorithm. Energetically more favorable structures were generated by using the distance geometry structures as input for a constrained energy minimization program. The results of both of these calculations indicate that the overall backbone conformation of the molecule is well-defined by the NMR data whereas the side-chain conformations are generally less well-defined. The main structural features derived from the NMR data were the presence of tight turns centered on residues Pro 5 and Arg 9 . The solution structures are compared with previous proposed models of conotoxin G1, and the NMR data are interpreted in conjunction with chemical modification studies and structural properties of other antagonists of the acetylcholine receptor to gain insight into structure-activity relationships in these peptide toxins
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
Chen, Kewei; Zhan, Hongbin
2018-06-01
The reactive solute transport in a single fracture bounded by upper and lower matrixes is a classical problem that captures the dominant factors affecting transport behavior beyond pore scale. A parallel fracture-matrix system which considers the interaction among multiple paralleled fractures is an extension to a single fracture-matrix system. The existing analytical or semi-analytical solution for solute transport in a parallel fracture-matrix simplifies the problem to various degrees, such as neglecting the transverse dispersion in the fracture and/or the longitudinal diffusion in the matrix. The difficulty of solving the full two-dimensional (2-D) problem lies in the calculation of the mass exchange between the fracture and matrix. In this study, we propose an innovative Green's function approach to address the 2-D reactive solute transport in a parallel fracture-matrix system. The flux at the interface is calculated numerically. It is found that the transverse dispersion in the fracture can be safely neglected due to the small scale of fracture aperture. However, neglecting the longitudinal matrix diffusion would overestimate the concentration profile near the solute entrance face and underestimate the concentration profile at the far side. The error caused by neglecting the longitudinal matrix diffusion decreases with increasing Peclet number. The longitudinal matrix diffusion does not have obvious influence on the concentration profile in long-term. The developed model is applied to a non-aqueous-phase-liquid (DNAPL) contamination field case in New Haven Arkose of Connecticut in USA to estimate the Trichloroethylene (TCE) behavior over 40 years. The ratio of TCE mass stored in the matrix and the injected TCE mass increases above 90% in less than 10 years.
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.)
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Jin, Li; Hongxia, Liu; Bin, Li; Lei, Cao; Bo, Yuan
2010-08-01
For the first time, a simple and accurate two-dimensional analytical model for the surface potential variation along the channel in fully depleted dual-material gate strained-Si-on-insulator (DMG SSOI) MOSFETs is developed. We investigate the improved short channel effect (SCE), hot carrier effect (HCE), drain-induced barrier-lowering (DIBL) and carrier transport efficiency for the novel structure MOSFET. The analytical model takes into account the effects of different metal gate lengths, work functions, the drain bias and Ge mole fraction in the relaxed SiGe buffer. The surface potential in the channel region exhibits a step potential, which can suppress SCE, HCE and DIBL. Also, strained-Si and SOI structure can improve the carrier transport efficiency, with strained-Si being particularly effective. Further, the threshold voltage model correctly predicts a “rollup" in threshold voltage with decreasing channel length ratios or Ge mole fraction in the relaxed SiGe buffer. The validity of the two-dimensional analytical model is verified using numerical simulations.
International Nuclear Information System (INIS)
Schunert, Sebastian; Azmy, Yousry Y.
2011-01-01
The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally ne mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite rst eliminates the aforementioned limitation of ne mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme. (author)
Wang, Tiansi; Zhang, Chong; Aleksov, Aleksandar; Salama, Islam; Kar, Aravinda
2017-04-01
Phased array ultrasonic transducers enable modulating the focal position of the acoustic waves, and this capability is utilized in many applications, such as medical imaging and non-destructive testing. This type of transducers also provides a mechanism to generate tilted wavefronts in acousto-optic deflectors to deflect laser beams for high precision advanced laser material processing. In this paper, a theoretical model is presented for the diffraction of ultrasonic waves emitted by several phased array transducers into an acousto-optic medium such as TeO 2 crystal. A simple analytic expression is obtained for the distribution of the ultrasonic displacement field in the crystal. The model prediction is found to be in good agreement with the results of a numerical model that is based on a non-paraxial multi-Gaussian beam (NMGB) model. Published by Elsevier B.V.
Analytical method for steady state heat transfer in two-dimensional porous media
Energy Technology Data Exchange (ETDEWEB)
Siegal, R.; Goldstein, M.E.
1970-07-01
A general technique has been devised for obtaining exact solutions for the heat transfer behavior of a 2- dimensional porous cooled medium. Fluid flows through the porous medium from a reservoir at constant pressure and temperature to a second reservoir at a lower pressure. For the type of flow involved, the surfaces of the porous region that are each at constant pressure are boundaries of constant velocity potential. This fact is used to map the porous region into a strip bounded by parallel potential lines in a complex potential plane. The energy equation, derived by assuming the local matrix and fluid temperatures are equal, is transformed into a separable equation when its independent variables are changed to the coordinates of the potential plane. This allows the general solution for the temperature distribution to be found in the potential plane. The solution is then mapped into the physical plane to yield the heat transfer characteristics of the porous region. An example problem of a porous wall having a step in thickness and a specified surface temperature or heat flux is worked out in detail.
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
Two-dimensional analytical model for dual-material control-gate tunnel FETs
Xu, Hui Fang; Dai, Yue Hua; Gui Guan, Bang; Zhang, Yong Feng
2016-09-01
An analytical model for a dual-material control-gate (DMCG) tunnel field effect transistor (TFET) is presented for the first time in this paper, and the influence of the mobile charges on the potential profile is taken into account. On the basis of the potential profile, the lateral electric field is derived and the expression for the drain current is obtained by integrating the band-to-band tunneling (BTBT) generation rate applicable to low-bandgap and high-bandgap materials over the tunneling region. The model also predicts the impacts of the control-gate work function on the potential and drain current. The advantage of this work is that it not only offers physical insight into device physics but also provides the basic designing guideline for DMCG TFETs, enabling the designer to optimize the device in terms of the on-state current, the on-off current ratio, and suppressed ambipolar behavior. Very good agreements for both the potential and drain current are observed between the model calculations and the simulated results.
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.
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)
Cresti, Alessandro; Grosso, Giuseppe; Parravicini, Giuseppe Pastori
2006-01-01
We have derived closed analytic expressions for the Green's function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green's functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green's function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of the Green's function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green's function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems
Directory of Open Access Journals (Sweden)
J. Kalas
2012-01-01
Full Text Available The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for $t$ approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.
Superintegrability in two-dimensional Euclidean space and associated polynomial solutions
International Nuclear Information System (INIS)
Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.
1996-01-01
In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab
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
A solution of two-dimensional magnetohydrodynamic flow using the finite volume method
Directory of Open Access Journals (Sweden)
Naceur Sonia
2014-01-01
Full Text Available This paper presents the two dimensional numerical modeling of the coupling electromagnetic-hydrodynamic phenomena in a conduction MHD pump using the Finite volume Method. Magnetohydrodynamic problems are, thus, interdisciplinary and coupled, since the effect of the velocity field appears in the magnetic transport equations, and the interaction between the electric current and the magnetic field appears in the momentum transport equations. The resolution of the Maxwell's and Navier Stokes equations is obtained by introducing the magnetic vector potential A, the vorticity z and the stream function y. The flux density, the electromagnetic force, and the velocity are graphically presented. Also, the simulation results agree with those obtained by Ansys Workbench Fluent software.
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
International Nuclear Information System (INIS)
Widom, Julia R; Marcus, Andrew H; Johnson, Neil P; Von Hippel, Peter H
2013-01-01
We have observed the conformation-dependent electronic coupling between the monomeric subunits of a dinucleotide of 2-aminopurine (2-AP), a fluorescent analogue of the nucleic acid base adenine. This was accomplished by extending two-dimensional fluorescence spectroscopy (2D FS)—a fluorescence-detected variation of 2D electronic spectroscopy—to excite molecular transitions in the ultraviolet (UV) regime. A collinear sequence of four ultrafast laser pulses centered at 323 nm was used to resonantly excite the coupled transitions of 2-AP dinucleotide. The phases of the optical pulses were continuously swept at kilohertz frequencies, and the ensuing nonlinear fluorescence was phase-synchronously detected at 370 nm. Upon optimization of a point–dipole coupling model to our data, we found that in aqueous buffer the 2-AP dinucleotide adopts an average conformation in which the purine bases are non-helically stacked (center-to-center distance R 12 = 3.5 ± 0.5 Å , twist angle θ 12 = 5° ± 5° ), which differs from the conformation of such adjacent bases in duplex DNA. These experiments establish UV–2D FS as a method for examining the local conformations of an adjacent pair of fluorescent nucleotides substituted into specific DNA or RNA constructs, which will serve as a powerful probe to interpret, in structural terms, biologically significant local conformational changes within the nucleic acid framework of protein–nucleic acid complexes. (paper)
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
Numerical solution of two-dimensional non-linear partial differential ...
African Journals Online (AJOL)
linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...
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
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
Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies
Fuller, Franklyn B.
1961-01-01
The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.
A matrix integral solution to two-dimensional Wp-gravity
International Nuclear Information System (INIS)
Adler, M.; Moerbeke, P. van; Louvain Univ., Louvain-la-Neuve
1992-01-01
The p th Gel'fand-Dickey equation and the string equation [L.P.] = 1 have a common solution τ experessible in terms of an integral over n x n Hermitean matrices (for large n). the integrand being a perturbation of a Gaussian. generalizing Kontsevich's inegral beyond the KdV-case; it is equivalent to showing that τ is a vacuum vector for a Q p + -algebra, generated from the coefficients of the vertex operator. This connectionis established via a quadratic identity involving the wave function and the vertex operator, which is disguised differential version of the Fay identity. The latter is also the key to the spectral theory for the two compatible symplectic structures of KdV in terms of the stress-energy tensor associated with the Virasoro algebra. Given a differential operator L=D p +q 2 (t)D p-2 +...+q p (t), with D=d/dx, t=(t 1 , t 2 , t 3 , ...), x=t 1 , consider the deformation equations dL/dt n =[(L n/p ) + , L] n=1, 2, ..., n≠0(mod p) (p-reduced KP-equation) of L, for which there exists a differential operator P (possibly of infinite order) such that [L, P]=1 (string equation). In this note, we give a complete solution to this problem. (orig./HSI)
Directory of Open Access Journals (Sweden)
Giao N. Pham
2018-05-01
Full Text Available Nowadays, three-dimensional (3D printing technology is applied to many areas of life and changes the world based on the creation of complex structures and shapes that were not feasible in the past. But, the data of 3D printing is often attacked in the storage and transmission processes. Therefore, 3D printing must be ensured security in the manufacturing process, especially the data of 3D printing to prevent attacks from hackers. This paper presents a security solution for 3D printing based on two-dimensional (2D slices encryption. The 2D slices of 3D printing data is encrypted in the frequency domain or in the spatial domain by the secret key to generate the encrypted data of 3D printing. We implemented the proposed solution in both the frequency domain based on the Discrete Cosine Transform and the spatial domain based on geometric transform. The entire 2D slices of 3D printing data is altered and secured after the encryption process. The proposed solution is responsive to the security requirements for the secured storage and transmission. Experimental results also verified that the proposed solution is effective to 3D printing data and is independent on the format of 3D printing models. When compared to the conventional works, the security and performance of the proposed solution is also better.
Directory of Open Access Journals (Sweden)
Marco Rosales-Vera
2012-01-01
Full Text Available The problem of a hydromagnetic hot two-dimensional laminar jet issuing vertically into an otherwise quiescent fluid of a lower temperature is studied. We propose solutions to the boundary layer equations using the classical Fourier series. The method is essentiall to transform the boundary layer equations to a coupled set of nonlinear first-order ordinary differential equations through the Fourier series. The accuracy of the results has been tested by the comparison of the velocity distributions obtained by the Fourier series with those calculated by finite difference method. The results show that the present method, based on the Fourier series, is an efficient method, suitable to solve boundary layer equations applied to plane jet flows with high accuracy.
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
Directory of Open Access Journals (Sweden)
Shoubin Wang
2017-01-01
Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.
Analytic solutions of hydrodynamics equations
International Nuclear Information System (INIS)
Coggeshall, S.V.
1991-01-01
Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions
Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube
Zhou, Guangzhao; Xu, Kun; Liu, Feng
2018-01-01
The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics are of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru and Tenaud ["Evaluation of TVD high resolution schemes for unsteady viscous shocked flows," Comput. Fluids 30, 89-113 (2001)] proposed a two-dimensional model problem as a numerical test case for high-resolution schemes to simulate the flow field in a square closed shock tube. Though many researchers attempted this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting grid-converged solutions for this problem by using a newly developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analyzed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface. Presentation and analysis of those flow processes provide important physical insight into the complex flow physics occurring in a shock tube.
International Nuclear Information System (INIS)
Setare, M R; Kamali, V
2011-01-01
We show that a BTZ black hole solution of cosmological topological massive gravity has a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in BTZ spacetime and find that the wave equation could be written in terms of the SL(2, R) quadratic Casimir. From the conformal coordinates, the temperatures of the dual conformal field theories (CFTs) could be read directly. Moreover, we compute the microscopic entropy of the dual CFT by the Cardy formula and find a perfect match to the Bekenstein-Hawking entropy of a BTZ black hole. Then, we consider Galilean conformal algebras (GCA), which arises as a contraction of relativistic conformal algebras (x → εx, t → t, ε → 0). We show that there is a correspondence between GCA 2 on the boundary and contracted BTZ in the bulk. For this purpose we obtain the central charges and temperatures of GCA 2 . Then, we compute the microscopic entropy of the GCA 2 by the Cardy formula and find a perfect match to the Bekenstein-Hawking entropy of a BTZ black hole in a non-relativistic limit. The absorption cross section of a near-region scalar field also matches the microscopic absorption cross section of the dual GCA 2 . So we find further evidence that shows correspondence between a contracted BTZ black hole and two-dimensional GCA.
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)
Lin, Zhaoyang; Yin, Anxiang; Mao, Jun; Xia, Yi; Kempf, Nicholas; He, Qiyuan; Wang, Yiliu; Chen, Chih-Yen; Zhang, Yanliang; Ozolins, Vidvuds; Ren, Zhifeng; Huang, Yu; Duan, Xiangfeng
2016-10-01
Epitaxial heterostructures with precisely controlled composition and electronic modulation are of central importance for electronics, optoelectronics, thermoelectrics, and catalysis. In general, epitaxial material growth requires identical or nearly identical crystal structures with small misfit in lattice symmetry and parameters and is typically achieved by vapor-phase depositions in vacuum. We report a scalable solution-phase growth of symmetry-mismatched PbSe/Bi 2 Se 3 epitaxial heterostructures by using two-dimensional (2D) Bi 2 Se 3 nanoplates as soft templates. The dangling bond-free surface of 2D Bi 2 Se 3 nanoplates guides the growth of PbSe crystal without requiring a one-to-one match in the atomic structure, which exerts minimal restriction on the epitaxial layer. With a layered structure and weak van der Waals interlayer interaction, the interface layer in the 2D Bi 2 Se 3 nanoplates can deform to accommodate incoming layer, thus functioning as a soft template for symmetry-mismatched epitaxial growth of cubic PbSe crystal on rhombohedral Bi 2 Se 3 nanoplates. We show that a solution chemistry approach can be readily used for the synthesis of gram-scale PbSe/Bi 2 Se 3 epitaxial heterostructures, in which the square PbSe (001) layer forms on the trigonal/hexagonal (0001) plane of Bi 2 Se 3 nanoplates. We further show that the resulted PbSe/Bi 2 Se 3 heterostructures can be readily processed into bulk pellet with considerably suppressed thermal conductivity (0.30 W/m·K at room temperature) while retaining respectable electrical conductivity, together delivering a thermoelectric figure of merit ZT three times higher than that of the pristine Bi 2 Se 3 nanoplates at 575 K. Our study demonstrates a unique epitaxy mode enabled by the 2D nanocrystal soft template via an affordable and scalable solution chemistry approach. It opens up new opportunities for the creation of diverse epitaxial heterostructures with highly disparate structures and functions.
Eftekhari, Ali; Parastar, Hadi
2016-09-30
The present contribution is devoted to develop multivariate analytical figures of merit (AFOMs) as a new metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography-mass spectrometry (GC×GC-MS). In this regard, new definition of sensitivity (SEN) is extended to GC×GC-MS data and then, other multivariate AFOMs including analytical SEN (γ), selectivity (SEL) and limit of detection (LOD) are calculated. Also, two frequently used second- and third-order calibration algorithms of multivariate curve resolution-alternating least squares (MCR-ALS) as representative of multi-set methods and parallel factor analysis (PARAFAC) as representative of multi-way methods are discussed to exploit pure component profiles and to calculate multivariate AFOMs. Different GC×GC-MS data sets with different number of components along with various levels of artifacts are simulated and analyzed. Noise, elution time shifts in both chromatographic dimensions, peak overlap and interferences are considered as the main artifacts in this work. Additionally, a new strategy is developed to estimate the noise level using variance-covariance matrix of residuals which is very important to calculate multivariate AFOMs. Finally, determination of polycyclic aromatic hydrocarbons (PAHs) in aromatic fraction of heavy fuel oil (HFO) analyzed by GC×GC-MS is considered as real case to confirm applicability of the proposed metric in real samples. It should be pointed out that the proposed strategy in this work can be used for other types of comprehensive two-dimensional chromatographic (CTDC) techniques like comprehensive two dimensional liquid chromatography (LC×LC). Copyright © 2016 Elsevier B.V. All rights reserved.
Suemitsu, Yoshikazu; Nara, Shigetoshi
2004-09-01
Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.
Basic problems and solution methods for two-dimensional continuous 3 × 3 order hidden Markov model
International Nuclear Information System (INIS)
Wang, Guo-gang; Tang, Gui-jin; Gan, Zong-liang; Cui, Zi-guan; Zhu, Xiu-chang
2016-01-01
A novel model referred to as two-dimensional continuous 3 × 3 order hidden Markov model is put forward to avoid the disadvantages of the classical hypothesis of two-dimensional continuous hidden Markov model. This paper presents three equivalent definitions of the model, in which the state transition probability relies on not only immediate horizontal and vertical states but also immediate diagonal state, and in which the probability density of the observation relies on not only current state but also immediate horizontal and vertical states. The paper focuses on the three basic problems of the model, namely probability density calculation, parameters estimation and path backtracking. Some algorithms solving the questions are theoretically derived, by exploiting the idea that the sequences of states on rows or columns of the model can be viewed as states of a one-dimensional continuous 1 × 2 order hidden Markov model. Simulation results further demonstrate the performance of the algorithms. Because there are more statistical characteristics in the structure of the proposed new model, it can more accurately describe some practical problems, as compared to two-dimensional continuous hidden Markov model.
International Nuclear Information System (INIS)
Mao Wei; She Wei-Bo; Zhang Chao; Zhang Jin-Cheng; Zhang Jin-Feng; Liu Hong-Xia; Yang Lin-An; Zhang Kai; Zhao Sheng-Lei; Chen Yong-He; Zheng Xue-Feng; Hao Yue; Yang Cui; Ma Xiao-Hua
2014-01-01
In this paper, we present a two-dimensional (2D) fully analytical model with consideration of polarization effect for the channel potential and electric field distributions of the gate field-plated high electron mobility transistor (FP-HEMT) on the basis of 2D Poisson's solution. The dependences of the channel potential and electric field distributions on drain bias, polarization charge density, FP structure parameters, AlGaN/GaN material parameters, etc. are investigated. A simple and convenient approach to designing high breakdown voltage FP-HEMTs is also proposed. The validity of this model is demonstrated by comparison with the numerical simulations with Silvaco—Atlas. The method in this paper can be extended to the development of other analytical models for different device structures, such as MIS-HEMTs, multiple-FP HETMs, slant-FP HEMTs, etc. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Energy Technology Data Exchange (ETDEWEB)
Sawyer, Karma Rae [Univ. of California, Berkeley, CA (United States)
2008-12-01
Understanding chemical reactions requires the knowledge of the elementary steps of breaking and making bonds, and often a variety of experimental techniques are needed to achieve this goal. The initial steps occur on the femto- through picosecond time-scales, requiring the use of ultrafast spectroscopic methods, while the rate-limiting steps often occur more slowly, requiring alternative techniques. Ultrafast one and two-dimensional infrared and step-scan FTIR spectroscopies are used to investigate the photochemical reactions of four organometallic complexes. The analysis leads to a detailed understanding of mechanisms that are general in nature and may be applicable to a variety of reactions.
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
Yan, Xia; Wang, Li-Juan; Wu, Zhen; Wu, Yun-Long; Liu, Xiu-Xiu; Chang, Fang-Rong; Fang, Mei-Juan; Qiu, Ying-Kun
2016-10-15
Microbial metabolites represent an important source of bioactive natural products, but always exhibit diverse of chemical structures or complicated chemical composition with low active ingredients content. Traditional separation methods rely mainly on off-line combination of open-column chromatography and preparative high performance liquid chromatography (HPLC). However, the multi-step and prolonged separation procedure might lead to exposure to oxygen and structural transformation of metabolites. In the present work, a new two-dimensional separation workflow for fast isolation and analysis of microbial metabolites from Chaetomium globosum SNSHI-5, a cytotoxic fungus derived from extreme environment. The advantage of this analytical comprehensive two-dimensional liquid chromatography (2D-LC) lies on its ability to analyze the composition of the metabolites, and to optimize the separation conditions for the preparative 2D-LC. Furthermore, gram scale preparative 2D-LC separation of the crude fungus extract could be performed on a medium-pressure liquid chromatograph×preparative high-performance liquid chromatography system, under the optimized condition. Interestingly, 12 cytochalasan derivatives, including two new compounds named cytoglobosin Ab (3) and isochaetoglobosin Db (8), were successfully obtained with high purity in a short period of time. The structures of the isolated metabolites were comprehensively characterized by HR ESI-MS and NMR. To be highlighted, this is the first report on the combination of analytical and preparative 2D-LC for the separation of microbial metabolites. The new workflow exhibited apparent advantages in separation efficiency and sample treatment capacity compared with conventional methods. Copyright © 2016 Elsevier B.V. All rights reserved.
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.
Directory of Open Access Journals (Sweden)
2015-12-01
Full Text Available Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
Analytical Solution of a Generalized Hirota-Satsuma Equation
Kassem, M.; Mabrouk, S.; Abd-el-Malek, M.
A modified version of generalized Hirota-Satsuma is here solved using a two parameter group transformation method. This problem in three dimensions was reduced by Estevez [1] to a two dimensional one through a Lie transformation method and left unsolved. In the present paper, through application of symmetry transformation the Lax pair has been reduced to a system of ordinary equations. Three transformations cases are investigated. The obtained analytical solutions are plotted and show a profile proper to deflagration processes, well described by Degasperis-Procesi equation.
Kwak, Kyungwon; Rosenfeld, Daniel E; Chung, Jean K; Fayer, Michael D
2008-11-06
Hydrogen bonds formed between C-H and various hydrogen bond acceptors play important roles in the structure of proteins and organic crystals, and the mechanisms of C-H bond cleavage reactions. Chloroform, a C-H hydrogen bond donor, can form weak hydrogen-bonded complexes with acetone and with dimethylsulfoxide (DMSO). When chloroform is dissolved in a mixed solvent consisting of acetone and DMSO, both types of hydrogen-bonded complexes exist. The two complexes, chloroform-acetone and chloroform-DMSO, are in equilibrium, and they rapidly interconvert by chloroform exchanging hydrogen bond acceptors. This fast hydrogen bond acceptor substitution reaction is probed using ultrafast two-dimensional infrared (2D-IR) vibrational echo chemical exchange spectroscopy. Deuterated chloroform is used in the experiments, and the 2D-IR spectrum of the C-D stretching mode is measured. The chemical exchange of the chloroform hydrogen bonding partners is tracked by observing the time-dependent growth of off-diagonal peaks in the 2D-IR spectra. The measured substitution rate is 1/30 ps for an acetone molecule to replace a DMSO molecule in a chloroform-DMSO complex and 1/45 ps for a DMSO molecule to replace an acetone molecule in a chloroform-acetone complex. Free chloroform exists in the mixed solvent, and it acts as a reactive intermediate in the substitution reaction, analogous to a SN1 type reaction. From the measured rates and the equilibrium concentrations of acetone and DMSO, the dissociation rates for the chloroform-DMSO and chloroform-acetone complexes are found to be 1/24 ps and 1/5.5 ps, respectively. The difference between the measured rate for the complete substitution reaction and the rate for complex dissociation corresponds to the diffusion limited rate. The estimated diffusion limited rate agrees well with the result from a Smoluchowski treatment of diffusive reactions.
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
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.
Xu, Huifang; Dai, Yuehua
2017-02-01
A two-dimensional analytical model of double-gate (DG) tunneling field-effect transistors (TFETs) with interface trapped charges is proposed in this paper. The influence of the channel mobile charges on the potential profile is also taken into account in order to improve the accuracy of the models. On the basis of potential profile, the electric field is derived and the expression for the drain current is obtained by integrating the BTBT generation rate. The model can be used to study the impact of interface trapped charges on the surface potential, the shortest tunneling length, the drain current and the threshold voltage for varying interface trapped charge densities, length of damaged region as well as the structural parameters of the DG TFET and can also be utilized to design the charge trapped memory devices based on TFET. The biggest advantage of this model is that it is more accurate, and in its expression there are no fitting parameters with small calculating amount. Very good agreements for both the potential, drain current and threshold voltage are observed between the model calculations and the simulated results. Project supported by the National Natural Science Foundation of China (No. 61376106), the University Natural Science Research Key Project of Anhui Province (No. KJ2016A169), and the Introduced Talents Project of Anhui Science and Technology University.
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)
Bloem, Robbert; Dijkstra, Arend G.; Jansen, Thomas La Cour; Knoester, Jasper
2008-01-01
Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to
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
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.
Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors
Energy Technology Data Exchange (ETDEWEB)
Rivard, J B [Sandia Laboratories (United States)
1974-07-01
If azimuthal power density variations are ignored, the steady-state temperature distribution within a TRIGA-type fuel element is given by the solution of the Poisson equation in two dimensions (r and z) . This paper presents a closed-form solution of this equation as a function of the axial and radial power density profiles, the conductivity of the U-ZrH, the inlet temperature, specific heat and flow rate of the coolant, and the overall heat transfer coefficient. The method begins with the development of a system of linear ordinary differential equations describing mass and energy balances in the fuel and coolant. From the solution of this system, an expression for the second derivative of the fuel temperature distribution in the axial (z) direction is found. Substitution of this expression into the Poisson equation for T(r,z) reduces it from a partial differential equation to an ordinary differential equation in r, which is subsequently solved in closed-form. The results of typical calculations using the model are presented. (author)
Directory of Open Access Journals (Sweden)
Lulu Deng
2011-07-01
Full Text Available The phase and texture of a newly developed solution-processed copper phthalocyanine (CuPc thin film have been investigated by two-dimensional grazing incidence X-ray diffraction. The results show that it has β phase crystalline structure, with crystallinity greater than 80%. The average size of the crystallites is found to be about 24 nm. There are two different arrangements of crystallites, with one dominating the diffraction pattern. Both of them have preferred orientation along the thin film normal. Based on the similarities to the vacuum deposited CuPc thin films, the new solution processing method is verified to offer a good alternative to vacuum process, for the fabrication of low cost small molecule based organic photovoltaics.
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
Energy Technology Data Exchange (ETDEWEB)
Prinja, A.K.
1998-09-01
In this work, it has been shown that, for the given sets of parameters (transport coefficients), the Tangent-Predictor (TP) continuation method, which was used in the coarsest grid, works remarkably well. The problems in finding an initial guess that resides well within Newton`s method radius of convergence are alleviated by correcting the initial guess by the predictor step of the TP method. The TP method works well also in neutral gas puffing and impurity simulations. The neutral gas puffing simulation is performed by systematically increasing the fraction of puffing rate according to the TP method until it reaches a desired condition. Similarly, the impurity simulation characterized by using the fraction of impurity density as the continuation parameter, is carried out in line with the TP method. Both methods show, as expected, a better performance than the classical embedding (CE) method. The convergence criteria {epsilon} is set to be 10{sup {minus}9} based on the fact that lower value of {epsilon} does not alter the solution significantly. Correspondingly, the number of Newton`s iterations in the corrector step of the TP method decrease substantially, an extra point in terms of code speed. The success of the TP method enlarges the possibility of including other sets of parameters (operations and physics). With the availability of the converged coarsest grid solution, the next forward step to the multigrid cycle becomes possible. The multigrid method shows that the memory storage problems that plagued the application of Newton`s method on fine grids, are of no concern. An important result that needs to be noted here is the performance of the FFCD model. The FFCD model is relatively simple and is based on the overall results the model has shown to predict different divertor plasma parameters. The FFCD model treats exactly the implementation of the deep penetration of energetic neutrals emerging from the divertor plate. The resulting ionization profiles are
International Nuclear Information System (INIS)
Prinja, A.K.
1998-01-01
In this work, it has been shown that, for the given sets of parameters (transport coefficients), the Tangent-Predictor (TP) continuation method, which was used in the coarsest grid, works remarkably well. The problems in finding an initial guess that resides well within Newton's method radius of convergence are alleviated by correcting the initial guess by the predictor step of the TP method. The TP method works well also in neutral gas puffing and impurity simulations. The neutral gas puffing simulation is performed by systematically increasing the fraction of puffing rate according to the TP method until it reaches a desired condition. Similarly, the impurity simulation characterized by using the fraction of impurity density as the continuation parameter, is carried out in line with the TP method. Both methods show, as expected, a better performance than the classical embedding (CE) method. The convergence criteria ε is set to be 10 -9 based on the fact that lower value of ε does not alter the solution significantly. Correspondingly, the number of Newton's iterations in the corrector step of the TP method decrease substantially, an extra point in terms of code speed. The success of the TP method enlarges the possibility of including other sets of parameters (operations and physics). With the availability of the converged coarsest grid solution, the next forward step to the multigrid cycle becomes possible. The multigrid method shows that the memory storage problems that plagued the application of Newton's method on fine grids, are of no concern. An important result that needs to be noted here is the performance of the FFCD model. The FFCD model is relatively simple and is based on the overall results the model has shown to predict different divertor plasma parameters. The FFCD model treats exactly the implementation of the deep penetration of energetic neutrals emerging from the divertor plate. The resulting ionization profiles are relatively smooth as a
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
Stewart, A. L.; Dellar, P. J.
The component of the Coriolis force due to the locally horizontal component of the Earth's rotation vector is commonly neglected, under the so-called traditional approximation. We investigate the role of this "non-traditional" component of the Coriolis force in cross-equatorial flow of abyssal ocean currents. We focus on the Antarctic Bottom Water (AABW), which crosses from the southern to the northern hemisphere through the Ceara abyssal plain in the western Atlantic ocean. The bathymetry in this region resembles a northwestward channel, connecting the Brazil Basin in the south to the Guyana Basin in the north. South of the equator, the AABW leans against the western continental rise, consistent with a northward flow in approximate geostrophic balance. The AABW then crosses to the other side of the abyssal channel as it crosses the equator, and flows into the northern hemisphere leaning towards the east against the Mid-Atlantic Ridge. The non-traditional component of the Coriolis force is strongest close to the equator. The traditional component vanishes at the equator, being proportional to the locally vertical component of the Earth's rotation vector. The weak stratification of the abyssal ocean, and subsequent small internal deformation radius, defines a relatively short characteristic horizontal lengthscale that tends to make non-traditional effects more prominent. Additionally, the steep gradients of the channel bathymetry induce large vertical velocities, which are linked to zonal accelerations by the non-traditional components of the Coriolis force. We therefore expect non-traditional effects to play a substantial role in cross-equatorial transport of the AABW. We present asymptotic steady solutions for non-traditional shallow water flow through an idealised abyssal channel, oriented at an oblique angle to the equator. The current enters from the south, leaning up against the western side of the channel in approximate geostrophic balance, and crosses the
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.
Insight solutions are correct more often than analytic solutions
Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark
2016-01-01
How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
This paper presents an effective analytical simulation to solve population .... considering spatial dependence and growth, based on the so-called LPA formulation as .... But the particle size distribution is defined so that n(v,t) dx is the number of ..... that was made beforehand in the construction of the analytical solutions ...
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.
Analytic solutions of nonlinear Cournot duopoly game
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2005-01-01
Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.
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)
Thomas, P.D.; Basus, V.J.; James, T.L.
1991-01-01
Solution structures for many proteins have been determined to date utilizing interproton distance constraints estimated from two-dimensional nuclear Overhauser effect (2D NOE) spectra. Although the simple isolated spin pair approximation (ISPA) generally used can result in systematic errors in distances, the large number of constraints enables proteins structure to be defined with reasonably high resolution. Effects of these systematic errors on the resulting protein structure are examined. Iterative relaxation matrix calculations, which account for dipolar interactions between all protons in a molecule, can accurately determine internuclear distances with little or no a priori knowledge of the molecular structure. The value of this additional complexity is also addressed. To assess these distance determination methods, hypothetical experimental data, including random noise and peak overlap, are calculated for an arbitrary true protein structure. Three methods of obtaining distance constraints from 2D NOE peak intensities are examined: one entails a conservative use of ISPA, one assumes the ISPA to be fairly accurate, and on utilizes an iterative relaxation matrix method called MARDIGRAS (matrix analysis of relaxation for discerning the geometry of an aqueous structure), developed in this laboratory. An R factor for evaluating fit between experimental and calculated 2D NOE intensities is proposed
Bodin, Jacques
2015-03-01
In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.
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 ...
Analytic solution for a quartic electron mirror
Energy Technology Data Exchange (ETDEWEB)
Straton, Jack C., E-mail: straton@pdx.edu
2015-01-15
A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z{sup 2}−r{sup 2}/2) to which we add a quartic term (kλz{sup 4}). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile. - Highlights: • We find the analytical solution for electron mirrors whose curvature has z4 dependence added to the usual z{sup 2} – r{sup 2}/2 terms. • The resulting Jacobi cosine-amplitude function reduces to the well-known cosh solution in the limit where the new term is 0. • This quartic term gives a mirror designer additional flexibility for eliminating spherical and chromatic aberrations. • The possibility of using these analytical results to approximately model spherical tetrode mirrors close to axis is noted.
Closed form analytic solutions describing glow discharge plasma
International Nuclear Information System (INIS)
Pai, S.T.; Guo, X.M.; Zhou, T.D.
1996-01-01
On the basis of an analytic model developed previously [S. T. Pai, J. Appl. Phys. 71, 5820 (1992)], an improved version of the model for the description of dc glow discharge plasma was successfully developed. A set of closed form solutions was obtained from the governing equations. The two-dimensional, analytic solutions are functional and completely satisfy the governing equations, the actual boundary conditions, and Maxwell equations. They can be readily used to carry out numerical calculations without the necessity of employing any assumed boundary conditions. Results obtained from the model reveal that as the discharge gap spacing or pressure increases the maximum value in the electron density distribution moves toward the cathode. At a sufficiently large value of gap spacing, the positive column phenomenon begins to appear in the discharge region. The model has the capability of treating the positive column and negative glow as a continuous system without the necessity of studying them separately. The model also predicts a sharp rise of the positive ion density near the cathode and field reversal in the anode region. Variation of the electrode radius produces little effect on the axial spatial distribution of physical quantities studied. copyright 1996 American Institute of Physics
Surface solitons in waveguide arrays: Analytical solutions.
Kominis, Yannis; Papadopoulos, Aristeidis; Hizanidis, Kyriakos
2007-08-06
A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear or nonlinear homogeneous medium as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of each part in order to assure existence of solutions with specific profile characteristics. The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations and interesting features are presented such as their remarkable robustness which could facilitate their experimental observation.
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)
International Nuclear Information System (INIS)
Gureghian, A.B.
1979-01-01
A mathematical model of ground water transport through an aquifer is presented. The solute of interest is a metal tracer or radioactive material which may undergo decay through a sorbing unconfined aquifer. The subject is developed under the following headings: flow equation, solute equation, boundary conditions, finite element formulation, element formulation, solution scheme (flow equation, solute equation), results and discussions, water movement in a ditch drained aquifer under transient state, water and solute movement in a homogeneous and unsaturated soil, transport of 226 Ra in nonhomogeneous aquifer, tailings pond lined, and tailings pond unlined. It is concluded that this mathematical model may have a wide variety of applications. The uranium milling industry may find it useful to evaluate the hydrogeological suitability of their disposal sites. It may prove suited for the design of clay disposal ponds destined to hold hazardous liquids. It may also provide a means of estimating the long-term impact of radionuclides or other pollutants on the quality of ground water. 31 references, 9 figures, 3 tables
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 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
Analytic vortex solutions on compact hyperbolic surfaces
International Nuclear Information System (INIS)
Maldonado, Rafael; Manton, Nicholas S
2015-01-01
We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations. (paper)
Demirci, İsmail; Dikmen, Ünal; Candansayar, M. Emin
2018-02-01
Joint inversion of data sets collected by using several geophysical exploration methods has gained importance and associated algorithms have been developed. To explore the deep subsurface structures, Magnetotelluric and local earthquake tomography algorithms are generally used individually. Due to the usage of natural resources in both methods, it is not possible to increase data quality and resolution of model parameters. For this reason, the solution of the deep structures with the individual usage of the methods cannot be fully attained. In this paper, we firstly focused on the effects of both Magnetotelluric and local earthquake data sets on the solution of deep structures and discussed the results on the basis of the resolving power of the methods. The presence of deep-focus seismic sources increase the resolution of deep structures. Moreover, conductivity distribution of relatively shallow structures can be solved with high resolution by using MT algorithm. Therefore, we developed a new joint inversion algorithm based on the cross gradient function in order to jointly invert Magnetotelluric and local earthquake data sets. In the study, we added a new regularization parameter into the second term of the parameter correction vector of Gallardo and Meju (2003). The new regularization parameter is enhancing the stability of the algorithm and controls the contribution of the cross gradient term in the solution. The results show that even in cases where resistivity and velocity boundaries are different, both methods influence each other positively. In addition, the region of common structural boundaries of the models are clearly mapped compared with original models. Furthermore, deep structures are identified satisfactorily even with using the minimum number of seismic sources. In this paper, in order to understand the future studies, we discussed joint inversion of Magnetotelluric and local earthquake data sets only in two-dimensional space. In the light of these
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 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
Analytic Solutions of Special Functional Equations
Directory of Open Access Journals (Sweden)
Octav Olteanu
2013-07-01
Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.
Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations
Wagenmaker, Timothy Roger
This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of
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
Hasei, Tomohiro; Nakanishi, Haruka; Toda, Yumiko; Watanabe, Tetsushi
2012-08-31
3-Nitrobenzanthrone (3-NBA) is an extremely strong mutagen and carcinogen in rats inducing squamous cell carcinoma and adenocarcinoma. We developed a new sensitive analytical method, a two-dimensional HPLC system coupled with on-line reduction, to quantify non-fluorescent 3-NBA as fluorescent 3-aminobenzanthrone (3-ABA). The two-dimensional HPLC system consisted of reversed-phase HPLC and normal-phase HPLC, which were connected with a switch valve. 3-NBA was purified by reversed-phase HPLC and reduced to 3-ABA with a catalyst column, packed with alumina coated with platinum, in ethanol. An alcoholic solvent is necessary for reduction of 3-NBA, but 3-ABA is not fluorescent in the alcoholic solvent. Therefore, 3-ABA was separated from alcohol and impurities by normal-phase HPLC and detected with a fluorescence detector. Extracts from surface soil, airborne particles, classified airborne particles, and incinerator dust were applied to the two-dimensional HPLC system after clean-up with a silica gel column. 3-NBA, detected as 3-ABA, in the extracts was found as a single peak on the chromatograms without any interfering peaks. 3-NBA was detected in 4 incinerator dust samples (n=5). When classified airborne particles, that is, those 7.0 μm in size, were applied to the two-dimensional HPLC system after purified using a silica gel column, 3-NBA was detected in those particles with particle sizes NBA in airborne particles and the detection of 3-NBA in incinerator dust. Copyright © 2012 Elsevier B.V. All rights reserved.
Bitzer, Klaus
1999-05-01
Geological processes that create sedimentary basins or act during their formation can be simulated using the public domain computer code `BASIN'. For a given set of geological initial and boundary conditions the sedimentary basin evolution is calculated in a forward modeling approach. The basin is represented in a two-dimensional vertical cross section with individual layers. The stratigraphic, tectonic, hydrodynamic and thermal evolution is calculated beginning at an initial state, and subsequent changes of basin geometry are calculated from sedimentation rates, compaction and pore fluid mobilization, isostatic compensation, fault movement and subsidence. The sedimentologic, hydraulic and thermal parameters are stored at discrete time steps allowing the temporal evolution of the basin to be analyzed. A maximum flexibility in terms of geological conditions is achieved by using individual program modules representing geological processes which can be switched on and off depending on the data available for a specific simulation experiment. The code incorporates a module for clastic and carbonate sedimentation, taking into account the impact of clastic sediment supply on carbonate production. A maximum of four different sediment types, which may be mixed during sedimentation, can be defined. Compaction and fluid flow are coupled through the consolidation equation and the nonlinear form of the equation of state for porosity, allowing nonequilibrium compaction and overpressuring to be calculated. Instead of empirical porosity-effective stress equations, a physically consistent consolidation model is applied which incorporates a porosity dependent sediment compressibility. Transient solute transport and heat flow are calculated as well, applying calculated fluid flow rates from the hydraulic model. As a measure for hydrocarbon generation, the Time-Temperature Index (TTI) is calculated. Three postprocessing programs are available to provide graphic output in Post
Analytical solutions to matrix diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Kekäläinen, Pekka, E-mail: pekka.kekalainen@helsinki.fi [Laboratory of Radiochemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki (Finland)
2014-10-06
We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.
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.
International Nuclear Information System (INIS)
Eschke, Andy
2015-01-01
Examination object of the present thesis was the determination of local distributions of crystallographic texture and mechanical (eigen-)stresses in submicro-/nan0crystalline many-phase gradient materials. For this at the one hand experimental methods of the two-dimensional X-ray diffraction were applied as well as at the other hand theoretical calculations performed by means of analytical and numerical modeling approaches. The interest for the material is founded on the fact that ultrafine-granular materials because of their mechanical propertier (for instance hardness, ductility) ar to be stressed for advanced engineering application purposes. Furthermore the application of many-phase gradient materials makes to some extent possible a manufacture for measure concerning physical properties and by this a manifold of application potentials as well as a tuning of the material properties to the differential requirements in the application fields. This measure tailoring is related both to the degree of gradiation and to the special composition of the composite materials by the chosen starting materials. The work performed in the framework of the excellence cluster ''European Centre for Emerging Materials and Processes Dresden (ECEMP)'' of the Saxonian excellence initiative aimed especially to the analysis of an especially processed, ultrafine-granular Ti/Al composite, which was and is research object of the partial ECEMP project ''High strength metallic composites'' (HSMetComp). Thereby were process as well as materials in the focus of the above mentioned (indirect) examination methods. which were adapted and further developed for these purposes. The results of the experimental as well as theoretical studies could contribute to an increased understanding of the technological process as well as the material behaviour and can by this also used for hints concerning process- and/or material-sided optimizations. Altogether they
Narendar, Vadthiya; Rai, Saurabh; Tiwari, Siddharth; Mishra, R. A.
2016-12-01
The double-gate (DG) metal-oxide-semiconductor field effect transistors (MOSFETs) are the choice of technology in sub -100 nm regime of leading microelectronics industry. To enhance the analog and RF performance of DG MOSFET, an underlap dual-material (DM) DG MOSFET device structure has been considered because, it has the advantages of both underlap as well as that of dual-material gate (DMG). A 2D analytical surface potential, subthreshold current, subthreshold swing as well as transconductance modelling of underlap DMDG MOSFET has been done by solving the Poisson's equation. It has also been found that, numerically simulated data approves the analytically modelled data with commendable accuracy. As underlap length (Lun) increases, a substantial reduction of subthreshold current due to enhanced gate control over channel regime is observed. DMG structure facilitates to improve the average velocity of carriers which leads to superior drive current of the device. The underlap DMDG MOSFET device structure demonstrates an ameliorated subthreshold characteristic. The analog figure of merits (FOMs) such as transconductance (gm), transconductance generation factor (TGF), output conductance (gd), early voltage (VEA), intrinsic gain (AV) and RF FOMs namely cut-off frequency (fT), gain frequency product (GFP), transconductance frequency product (TFP) and gain transconductance frequency product (GTFP) have been evaluated. The aforesaid analysis revels that, the device is best suited for communication related Analog/RF applications.
Priya, Anjali; Mishra, Ram Awadh
2016-04-01
In this paper, analytical modeling of surface potential is proposed for new Triple Metal Gate (TMG) fully depleted Recessed-Source/Dain Silicon On Insulator (SOI) Metal Oxide Semiconductor Field Effect Transistor (MOSFET). The metal with the highest work function is arranged near the source region and the lowest one near the drain. Since Recessed-Source/Drain SOI MOSFET has higher drain current as compared to conventional SOI MOSFET due to large source and drain region. The surface potential model developed by 2D Poisson's equation is verified by comparison to the simulation result of 2-dimensional ATLAS simulator. The model is compared with DMG and SMG devices and analysed for different device parameters. The ratio of metal gate length is varied to optimize the result.
International Nuclear Information System (INIS)
Auluck, S. K. H.
2013-01-01
Recent resurgence of interest in applications of dense plasma focus and doubts about the conventional view of dense plasma focus as a purely irrotational compressive flow have re-opened questions concerning device optimization. In this context, this paper re-appraises and extends the analytical snowplow model of plasma focus sheath evolution developed by F. Gratton and J. M. Vargas [Energy Storage, Compression and Switching, edited by V. Nardi, H. Sahlin, and W. H. Bostick (Plenum, New York, 1983), Vol. 2, p. 353)] and shows its relevance to contemporary research. The Gratton-Vargas (GV) model enables construction of a special orthogonal coordinate system in which the plasma flow problem can be simplified and a model of sheath structure can be formulated. The Lawrenceville Plasma Physics (LPP) plasma focus facility, which reports neutron yield better than global scaling law, is shown to be operating closer to an optimum operating point of the GV model as compared with PF-1000
DEFF Research Database (Denmark)
Pagès, Anais; Grice, Kliti; Vacher, Michael
2014-01-01
Summary: Modern microbial mats are highly complex and dynamic ecosystems. Diffusive equilibration in thin films (DET) and diffusive gradients in thin films (DGT) samplers were deployed in a modern smooth microbial mat from Shark Bay in order to observe, for the first time, two-dimensional distrib......Summary: Modern microbial mats are highly complex and dynamic ecosystems. Diffusive equilibration in thin films (DET) and diffusive gradients in thin films (DGT) samplers were deployed in a modern smooth microbial mat from Shark Bay in order to observe, for the first time, two...
International Nuclear Information System (INIS)
Tripathi Shweta
2014-01-01
An analytical model for the channel potential and the threshold voltage of the short channel dual-material-gate lightly doped drain (DMG-LDD) metal—oxide—semiconductor field-effect transistor (MOSFET) is presented using the parabolic approximation method. The proposed model takes into account the effects of the LDD region length, the LDD region doping, the lengths of the gate materials and their respective work functions, along with all the major geometrical parameters of the MOSFET. The impact of the LDD region length, the LDD region doping, and the channel length on the channel potential is studied in detail. Furthermore, the threshold voltage of the device is calculated using the minimum middle channel potential, and the result obtained is compared with the DMG MOSFET threshold voltage to show the improvement in the threshold voltage roll-off. It is shown that the DMG-LDD MOSFET structure alleviates the problem of short channel effects (SCEs) and the drain induced barrier lowering (DIBL) more efficiently. The proposed model is verified by comparing the theoretical results with the simulated data obtained by using the commercially available ATLAS™ 2D device simulator. (interdisciplinary physics and related areas of science and technology)
Shweta, Tripathi
2014-11-01
An analytical model for the channel potential and the threshold voltage of the short channel dual-material-gate lightly doped drain (DMG-LDD) metal—oxide—semiconductor field-effect transistor (MOSFET) is presented using the parabolic approximation method. The proposed model takes into account the effects of the LDD region length, the LDD region doping, the lengths of the gate materials and their respective work functions, along with all the major geometrical parameters of the MOSFET. The impact of the LDD region length, the LDD region doping, and the channel length on the channel potential is studied in detail. Furthermore, the threshold voltage of the device is calculated using the minimum middle channel potential, and the result obtained is compared with the DMG MOSFET threshold voltage to show the improvement in the threshold voltage roll-off. It is shown that the DMG-LDD MOSFET structure alleviates the problem of short channel effects (SCEs) and the drain induced barrier lowering (DIBL) more efficiently. The proposed model is verified by comparing the theoretical results with the simulated data obtained by using the commercially available ATLAS™ 2D device simulator.
Recovery of uranium from analytical waste solution
International Nuclear Information System (INIS)
Kumar, Pradeep; Anitha, M.; Singh, D.K.
2016-01-01
Dispersion fuels are considered as advance fuel for the nuclear reactor. Liquid waste containing significant quantity of uranium gets generated during chemical characterization of dispersion fuel. The present paper highlights the effort in devising a counter current solvent extraction process based on the synergistic mixture of D2EHPA and Cyanex 923 to recover uranium from such waste solutions. A typical analytical waste solution was found to have the following composition: U 3 O 8 (∼3 g/L), Al: 0.3 g/L, V: 15 ppm, Phosphoric acid: 3M, sulphuric acid : 1M and nitric acid : 1M. The aqueous solution is composed of mixture of either 3M phosphoric acid and 1M sulphuric acid or 1M sulphuric acid and 1M nitric acid, keeping metallic concentrations in the above mentioned range. Different organic solvents were tested. Based on the higher extraction of uranium with synergistic mixture of 0.5M D2EHPA + 0.125M Cyanex 923, it was selected for further investigation in the present work
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
Arletti, Rossella; Fois, Ettore; Gigli, Lara; Vezzalini, Giovanna; Quartieri, Simona; Tabacchi, Gloria
2017-02-13
Turning disorder into organization is a key issue in science. By making use of X-ray powder diffraction and modeling studies, we show herein that high pressures in combination with the shape and space constraints of the hydrophobic all-silica zeolite ferrierite separate an ethanol-water liquid mixture into ethanol dimer wires and water tetramer squares. The confined supramolecular blocks alternate in a binary two-dimensional (2D) architecture that remains stable upon complete pressure release. These results support the combined use of high pressures and porous networks as a viable strategy for driving the organization of molecules or nano-objects towards complex, pre-defined patterns relevant for the realization of novel functional nanocomposites. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis
Directory of Open Access Journals (Sweden)
Przemysław Korohoda
2013-01-01
Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.
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.
Analytic structure of solutions to multiconfiguration equations
Energy Technology Data Exchange (ETDEWEB)
Fournais, Soeren [Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, DK-8000 Arhus C (Denmark); Hoffmann-Ostenhof, Maria [Fakultaet fuer Mathematik, Universitaet Wien, Nordbergstrasse 15, A-1090 Vienna (Austria); Hoffmann-Ostenhof, Thomas [Institut fuer Theoretische Chemie, Waehringerstrasse 17, Universitaet Wien, A-1090 Vienna (Austria); Soerensen, Thomas Oestergaard [Department of Mathematics, Imperial College London, Huxley Building, 180 Queen' s Gate, London SW7 2AZ (United Kingdom)], E-mail: fournais@imf.au.dk, E-mail: Maria.Hoffmann-Ostenhof@univie.ac.at, E-mail: thoffman@esi.ac.at, E-mail: t.sorensen@imperial.ac.uk
2009-08-07
We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree-Fock) of Coulomb systems. We prove the following: let {l_brace}{psi}{sub 1}, ..., {psi}{sub M}{r_brace} be any solution to the rank-M multiconfiguration equations for a molecule with L fixed nuclei at R{sub 1},...,R{sub L} element of R{sup 3}. Then, for any j in {l_brace}1, ..., M{r_brace}, k in {l_brace}1, ..., L{r_brace}, there exists a neighborhood U{sub j,k} subset or equal R{sup 3} of R{sub k}, and functions {psi}{sup (1)}{sub j,k}, {psi}{sup (2)}{sub j,k}, real analytic in U{sub j,k}, such that {phi}{sub j}(x)={phi}{sub j,k}{sup (1)}(x)+|x-R{sub k}|{phi}{sub j,k}{sup (2)}(x), x element of U{sub j,k}. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo-Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schroedinger operator of atoms and molecules near two-particle coalescence points.
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
Energy Technology Data Exchange (ETDEWEB)
Monsefi, Farid [Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, MDH, Västerås, Sweden and School of Innovation, Design and Engineering, IDT, Mälardalen University, MDH Väs (Sweden); Carlsson, Linus; Silvestrov, Sergei [Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, MDH, Västerås (Sweden); Rančić, Milica [Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, MDH, Västerås, Sweden and Department of Theoretical Electrical Engineering, Faculty of Electronic Engineering, University (Serbia); Otterskog, Magnus [School of Innovation, Design and Engineering, IDT, Mälardalen University, MDH Västerås (Sweden)
2014-12-10
To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD) method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations, is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTD scheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source of electromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of Absorbing Boundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC) surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTD scheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of the computer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can be rather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTD algorithm.
International Nuclear Information System (INIS)
Monsefi, Farid; Carlsson, Linus; Silvestrov, Sergei; Rančić, Milica; Otterskog, Magnus
2014-01-01
To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD) method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations, is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTD scheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source of electromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of Absorbing Boundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC) surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTD scheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of the computer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can be rather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTD algorithm
ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS
International Nuclear Information System (INIS)
Chu Zhe; Lin, W. P.; Yang Xiaofeng
2013-01-01
Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.
Directory of Open Access Journals (Sweden)
Jorge Rodolfo Silva Zabadal
2006-06-01
Full Text Available Neste trabalho são apresentados métodos híbridos para solução de problemas difusivos relativos à dispersão de poluentes em meio aquático. Estes métodos aplicam variáveis complexas a fim de executar mapeamentos sobre a equação diferencial a ser resolvida bem como sobre o domínio considerado. O mapeamento sobre a equação diferencial converte o operador laplaciano bidimensional em uma derivada cruzada de segunda ordem na variável espacial. O mapeamento do domínio transforma regiões de formato complexo em regiões retangulares. Ambos mapeamentos são usados a fim de reduzir o tempo total requerido de processamento para solução de problemas difusivos não-homogêneos. Resultados numéricos são apresentados.In this work hybrid methods for solving diffusion problems related to pollutants dispersion in water bodies are presented. These methods employ complex variables in order to perform mappings over the differential equation to be solved as well as over the considered domain. The mapping over the differential equation converts the two dimensional laplacian operator into a second order mixed derivative in the complex variables. The mapping of the domain transforms complex-shaped regions into rectangular ones. Both mappings are used in order to reduce the total time proccessing required for solving non-homogeneous diffusion problems. Numerical results are reported.
Analytic solutions of a class of nonlinearly dynamic systems
International Nuclear Information System (INIS)
Wang, M-C; Zhao, X-S; Liu, X
2008-01-01
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently
New analytic solutions of stochastic coupled KdV equations
International Nuclear Information System (INIS)
Dai Chaoqing; Chen Junlang
2009-01-01
In this paper, firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures.
Seadawy, Aly R.
2017-12-01
In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.
Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming
1990-01-01
A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.
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
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
International Nuclear Information System (INIS)
Alvarenga, M.A.B.
1980-12-01
An analytical procedure to solve the neutron diffusion equation in two dimensions and two energy groups was developed. The response matrix method was used coupled with an expansion of the neutron flux in finite Fourier series. A computer code 'MRF2D' was elaborated to implement the above mentioned procedure for PWR reactor core calculations. Different core symmetry options are allowed by the code, which is also flexible enough to allow for improvements by means of algorithm optimization. The code performance was compared with a corner mesh finite difference code named TVEDIM by using a International Atomic Energy Agency (IAEA) standard problem. Computer processing time 12,7% smaller is required by the MRF2D code to reach the same precision on criticality eigenvalue. (Author) [pt
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)
Menezes, Welton Alves de
2009-01-01
In this dissertation the spectral nodal method SD-SGF-CN, cf. spectral diamond - spectral Green's function - constant nodal, is used to determine the angular fluxes averaged along the edges of the homogenized nodes in heterogeneous domains. Using these results, we developed an algorithm for the reconstruction of the node-edge average angular fluxes within the nodes of the spatial grid set up on the domain, since more localized numerical solutions are not generated by coarse-mesh numerical methods. Numerical results are presented to illustrate the accuracy of the algorithm we offer. (author)
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
Semi-analytic solution to planar Helmholtz equation
Directory of Open Access Journals (Sweden)
Tukač M.
2013-06-01
Full Text Available Acoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costs.
Energy Technology Data Exchange (ETDEWEB)
Fan, T.W.M.; Higashi, R.M.; Lane, A.N.
2000-05-01
A California forest soil used for contaminant bioavailability studies was extracted for humic substances (HS) and then treated with 4,5-dihydroxy-1,3-benzene disulfonate (Tiron) to remove exchangeable metal ions. This yielded HS that was readily water-soluble at neutral pH without residual Tiron contamination, and the gel electrophoretic pattern was very similar to an international reference HS. The improved solubility facilitated analysis of HS by solution-state 1-D and 2-D {sup 1}H, {sup 13}C, {sup 31}P, and {sup 13}C-{sup 1}H NMR. The amino acids Gly, Ala, Leu, lle, Val, Asp, Ser, Thr, Glu, and Pro were identified in intact HS as peptidic from scalar coupling in TOCSY and dipolar interactions in NOESY and then confirmed by acid digestion of HS with 2-D {sup 1}H NMR and GCMS analysis. The presence of peptides was also corroborated by FT-IR and pyrolysis-GCMS results. Carbohydrates containing {alpha}- and {beta}-pyranoses, methoxy-phenylpropanyl structures, phosphate mono/diesters, polyphosphates, plus phosphatidic acid esters were also evident. Furthermore, the {sup 1}H NOESY, TOCSY, and HSQC together indicated that the peptidic side chains were mobile, whereas aromatic groups were relatively rigid. Thus the peptidic moieties may be more readily accessible to aqueous contaminants than aromatic groups.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use ... The domain part of the email address of all email addresses used by the office of Indian Academy of Sciences, including those of the staff, the journals, various ...
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.
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....
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
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
Analytical solution of one dimensional temporally dependent ...
African Journals Online (AJOL)
user
transfer of heat in fluids, flow through porous media, and the spread of ... In present paper, advection-dispersion equation is considered one dimensional longitudinal initially solute free semi- .... free. Thus initial and boundary conditions for eq.
Analytical solutions of one-dimensional advection–diffusion
Indian Academy of Sciences (India)
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the ...
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
Two-dimensional transient far-field analysis for the excess temperature from an arbitrary source
Energy Technology Data Exchange (ETDEWEB)
Witten, A.J.; Long, E.C.
1978-07-01
An analytic solution is presented for the two-dimensional time-dependent advective diffusion equation governing the distribution of excess temperature in a river of uniform width, depth, and downstream flow. The solution is also applicable to a straight coastline with uniform longshore flow. Exact solutions are obtained for a point heat source and a particular line heat source, while an approximate representation is given for an arbitrary time-varying heat source. These solutions are incorporated into a computer program which calculates excess temperature and time rate-of-change of excess temperature in a river or coast as a result of waste heat discharged from various transient sources.
Bing, Xue; Yicai, Ji
2018-06-01
In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.
Analytical solution of strongly nonlinear Duffing oscillators
Directory of Open Access Journals (Sweden)
A.M. El-Naggar
2016-06-01
Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.
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)
Analytical solution of strongly nonlinear Duffing oscillators
El-Naggar, A.M.; Ismail, G.M.
2016-01-01
In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...
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.
Analytic solutions for marginal deformations in open superstring field theory
International Nuclear Information System (INIS)
Okawa, Y.
2007-04-01
We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular. (orig.)
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)
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.
Spin precession in inversion-asymmetric two-dimensional systems
International Nuclear Information System (INIS)
Liu, M.-H.; Chang, C.-R.
2006-01-01
We present a theoretical method to calculate the expectation value of spin in an inversion-asymmetric two-dimensional (2D) system with respect to an arbitrarily spin-polarized electron state, injected via an ideal point contact. The 2D system is confined in a [0 0 1]-grown quantum well, where both the Rashba and the Dresselhaus spin-orbit couplings are taken into account. The obtained analytical results allow more concrete description of the spatial behaviors of the spin precession caused individually by the Rashba and the Dresselhaus terms. Applying the calculation on the Datta-Das spin-FET, whose original design considers only the Rashba effect inside the channel, we investigate the possible influence due to the Dresselhaus spin-orbit coupling. Concluded solution is the choice of ±[1±10], in particular [1 1 0], as the channel direction
Analytic solutions of QCD motivated Hamiltonians at low energy
International Nuclear Information System (INIS)
Yepez, T.; Amor, A.; Hess, P.O.; Szczepaniak, A.; Civitarese, O.
2011-01-01
A model Hamiltonian, motivated by QCD, is investigated in order to study only the quark sector, then only the gluon sector and finally both together. Restricting to the pure quark sector and setting the mass of the quarks to zero, we find analytic solutions, involving two to three orbitals. Allowing the mass of the quarks to be different to zero, we find semi-analytic solutions involving an arbitrary number of orbitals. Afterwards, we indicate on how to incorporate gluons. (author)
Analytical solution of dispersion relations for the nuclear optical model
Energy Technology Data Exchange (ETDEWEB)
VanderKam, J.M. [Center for Communications Research, Thanet Road, Princeton, NJ 08540 (United States); Weisel, G.J. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States); Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 (United States); Tornow, W. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States)
2000-12-01
Analytical solutions of dispersion integral relations, linking the real and imaginary parts of the nuclear optical model, have been derived. These are displayed for some widely used forms of the volume- and surface-absorptive nuclear potentials. When the analytical solutions are incorporated into the optical-model search code GENOA, replacing a numerical integration, the code runs three and a half to seven times faster, greatly aiding the analysis of direct-reaction, elastic scattering data. (author)
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...
International Nuclear Information System (INIS)
Yabushita, Kazuki; Yamashita, Mariko; Tsuboi, Kazuhiro
2007-01-01
We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 x 10 3 ∼ 2 x 10 5 (for instance, a sphere) for practical situations, such as throwing a ball. It has been considered that the equations of motion of this case are unsolvable for a general projectile angle, although some solutions have been obtained for a small projectile angle using perturbation techniques. To obtain a general analytic solution, we apply Liao's homotopy analysis method to this problem. The homotopy analysis method, which is different from a perturbation technique, can be applied to a problem which does not include small parameters. We apply the homotopy analysis method for not only governing differential equations, but also an algebraic equation of a velocity vector to extend the radius of convergence. Ultimately, we obtain the analytic solution to this problem and investigate the validation of the solution
Analytic solution of the lifeguard problem
De Luca, Roberto; Di Mauro, Marco; Naddeo, Adele
2018-03-01
A simple version due to Feynman of Fermat’s principle is analyzed. It deals with the path a lifeguard on a beach must follow to reach a drowning swimmer. The solution for the exact point, P(x, 0) , at the beach-sea boundary, corresponding to the fastest path to the swimmer, is worked out in detail and the analogy with light traveling at the air-water boundary is described. The results agree with the known conclusion that the shortest path does not coincide with the fastest one. The relevance of the subject for a basic physics course, at an advanced high school level, is pointed out.
Analytical solutions to SSC coil end design
International Nuclear Information System (INIS)
Bossert, R.C.; Brandt, J.S.; Carson, J.A.; Fulton, H.J.; Lee, G.C.; Cook, J.M.
1989-03-01
As part of the SCC magnet effort, Fermilab will build and test a series of one meter model SSC magnets. The coils in these magnets will be constructed with several different end configurations. These end designs must satisfy both mechanical and magnetic criteria. Only the mechanical problem will be addressed. Solutions will attempt to minimize stresses and provide internal support for the cable. Different end designs will be compared in an attempt to determine which is most appropriate for the SSC dipole. The mathematics required to create each end configuration will be described. The computer aided design, programming and machine technology needed to make the parts will be reviewed. 2 refs., 10 figs
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)].
Analytic solution of integral equations for molecular fluids
International Nuclear Information System (INIS)
Cummings, P.T.
1984-01-01
We review some recent progress in the analytic solution of integral equations for molecular fluids. The site-site Ornstein-Zernike (SSOZ) equation with approximate closures appropriate to homonuclear diatomic fluids both with and without attractive dispersion-like interactions has recently been solved in closed form analytically. In this paper, the close relationship between the SSOZ equation for homonuclear dumbells and the usual Ornstein-Zernike (OZ) equation for atomic fluids is carefully elucidated. This relationship is a key motivation for the analytic solutions of the SSOZ equation that have been obtained to date. (author)
Analytic plane wave solutions for the quaternionic potential step
International Nuclear Information System (INIS)
De Leo, Stefano; Ducati, Gisele C.; Madureira, Tiago M.
2006-01-01
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in the presence of a quaternionic step potential. The analytic solution for the stationary states allows one to explicitly show the qualitative and quantitative differences between this quaternionic quantum dynamical system and its complex counterpart. A brief discussion on reflected and transmitted times, performed by using the stationary phase method, and its implication on the experimental evidence for deviations of standard quantum mechanics is also presented. The analytic solution given in this paper represents a fundamental mathematical tool to find an analytic approximation to the quaternionic barrier problem (up to now solved by numerical method)
Speciation—targets, analytical solutions and markets
Łobiński, Ryszard
1998-02-01
An analysis of speciation-relevant issues leads to the conclusion that, despite the rapidly increasing number of reports, the field has reached a level of virtual stagnation in terms of research originality and market perspectives. A breakthrough is in sight but requires an advanced interdisciplinary collaboration of chemists-analysts with clinicians, ecotoxicologists and nutricionists aimed at the definition of metal (metalloid)-dependent problems relevant to human health. The feedback from analytical chemists will be stimulated by a wider availability of efficient HPLC (CZE)-inductively coupled plasma mass spectrometry (ICP MS) interfaces, chromatographic software for ICP AES and MS and sensitive on-line methods for compound identification (electrospray MS/MS). The maturity of purge and trap thermal desorption techniques and capillary GC chromatography is likely to be reflected by an increasing number of commercial dedicated systems for small molecules containing Hg, Pb, Sn and metalloids. The pre-requisite of success for such systems is the integration of a sample preparation step (based on focused low-power microwave technology) into the marketed set-up.
Analytical solutions of advection-dispersion equation for varying ...
African Journals Online (AJOL)
Analytical solutions are obtained for a one-dimensional advection–dispersion equation with variable coefficients in a longitudinal domain. Two cases are considered. In the first one the solute dispersion is time dependent along a uniform flow in a semi-infinite domain while in the second case the dispersion and the velocity ...
Analytical solutions for one-dimensional advection–dispersion ...
Indian Academy of Sciences (India)
We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0.
Analytical solutions in the two-cavity coupling problem
International Nuclear Information System (INIS)
Ayzatsky, N.I.
2000-01-01
Analytical solutions of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases.For their derivation we have used the method of solution of an infinite set of linear algebraic equations,based on its transformation into dual integral equations
On Analytic Solution of resonant Mixing for Solar Neutrino Oscillations
Masatoshi, ITO; Takao, KANEKO; Masami, NAKAGAWA; Department of Physics, Meijo University; Department of Physics, Meijo University; Department of Physics, Meijo University
1988-01-01
Behavior of resonant mixing in matter-enhancing region for solar neutrino oscillation, the Mikheyev-Smirnov-Wolfenstein mechanism, is reanalyzed by means of an analytic treatment recently proposed. We give solutions in terms of confluent hypergeometric functions, which agree with "exact" solutions of coupled differential equations.
Analytical Solutions of the KDV-KZK Equation
Gan, W. S.
The KdV-KZK equation for fluids developed by me was presented at the ICSV 11 in St. Petersburg in July 2004. In this paper, I made an attempt on the analytical solutions of this equation using the perturbation method. Some physical interpretation of the solutions is given. A brief introduction to KdV-KZK equation for solids is given
Transmission Line Adapted Analytical Power Charts Solution
Sakala, Japhet D.; Daka, James S. J.; Setlhaolo, Ditiro; Malichi, Alec Pulu
2017-08-01
The performance of a transmission line has been assessed over the years using power charts. These are graphical representations, drawn to scale, of the equations that describe the performance of transmission lines. Various quantities that describe the performance, such as sending end voltage, sending end power and compensation to give zero voltage regulation, may be deduced from the power charts. Usually required values are read off and then converted using the appropriate scales and known relationships. In this paper, the authors revisit this area of circle diagrams for transmission line performance. The work presented here formulates the mathematical model that analyses the transmission line performance from the power charts relationships and then uses them to calculate the transmission line performance. In this proposed approach, it is not necessary to draw the power charts for the solution. However the power charts may be drawn for the visual presentation. The method is based on applying derived equations and is simple to use since it does not require rigorous derivations.
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.
A comprehensive analytical solution of the nonlinear pendulum
International Nuclear Information System (INIS)
Ochs, Karlheinz
2011-01-01
In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.
An analytical solution for improved HIFU SAR estimation
International Nuclear Information System (INIS)
Dillon, C R; Vyas, U; Christensen, D A; Roemer, R B; Payne, A
2012-01-01
Accurate determination of the specific absorption rates (SARs) present during high intensity focused ultrasound (HIFU) experiments and treatments provides a solid physical basis for scientific comparison of results among HIFU studies and is necessary to validate and improve SAR predictive software, which will improve patient treatment planning, control and evaluation. This study develops and tests an analytical solution that significantly improves the accuracy of SAR values obtained from HIFU temperature data. SAR estimates are obtained by fitting the analytical temperature solution for a one-dimensional radial Gaussian heating pattern to the temperature versus time data following a step in applied power and evaluating the initial slope of the analytical solution. The analytical method is evaluated in multiple parametric simulations for which it consistently (except at high perfusions) yields maximum errors of less than 10% at the center of the focal zone compared with errors up to 90% and 55% for the commonly used linear method and an exponential method, respectively. For high perfusion, an extension of the analytical method estimates SAR with less than 10% error. The analytical method is validated experimentally by showing that the temperature elevations predicted using the analytical method's SAR values determined for the entire 3D focal region agree well with the experimental temperature elevations in a HIFU-heated tissue-mimicking phantom. (paper)
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.
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.
Analytic Solution to Shell Boundary – Value Problems
Directory of Open Access Journals (Sweden)
Yu. I. Vinogradov
2015-01-01
Full Text Available Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.
Analytical Solution of General Bagley-Torvik Equation
William Labecca; Osvaldo Guimarães; José Roberto C. Piqueira
2015-01-01
Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomoge...
Analytical solution to the hybrid diffusion-transport equation
International Nuclear Information System (INIS)
Nanneh, M.M.; Williams, M.M.R.
1986-01-01
A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.
2016-09-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.
2016-01-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
International Nuclear Information System (INIS)
Gesell, Jennifer; Zasloff, Michael; Opella, Stanley J.
1997-01-01
Magainin2 is a 23-residue antibiotic peptide that disrupts the ionic gradient across certain cell membranes. Two-dimensional 1H NMR spectroscopy was used to investigate the structure of the peptide in three of the membrane environments most commonly employed in biophysical studies. Sequence-specific resonance assignments were determined for the peptide in perdeuterated dodecylphosphocholine (DPC) and sodium dodecylsulfate micelles and confirmed for the peptide in 2,2,2-trifluoroethanol solution. The secondary structure is shown to be helical in all of the solvent systems. The NMR data were used as a set of restraints for a simulated annealing protocol that generated a family of three-dimensional structures of the peptide in DPC micelles, which superimposed best between residues 4 and 20. For these residues, the mean pairwise rms difference for the backbone atoms is 0.47 ± 0.10A from the average structure. The calculated peptide structures appear to be curved,with the bend centered at residues Phe12 and Gly13
Analytical solutions for systems of partial differential-algebraic equations.
Benhammouda, Brahim; Vazquez-Leal, Hector
2014-01-01
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
Analytical solution for a coaxial plasma gun: Weak coupling limit
International Nuclear Information System (INIS)
Dietz, D.
1987-01-01
The analytical solution of the system of coupled ODE's which describes the time evolution of an ideal (i.e., zero resistance) coaxial plasma gun operating in the snowplow mode is obtained in the weak coupling limit, i.e, when the gun is fully influenced by the driving (RLC) circuit in which it resides but the circuit is negligibly influenced by the gun. Criteria for the validity of this limit are derived and numerical examples are presented. Although others have obtained approximate, asymptotic and numerical solutions of the equations, the present analytical results seem not to have appeared previously in the literature
Analytical Solution of General Bagley-Torvik Equation
Directory of Open Access Journals (Sweden)
William Labecca
2015-01-01
Full Text Available Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomogeneous case is solved without restrictions in boundary and initial conditions. The generalized Mittag-Leffler functions with three parameters are used and the solutions presented are expressed in terms of Wiman’s functions and their derivatives.
Analytical solution for Van der Pol-Duffing oscillators
International Nuclear Information System (INIS)
Kimiaeifar, A.; Saidi, A.R.; Bagheri, G.H.; Rahimpour, M.; Domairry, D.G.
2009-01-01
In this paper, the problem of single-well, double-well and double-hump Van der Pol-Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the 'Homotopy Analysis Method' (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. This method is a capable tool for solving this kind of nonlinear problems.
Analytic solution to variance optimization with no short positions
Kondor, Imre; Papp, Gábor; Caccioli, Fabio
2017-12-01
We consider the variance portfolio optimization problem with a ban on short selling. We provide an analytical solution by means of the replica method for the case of a portfolio of independent, but not identically distributed, assets. We study the behavior of the solution as a function of the ratio r between the number N of assets and the length T of the time series of returns used to estimate risk. The no-short-selling constraint acts as an asymmetric \
Decision Exploration Lab : A Visual Analytics Solution for Decision Management
Broeksema, Bertjan; Baudel, Thomas; Telea, Alex; Crisafulli, Paolo
2013-01-01
We present a visual analytics solution designed to address prevalent issues in the area of Operational Decision Management (ODM). In ODM, which has its roots in Artificial Intelligence (Expert Systems) and Management Science, it is increasingly important to align business decisions with business
Foam for Enhanced Oil Recovery : Modeling and Analytical Solutions
Ashoori, E.
2012-01-01
Foam increases sweep in miscible- and immiscible-gas enhanced oil recovery by decreasing the mobility of gas enormously. This thesis is concerned with the simulations and analytical solutions for foam flow for the purpose of modeling foam EOR in a reservoir. For the ultimate goal of upscaling our
Analytical construction of peaked solutions for the nonlinear ...
African Journals Online (AJOL)
These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schrödinger type.
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
data processing, and using the machine learning toolkit, MADlib, for doing in-database data analytics in PostgreSQL database. This paper evaluates the key technologies of the proposed ICT-solution, and the results show the effectiveness and efficiency of using the system for both batch and online...
Analytical solution for the convectively-mixed atmospheric boundary layer
Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.
2013-01-01
Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation
General analytical shakedown solution for structures with kinematic hardening materials
Guo, Baofeng; Zou, Zongyuan; Jin, Miao
2016-09-01
The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.
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
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 ...
Triangular dislocation: an analytical, artefact-free solution
Nikkhoo, Mehdi; Walter, Thomas R.
2015-05-01
Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.
The big bang and inflation united by an analytic solution
International Nuclear Information System (INIS)
Bars, Itzhak; Chen, Shih-Hung
2011-01-01
Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index, and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the big bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Friedmann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in the 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow-roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time; rather, it oscillates around the potential minimum while settling down, unlike the slow-roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.
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
Analytical solutions to orthotropic variable thickness disk problems
Directory of Open Access Journals (Sweden)
Ahmet N. ERASLAN
2016-02-01
Full Text Available An analytical model is developed to estimate the mechanical response of nonisothermal, orthotropic, variable thickness disks under a variety of boundary conditions. Combining basic mechanical equations of disk geometry with the equations of orthotropic material, the elastic equation of the disk is obtained. This equation is transformed into a standard hypergeometric differential equation by means of a suitable transformation. An analytical solution is then obtained in terms of hypergeometric functions. The boundary conditions used to complete the solutions simulate rotating annular disks with two free surfaces, stationary annular disks with pressurized inner and free outer surfaces, and free inner and pressurized outer surfaces. The results of the solutions to each of these cases are presented in graphical forms. It is observed that, for the three cases investigated the elastic orthotropy parameter turns out to be an important parameter affecting the elastic behaviorKeywords: Orthotropic disk, Variable thickness, Thermoelasticity, Hypergeometric equation
International Nuclear Information System (INIS)
Goncalves, Glenio Aguiar
2003-01-01
In this work, we are reported analytical solutions for the transport equation for neutral particles in cylindrical and cartesian geometry. For the cylindrical geometry, it is applied the Hankel transform of order zero in the S N approximation of the one-dimensional cylindrical transport equation, assuming azimuthal symmetry and isotropic scattering. This procedure is coined HTSN method. The anisotropic problem is handled using the decomposition method, generating a recursive approach, which the HTSN solution is used as initial condition. For cartesian geometry, the one and two dimensional transport equation is derived in the angular variable as many time as the degree of the anisotropic scattering. This procedure leads to set of integro-differential plus one differential equation that can be really solved by the variable separation method. Following this procedure, it was possible to come out with the Case solution for the one-dimensional problem. Numerical simulations are reported for the cylindrical transport problem both isotropic and anisotropic case of quadratic degree. (author)
Analytic study of nonperturbative solutions in open string field theory
International Nuclear Information System (INIS)
Bars, I.; Kishimoto, I.; Matsuo, Y.
2003-01-01
We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution
On the Partial Analytical Solution of the Kirchhoff Equation
Michels, Dominik L.
2015-09-01
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.
Analytical exact solution of the non-linear Schroedinger equation
International Nuclear Information System (INIS)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da
2011-01-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
On the Partial Analytical Solution of the Kirchhoff Equation
Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Sobottka, Gerrit A.; Weber, Andreas G.
2015-01-01
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.
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
Explicit analytical solution of a pendulum with periodically varying length
International Nuclear Information System (INIS)
Yang Tianzhi; Fang Bo; Li Song; Huang Wenhu
2010-01-01
A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper, we use the homotopy analysis method to explore the approximate solution to this system. The method can easily self-adjust and control the convergence region. By applying the method to the governing equation of the pendulum, we obtain the approximation solution in a closed form. It is shown by the numerical method that the homotopy analysis method supplies a more accurate analytical solution for predicting the long-term behaviour of the pendulum. We believe that this system may be a good example for undergraduate and graduate students for better understanding of nonlinear oscillations.
Analytical solution of the PNP equations at AC applied voltage
International Nuclear Information System (INIS)
Golovnev, Anatoly; Trimper, Steffen
2012-01-01
A symmetric binary polymer electrolyte subjected to an AC voltage is considered. The analytical solution of the Poisson–Nernst–Planck equations (PNP) is found and analyzed for small applied voltages. Three distinct time regimes offering different behavior can be discriminated. The experimentally realized stationary behavior is discussed in detail. An expression for the external current is derived. Based on the theoretical result a simple method is suggested of measuring the ion mobility and their concentration separately. -- Highlights: ► Analytical solution of Poisson–Nernst–Planck equations. ► Binary polymer electrolyte subjected to an external AC voltage. ► Three well separated time scales exhibiting different behavior. ► The experimentally realized stationary behavior is discussed in detail. ► A method is proposed measuring the mobility and the concentration separately.
Quantum decay model with exact explicit analytical solution
Marchewka, Avi; Granot, Er'El
2009-01-01
A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
Explicit analytical solution of the nonlinear Vlasov Poisson system
International Nuclear Information System (INIS)
Skarka, V.; Mahajan, S.M.; Fijalkow, E.
1993-10-01
In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs
Analytic solution of the Starobinsky model for inflation
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)
2017-07-15
We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lemaitre-Robertson-Walker metric constitute an integrable system. The analytical solution in terms of a Painleve series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory. (orig.)
Semi-analytical solution to arbitrarily shaped beam scattering
Wang, Wenjie; Zhang, Huayong; Sun, Yufa
2017-07-01
Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.
Muonium hyperfine structure : An analytical solution to perturbative calculations
International Nuclear Information System (INIS)
Wotzasek, C.J.; Gregorio, M.A.; Reinecke, S.
1982-01-01
The purely coulombian contribution to the terms of order E sub(F) (α 2 m sub(e)/m sub(μ))ln α - 1 of the hyperfine splitting of muonium is computed. Results agree with those of other authors. The goal of the work was twofold: first, to confirm that contribution; second, and perhaps more important, to check the analytic solution of the relativistic coulombian problem of the Bethe-Salpeter equation with instantaneous kernel. (Author) [pt
Control Operator for the Two-Dimensional Energized Wave Equation
Directory of Open Access Journals (Sweden)
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.
The ADO-nodal method for solving two-dimensional discrete ordinates transport problems
International Nuclear Information System (INIS)
Barichello, L.B.; Picoloto, C.B.; Cunha, R.D. da
2017-01-01
Highlights: • Two-dimensional discrete ordinates neutron transport. • Analytical Discrete Ordinates (ADO) nodal method. • Heterogeneous media fixed source problems. • Local solutions. - Abstract: In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.
International Nuclear Information System (INIS)
Leal, M.A.; Ruperti Junior, N.J.; Cotta, R.M.
1997-01-01
A two-dimensional model for the flow and mass transfer of radioactive waste in porous media is investigated. The flow equations are modeled under steady-state Darcy regime assumptions, subjected to discrete boundary source terms. The mass transfer of the contaminant is modeled through the transient convection-diffusion equation, allowing for variable dispersivity coefficients and boundary source functions. The Generalized Integral Transform Technique (GITT) is utilized to provide the proposed hybrid numerical-analytical solution . (author)
Energy Technology Data Exchange (ETDEWEB)
Leal, M.A.; Ruperti Junior, N.J. [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil). Coordenacao de Rejeitos Radioativos; Cotta, R.M. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Lab. de Transmissao e Tecnologia do Calor
1997-12-31
A two-dimensional model for the flow and mass transfer of radioactive waste in porous media is investigated. The flow equations are modeled under steady-state Darcy regime assumptions, subjected to discrete boundary source terms. The mass transfer of the contaminant is modeled through the transient convection-diffusion equation, allowing for variable dispersivity coefficients and boundary source functions. The Generalized Integral Transform Technique (GITT) is utilized to provide the proposed hybrid numerical-analytical solution . (author) 12 refs., 3 figs.
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....
Analytic solution of pseudocolloid migration in fractured rock
International Nuclear Information System (INIS)
Hwang, Y.; Pigford, T.H.; Lee, W.W.L.; Chambre, P.L.
1989-06-01
A form of colloid migration that can enhance or retard the migration of a dissolved contaminant in ground water is the sorption of the contaminant on the moving colloidal particulate to form pseudocolloids. In this paper we develop analytical solutions for the interactive migration of radioactive species dissolved in ground water and sorbed as pseudocolloids. The solute and pseudocolloids are assumed to undergo advection and dispersion in a one-dimensional flow field in planar fractures in porous rock. Interaction between pseudocolloid and dissolved species is described by equilibrium sorption. Sorbed species on the pseudocolloids undergo radioactive decay, and pseudocolloids can sorb on fracture surfaces and sediments. Filtration is neglected. The solute can decay and sorb on pseudocolloids, on the fracture surfaces, and on sediments and can diffuse into the porous rock matrix. 1 fig
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)
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...
Analytical Solution for Optimum Design of Furrow Irrigation Systems
Kiwan, M. E.
1996-05-01
An analytical solution for the optimum design of furrow irrigation systems is derived. The non-linear calculus optimization method is used to formulate a general form for designing the optimum system elements under circumstances of maximizing the water application efficiency of the system during irrigation. Different system bases and constraints are considered in the solution. A full irrigation water depth is considered to be achieved at the tail of the furrow line. The solution is based on neglecting the recession and depletion times after off-irrigation. This assumption is valid in the case of open-end (free gradient) furrow systems rather than closed-end (closed dike) systems. Illustrative examples for different systems are presented and the results are compared with the output obtained using an iterative numerical solution method. The final derived solution is expressed as a function of the furrow length ratio (the furrow length to the water travelling distance). The function of water travelling developed by Reddy et al. is considered for reaching the optimum solution. As practical results from the study, the optimum furrow elements for free gradient systems can be estimated to achieve the maximum application efficiency, i.e. furrow length, water inflow rate and cutoff irrigation time.
Small-scale engagement model with arrivals: analytical solutions
International Nuclear Information System (INIS)
Engi, D.
1977-04-01
This report presents an analytical model of small-scale battles. The specific impetus for this effort was provided by a need to characterize hypothetical battles between guards at a nuclear facility and their potential adversaries. The solution procedure can be used to find measures of a number of critical parameters; for example, the win probabilities and the expected duration of the battle. Numerical solutions are obtainable if the total number of individual combatants on the opposing sides is less than 10. For smaller force size battles, with one or two combatants on each side, symbolic solutions can be found. The symbolic solutions express the output parameters abstractly in terms of symbolic representations of the input parameters while the numerical solutions are expressed as numerical values. The input parameters are derived from the probability distributions of the attrition and arrival processes. The solution procedure reduces to solving sets of linear equations that have been constructed from the input parameters. The approach presented in this report does not address the problems associated with measuring the inputs. Rather, this report attempts to establish a relatively simple structure within which small-scale battles can be studied
Analytic solutions for neutrino momenta in decay of top quarks
Energy Technology Data Exchange (ETDEWEB)
Betchart, Burton A., E-mail: bbetchar@pas.rochester.edu; Demina, Regina, E-mail: regina@pas.rochester.edu; Harel, Amnon, E-mail: amnon.harel@cern.ch
2014-02-01
We employ a geometric approach to analytically solve equations of constraint on the decay of top quarks involving leptons. The neutrino momentum is found as a function of the 4-vectors of the associated bottom quark and charged lepton, the masses of the top quark and W boson, and a single parameter, which constrains it to an ellipse. We show how the measured imbalance of momenta in the event reduces the solutions for neutrino momenta to a discrete set, in the cases of one or two top quarks decaying to leptons. The algorithms can be implemented concisely with common linear algebra routines. -- Highlights: • Neutrino momentum from top quark decay is constrained to an ellipse. • We find analytically the best neutrino momenta given the momentum imbalance. • A reference implementation of the algorithms is included.
Analytical solution of Mori's equation with secant hyperbolic memory
International Nuclear Information System (INIS)
Tankeshwar, K.; Pathak, K.N.
1993-07-01
The equation of motion of the auto-correlation function has been solved analytically using a secant-hyperbolic form of the memory function. The analytical results obtained for the long time expansion together with the short time expansion provide a good description over the whole time domain as judged by their comparison with the numerical solution of Mori's equation of motion. We also find that the time evolution of the auto-correlation function is determined by a single parameter τ which is related to the frequency sum rules up to the fourth order. The auto-correlation function has been found to show simple decaying or oscillatory behaviour depending on whether the parameter τ is greater than or less than some critical values. Similarities as well as differences in time evolution of the auto-correlation have been discussed for exponential, secant-hyperbolic and Gaussian approaches of the memory function. (author). 16 refs, 5 figs
Biological and analytical studies of peritoneal dialysis solutions
Directory of Open Access Journals (Sweden)
N. Hudz
2018-04-01
Full Text Available The purpose of our work was to conduct biological and analytical studies of the peritoneal dialysis (PD solutions containing glucose and sodium lactate and establish correlations between cell viability of the Vero cell line and values of analytical indexes of the tested solutions. The results of this study confirm the cytotoxicity of the PD solutions even compared with the isotonic solution of sodium chloride, which may be due to the low pH of the solutions, presence of glucose degradation products (GDPs and high osmolarity of the solutions, and unphysiological concentrations of glucose and sodium lactate. However, it is not yet known what factors or their combination and to what extent cause the cytotoxicity of PD solutions. In the neutral red (NR test the weak, almost middle (r = -0.496 and 0.498, respectively and unexpected correlations were found between reduced viability of monkey kidney cells and increased pH of the PD solutions and between increased cell viability and increased absorbance at 228 nm of the tested PD solutions. These two correlations can be explained by a strong correlation (r = -0.948 between a decrease in pH and an increase in the solution absorbance at 228 nm. The opposite effect was observed in the MTT test. The weak, but expected correlations (r = 0.32 and -0.202, respectively were found between increased cell viability and increased pH in the PD solutions and between decreased cell viability and increased absorbance at 228 nm of the tested PD solutions. The middle and weak correlations (r = 0.56 and 0.29, respectively were detected between increased cell viability and increased lactate concentration in the NR test and MTT test. The data of these correlations can be partially explained by the fact that a correlation with a coefficient r = -0.34 was found between decreased pH in the solutions and increased lactate concentration. The very weak correlations (0.138 and 0.196, respectively were found between increased cell
Parrish, K. E.; Zhang, J.; Teasdale, E.
2007-12-01
An exact analytical solution to the ordinary one-dimensional partial differential equation is derived for transient groundwater flow in a homogeneous, confined, horizontal aquifer using Laplace transformation. The theoretical analysis is based on the assumption that the aquifer is homogeneous and one-dimensional (horizontal); confined between impermeable formations on top and bottom; and of infinite horizontal extent and constant thickness. It is also assumed that there is only a single pumping well penetrating the entire aquifer; flow is everywhere horizontal within the aquifer to the well; the well is pumping with a constant discharge rate; the well diameter is infinitesimally small; and the hydraulic head is uniform throughout the aquifer before pumping. Similar to the Theis solution, this solution is suited to determine transmissivity and storativity for a two- dimensional, vertically confined aquifer, such as a long vertically fractured zone of high permeability within low permeable rocks or a long, high-permeability trench inside a low-permeability porous media. In addition, it can be used to analyze time-drawdown responses to pumping and injection in similar settings. The solution can also be used to approximate the groundwater flow for unconfined conditions if (1) the variation of transmissivity is negligible (groundwater table variation is small in comparison to the saturated thickness); and (2) the unsaturated flow is negligible. The errors associated with the use of the solution to unconfined conditions depend on the accuracies of the above two assumptions. The solution can also be used to assess the impacts of recharge from a seasonal river or irrigation canal on the groundwater system by assuming uniform, time- constant recharge along the river or canal. This paper presents the details for derivation of the analytical solution. The analytical solution is compared to numerical simulation results with example cases. Its accuracy is also assessed and
Numerical and analytical solutions for problems relevant for quantum computers
International Nuclear Information System (INIS)
Spoerl, Andreas
2008-01-01
Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)
Analytical solution of the toroidal constant tension solenoid
International Nuclear Information System (INIS)
Gralnick, S.L.; Tenney, F.H.
1975-01-01
The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 percent
Analytical solutions for tsunami runup on a plane beach
DEFF Research Database (Denmark)
Madsen, Per A.; Schäffer, Hemming Andreas
2010-01-01
wavetrains generated by monopole and dipole disturbances in the deep ocean. The evolution of these wavetrains, while travelling a considerable distance over a constant depth, is influenced by weak dispersion and is governed by the linear Korteweg-De Vries (KdV) equation. This process is described......) of the wave, which is not realistic for geophysical tsunamis. To resolve this problem, we first derive analytical solutions to the nonlinear shallow-water (NSW) equations for the runup/rundown of single waves, where the duration and the wave height can be specified separately. The formulation is then extended...
An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester
Directory of Open Access Journals (Sweden)
H. Salmani
2015-01-01
Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.
Stochastic and collisional diffusion in two-dimensional periodic flows
International Nuclear Information System (INIS)
Doxas, I.; Horton, W.; Berk, H.L.
1990-05-01
The global effective diffusion coefficient D* for a two-dimensional system of convective rolls with a time dependent perturbation added, is calculated. The perturbation produces a background diffusion coefficient D, which is calculated analytically using the Menlikov-Arnold integral. This intrinsic diffusion coefficient is then enhanced by the unperturbed flow, to produce the global effective diffusion coefficient D*, which we can calculate theoretically for a certain range of parameters. The theoretical value agrees well with numerical simulations. 23 refs., 4 figs
Two-dimensional correlation spectroscopy in polymer study
Park, Yeonju; Noda, Isao; Jung, Young Mee
2015-01-01
This review outlines the recent works of two-dimensional correlation spectroscopy (2DCOS) in polymer study. 2DCOS is a powerful technique applicable to the in-depth analysis of various spectral data of polymers obtained under some type of perturbation. The powerful utility of 2DCOS combined with various analytical techniques in polymer studies and noteworthy developments of 2DCOS used in this field are also highlighted. PMID:25815286
Two-dimensional manifolds with metrics of revolution
International Nuclear Information System (INIS)
Sabitov, I Kh
2000-01-01
This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)
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.
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
Oblique propagation of nonlinear hydromagnetic waves: One- and two-dimensional behavior
International Nuclear Information System (INIS)
Malara, F.; Elaoufir, J.
1991-01-01
The one- and two-dimensional behavior of obliquely propagating hydromagnetic waves is analyzed by means of analytical theory and numerical simulations. It is shown that the nonlinear evolution of a one-dimensional MHD wave leads to the formation of a rotational discontinuity and a compressive steepened quasi-linearly polarized pulse whose structure is similar to that of a finite amplitude magnetosonic simple wave. For small propagation angles, the pulse mode (fast or slow) depends on the value of β with respect to unity while for large propagation angles the wave mode is fixed by the sign of the initial density-field correlation. The two-dimensional evolution shows that an MHD wave is unstable against a small-amplitude long-wavelength modulation in the direction transverse to the wave propagation direction. A two-dimensional magnetosonic wave solution is found, in which the density fluctuation is driven by the corresponding total pressure fluctuation, exactly as in the one-dimensional simple wave. Along with the steepening effect, the wave experiences both wave front deformation and a self-focusing effect which may eventually lead to the collapse of the wave. The results compare well with observations of MHD waves in the Earth's foreshock and at comets
Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices
International Nuclear Information System (INIS)
Rojas-Rojas, Santiago; Naether, Uta; Delgado, Aldo; Vicencio, Rodrigo A.
2016-01-01
Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.
Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices
Energy Technology Data Exchange (ETDEWEB)
Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2016-09-16
Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.
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)
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
Measurement of Actinides in Molybdenum-99 Solution Analytical Procedure
Energy Technology Data Exchange (ETDEWEB)
Soderquist, Chuck Z. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Weaver, Jamie L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2015-11-01
This document is a companion report to a previous report, PNNL 24519, Measurement of Actinides in Molybdenum-99 Solution, A Brief Review of the Literature, August 2015. In this companion report, we report a fast, accurate, newly developed analytical method for measurement of trace alpha-emitting actinide elements in commercial high-activity molybdenum-99 solution. Molybdenum-99 is widely used to produce ^{99m}Tc for medical imaging. Because it is used as a radiopharmaceutical, its purity must be proven to be extremely high, particularly for the alpha emitting actinides. The sample of ^{99}Mo solution is measured into a vessel (such as a polyethylene centrifuge tube) and acidified with dilute nitric acid. A gadolinium carrier is added (50 µg). Tracers and spikes are added as necessary. Then the solution is made strongly basic with ammonium hydroxide, which causes the gadolinium carrier to precipitate as hydrous Gd(OH)_{3}. The precipitate of Gd(OH)_{3} carries all of the actinide elements. The suspension of gadolinium hydroxide is then passed through a membrane filter to make a counting mount suitable for direct alpha spectrometry. The high-activity ^{99}Mo and ^{99m}Tc pass through the membrane filter and are separated from the alpha emitters. The gadolinium hydroxide, carrying any trace actinide elements that might be present in the sample, forms a thin, uniform cake on the surface of the membrane filter. The filter cake is first washed with dilute ammonium hydroxide to push the last traces of molybdate through, then with water. The filter is then mounted on a stainless steel counting disk. Finally, the alpha emitting actinide elements are measured by alpha spectrometry.
Measurement of Actinides in Molybdenum-99 Solution Analytical Procedure
International Nuclear Information System (INIS)
Soderquist, Chuck Z.; Weaver, Jamie L.
2015-01-01
This document is a companion report to a previous report, PNNL 24519, Measurement of Actinides in Molybdenum-99 Solution, A Brief Review of the Literature, August 2015. In this companion report, we report a fast, accurate, newly developed analytical method for measurement of trace alpha-emitting actinide elements in commercial high-activity molybdenum-99 solution. Molybdenum-99 is widely used to produce 99m Tc for medical imaging. Because it is used as a radiopharmaceutical, its purity must be proven to be extremely high, particularly for the alpha emitting actinides. The sample of 99 Mo solution is measured into a vessel (such as a polyethylene centrifuge tube) and acidified with dilute nitric acid. A gadolinium carrier is added (50 µg). Tracers and spikes are added as necessary. Then the solution is made strongly basic with ammonium hydroxide, which causes the gadolinium carrier to precipitate as hydrous Gd(OH) 3 . The precipitate of Gd(OH) 3 carries all of the actinide elements. The suspension of gadolinium hydroxide is then passed through a membrane filter to make a counting mount suitable for direct alpha spectrometry. The high-activity 99 Mo and 99m Tc pass through the membrane filter and are separated from the alpha emitters. The gadolinium hydroxide, carrying any trace actinide elements that might be present in the sample, forms a thin, uniform cake on the surface of the membrane filter. The filter cake is first washed with dilute ammonium hydroxide to push the last traces of molybdate through, then with water. The filter is then mounted on a stainless steel counting disk. Finally, the alpha emitting actinide elements are measured by alpha spectrometry.
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
A two-dimensional model with three regions for the reflooding study
International Nuclear Information System (INIS)
Motta, A.M.T.; Kinrys, S.; Roberty, N.C.; Carmo, E.G.D. do; Oliveira, L.F.S. de.
1983-02-01
A two-dimensional semi-analytical model, with three heat transfer regions is described for the calculation of flood ratio, the lenght of quenching front and the temperature distribution in the cladding. (E.G.) [pt
A two-dimensional model with three regions for the reflooding study
International Nuclear Information System (INIS)
Motta, A.M.T.; Kinrys, S.; Roberty, N.C.; Carmo, E.G.D. do; Oliveira, L.F.S. de
1982-01-01
A two-dimensional semi-analytical model, with three heat transfer regions is described for the calculation of flood ratio, the length of quenching front and the temperature distribution in the cladding. (E.G.) [pt
An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows
Energy Technology Data Exchange (ETDEWEB)
Snider, D.M. [SAIC, Albuquerque, NM (United States); O`Rourke, P.J. [Los Alamos National Lab., NM (United States); Andrews, M.J. [Texas A and M Univ., College Station, TX (United States). Dept. of Mechanical Engineering
1997-06-01
A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.
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
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 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…
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.
International Nuclear Information System (INIS)
Grekov, D.; Kasilov, S.; Kernbichler, W.
2016-01-01
A two dimensional numerical code for computation of the electromagnetic field of a fast magnetosonic wave in a tokamak at high harmonics of the ion cyclotron frequency has been developed. The code computes the finite difference solution of Maxwell equations for separate toroidal harmonics making use of the toroidal symmetry of tokamak plasmas. The proper boundary conditions are prescribed at the realistic tokamak vessel. The currents in the RF antenna are specified externally and then used in Ampere law. The main poloidal tokamak magnetic field and the ''kinetic'' part of the dielectric permeability tensor are treated iteratively. The code has been verified against known analytical solutions and first calculations of current drive in the spherical torus are presented.
Analytical Solution and Physics of a Propellant Damping Device
Yang, H. Q.; Peugeot, John
2011-01-01
NASA design teams have been investigating options for "detuning" Ares I to prevent oscillations originating in the vehicle solid-rocket main stage from synching up with the natural resonance of the rest of the vehicle. An experimental work started at NASA MSFC center in 2008 using a damping device showed great promise in damping the vibration level of an 8 resonant tank. However, the mechanisms of the vibration damping were not well understood and there were many unknowns such as the physics, scalability, technology readiness level (TRL), and applicability for the Ares I vehicle. The objectives of this study are to understand the physics of intriguing slosh damping observed in the experiments, to further validate a Computational Fluid Dynamics (CFD) software in propellant sloshing against experiments with water, and to study the applicability and efficiency of the slosh damper to a full scale propellant tank and to cryogenic fluids. First a 2D fluid-structure interaction model is built to model the system resonance of liquid sloshing and structure vibration. A damper is then added into the above model to simulate experimentally observed system damping phenomena. Qualitative agreement is found. An analytical solution is then derived from the Newtonian dynamics for the thrust oscillation damper frequency, and a slave mass concept is introduced in deriving the damper and tank interaction dynamics. The paper will elucidate the fundamental physics behind the LOX damper success from the derivation of the above analytical equation of the lumped Newtonian dynamics. Discussion of simulation results using high fidelity multi-phase, multi-physics, fully coupled CFD structure interaction model will show why the LOX damper is unique and superior compared to other proposed mitigation techniques.
Directory of Open Access Journals (Sweden)
Hasan Bulut
2013-01-01
Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.
Kacimov, A. R.; Obnosov, Y. V.
2018-01-01
A study is made of a steady, two-dimensional groundwater flow with a horizontal well (drain), which pumps out freshwater from an aquifer sandwiched between a horizontal bedrock and ponded soil surface, and containing a lens-shaped static volume of a heavier saline water (DNAPL-dense nonaqueous phase liquid) as a free surface. For flow toward a line sink, an explicit analytical solution is obtained by a conformal mapping of the hexagon in the complex potential plane onto a reference plane and the Keldysh-Sedov integral representation of a mixed boundary-value problem for a complex physical coordinate. The interface is found as a function of the pumping rate, the well locus, the ratio of liquid densities, and the hydraulic heads at the soil surface and in the well. The shape with two inflexion points and fronts varies from a small-thickness bedrock-spread pancake to a critical curvilinear triangle, which cusps toward the sink. The problem is mathematically solvable in a relatively narrow band of geometric and hydraulic parameters. A similar analytic solution for a static heavy bubble confined by a closed-curve interface (no contact with the bedrock) is outlined as an illustration of the method to solve a mixed boundary-value problem.
Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem
Younis, Mohammad I.
2014-01-01
We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions
Analytical solutions for peak and residual uplift resistance of pipelines
Energy Technology Data Exchange (ETDEWEB)
Nixon, J.F. [Nixon Geotech Ltd., Calgary, AB (Canada); Oswell, J.M. [Naviq Consulting Inc., Calgary, AB (Canada)
2010-07-01
Frost heave can occur on cold pipelines that traverse unfrozen, non permafrost terrain. The stresses experienced by the pipeline are partly a function of the strength of the soil on the non heaving side of the frozen-unfrozen interface. This paper proposed three analytical solutions to estimate the soil uplift resistance by considering the pipeline and soil to act similar to a strip footing, a punching shear failure, and by considering the formation of horizontal crack emanating from the spring line of the pipe. Peak uplift resistance and residual uplift resistance were discussed. Results for full scale pipe and for laboratory scale model pipes were presented, with particular reference to cover depth, temperature and crack width; and limits to residual uplift resistance. It was concluded that the peak uplift resistance and the residual uplift resistance are generally independent and controlled by different factors. The peak resistance is related directly to pipe diameter, and less strongly dependent on springline depth. It is also strongly dependent on soil temperature. However, the residual uplift resistance is strongly dependent on burial depth, weakly dependent on pipe displacement rate and also on soil temperature. 15 refs., 19 figs.
Electronic states of graphene nanoribbons and analytical solutions
Directory of Open Access Journals (Sweden)
Katsunori Wakabayashi, Ken-ichi Sasaki, Takeshi Nakanishi and Toshiaki Enoki
2010-01-01
Full Text Available Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.
Solution of the isotopic depletion equation using decomposition method and analytical solution
Energy Technology Data Exchange (ETDEWEB)
Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: fprata@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear
2011-07-01
In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)
Solution of the isotopic depletion equation using decomposition method and analytical solution
International Nuclear Information System (INIS)
Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S.
2011-01-01
In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)
Numerical studies of unsteady coherent structures and transport in two-dimensional flows
Energy Technology Data Exchange (ETDEWEB)
Hesthaven, J.S.
1995-08-01
The dynamics of unsteady two-dimensional coherent structures in various physical systems is studied through direct numerical solution of the dynamical equations using spectral methods. The relation between the Eulerian and the Lagrangian auto-correlation functions in two-dimensional homogeneous, isotropic turbulence is studied. A simple analytic expression for the Eulerian and Lagrangian auto-correlation function for the fluctuating velocity field is derived solely on the basis of the one-dimensional power spectrum. The long-time evolution of monopolar and dipolar vortices in anisotropic systems relevant for geophysics and plasma physics is studied by direct numerical solution. Transport properties and spatial reorganization of vortical structures are found to depend strongly on the initial conditions. Special attention is given to the dynamics of strong monopoles and the development of unsteady tripolar structures. The development of coherent structures in fluid flows, incompressible as well as compressible, is studied by novel numerical schemes. The emphasis is on the development of spectral methods sufficiently advanced as to allow for detailed and accurate studies of the self-organizing processes. (au) 1 ill., 94 refs.
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...
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.
Two-Dimensional One-Component Plasma on Flamm's Paraboloid
Fantoni, Riccardo; Téllez, Gabriel
2008-11-01
We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Γ=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.
Anisotropic mass density by two-dimensional acoustic metamaterials
Energy Technology Data Exchange (ETDEWEB)
Torrent, Daniel; Sanchez-Dehesa, Jose [Wave Phenomena Group, Department of Electronic Engineering, Polytechnic University of Valencia, C/Camino de Vera s/n, E-46022 Valencia (Spain)], E-mail: jsdehesa@upvnet.upv.es
2008-02-15
We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.
Linear and nonlinear viscous flow in two-dimensional fluids
International Nuclear Information System (INIS)
Gravina, D.; Ciccotti, G.; Holian, B.L.
1995-01-01
We report on molecular dynamics simulations of shear viscosity η of a dense two-dimensional fluid as a function of the shear rate γ. We find an analytic dependence of η on γ, and do not find any evidence whatsoever of divergence in the Green-Kubo (GK) value that would be caused by the well-known long-time tail for the shear-stress autocorrelation function, as predicted by the mode-coupling theory. In accordance with the linear response theory, the GK value of η agrees remarkably well with nonequilibrium values at small shear rates. (c) 1995 The American Physical Society
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....
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
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....
An analytical solution for the Marangoni mixed convection boundary layer flow
DEFF Research Database (Denmark)
Moghimi, M. A.; Kimiaeifar, Amin; Rahimpour, M.
2010-01-01
In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier-Stokes equations to a set of nonlinear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM...... the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....
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.
Relaxation and self-organization in two-dimensional plasma and neutral fluid flow systems
International Nuclear Information System (INIS)
Das, Amita
2008-01-01
Extensive numerical studies in the framework of a simplified two-dimensional model for neutral and plasma fluid for a variety of initial configurations and for both decaying and driven cases are carried out to illustrate relaxation toward a self-organized state. The dynamical model equation constitutes a simple choice for this purpose, e.g., the vorticity equation of the Navier-Stokes dynamics for the incompressible neutral fluids and the Hasegawa-Mima equation for plasma fluid flow system. Scatter plots are employed to observe a development of functional relationship, if any, amidst the generalized vorticity and its Laplacian. It is seen that they do not satisfy a linear relationship as the well known variational approach of enstrophy minimization subject to constancy of the energy integral for the two-dimensional (2D) system suggests. The observed nonlinear functional relationship is understood by separating the contribution to the scatter plot from spatial regions with intense vorticity patches and those of the background flow region where the background vorticity is weak or absent altogether. It is shown that such a separation has close connection with the known exact analytical solutions of the system. The analytical solutions are typically obtained by assuming a finite source of vorticity for the inner core of the localized structure, which is then matched with the solution in the outer region where vorticity is chosen to be zero. The work also demonstrates that the seemingly ad hoc choice of the linear vorticity source function for the inner region is in fact consistent with the self-organization paradigm of the 2D systems
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.
Directory of Open Access Journals (Sweden)
D. A. Fetisov
2015-01-01
Full Text Available The controllability conditions are well known if we speak about linear stationary systems: a linear stationary system is controllable if and only if the dimension of the state vector is equal to the rank of the controllability matrix. The concept of the controllability matrix is extended to affine systems, but relations between affine systems controllability and properties of this matrix are more complicated. Various controllability conditions are set for affine systems, but they deal as usual either with systems of some special form or with controllability in some small neighborhood of the concerned point. An affine system is known to be controllable if the system is equivalent to a system of a canonical form, which is defined and regular in the whole space of states. In this case, the system is said to be feedback linearizable in the space of states. However there are examples, which illustrate that a system can be controllable even if it is not feedback linearizable in any open subset in the space of states. In this article we deal with such systems.Affine systems with two-dimensional control are considered. The system in question is assumed to be equivalent to a system of a quasicanonical form with two-dimensional zero dynamics which is defined and regular in the whole space of states. Therefore the controllability of the original system is equivalent to the controllability of the received system of a quasicanonical form. In this article the sufficient condition for an available solution of the terminal problem is proven for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. The condition is valid in the case of an arbitrary time interval and arbitrary initial and finite states of the system. Therefore the controllability condition is set for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. An example is given which illustrates how the proved
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
International Nuclear Information System (INIS)
Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro
2010-01-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro
2010-10-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk
International Nuclear Information System (INIS)
Milinazzo, F.; Saffman, P.G.
1977-01-01
The numerical calculation of two-dimensional rotational flow at large Reynolds number is considered. The method of replacing a continuous distribution of vorticity by a finite number, N, of discrete vortices is examined, where the vortices move under their mutually induced velocities plus a random component to simulate effects of viscosity. The accuracy of the method is studied by comparison with the exact solution for the decay of a circular vortex. It is found, and analytical arguments are produced in support, that the quantitative error is significant unless N is large compared with a characteristic Reynolds number. The mutually induced velocities are calculated by both direct summation and by the ''cloud in cell'' technique. The latter method is found to produce comparable error and to be much faster
International Nuclear Information System (INIS)
Christodoulakis, T; Doulis, G; Terzis, Petros A; Melas, E; Grammenos, Th; Papadopoulos, G O; Spanou, A
2010-01-01
The canonical decomposition of all 3+1 geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific renormalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchar's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-DeWitt equation is based on a renormalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible through the exploitation of the residual freedom in the choice of the third functional, which is left by the imposition of the Requirement, and is proven to correspond to a general coordinate transformation in the renormalized manifold.
FEAST: a two-dimensional non-linear finite element code for calculating stresses
International Nuclear Information System (INIS)
Tayal, M.
1986-06-01
The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%
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...
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.
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.
International Nuclear Information System (INIS)
Chen, C.S.; Yates, S.R.
1989-01-01
In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. It has been reported that by treating the radioactive decay constant as the appropriate first-order rate constant, these solutions can also be used to study injection problems of a similar nature subject to first-order chemical or biological reactions. The fracture is idealized by a pair of parallel, smooth plates separated by an aperture of constant thickness. Groundwater was assumed to be immobile in the underlying and overlying porous formations due to their low permeabilities. However, the injected radionuclides were able to move from the fracture into the porous matrix by molecular diffusion (the matrix diffusion) due to possible concentration gradients across the interface between the fracture and the porous matrix. Calculation of the transient solutions is not straightforward, and the paper documents a contained Fortran program, which computes the Stehfest inversion, the Airy functions, and gives the concentration distributions in the fracture as well as in the porous matrix for both transient and steady-state cases
Analysis of the two dimensional Datta-Das Spin Field Effect Transistor
Bandyopadhyay, S.
2010-01-01
An analytical expression is derived for the conductance modulation of a ballistic two dimensional Datta-Das Spin Field Effect Transistor (SPINFET) as a function of gate voltage. Using this expression, we show that the recently observed conductance modulation in a two-dimensional SPINFET structure does not match the theoretically expected result very well. This calls into question the claimed demonstration of the SPINFET and underscores the need for further careful investigation.
Analysis of the two-dimensional Datta-Das spin field effect transistor
Agnihotri, P.; Bandyopadhyay, S.
2010-03-01
An analytical expression is derived for the conductance modulation of a ballistic two-dimensional Datta-das spin field effect transistor (SPINFET) as a function of gate voltage. Using this expression, we show that the recently observed conductance modulation in a two-dimensional SPINFET structure does not match the theoretically expected result very well. This calls into question the claimed demonstration of the SPINFET and underscores the need for further careful investigation.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.
Two-dimensional and relativistic effects in lower-hybrid current drive
International Nuclear Information System (INIS)
Hewett, D.; Hizanidis, K.; Krapchev, V.; Bers, A.
1983-06-01
We present new numerical and analytic solutions of the two-dimensional Fokker-Planck equation supplemented by a parallel quasilinear diffusion term. The results show a large enhancement of the perpendicular temperature of both the electrons resonant with the applied RF fields and the more energetic electrons in the tail. Both the RF-generated current and power dissipated are substantially increased by the perpendicular energy broadening in the resonant region. In the presence of a small DC electric field the RF current generated is very much enhanced, much more than in a simple additive fashion. In addition, we present a relativistic formulation of the two-dimensional Fokker-Planck quasilinear equation. From conservation equations, based upon this formulation, we derive the characteristics of RF current drive with energetic electrons. These show how the RF-driven current and its figure of merit (I/P/sub d/) increase with the energy of the current-carrying electrons, and that their perpendicular, random momentum must also increase
Analytical solutions of the electrostatically actuated curled beam problem
Younis, Mohammad I.
2014-01-01
This works presents analytical expressions of the electrostatically actuated initially deformed cantilever beam problem. The formulation is based on the continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We
International Nuclear Information System (INIS)
Liu Chunliang; Xie Xi; Chen Yinbao
1991-01-01
The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation
International Nuclear Information System (INIS)
Banks, K.M.; Hare, D.R.; Reid, B.R.
1989-01-01
A three-dimensional solution structure for the self-complementary dodecanucleotide [(d-GCCTGATCAGGC)] 2 has been determined by distance geometry with further refinements being performed after back-calculation of the NOESY spectrum. This DNA dodecamer contains the hexamer [d(TGATCA)] 2 recognized and cut by the restriction endonuclease BclI, and its structure was determined in hopes of obtaining a better understanding of the sequence-specific interactions which occur between proteins and DNA. Preliminary examination of the structure indicates the structure is underwound with respect to idealized B-form DNA though some of the local structural parameters (glycosyl torsion angle and pseudorotation angle) suggest a B-family type of structure is present. This research demonstrates the requirements (resonance assignments, interproton distance measurements, distance geometry calculations, and NOESY spectra back-calculation) to generate experimentally self-consistent solution structures for short DNA sequences
Fraction transfer process in on-line comprehensive two-dimensional liquid phase separations
Czech Academy of Sciences Publication Activity Database
Česla, P.; Křenková, Jana
2017-01-01
Roč. 40, č. 1 (2017), s. 109-123 ISSN 1615-9306 R&D Projects: GA ČR(CZ) GA14-06319S Institutional support: RVO:68081715 Keywords : capillary electrophoresis * comprehensive liquid chromatography * fraction transfer * two-dimensional separations * liquid chromatography Subject RIV: CB - Analytical Chemistry, Separation OBOR OECD: Analytical chemistry Impact factor: 2.557, year: 2016
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 ...
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.
Repulsion of polarized particles from two-dimensional materials
Rodríguez-Fortuño, Francisco J.; Picardi, Michela F.; Zayats, Anatoly V.
2018-05-01
Repulsion of nanoparticles, molecules, and atoms from surfaces can have important applications in nanomechanical devices, microfluidics, optical manipulation, and atom optics. Here, through the solution of a classical scattering problem, we show that a dipole source oscillating at a frequency ω can experience a robust and strong repulsive force when its near-field interacts with a two-dimensional material. As an example, the case of graphene is considered, showing that a broad bandwidth of repulsion can be obtained at frequencies for which propagation of plasmon modes is allowed 0 chemical potential tunable electrically or by chemical doping.
Minimal quantization of two-dimensional models with chiral anomalies
International Nuclear Information System (INIS)
Ilieva, N.
1987-01-01
Two-dimensional gauge models with chiral anomalies - ''left-handed'' QED and the chiral Schwinger model, are quantized consistently in the frames of the minimal quantization method. The choice of the cone time as a physical time for system of quantization is motivated. The well-known mass spectrum is found but with a fixed value of the regularization parameter a=2. Such a unique solution is obtained due to the strong requirement of consistency of the minimal quantization that reflects in the physically motivated choice of the time axis
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.
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 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.
Ding, Xiao-Li; Nieto, Juan J.
2017-11-01
In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.
Analytic solution of the potential and electric field of a jet type drift chamber
Energy Technology Data Exchange (ETDEWEB)
Weltin, A
1988-02-15
Starting from the known two-dimensional potential of a multiwire proportional chamber, the analytic expressions of the potential and the electric field are derived for a jet type drift chamber with a central wire plane of alternating sense and potential wires. The design goal of any jet chamber, namely the periodicity of the electric drift field, is imposed as a boundary condition at the beginning. In this way, the formulae are short and can be easily evaluated. In particular, expressions are given for the mean potential of the central wire plane, the drift field and the wire surface fields. Moreover, wire cathodes frequently used in jet chambers are described by analytic expressions. For a given drift field the difference of the potential as compared to a continuous metal cathode is presented. These results allowed to construct a two-dimensional computer simulation of the full OPAL jet chamber with no explicit periodicity but all its boundaries. Using field shaping electrodes a geometrically short yet quite satisfactory termination of a sense wire plane is demonstrated. Finally an example is presented, which is calculated in detail.
Global geometry of two-dimensional charged black holes
International Nuclear Information System (INIS)
Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus
2006-01-01
The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation
Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-01-01
2 and Q 0 2 , being equally accurate in devolution (Q 2 0 2 ) as in evolution (Q 2 >Q 0 2 ). Further, it can also be used for nonsinglet distributions, thus giving LO analytic solutions for individual quark and gluon distributions at a given x and Q 2 , rather than the numerical solutions of the coupled integral-differential equations on a large, but fixed, two-dimensional grid that are currently available.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
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.
Analytic continuation of solutions of some nonlinear convolution partial differential equations
Directory of Open Access Journals (Sweden)
Hidetoshi Tahara
2015-01-01
Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of ...
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)
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
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 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 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
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.
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.
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.
On analytical solution of the Navier-Stokes equations
International Nuclear Information System (INIS)
Scheffel, J.
2001-04-01
An analytical method for solving the dissipative, nonlinear and non-stationary Navier-Stokes equations is presented. Velocity and pressure is expanded in power series of cartesian coordinates and time. The method is applied to 2-D incompressible gravitational flow in a bounded, rectangular domain
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)
Zheng, Jun; Han, Xinyue; Wang, ZhenTao; Li, Changfeng; Zhang, Jiazhong
2017-06-01
For about a century, people have been trying to seek for a globally convergent and closed analytical solution (CAS) of the Blasius Equation (BE). In this paper, we proposed a formally satisfied solution which could be parametrically expressed by two power series. Some analytical results of the laminar boundary layer of a flat plate, that were not analytically given in former studies, e.g. the thickness of the boundary layer and higher order derivatives, could be obtained based on the solution. Besides, the heat transfer in the laminar boundary layer of a flat plate with constant temperature could also be analytically formulated. Especially, the solution of the singular situation with Prandtl number Pr=0, which seems impossible to be analyzed in prior studies, could be given analytically. The method for finding the CAS of Blasius equation was also utilized in the problem of the boundary layer regulation through wall injection and slip velocity on the wall surface.
Energy Technology Data Exchange (ETDEWEB)
Yamasaki, Ryohei; Bacon, B. (Univ. of California, San Francisco (USA) Veterans Administration Medical Center, San Francisco, CA (USA))
1991-01-22
The solution conformations of the group B polysaccharide of Neisseria meningitidis were analyzed by DQF-COSY and pure absorption 2D NOE NMR with three mixing times. The pyranose ring of the sialic acid residue was found to be in the {sup 2}C{sub 5} conformation. The DQF-COSY analysis indicated that the orientations of H6 and H7 and of H7 and H8 are both gauche. In order to overcome the difficulties in analyzing the NOE data due to the two sets of proton overlaps, molecular modeling of {alpha}-2,8-linked sialic acid oligomers was carried out to investigate possible conformers, and theoretical NOE calculations were performed by using CORMA (complete relaxation matrix analysis). The analysis suggests that the polysaccharide adopts helical structures for which the {phi} (defined by O6-C2-O8-C8) and {psi} (C2-O8-C8-C7) angles are in the following ranges: {phi}-60 to 0{degree}, {psi} 115-175{degree} or {phi} 90-120{degree}, {psi}55-175{degree}. The weak affinity of anti-B antibodies for smaller {alpha}-2,8-linked oligosaccharides may be due to the fact that such oligomers are more flexible and may not form an ordered structure as the poly(sialic acid) does.
International Nuclear Information System (INIS)
Kuddusi, Luetfullah; Denton, Jesse C.
2007-01-01
The constructal solution for cooling of electronics requires solution of a fundamental heat conduction problem in a composite slab composed of a heat generating slab and a thin strip of high conductivity material that is responsible for discharging the generated heat to a heat sink located at one end of the strip. The fundamental 2D heat conduction problem is solved analytically by applying an integral transform method. The analytical solution is then employed in a constructal solution, following Bejan, for cooling of electronics. The temperature and heat flux distributions of the elemental heat generating slabs are assumed to be the same as those of the analytical solution in all the elemental volumes and the high conductivity strips distributed in the different constructs. Although the analytical solution of the fundamental 2D heat conduction problem improves the accuracy of the distributions in the elemental slabs, the results following Bejan's strategy do not affirm the accuracy of Bejan's constructal solution itself as applied to this problem of cooling of electronics. Several different strategies are possible for developing a constructal solution to this problem as is indicated
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor ... It is to observe the layer behavior of the solution for smaller values of ε leading to singular ...... Burger equation, momentum gas equation and heat equation.
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
Selva Balaji Munusamy
2017-07-29
Jul 29, 2017 ... higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation .... reality, seepage face formation is common for tide–aquifer interaction problems. To simplify the complexity of the.
A family of analytical solutions of a nonlinear diffusion-convection equation
Hayek, Mohamed
2018-01-01
Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.
Analytical Solution of Pantograph Equation with Incommensurate Delay
Patade, Jayvant; Bhalekar, Sachin
2017-08-01
Pantograph equation is a delay differential equation (DDE) arising in electrodynamics. This paper studies the pantograph equation with two delays. The existence, uniqueness, stability and convergence results for DDEs are presented. The series solution of the proposed equation is obtained by using Daftardar-Gejji and Jafari method and given in terms of a special function. This new special function has several properties and relations with other functions. Further, we generalize the proposed equation to fractional-order case and obtain its solution.
Selecting analytical tools for characterization of polymersomes in aqueous solution
DEFF Research Database (Denmark)
Habel, Joachim Erich Otto; Ogbonna, Anayo; Larsen, Nanna
2015-01-01
Selecting the appropriate analytical methods for characterizing the assembly and morphology of polymer-based vesicles, or polymersomes are required to reach their full potential in biotechnology. This work presents and compares 17 different techniques for their ability to adequately report size....../purification. Of the analytical methods tested, Cryo-transmission electron microscopy and atomic force microscopy (AFM) turned out to be advantageous for polymersomes with smaller diameter than 200 nm, whereas confocal microscopy is ideal for diameters >400 nm. Polymersomes in the intermediate diameter range can be characterized...... using freeze fracture Cryo-scanning electron microscopy (FF-Cryo-SEM) and nanoparticle tracking analysis (NTA). Small angle X-ray scattering (SAXS) provides reliable data on bilayer thickness and internal structure, Cryo-TEM on multilamellarity. Taken together, these tools are valuable...
Analytical solutions of the electrostatically actuated curled beam problem
Younis, Mohammad I.
2014-07-24
This works presents analytical expressions of the electrostatically actuated initially deformed cantilever beam problem. The formulation is based on the continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximation. In such cases, multi-mode reduced order models are shown to yield accurate results. © 2014 Springer-Verlag Berlin Heidelberg.
Yang, Jianwen
2012-04-01
A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.
SIMULATIONS OF VISCOUS ACCRETION FLOW AROUND BLACK HOLES IN A TWO-DIMENSIONAL CYLINDRICAL GEOMETRY
Energy Technology Data Exchange (ETDEWEB)
Lee, Seong-Jae; Hyung, Siek [School of Science Education (Astronomy), Chungbuk National University, Chungbuk 28644 (Korea, Republic of); Chattopadhyay, Indranil; Kumar, Rajiv [ARIES, Manora Peak, Nainital-263002, Uttarakhand (India); Ryu, Dongsu, E-mail: seong@chungbuk.ac.kr [Department of Physics, School of Natural Sciences UNIST, Ulsan 44919 (Korea, Republic of)
2016-11-01
We simulate shock-free and shocked viscous accretion flows onto a black hole in a two-dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian total variation diminishing plus remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. The inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any quasi-periodic oscillation (QPO)-like activity developed. The steady-state shocked solution in the inviscid as well as in the viscous regime matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large-amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. This oscillation of the inner part of the disk is interpreted as the source of QPO in hard X-rays observed in micro-quasars. Strong shock oscillation induces strong episodic jet emission. The jets also show the existence of shocks, which are produced as one shell hits the preceding one. The periodicities of the jets and shock oscillation are similar; the jets for the higher viscosity parameter appear to be stronger and faster.
Two-dimensional fluid-hammer analysis by the method of nearcharacteristics
International Nuclear Information System (INIS)
Shin, Y.W.; Kot, C.A.
1975-05-01
A numerical technique based on the method of nearcharacteristics is considered for solving propagation of fluid-hammer waves in a two-dimensional geometry. The solution is constructed by relating flow conditions by compatibility equations along lines called nearcharacteristics. Three choices are considered in the numerical scheme that are accurate within an error of the order of magnitude of the time step. Since the nearcharacteristics lie in the coordinate planes, the technique provides an efficient method requiring only simple interpolations in the initial plane. On the other hand, the nearcharacteristics fall outside the characteristics cone. Thus the solution procedure directly refers to conditions outside the true domain of dependence. The effect of this is studied through numerical calculation of a simple example problem and comparison with results obtained by a bicharacteristic method. Comparison is also made with existing analytical solutions and experiments. Furthermore, the three solution schemes considered are examined for numerical stability by the vonNeumann test. Two of the schemes were found to be unstable; the third yielded a stability criterion equivalent to that of the bicharacteristic formulation. The stability-analysis results were confirmed by numerical experimentation. (auth)
International Nuclear Information System (INIS)
1983-04-01
SALT4 is a two-dimensional analytical/displacement-discontinuity code designed to evaluate temperatures, deformation, and stresses associated with underground disposal of radioactive waste in bedded salt. This code was developed by the University of Minnesota. This documentation describes the mathematical equations of the physical system being modeled, the numerical techniques utilized, and the organization of the computer code, SALT4. The SALT4 code takes into account: (1) viscoelastic behavior in the pillars adjacent to excavations; (2) transversely isotropic elastic moduli such as those exhibited by bedded or stratified rock; and (2) excavation sequence. Major advantages of the SALT4 code are: (1) computational efficiency; (2) the small amount of input data required; and (3) a creep law consistent with laboratory experimental data for salt. The main disadvantage is that some of the assumptions in the formulation of SALT4, i.e., temperature-independent material properties, render it unsuitable for canister-scale analysis or analysis of lateral deformation of the pillars. The SALT4 code can be used for parameter sensitivity analyses of two-dimensional, repository-scale, thermal and thermomechanical response in bedded salt during the excavation, operational, and post-closure phases. It is especially useful in evaluating alternative patterns and sequences of excavation or waste canister placement. SALT4 can also be used to verify fully numerical codes. This is similar to the use of analytic solutions for code verification. Although SALT4 was designed for analysis of bedded salt, it is also applicable to crystalline rock if the creep calculation is suppressed. In Section 1.5 of this document the code custodianship and control is described along with the status of verification, validation and peer review of this report
Two-dimensional analysis of motion artifacts, including flow effects
International Nuclear Information System (INIS)
Litt, A.M.; Brody, A.S.; Spangler, R.A.; Scott, P.D.
1990-01-01
The effects of motion on magnetic resonance images have been theoretically analyzed for the case of a point-like object in simple harmonic motion and for other one-dimensional trajectories. The authors of this paper extend this analysis to a generalized two-dimensional magnetization with an arbitrary motion trajectory. The authors provide specific solutions for the clinically relevant cases of the cross-sections of cylindrical objects in the body, such as the aorta, which has a roughly one-dimensional, simple harmonic motion during respiration. By extending the solution to include inhomogeneous magnetizations, the authors present a model which allows the effects of motion artifacts and flow artifacts to be analyzed simultaneously
Tachyon hair on two-dimensional black holes
International Nuclear Information System (INIS)
Peet, A.; Susskind, L.; Thorlacius, L.
1993-01-01
Static black holes in two-dimensional string theory can carry tachyon hair. Configurations which are nonsingular at the event horizon have a nonvanishing asymptotic energy density. Such solutions can be smoothly extended through the event horizon and have a nonvanishing energy flux emerging from the past singularity. Dynamical processes will not change the amount of tachyon hair on a black hole. In particular, there will be no tachyon hair on a black hole formed in gravitational collapse if the initial geometry is the linear dilaton vacuum. There also exist static solutions with a finite total energy, which have singular event horizons. Simple dynamical arguments suggest that black holes formed in gravitational collapse will not have tachyon hair of this type
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.
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.; Aarts, D. G. A. L.; Howell, P. D.; Majumdar, A.
2017-01-01
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Advancements of two dimensional correlation spectroscopy in protein researches
Tao, Yanchun; Wu, Yuqing; Zhang, Liping
2018-05-01
The developments of two-dimensional correlation spectroscopy (2DCOS) applications in protein studies are discussed, especially for the past two decades. The powerful utilities of 2DCOS combined with various analytical techniques in protein studies are summarized. The emphasis is on the vibration spectroscopic techniques including IR, NIR, Raman and optical activity (ROA), as well as vibration circular dichroism (VCD) and fluorescence spectroscopy. In addition, some new developments, such as hetero-spectral 2DCOS, moving-window correlation, and model based correlation, are also reviewed for their utility in the investigation of the secondary structure, denaturation, folding and unfolding changes of protein. Finally, the new possibility and challenges of 2DCOS in protein research are highlighted as well.
Two-dimensional fruit ripeness estimation using thermal imaging
Sumriddetchkajorn, Sarun; Intaravanne, Yuttana
2013-06-01
Some green fruits do not change their color from green to yellow when being ripe. As a result, ripeness estimation via color and fluorescent analytical approaches cannot be applied. In this article, we propose and show for the first time how a thermal imaging camera can be used to two-dimensionally classify fruits into different ripeness levels. Our key idea relies on the fact that the mature fruits have higher heat capacity than the immature ones and therefore the change in surface temperature overtime is slower. Our experimental proof of concept using a thermal imaging camera shows a promising result in non-destructively identifying three different ripeness levels of mangoes Mangifera indica L.
Normal Modes of Magnetized Finite Two-Dimensional Yukawa Crystals
Marleau, Gabriel-Dominique; Kaehlert, Hanno; Bonitz, Michael
2009-11-01
The normal modes of a finite two-dimensional dusty plasma in an isotropic parabolic confinement, including the simultaneous effects of friction and an external magnetic field, are studied. The ground states are found from molecular dynamics simulations with simulated annealing, and the influence of screening, friction, and magnetic field on the mode frequencies is investigated in detail. The two-particle problem is solved analytically and the limiting cases of weak and strong magnetic fields are discussed.[4pt] [1] C. Henning, H. K"ahlert, P. Ludwig, A. Melzer, and M.Bonitz. J. Phys. A 42, 214023 (2009)[2] B. Farokhi, M. Shahmansouri, and P. K. Shukla. Phys.Plasmas 16, 063703 (2009)[3] L. Cândido, J.-P. Rino, N. Studart, and F. M. Peeters. J. Phys.: Condens. Matter 10, 11627--11644 (1998)
Drifting plasmons in open two-dimensional channels: modal analysis
International Nuclear Information System (INIS)
Sydoruk, O
2013-01-01
Understanding the properties of plasmons in two-dimensional channels is important for developing methods of terahertz generation. This paper presents a modal analysis of plasmonic reflection in open channels supporting dc currents. As it shows, the plasmons can be amplified upon reflection if a dc current flows away from a conducting boundary; de-amplification occurs for the opposite current direction. The problem is solved analytically, based on a perturbation calculation, and numerically, and agreement between the methods is demonstrated. The power radiated by a channel is found to be negligible, and plasmon reflection in open channels is shown to be similar to that in closed channels. Based on this similarity, the oscillator designs developed earlier for closed channels could be applicable also for open ones. The results develop the modal-decomposition technique further as an instrument for the design of terahertz plasmonic sources. (paper)
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.
2017-01-16
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Acoustic resonances in two-dimensional radial sonic crystal shells
Energy Technology Data Exchange (ETDEWEB)
Torrent, Daniel; Sanchez-Dehesa, Jose, E-mail: jsdehesa@upvnet.upv.e [Wave Phenomena Group, Departamento de Ingenieria Electronica, Universidad Politecnica de Valencia, C/Camino de Vera s.n., E-46022 Valencia (Spain)
2010-07-15
Radial sonic crystals (RSC) are fluidlike structures infinitely periodic along the radial direction that verify the Bloch theorem and are possible only if certain specially designed acoustic metamaterials with mass density anisotropy can be engineered (see Torrent and Sanchez-Dehesa 2009 Phys. Rev. Lett. 103 064301). A comprehensive analysis of two-dimensional (2D) RSC shells is reported here. A given shell is in fact a circular slab with a central cavity. These finite crystal structures contain Fabry-Perot-like resonances and modes strongly localized at the central cavity. Semi-analytical expressions are developed to obtain the quality factors of the different resonances, their symmetry features and their excitation properties. The results reported here are completely general and can be extended to equivalent 3D spherical shells and to their photonic counterparts.
Two-dimensional dynamics of a free molecular chain with a secondary structure
DEFF Research Database (Denmark)
Zolotaryuk, Alexander; Christiansen, Peter Leth; Savin, A.V.
1996-01-01
A simple two-dimensional (2D) model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model of an anharmo......A simple two-dimensional (2D) model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model...
Analytical solution using computer algebra of a biosensor for detecting toxic substances in water
Rúa Taborda, María. Isabel
2014-05-01
In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.
Unsteady analytical solutions to the Poisson–Nernst–Planck equations
International Nuclear Information System (INIS)
Schönke, Johannes
2012-01-01
It is shown that the Poisson–Nernst–Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unsteady exact solutions for one and multidimensional cases are presented. Besides new mathematical insights which these first known unsteady solutions give, they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code. (paper)
Analytical solutions of hypersonic type IV shock - shock interactions
Frame, Michael John
An analytical model has been developed to predict the effects of a type IV shock interaction at high Mach numbers. This interaction occurs when an impinging oblique shock wave intersects the most normal portion of a detached bow shock. The flowfield which develops is complicated and contains an embedded jet of supersonic flow, which may be unsteady. The jet impinges on the blunt body surface causing very high pressure and heating loads. Understanding this type of interaction is vital to the designers of cowl lips and leading edges on air- breathing hypersonic vehicles. This analytical model represents the first known attempt at predicting the geometry of the interaction explicitly, without knowing beforehand the jet dimensions, including the length of the transmitted shock where the jet originates. The model uses a hyperbolic equation for the bow shock and by matching mass continuity, flow directions and pressure throughout the flowfield, a prediction of the interaction geometry can be derived. The model has been shown to agree well with the flowfield patterns and properties of experiments and CFD, but the prediction for where the peak pressure is located, and its value, can be significantly in error due to a lack of sophistication in the model of the jet fluid stagnation region. Therefore it is recommended that this region of the flowfield be modeled in more detail and more accurate experimental and CFD measurements be used for validation. However, the analytical model has been shown to be a fast and economic prediction tool, suitable for preliminary design, or for understanding the interactions effects, including the basic physics of the interaction, such as the jet unsteadiness. The model has been used to examine a wide parametric space of possible interactions, including different Mach number, impinging shock strength and location, and cylinder radius. It has also been used to examine the interaction on power-law shaped blunt bodies, a possible candidate for
Analytical solution of a stochastic content-based network model
International Nuclear Information System (INIS)
Mungan, Muhittin; Kabakoglu, Alkan; Balcan, Duygu; Erzan, Ayse
2005-01-01
We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour
Analytical Solutions for Predicting Underwater Explosion Gas Bubble Behaviour
2010-11-01
décrit différents modèles analytiques élaborés antérieurement pour prévoir la croissance et l’implosion radiales en champ libre des bulles gazeuses...9.80665 Air pressure (kPa), Pair 101.325 101.325 4.4 Code Development The visualization software IDL was used to develop a code for calculating the...models and assumptions provide better predictions. Using the visualization software IDL the various analytical models and similitude equations, a code
Selecting analytical tools for characterization of polymersomes in aqueous solution
DEFF Research Database (Denmark)
Habel, Joachim Erich Otto; Ogbonna, Anayo; Larsen, Nanna
2015-01-01
/purification. Of the analytical methods tested, Cryo-transmission electron microscopy and atomic force microscopy (AFM) turned out to be advantageous for polymersomes with smaller diameter than 200 nm, whereas confocal microscopy is ideal for diameters >400 nm. Polymersomes in the intermediate diameter range can be characterized...... using freeze fracture Cryo-scanning electron microscopy (FF-Cryo-SEM) and nanoparticle tracking analysis (NTA). Small angle X-ray scattering (SAXS) provides reliable data on bilayer thickness and internal structure, Cryo-TEM on multilamellarity. Taken together, these tools are valuable...
Towards an analytic solution of QCD: The glueball mass gap
International Nuclear Information System (INIS)
West, G.B.
1987-01-01
Certain general features and beliefs concerning quantum chromodynamics are reviewed with he view to seeing whether the theory sense and whether its physical spectrum can be determined. A typical Green's function is represented as an expansion around the minima of the action, each term of which is divergent and requires renormalization. It is shown that even after renormalization, each of the series generated by expansion around a minimum is divergent and requires a summability procedure to make sense. The causality and analyticity of the resulting Green's function is then discussed. The ideas thus developed are shown to determine the position of the first singularity of the Green's function
Applicability of the Analytical Solution to N-Person Social Dilemma Games
Directory of Open Access Journals (Sweden)
Ugo Merlone
2018-05-01
Full Text Available The purpose of this study is to present an analysis of the applicability of an analytical solution to the N−person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent based simulation. However, no discussion has been offered for the applicability of this result in all Prisoners' Dilemma game scenarios or in other N−person social dilemma games such as Chicken or Stag Hunt. In this paper it is shown that the analytical solution works in all social games where the linear payoff functions are such that each agent's cooperating probability fluctuates around the analytical solution without cooperating or defecting with certainty. The social game regions where this determination holds are explored by varying payoff function parameters. It is found by both simulation and a special method that the analytical solution applies best in Chicken when the payoff parameter S is slightly negative and then the analytical solution slowly degrades as S becomes more negative. It turns out that the analytical solution is only a good estimate for Prisoners' Dilemma games and again becomes worse as S becomes more negative. A sensitivity analysis is performed to determine the impact of different initial cooperating probabilities, learning factors, and neighborhood size.
Analytical travelling wave solutions and parameter analysis for the ...
Indian Academy of Sciences (India)
done in the past few decades to improve this equation. Especially, in ... For exam- ple, the solutions of DS equation could describe the interaction between a ... In this paper, we consider the following (2+1)-dimensional Davey–Stewartson-type.
General scalar-tensor cosmology: analytical solutions via noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-02-15
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system. (orig.)
Analytical solutions of weakly coupled map lattices using recurrence relations
Energy Technology Data Exchange (ETDEWEB)
Sotelo Herrera, Dolores, E-mail: dsh@dfmf.uned.e [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); San Martin, Jesus [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); Dep. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9-28040 Madrid (Spain)
2009-07-20
By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C{sup 2} function.
Analytic method for solitary solutions of some partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya@firat.edu.tr
2007-10-22
In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation.
Analytic method for solitary solutions of some partial differential equations
International Nuclear Information System (INIS)
Ugurlu, Yavuz; Kaya, Dogan
2007-01-01
In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation
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 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 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.
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
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.
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback
Al Noufaey, K. S.
2018-06-01
This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.
An analytic solution for the enrichment of uranium hexafluoride in long countercurrent centrifuges
International Nuclear Information System (INIS)
Raetz, E.
1977-01-01
The paper describes an analytic solution for the enrichment and the separative power of long countercurrent centrifuges. Equations to derive optimal operation parameters like feed and feed input height are derived and solved. (orig.) [de
A Quantum Dot with Spin-Orbit Interaction--Analytical Solution
Basu, B.; Roy, B.
2009-01-01
The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.
Analytical solutions for ozone generation by point to plane corona discharge
International Nuclear Information System (INIS)
Bestman, A.R.
1990-12-01
A recent mathematical model developed for ozone production is tackled analytically by asymptotic approximation. The results obtained are compared with existing numerical solutions. The comparison shows good agreement. (author). 3 refs, 1 fig
Two dimensional kinetic analysis of electrostatic harmonic plasma waves
Energy Technology Data Exchange (ETDEWEB)
Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R. [Instituto de Física, UFRGS, 91501-970 Porto Alegre, RS (Brazil); Yoon, P. H. [IPST, University of Maryland, College Park, Maryland 20742 (United States); SSR, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of)
2016-06-15
Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.
International Nuclear Information System (INIS)
Chen Changyuan; Sun Dongsheng; Lu Falin
2007-01-01
Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given
Non-perturbative analytical solutions of the space- and time-fractional Burgers equations
International Nuclear Information System (INIS)
Momani, Shaher
2006-01-01
Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0 < α, β ≤ 1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed
Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.
A Novel Method for Analytical Solutions of Fractional Partial Differential Equations
Mehmet Ali Akinlar; Muhammet Kurulay
2013-01-01
A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...
The presentation of explicit analytical solutions of a class of nonlinear evolution equations
International Nuclear Information System (INIS)
Feng Jinshun; Guo Mingpu; Yuan Deyou
2009-01-01
In this paper, we introduce a function set Ω m . There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ω m . A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.
Analytical solution for dynamic pressurization of viscoelastic fluids
International Nuclear Information System (INIS)
Hashemabadi, S.H.; Etemad, S.Gh.; Thibault, J.; Golkar Naranji, M.R.
2003-01-01
The flow of simplified Phan-Thien-Tanner model fluid between parallel plates is studied analytically for the case where the upper plate moves at constant velocity. Two forms of the stress coefficient, linear and exponential, are used in the constitutive equation. For the linear stress coefficient, the dimensionless pressure gradient, the velocity profile and the product of friction factor and Reynolds number are obtained for a wide range of flow rate, Deborah number and elongational parameter. The results indicate the strong effects of the viscoelastic parameter on the velocity profile, the extremum of the velocity, and the friction factor. A correlation for the maximum pressure rise in single screw extruders is proposed. For the exponential stress coefficient, only velocity profiles were obtained and compared with velocity profiles obtained with the linear stress coefficient
Analytic electrostatic solution of an axisymmetric accelerator gap
International Nuclear Information System (INIS)
Boyd, J.K.
1995-01-01
Numerous computer codes calculate beam dynamics of particles traversing an accelerating gap. In order to carry out these calculations the electric field of a gap must be determined. The electric field is obtained from derivatives of the scalar potential which solves Laplace's equation and satisfies the appropriate boundary conditions. An integral approach for the solution of Laplace's equation is used in this work since the objective is to determine the potential and fields without solving on a traditional spatial grid. The motivation is to quickly obtain forces for particle transport, and eliminate the need to keep track of a large number of grid point fields. The problem then becomes one of how to evaluate the appropriate integral. In this work the integral solution has been converted to a finite sum of easily computed functions. Representing the integral solution in this manner provides a readily calculable formulation and avoids a number of difficulties inherent in dealing with an integral that can be weakly convergent in some regimes, and is, in general, highly oscillatory
Analytical solution to the coupled evolution of multidimensional NMR data
International Nuclear Information System (INIS)
Mueller, Geoffrey A.
2009-01-01
A substantial time savings in the collection of multidimensional NMR data can be achieved by coupling the evolution of nuclei in the indirect dimensions. In order to save time, the sampling of the indirect dimensions is inherently incomplete. Therefore, many algorithms and samplings schemes have been developed aimed at separating the coevolved frequencies into analyzable data with limited artifacts. This paper extends the use of circulant matrices to describe coupled evolution with convolutions. By understanding the data in terms of convolutions, there is an exact solution to the inversion problem of extracting the orthogonal vectors from the coupled dimensions. Previously, this inversion problem has been solved using peak coordinates extracted from spectra. In contrast, the method described here uses spectra directly. This solution suggests a simple sampling scheme of collecting N orthogonal spectra, and N + 1 projections at specific projection angles, however, the theory developed can be extended generally to arbitrary projection angles. The circulant matrix methodology is demonstrated for simulated and real data. Further, an algorithm for separating overlapped signals in the detected dimension is presented. The algorithm involves the forward calculation of the coupled spectra from the orthogonal spectra, followed by back calculation of the orthogonal spectra from the coupled spectra, thus permitting rigorous cross-validation. This algorithm is shown to be robust in that erroneous solutions give rise to large artifacts
A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt
Directory of Open Access Journals (Sweden)
Xin Yang
2017-01-01
Full Text Available By calculating the concentration distributions of rock salt solutions at the boundary layer, an ordinary differential equation for describing a special dissolution rate model of rock salt under the assumption of an instantaneous diffusion process was established to investigate the dissolution mechanism of rock salt under transient but stable conditions. The ordinary differential equation was then solved mathematically to give an analytical solution and related expressions for the dissolved radius and solution concentration. Thereafter, the analytical solution was fitted with transient dissolution test data of rock salt to provide the dissolution parameters at different flow rates, and the physical meaning of the analytical formula was also discussed. Finally, the influential factors of the analytical formula were investigated. There was approximately a linear relationship between the dissolution parameters and the flow rate. The effects of the dissolution area and initial volume of the solution on the dissolution rate equation of rock salt were computationally investigated. The results showed that the present analytical solution gives a good description of the dissolution mechanism of rock salt under some special conditions, which may provide a primary theoretical basis and an analytical way to investigate the dissolution characteristics of rock salt.
A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics
Brovont, Aaron D.
The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.
The analytical solution to the 1D diffusion equation in heterogeneous media
International Nuclear Information System (INIS)
Ganapol, B.D.; Nigg, D.W.
2011-01-01
The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares
2015-07-01
This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)
An Analytical Solution for Cylindrical Concrete Tank on Deformable Soil
Directory of Open Access Journals (Sweden)
Shirish Vichare
2010-07-01
Full Text Available Cylindrical concrete tanks are commonly used in wastewater treatment plants. These are usually clarifier tanks. Design codes of practice provide methods to calculate design forces in the wall and raft of such tanks. These methods neglect self-weight of tank material and assume extreme, namely ‘fixed’ and ‘hinged’ conditions for the wall bottom. However, when founded on deformable soil, the actual condition at the wall bottom is neither fixed nor hinged. Further, the self-weight of the tank wall does affect the design forces. Thus, it is required to offer better insight of the combined effect of deformable soil and bottom raft stiffness on the design forces induced in such cylindrical concrete tanks. A systematic analytical method based on fundamental equations of shells is presented in this paper. Important observations on variation of design forces across the wall and the raft with different soil conditions are given. Set of commonly used tanks, are analysed using equations developed in the paper and are appended at the end.
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.
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 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.
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
Atomically thin two-dimensional organic-inorganic hybrid perovskites
Dou, Letian; Wong, Andrew B.; Yu, Yi; Lai, Minliang; Kornienko, Nikolay; Eaton, Samuel W.; Fu, Anthony; Bischak, Connor G.; Ma, Jie; Ding, Tina; Ginsberg, Naomi S.; Wang, Lin-Wang; Alivisatos, A. Paul; Yang, Peidong
2015-09-01
Organic-inorganic hybrid perovskites, which have proved to be promising semiconductor materials for photovoltaic applications, have been made into atomically thin two-dimensional (2D) sheets. We report the solution-phase growth of single- and few-unit-cell-thick single-crystalline 2D hybrid perovskites of (C4H9NH3)2PbBr4 with well-defined square shape and large size. In contrast to other 2D materials, the hybrid perovskite sheets exhibit an unusual structural relaxation, and this structural change leads to a band gap shift as compared to the bulk crystal. The high-quality 2D crystals exhibit efficient photoluminescence, and color tuning could be achieved by changing sheet thickness as well as composition via the synthesis of related materials.
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.
Cutting solid figures by plane - analytical solution and spreadsheet implementation
Benacka, Jan
2012-07-01
In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and cosine rules. The basic problem is to find the section of the figure by a plane that is defined by three points related to the figure. In this article, a formula is derived that gives the positions of the intersection points of such a plane and the figure edges, that is, the vertices of the section polygon. Spreadsheet implementations of the formula for cuboid and right rectangular pyramids are presented. The user can check his/her graphical solution, or proceed if he/she is not able to complete the section.
Exact analytic solutions for Mikheyev-Smirnov-Wolfenstein level crossings
International Nuclear Information System (INIS)
Noetzold, D.
1987-01-01
An exact formula for the transition probability in level-crossing phenomena is derived for a general case, ranging from adiabatic to sudden crossings. This is done in the context of neutrino flavor oscillations for the Mikheyev-Smirnov-Wolfenstein (MSW) effect, where hitherto only numerical or approximate solutions were obtained. The matter density or level splitting is assumed to be governed by a hyperbolic-tangent function which, however, can change arbitrarily fast between two constant values. For example, in context of the MSW effect this furnishes a nice fit to the solar density determining the level crossing of solar neutrinos. In the quasiadiabatic limit the exact Landau-Zener factor can be read off, correcting some expressions obtained so far. Even in the opposite limit of a sudden level crossing a conversion is found, which can have far-reaching consequences for neutrino detection on Earth
Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean
Energy Technology Data Exchange (ETDEWEB)
Petrov, P.S., E-mail: petrov@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Prants, S.V., E-mail: prants@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Petrova, T.N., E-mail: petrova.tn@dvfu.ru [Far Eastern Federal University, 8 Sukhanova str., 690950, Vladivostok (Russian Federation)
2017-06-21
The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic equations are solved explicitly, and the analytical expressions for the modal coefficients are obtained using a Lie-algebraic technique. - Highlights: • A group-theoretical approach is applied to a problem of sound propagation in a shallow sea with variable bottom slope. • An analytical solution of this problem is obtained in the form of modal expansion with analytical expressions of the coefficients. • Our result is the only analytical solution of the 3D sound propagation problem with no translational invariance. • This solution can be used for the validation of the numerical propagation models.
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
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
New integrable models and analytical solutions in f (R ) cosmology with an ideal gas
Papagiannopoulos, G.; Basilakos, Spyros; Barrow, John D.; Paliathanasis, Andronikos
2018-01-01
In the context of f (R ) gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R ) theories for which new analytical solutions are given and closed-form solutions are provided.
Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow
Gonzalez, M.
2018-04-01
The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.
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...
Effective viscosity of two-dimensional suspensions: Confinement effects
Doyeux, Vincent; Priem, Stephane; Jibuti, Levan; Farutin, Alexander; Ismail, Mourad; Peyla, Philippe
2016-08-01
We study the rheology of a sheared two-dimensional (2D) suspension of non-Brownian disks in the presence of walls. Although it is of course possible today with modern computers and powerful algorithms to perform direct numerical simulations that fully account for multiparticle 3D interactions in the presence of walls, the analysis of the simple case of a 2D suspension provides valuable insights and helps in the understanding of 3D results. Due to the direct visualization of the whole 2D flow (the shear plane), we are able to give a clear interpretation of the full hydrodynamics of semidilute confined suspensions. For instance, we examine the role of disk-wall and disk-disk interactions to determine the dissipation of confined sheared suspensions whose effective viscosity depends on the area fraction ϕ of the disks as ηeff=η0[1 +[η ] ϕ +β ϕ2+O (ϕ3) ] . We provide numerical estimates of [η ] and β for a wide range of confinements. As a benchmark for our simulations, we compare the numerical results obtained for [η ] and β for very weak confinements with analytical values [η] ∞ and β∞ obtained for an infinite fluid. If the value [η] ∞=2 is well known in the literature, much less is published on the value of β . Here we analytically calculate with very high precision β∞=3.6 . We also reexamine the 3D case in the light of our 2D results.
Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers
Directory of Open Access Journals (Sweden)
Belkacem Meziane
2008-01-01
Full Text Available A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These solutions are shown to evolve in accordance with the driving frequency of the permanent solution that we recently reported to illustrate the system. The procedure amounts to analytically construct the signal Fourier transform by applying an iterative algorithm that reconstitutes the first few terms of its development.
International Nuclear Information System (INIS)
Khericha, Soli T.
2000-01-01
One-energy group, two-dimensional computer code was developed to calculate the response of a detector to a vibrating absorber in a reactor core. A concept of local/global components, based on the frequency dependent detector adjoint function, and a nodalization technique were utilized. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux is expanded into polynomials about the center point of each node. The phase angle and the magnitude of the one-energy group detector adjoint function were calculated for a detector located in the center of a 200x200 cm reactor using a two-dimensional nodalization technique, the computer code EXTERMINATOR, and the analytical solution. The purpose of this research was to investigate the applicability of a polynomial nodal model technique to the calculations of the real and the imaginary parts of the detector adjoint function for one-energy group two-dimensional polynomial nodal model technique. From the results as discussed earlier, it is concluded that the nodal model technique can be used to calculate the detector adjoint function and the phase angle. Using the computer code developed for nodal model technique, the magnitude of one energy group frequency dependent detector adjoint function and the phase angle were calculated for the detector located in the center of a 200x200 cm homogenous reactor. The real part of the detector adjoint function was compared with the results obtained from the EXTERMINATOR computer code as well as the analytical solution based on a double sine series expansion using the classical Green's Function solution. The values were found to be less than 1% greater at 20 cm away from the source region and about 3% greater closer to the source compared to the values obtained from the analytical solution and the EXTERMINATOR code. The currents at the node interface matched within 1% of the average
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....
Analytical SN solutions in heterogeneous slabs using symbolic algebra computer programs
International Nuclear Information System (INIS)
Warsa, J.S.
2002-01-01
A modern symbolic algebra computer program, MAPLE, is used to compute solutions to the well-known analytical discrete ordinates, or S N , solutions in one-dimensional, slab geometry. Symbolic algebra programs compute the solutions with arbitrary precision and are free of spatial discretization error so they can be used to investigate new discretizations for one-dimensional slab, geometry S N methods. Pointwise scalar flux solutions are computed for several sample calculations of interest. Sample MAPLE command scripts are provided to illustrate how easily the theory can be translated into a working solution and serve as a complete tool capable of computing analytical S N solutions for mono-energetic, one-dimensional transport problems
Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza
2018-06-01
Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.
Matching of analytical and numerical solutions for neutron stars of arbitrary rotation
International Nuclear Information System (INIS)
Pappas, George
2009-01-01
We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R ISCO ), the rotation frequency and the epicyclic frequencies Ω ρ , Ω z . Finally we present some results of the comparison.
Matching of analytical and numerical solutions for neutron stars of arbitrary rotation
Energy Technology Data Exchange (ETDEWEB)
Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)
2009-10-01
We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.
Directory of Open Access Journals (Sweden)
Soheil Salahshour
2015-02-01
Full Text Available In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville or a solution with increasing length of their support (Hukuhara difference. Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.