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Geologic sequestration is currently being practiced and scientifically evaluated as a critical component in a broad strategy, comprising new practices and technologies, for mitigating global climate change due to anthropogenic emissions of CO2. Demonstrating that geologic sequestration of CO2 is safe and effective, and gaining public acceptance of sequestration technologies are critically important in meeting these global climate change challenges. Monitored field-scale demonstrations of geologic sequestration of carbon dioxide will contribute greatly toward growing trust and confidence in the technology; however, pilot demonstrations ultimately will not be the norm for new geological sequestration deployments. Instead, scientists, engineers, regulators, and ultimately the public will rely on numerical simulations to predict the performance of geologic repositories for carbon dioxide sequestration. The U.S. Department of Energy (DOE), through the National Environmental Technology ...

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In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation, they use an i...

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The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 ) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

International Nuclear Information System (INIS)

In the procedure of the hydraulic control system analysis, a linearized approximate equation described by the first order term of Taylor's series has been widely used. Such a linearized equation is effective just near the operating point. In this study, the authors estimate computational errors in the process of applying the existing linearized equation stated above. For evaluating the computational accuracy in practical applications of the linearized equations, dynamic behaviors of hydraulic control systems are investigated through simulations with several kinds of representative hydraulic systems and the linearized equations suggested in this study.

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A method for calculating flow through an airfoil cascade drawn on a surface of revolution is discussed. The three-dimensional flow was assumed to be represented by part-channels of varying width. The basic equations are the equation of continuity and the ...

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... 4 II. INERTIAL NAVIGATION ERROR EQUATIONS ..... 5 ... 4- Page 20. Chapter II INERTIAL NAVIGATION ERROR EQUATIONS ...

CERN Document Server

In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite general third- order nonlinear vector differential equation, and one example is given for illustration of the subject.

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The hierarchy of integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of linearization of these equations and their conservation law in the terms of solutions of corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and conservation laws explicitly expressed through the variables of the nonlinear equations are derived. (author)

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No abstract prepared.

Energy Technology Data Exchange (ETDEWEB)

This two-volume reference uses many equations to provide detailed information on atomic and nuclear decay phenomena.

International Nuclear Information System (INIS)

The problem in perturbation theory in general relativity is finding a natural gauge which simplifies the equations considerably. We solved the first and second order perturbation equations in the ''Lorentz gauge'' using the two-timing method. The equations were deduced from the equations of Einstein in the presence of a matter energy-momentum tensor of a perfect fluid with equation of state p = (#gamma#-1) rho. It is found that the 0--0 component of the first order equations together with the gauge conditions are consistent with the Bianchi type V model, without axial symmetry. It represents a ''ground state'' situation of the Bianchi type IX model (Mixmaster model.) The second order equations, describing the reaction back of the gravitational waves on the slowly varying background, give rise to rotation and will disturb the isotropization ...

CERN Document Server

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.

CERN Document Server

n an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids {\\bf 19}, 016101 (2007)], to simulate non-equilibrium flows. In this paper, instead of using three temperatures in $x-$, $y-$, and $z$-directions, we are going to further define the translational temperature as a second-order symmetric tensor. Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The zeroth-order expansion gives the 10 moment closure equations of Levermore [C.D. Levermore, J. Stat. Phys {\\bf 83}, pp.1021 (1996)]. To the 1st-order expansion, the derived gas dynamic equations can be considered as a regularization of Levermore's 10 moments equations. The new gas dynamic equations have the same structure as the ...

International Nuclear Information System (INIS)

To develop the advanced subchannel analysis code, the dominant factors that influence the boiling transitional process must be taken into account in the mechanistic constitutive equations based on the flow geometries and the fluid properties. The dominant factors that influence the boiling transitional processes are (1) the gas-liquid re-distribution by cross flow, (2) the liquid film dryout, (3) the two-phase flow regime transition, (4) the droplet deposition, and (5) the spacer-droplet interaction. At first, we indicated the strategy for the development of the constitutive equations for the five dominant factors based on the experimental database by the latest measurement technique and the latest computational fluid dynamics method. Then, the problems of the present constitutive equations and the improvement plan of the constitutive equations were indicated. Finally, the layered structure for the ...

International Nuclear Information System (INIS)

The static thermophysical properties of the molten salt system like LiF-NaF-BeF_2 influence the design and construction of the fuel salt and coolant in the Molten Salt Reactor for the new generation. In this paper, the equation of state of the ternary system 0.15LiF-0.58NaF-0.27BeF_2, over the temperature range from 873.15K to 1073.15K at one atmosphere pressure, is described by using modified Peng-Robinson equation. The density of the ternary system is evaluated by this equation directly, and compared with the experimental data. Base on the equation of state, the other static thermophysical properties such as the enthalpy, entropy and heat capacity at constant pressure are evaluated by the fugacity coefficient and residual function methods respectively. The density calculated by Peng-Robinson equation is in highly agreement with the experimental data, and the enthalpy, entropy and ...

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The static thermophysical properties of the molten salt system like LiF-NaF-BeF2 influence the design and construction of the fuel salt and coolant in the Molten Salt Reactor for the new generation. In this paper, the equation of state of the ternary system 0.15LiF-0.58NaF-0.27BeF2, over the temperature range from 873.15K to 1073.15K at one atmosphere pressure, is described by using modified Peng-Robinson equation. The density of the ternary system is evaluated by this equation directly, and compared with the experimental data. Base on the equation of state, the other static thermophysical properties such as the enthalpy, entropy and heat capacity at constant pressure are evaluated by the fugacity coefficient and residual function methods respectively. The density calculated by Peng-Robinson equation is in highly agreement with the experimental data, and the enthalpy, entropy and ...

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An elliptic equation in a rectangle with coefficients depending on a fast variable and with its period being a small parameter is considered. An asymptotic expansion of the solution up to an arbitrary degree of the small parameter is constructed and substantiated by applying the two-scale expansion method.

UK PubMed Central (United Kingdom)

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population...Full Text Available

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We apply the group theory to Kadomtsev-Petviashvili-Burgers (KPBII) equation which is a natural model for the propagation of the two-dimensional damped waves. In correspondence with the generators of the symmetry group allowed by the equation, new types of symmetry reductions are performed. Some new exact solutions are obtained, which can be in the form of solitary waves and periodic waves. Specially, our solutions indicate that the equation may have time-dependent nonlinear shears. Such exact explicit solutions and symmetry reductions are important in both applications and the theory of nonlinear science.

International Nuclear Information System (INIS)

The wave equation for spin;1/2 tachyons is derived from the Dirac equation and the principle of relativity extended to superluminal Lorentz frames. From this wave equation and the Dirac equation infinite velocity spinor transformations are obtained. They yield bispinors of the plane-wave states of the tachyon, their interpretation and covariant orthogonality relations satisfied by them. The transformation properties of the bispinors under Lorentz transformation are discussed. The boundary conditions for the free propagator of wave functions of tachyons are obtained and the propagator is constructed. Then the covariant S-matrix for scattering from an electromagnetic field is derived. It is applied to the scattering of electron-tachyons from the Coulomb field.

CERN Document Server

P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on the solutions. Here we consider an initial and boundary value problem for this equation in a two-dimensional bounded domain. We prove a number of results related to well-posedness and large time behavior of solutions. In particular, we analyze the existence of bounded absorbing sets in two different phase spaces and, correspondingly, we establish the existence of the global attractor. We also demonstrate the existence of an exponential attractor.

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... Union (INTAS), Brussels (Belgium) Science and Technology Center in Unkraine,

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... AT 1170 DEG C. A UNIQUE CREEP CONSTITUTIVE EQUATION CONSISTING OF LINEAR AND POWER LAW TERMS WAS PROPOSED, AND ...

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down inertial navigation systemshavebeenreported. Shibata (1986)describesthe strapdown inertial navigation error equations basedon a quaternion relationship ...

International Nuclear Information System (INIS)

One normally identifies the prediction of tachyons with a higher spin problem. We show that the same phenomenon also happens with certain spin-1/2 equations, in exactly the same circumstances. Furthermore, we prove that these equations also have the defect of possessing solutions with complex energies, even with the smallest external fields. The consequences of these results are analyzed.

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A boundary value problem for Laplace?s equation in a bounded two-dimensional domain filled with a piecewise homogeneous medium is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem of determining the inhomogeneity boundary and the solution of the equation given the solution and its normal derivative on the boundary of the domain is discussed. Numerical methods are proposed for solving the inverse problem, and the results of numerical experiments are presented.

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In this paper we present a new efficient sixth-order scheme for nonlinear equations. The method is compared to several members of the family of methods developed by Neta (1979) [B. Neta, A sixth-order family of methods for nonlinear equations, Int. J. Comput. Math. 7 (1979) 157-161]. It is shown that the new method is an improvement over this well known scheme.

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The linearized collective Schroedinger equation for nuclear quadrupole surface vibrations incorporates a new spin degree of freeedom with a spin value of 3/2. We use this equation to describe the low energy spectrum of certain even-odd Ir nuclei which have a spin 3/2 in their ground state. For that purpose we explicitly introduce collective spin-dependent potentials which simulate the interaction of the valence nucleon with the core. The linearized Schroedinger equation is transformed into an effective Schroedinger equation with collective spin-dependent potentials. Already collective spin-orbit couplings of SO(3) and SO(5) type are sufficient to reproduce the lowest excited states of even-odd Ir nuclei. (orig.).

British Library Electronic Table of Contents (United Kingdom)

Abstract The importance of evaluating greenhouse gas (GHG) emissions from dairy cows within the whole farm setting is being realized as more important than evaluating these emissions in isolation. Current whole farm models aimed at evaluating GHG emissions make use of simple regression equations to predict enteric methane (CH4) production. The objective of the current paper is to evaluate the performance of nine CH4 prediction equations that are currently being used in whole farm GHG models. Data used to evaluate the prediction equations came from a collection of individual (IND) and treatment averaged (TRT) data. Equations were compared based on mean square prediction error (MSPE) and concordance correlation coefficient (CCC) analysis. In general, predictions were poor, with root MSPE (as...

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In this paper, a complete solution of the steady-state Newton-Euler equations describing the motion of the balls in high speed thrust bill bearings is presented. Kinematic equations are derived and used as ancillary equations to obtain the numerical solution of the Newton-Euler equations. This differs from previously reported work where extraneous assumptions (instead of kinematic analysis) are used to allow solutions of these equations. It is shown that the no-slip condition for the ball motion reported in the literature is based on an unnecessary assumption. The correct form of the condition is developed and used in the analysis of the ball motion. The analysis shows the importance of contact angle on both ball motion and contact force. An approximate theory is then developed for determining the optimum contact angle that would result in minimum contact force in high speed ball ...

International Nuclear Information System (INIS)

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the ...

International Nuclear Information System (INIS)

Combining the approaches given by Baldwin [Baldwin D et al. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J Symbol Comput 2004;37:669-705], Peng [Peng YZ. A polynomial expansion method and new general solitary wave solutions to KS equation. Comm Theor Phys 2003;39:641-2] and by Schuermann [Schuermann HW, Serov VS. Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc progress electromagnetics research symposium, 28-31 March 2004, Pisa. p. 651-4; Schuermann HW. Traveling-wave solutions to the cubic-quintic nonlinear Schroedinger equation. Phys Rev E 1996;54:4312-20] leads to a method for finding exact travelling wave solutions of nonlinear wave and evolution equations (NLWEE). The first idea is to generalize ansaetze given by Baldwin and Peng to find elliptic solutions of NLWEEs. Secondly, conditions used by ...

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The biosorption of Cu(II) from aqueous solutions by valonia tannin resin was investigated as a function of particle size, initial pH, contact time and initial metal ion concentration. The aim of this study was to understand the mechanisms that govern copper removal and find a suitable equilibrium isotherm and kinetic model for the copper removal in a batch reactor. The experimental isotherm data were analysed using the Langmuir, Freundlich and Temkin equations. The equilibrium data fit well in the Langmuir isotherm. The experimental data were analysed using four sorption kinetic models - the pseudo-first- and second-order equations, the Elovich and the intraparticle diffusion model equation - to determine the best fit equation for the biosorption of copper ions onto valonia tannin resin. Results show that the pseudo-second-order equation provides the best correlation for the ...

International Nuclear Information System (INIS)

Solving a coupled set of differential equations formed by a Fokker-Planck equation and a set of master equations, we can calculate the number of 'prefission' particles (n,p,a), which are emitted from a hot, rotating compound nucleus. Furthermore we get their energy spectrum and their angular momentum distribution. Our results depend sensitively on the friction parameter #gamma#, the inertia M and the fission potential. Comparing the results with experimental data, we may learn something about these quantities. The investigations have been made for "1"8"7Ir and "1"8"5Os. (orig.).

British Library Electronic Table of Contents (United Kingdom)

Necessary and sufficient conditions for a minimax solution to the Cauchy problem for the Hamilton-Jacobi-Bellman equation are obtained as viability conditions for classical characteristics inside the graph of this solution. Using this property, a representative formula for a one-dimensional conservation law in terms of classical characteristics is derived. An estimate of the numerical integration of the characteristic system is presented and errors of numerical realizations of representative formulas are determined for the conservation law and its potential equal to the minimax solution of the Hamilton-Jacobi-Bellman equation.

CERN Document Server

Exact solutions are found for the Chandrasekhar Page angular equation which results when the Dirac equation in a Kerr Newman space time is separated into its radial and angular parts. The solutions turn out to be remarkably simple in form while satisfying the asymptotic conditions deduced earlier. The eigenvalues are found to be the square root of the total angular momentum as first found by Dirac for flat space; supplemented by a term which is the product of the mass of the Dirac particle times the specific angular momentum of the black hole. The additional contribution is what is expected from frame dragging.

International Nuclear Information System (INIS)

The spherical harmonic analysis of cosmic ray neutron data from the worldwide network neutron monitor stations during the years 1966 to 1969 was carried out. The second zonal harmonic component obtained from the analysis corresponds to the Pole-Equator anisotropy of the cosmic ray neutron intensity. Such an anisotropy makes a semiannual variation. In addition to this, it is shown that the Pole-Equator anisotropy makes a variation depending on the interplanetary magnetic field (IMF) sector polarities around the passages of the IMF sector boundary. A mechanism to interpret these results is also discussed.

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pletely new PW fuel cell model had to be developed for CINDA. Several ...... following linear equation, which is used in the SINDA fuel cell model: ...

CERN Document Server

Within the framework of a modified Balitsky-Kovchegov equation, we calculated and provide estimates of non-linear saturation effects expected in the LHC range of energies.

International Nuclear Information System (INIS)

In this paper, research on pass schedule of tandem cold mill (TCM) is carried out. According to load (reduction, rolling force, motor power) balance, non-linear equations set with variables of inter-stand thickness is constructed. The pass schedule optimization is carried out by solving the non-linear equations set. As the traditional method, the Newton-Raphson method is used for solving the non-linear equations set. In this paper a new simple method is brought up. On basis of the monotone relations between thickness and load, the inter-stands thickness is adjusted dynamically. The solution of non-linear equations set can be converged by iterative calculation. This method can avoid the derivative calculation used by traditional method. So, this method is simple and calculation speed is high. It is suitable for on-line control. (author)

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The validity is given to the newly proposed two weighting {delta}f scheme (Wang et al., Research Report of National Institute for Fusion Science NIFS-588, 1999) for collisional or neoclassical transport calculations, which can solve the drift kinetic equation taking account of effects of steep plasma gradients, large radial electric field, finite banana width, and the non-standard orbit topology near the axis. The marker density functions in weight equations are successively solved by using the idea of {delta}f method and a hierarchy of equations for weight and marker density functions is obtained. These hierarchy equations are solved by choosing an appropriate source function for each marker density. Thus the validity of the two weighting {delta}f scheme is mathematically proved. (author)

Science.gov (United States)

... A. Fasano, SD Howison. JR Ockendon & M. Primicerio. Some remarks on the regularisation of the supercooled one-phase Stefan problem. Quart. ...

British Library Electronic Table of Contents (United Kingdom)

Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure ...

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In this report we present a suite of subroutines for the solution of sparse unsymmetric sets of linear equations using a variant of Gaussian elimination. The subroutines are divided into three distinct phases. The first phase optionally preorders the matrix to block triangular form and then performs a sparsity oriented factorization, the second factorizes a matrix of a similar sparsity pattern, while the third uses these decompositions to solve the equations. In this revised edition, the actual Fortran listings have been replaced by a reference to their availability in machine readable form. Other changes to the first edition are minor. This revision is essentially a reprint of the 1979 revision, the only changes being that the MA28A specification sheet has been typeset and has a few minor changes and the existence of a version of the package for complex equations is announced. 11 refs., 11 tabs.

CERN Document Server

No Kerr-like exact solution has yet been found in Chern-Simons modified gravity. Intrigued by this absence, we study stationary and axisymmetric metrics that could represent the exterior field of spinning black holes. For the standard choice of the background scalar, the modified field equations decouple into the Einstein equations and additional constraints. These constraints eliminate essentially all solutions except for Schwarzschild. For non-canonical choices of the background scalar, we find several exact solutions of the modified field equations, including mathematical black holes and pp-waves. We show that the ultrarelativistically boosted Kerr metric can satisfy the modified field equations, and we argue that physical spinning black holes may exist in Chern-Simons modified gravity only if the metric breaks stationarity, axisymmetry or energy-momentum conservation.

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major radius of the toroidal containment volume. The containment time was calculated using equation (4) as derived in references 16 and 17. The solid ...

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... 2.5.6 Development of Observation Equations . . . . . 25 2.6 Inertial Navigation Error Model . . . . . ... 2 , as expected. 2.6 Inertial Navigation Error Model ...

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... Abstract : The purpose of this paper is to introduce strapdown inertial navigation error equations based on a quaternion relation between body-fixed ...

CSIR Research Space (South Africa)

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In Randall-Sundrum-type brane-world cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of imbedding and of the free gravitational field in the five-dimensional bulk. Instead of starting from an ansatz for the metric, we derive the covariant nonlinear dynamical equations for the gravitational and matter fields on the brane. The local energy-momentum corrections are significant only at very high energies, and in this regime we show that fluid world-lines have a non-gravitational acceleration off the brane. The imprint on the brane of the nonlocal gravitational field in the bulk is more subtle, and we provide a careful decomposition of this effect. The nonlocal energy density determines the tidal acceleration in the off-brane direction, and can oppose singularity formation via the generalized Raychaudhuri equation. Unlike the ...

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The interaction of thermal radiation with conduction and convection in thermally developing absorbing, emitting, non-gray gas particulate turbulent suspension flow through a circular tube is investigated. The contribution of thermal radiation is obtained through evaluation of the total hemispherical emittance of the particulate cloud and through evaluation of single band absorptances for molecular gases, modified to account for the interaction with the particles. The governing differential equation is derived as a (nonlinear) energy equation, coupled with integral equations to find the thermal radiation contributions. The energy equation is solved numerically by an implicit finite difference with its iterative procedure. Qualitative results for Nusselt numbers are shown for a variety and range of parameters, such as optical thickness of particulates and single molecular gas bands, relative gas band ...

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The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

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We consider particle evaporation and fission of an ensemble of hot, rotating compound nuclei as a stochastic process. We derive a set of coupled differential equations formed by a Fokker-Planck equation describing fission, and master equations for calculating particle evaporation. From these equations, we are able to determine multiplicities of prefission neutrons, protons and {alpha}-particles, their energy spectra and their angular momentum distributions. A comparison of our results with experimental data provides us with information regarding the reduced friction coefficient {beta}, the fission barrier height and the level density parameter. For different iridium isotopes, ({sup 181,185,187}Ir), {sup 185}Os and {sup 158}Er, we obtain as an upper limit {beta}{<=}8.0x10{sup 21} s{sup -1}. (orig.).

CERN Document Server

A set of mode-coupled excitation equations for the slowly-growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser, or FEL, including the effects of longitudinal space-charge. This approach to describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of such eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. A simple transformation converts the coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant eigenmode, in the approximation that it consists of a single ...

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This book examines some of the basic principles behind chemical reactions kinetics. Topics considered include ab initio determination of potential energy for chemical reactions; semi-empirical potential energy surfaces; general theory of reactive scattering: different equation approach; and integral equation approach to reactive scattering.

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The pressure of a 6:12 fluid is obtained from the Percus-Yevick theory at the temperature kT/? = 1.35. The energy equation results are in excellent agreement with machine calculation results in contrast to the pressure and compressibility equation results. Present address: Diffusion Research Unit, The Australian National University, Canberra, ACT, Australia.

International Nuclear Information System (INIS)

An explicite PN solution of the multi-dimensional homogeneous neutron transport equation is given by expanding the angular flux into a series of geometry-independent spherical harmonics operators. An algorithm is developed for representing the spherical harmonic operators in orthogonal curvilinear coordinates. The general formulae are applied to two-dimensional spherical geometry; detailed P3 formulae are given. (orig.).

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The wave equation of a spinless tachyon is studied in Schwarzschild space-time. In contrast to earlier approaches to the problem, it is shown that tachyonic static solutions satisfy a simple second-order linear differential equation regardless of the mass of the black hole and the mass parameter of the tachyon. Physical implication of the present approach is discussed. Using Langer modification of the WKB (Wentzel-Kramers-Brillouin) boundary condition an expression similar to the Bohr-Sommerfeld quantization condition is derived.

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To simulate the effects of the breakup channel on rearrangement amplitudes, the conventional coupled-reaction-channel (CRC) expansion is augmented by pseudoreaction channels. The construction of the projector for the extended CRC space is discussed, and transition-operator equations on this space are given. By solving the full and post-approximation forms of the CRC equations for a model three-particle problem, the crucial role played by the nonorthogonality terms is demonstrated.

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Diffraction by an impermeable scatterer in ?3 with a Dirichlet boundary condition is considered. It is shown that the null field equation is equivalent to the original diffraction problem. The general theoretical constructions are illustrated by analyzing the excitation of a sphere by a point source. The evolution of the residual of the null field equation as the scatterer surface is approached by an auxiliary surface is estimated.

International Nuclear Information System (INIS)

1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real

British Library Electronic Table of Contents (United Kingdom)

By a variant version of Fountain Theorem due to Zou [W. Zou, Variant fountain theorems and their applications, Manuscripta Math. 104 (2001) 343-358], the existence of infinitely many solutions is obtained for a class of biharmonic equations where the nonlinearity involves a combination of superlinear and asymptotically linear terms.

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Zanker has recently presented nomographs for determining particle settling velocities in solid-liquid systems. These nomographs were based on the general correlations developed by Barnea and Mizrahi and Barnea and Mednick. This work presents an equation directly computing particle settling velocities, eliminating the uncertainty associated with nomographs.

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The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the ...

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This demonstration project uses modern simulation techniques to illustrate the important technologies and design variables that an auto-designer would consider in production a high efficiency, low emissions vehicle. Simulation and modeling techniques use the idea of capturing the relationships between real components of the systems with mathematical equations. These equations are then solved on a computer to simulate the behavior or performance of the system under various conditions. In the current demonstration project, we focus on many variations of a hydrogen-powered vehicle.

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Four solutions of the Cauchy problem for Mathieu?s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.

International Nuclear Information System (INIS)

To calculate the energy band structures in semiconductors using the relativistic augmented plane wave method, atomic potential and charge density are needed, which are calculated by self-consistent method. Wave function for one electron is determined by solving the Dirac equation with the Hartree-Fock equation based on the slater's exchange potential. The results of calculation for Cu"+"1 are given. (Author).

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The effect of finite gyroradius on the current diffusive ballooning mode is examined. Starting from the reduced MHD equations including turbulent transports, coupling with drift motion and finite gyroradius effect of ions, we derive a ballooning mode equation with complex transport coefficients. The eigenfrequency, saturation level and thermal diffusivity are evaluated numerically from the marginal stability condition. Preliminary results of their parameter dependence is presented. (author)

International Nuclear Information System (INIS)

A formula for calculating the Dirac S-matrix for central Lorentz scalar and vector potentials is derived by use of a new amplitude-phase method. The derivation also makes use of certain invariants of the reduced 2-spinor radial Dirac equations.

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We consider the problem of rotation in a homogeneous Bianchi type IX cosmological model. Studying the Wheeler-De Witt equation corresponding to this minisuperspace, and adopting a particular choice of the factor ordering, we are able to find a particular solution which is strongly peaked about isotropy. This result confirms all the previous investigations in this field, and suggests the conclusion that the machian nature of our universe is the natural, i.e. most likely, outcome of the Planck epoch. (orig.).

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Numerical simulations of compressible flows are commonly based on the Euler equations when effects of viscosity are thought to be negligible. These equations admit singular solutions, even in cases where the initial and boundary conditions are smooth. So-called ''Euler solvers'' rely on numerical dissipation, explicitly or implicitly present in the scheme, to regularize the problem, such that physical solutions are selected.

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The Schroedinger equation for nuclear quadruple surface vibrations is linearized with the consequence that a new spin degree of freedom appears in the wave function of the linearized equation. This spin is called collective spin and has a value of 3/2. The linearized Schroedinger equation for quadrupole vibrations is used for the description of certain collective aspects of even-odd {sup 187,189,191}Ir nuclei which have a spin 3/2 in their ground state. As a potential we use the {gamma}-soft collective potential of the neighboring even-even nuclei, which is inserted into the linearized Schroedinger equation via a scalar coupling. This leads to a collective spin-dependent fine structure splitting of the energy levels governed by a collective SO(5) spin-orbit coupling and a correction to the kinetic energy. Further, we consider explicitly spin-dependent potentials which effectively describe the ...

International Nuclear Information System (INIS)

We analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern theory. In the brane world models the four-dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the three-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations have properties quite distinct as compared to the standard black hole solutions of general relativity. We close the structure equations by assuming a simple linear equation of state for the dark pressure. In this case the vacuum is Jacobi stable only for a small range of values of the proportionality constant relating the dark pressure and the dark radiation. The ...

CERN Document Server

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation model can be uniquely recovered from the covariance matrix of the associated normal distribution. We treat the case of generic identifiability, where unique recovery is possible for almost every choice of parameters. We give a new graphical criterion that is sufficient for generic identifiability. It improves criteria from prior work and does not require the directed part of the graph to be acyclic. We also develop ...

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Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport ...

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A copyrighted computational fluid dynamics computer code, ICOMFLO, has been developed for the simulation of multiphase reacting flows. The code solves conservation equations for gaseous species and droplets (or solid particles) of various sizes. General conservation laws, expressed by elliptic type partial differential equations, are used in conjunction with rate equations governing the mass, momentum, enthalpy, species, turbulent kinetic energy, and turbulent dissipation. Associated phenomenological submodels of the code include integral combustion, two parameter turbulence, particle evaporation, and interfacial submodels. A newly developed integral combustion submodel replacing an Arrhenius type differential reaction submodel has been implemented to improve numerical convergence and enhance numerical stability. A two parameter turbulence submodel is modified for both gas and solid phases. An evaporation submodel treats ...

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VSP reverse-time migration is a well adaptable wave equation migration method. Its control equation not only describes all-direction propagation of seismic wave but also removes interbed multiples. Clearbout's image principle is generalized to determine image conditions, real VSP data are used to determine boundary condition, and two way reflection-free wave equation is solved by making reverse-time extrapolation. In each step of extrapolation, the migration value at relevant image point is obtained by using the image condition. The complete migration of a seismic section is achieved when reverse-time extrapolation reaches the minimum image time. In this paper it is proved theoretically and practically that this method is applicable to any velocity variation and makes the migrated section have both good resolution and high S/N ratio. Besides, this method results in high processing efficiency.

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A new formulation of the theory of tachyons using the same two postulates as in special relativity is applied to the electrodynamics of material media. A discussion of Lagrange`s equations and Hamilton`s equations for `classical` charged tachyons shows that such a formalism is a viable approach. An essay is included on why tachyons can be considered to be localised particles for the purpose of calculations. Tachyonic transformations of the electromagnetic fields D, P, H and M are shown to be the same as for bradyonic transformations. Examples discussed include the electric dipole moment of a tachyonic current loop, constitutive equations, polarisation in tachyonic dielectric materials and the velocity of light in tachyonic dielectric media. This is followed by discussions of the collision energy loss for charged tachyons interacting with a material medium and a mathematical proof that tachyons cannot emit Cherenkov ...

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The space derivation term of a wave equation is accurately calculated using Fourier transform method, and the wave equation only relating to time derivative in time-space domain is derived. Solving this equation with the aid of central difference method brings the numerical recursion formula for forward modeling or reverse time migration of seismic wave field in the medium in which seismic velocity varies. The key to this method lies in introducing two auxiliary wave fields relating to velocity and spacial frequency of Fourier transform respectively after multi-dimensional Fourier transform respectively after multi-dimensional Fourier transform of space vector is made. Theoretically, this method is suitable to the forward modeling and migration of seismic wave field in complex area where seismic velocity and structure shape vary arbitrarily. Theoretical results proved this method satisfactory.

CERN Document Server

We investigate the existence of time-periodic solutions of the Dirac equation in the Kerr-Newman background metric. To this end, the solutions are expanded in a Fourier series with respect to the time variable $t$ and the Chandrasekhar separation ansatz is applied so that the question of existence of a time-periodic solution is reduced to the solvability of a certain coupled system of ordinary differential equations. First, we prove the already known result that there are no time-periodic solutions in the non-extreme case. Then it is shown that in the extreme case for fixed black hole data there is a sequence of particle masses $(m_N)_{N\\in\\mathbb N}$ for which a time-periodic solution of the Dirac equation does exist. The period of the solution depends only on the data of the black hole described by the Kerr-Newman metric.

CERN Document Server

A macroscopic realization of the strange virtual particles is presented. The classical Helmholtz and the quantum mechanical Schr\\"odinger equations are analogous differential equations. Their imaginary solutions are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary solutions of this differential equation point to strange consequences: They are non local, they are not observable, and they described as virtual particles. During the last two decades QED calculations of the imaginary solutions have been experimentally confirmed for phonons, photons, and for electrons. The experimental proofs of the predictions of the non-relativistic quantum mechanics and of the Wigner phase time approach for the elastic, the electromagnetic and the Schr\\"odinger fields will be presented in this article. The ...

International Nuclear Information System (INIS)

We obtain x-ray absorption near-edge structures (XANES) by solving the equation of motion for the two-particle Green's function for the electron-hole pair, the Bethe-Salpeter equation (BSE), within the all-electron full-potential linearized augmented plane wave method (FPLAPW). The excited states are calculated for the Li K-edge in the insulating solids LiF, Li_2O and Li_2S, and absorption spectra are compared with independent particle results using the random phase approximation (RPA), as well as supercell calculations using the core-hole approximation within density functional theory (DFT). The binding energies of strongly bound excitations are determined in the materials, and core-exciton wavefunctions are demonstrated for LiF.

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This paper presents research work concerning the mathematical modelling of air pollution in the Athens basin. A mathematical model based on aerodynamics and conservation equations together with turbulence modelling in body-fitted coordinates is used to provide the necessary input information to a similar but more detailed (i.e. small scale) model around Athens. Both models consist of solving the full Navier-Stokes equations and take into account the precise topography of the region. Different roughness heights are used for sea, coastal regions and land. The smaller scale model makes use of a two-equation turbulence model ({kappa}-{epsilon}) and the large scale model assumes a constant turbulence viscosity. The pollutant sources used in these models are based on actual emissions in the Athens area and are distributed in space. The results of this work appear promising and demonstrate the capability of the model as a tool for ...

International Nuclear Information System (INIS)

Within the framework of the Bianchi type-IX homogeneous space, we set up a system of coupled equations for the cosmic scale factors, scalar field, and radiative energy density. At the tree level, the equations are written in a self-consistent, Hartree-Fock form. For phi"4 theory, the system of nine first-order differential equations is solved numerically for a varying ratio of the energy of anisotropy to the vacuum energy. As the vacuum energy increases, there appears to be less reheating, since the energy of anisotropy is more efficiently converted into isotropic expansion. If the energy of anisotropy is large enough, the inflationary phase is prevented. In this case, a series of cosmological phase transitions will take place each time the square of the effective mass changes its sign.

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The code is being developed starting from the steady-state finite element code FENDER for the solution of the diffusion equation by extending it to become time-dependent. The numerical solution of the time-dependent multigroup diffusion equations within TRANSFUSION is performed at the present stage of development by using a backward difference scheme for the time variable, leading to a rearrangement of FENDER by adding a new loop over time steps. The code retains the multigroup coupled neutron-gamma features of FENDER, and provides a consistent two-, and quasi three-dimensional numerical solution of both static and time-dependent multigroup diffusion equations. (orig./DG)

International Nuclear Information System (INIS)

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.

British Library Electronic Table of Contents (United Kingdom)

In this paper, the unsteady MHD free convection heat and mass transfer of viscous fluid flowing through a Darcian porous regime adjacent to a moving vertical semi-infinite plate under Soret and Dufour effect have been examined. Viscous dissipation effects are included in the energy equation. A uniform magnetic field is applied transversely to the direction of the flow. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. The influence of Grashof number (Gr), magnetic parameter (M), heat absorption parameter (Q), permeability parameter (K), Schmidt number (Sc), Soret number (Sr), and Dufour number (Du) on the velocity, tempera...

International Nuclear Information System (INIS)

A nodal integral method is derived for the monoenergetic, steady-state, fixed source neutron diffusion equation in hexagonal geometry based on a coordinate transformation that maps a parallelogram into a rectangle. The new hexagonal nodal diffusion method is implemented in the computer code HND where the discrete-variable equations are solved via an iterative scheme. Because the new method's equations are derived for a rhombus, they can be solved on a sequence of embedded meshes to study the method's error order. Indeed a preliminary numerical error analysis reveals a second-order error in the mesh size, and comparison with finite difference results obtained with the finite difference based BOLD-VENTURE code indicate the superior accuracy of our new nodal method.

CERN Document Server

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The said simultaneous equations are generated and updated using particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a ...

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A non-linear analysis of a Cerenkov maser is presented. The system consists of a ring configuration of a cylindrical waveguide filled with a dielectric material. A single transverse-magnetic mode is assumed to propagate in the system. A low-density pencil electron beam travels in part of the ring, confined by a strong axial magnetic field. Using the single-particle description for the beam and the wave equation for the field, we obtain a set of two coupled non-linear differential equations describing the slowly varying amplitude and phase of the electromagnetic mode. The gain per path is assumed to be small and the spatial growth of the field is neglected. The resulting time dependent amplitude includes the exponential gain of the linear stage and the saturation to its maximum value. The time dependent frequency is also calculated. The two equations are combined to a single Van Der Pol equation with a ...

International Nuclear Information System (INIS)

Determination of the specific surface of uranium oxides: UO_2 and U_3O_8 using a simplified equation derived from the Brunauer, Emmett and Teller theory. The method is suitable for samples having a surface between 6 to 50 m"2.

CERN Document Server

We solve the loop equations of the $\\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\\beta=1$. For \\beta=1$, the solution was expressed using the algebraic spectral curve of equation $y^2=U(x)$. For arbitrary $\\beta$, the spectral curve converts into a Schr\\"odinger equation $((\\hbar\\partial)^2-U(x))\\psi(x)=0$ with $\\hbar\\propto (\\sqrt\\beta-1/\\sqrt\\beta)/N$. This paper is similar to the sister paper~I, in particular, all the main ingredients specific for the algebraic solution of the problem remain the same, but here we present the second approach to finding a solution of loop equations using sectorwise definition of resolvents. Being technically more involved, it allows defining consistently the B-cycle structure of the obtained quantum algebraic curve (a D-module of the form $y^2-U(x)$, where $[y,x]=\\hbar$) and to construct explicitly the correlation ...

International Nuclear Information System (INIS)

An exact cosmological solution of Einstein's equations which has time-dependent rotation is presented. The t-constant sections are of Bianchi type II. The source of this geometry is a fluid which has not been thermalized. (Author).

CERN Document Server

We show that, in addition to radiation travelling at the speed of light, QED theory predicts a second type of radiation with an infinite velocity. We also show that charge, as it appears in the Dirac equation, may have a triune nature.

Science.gov (United States)

In order to reduce the air concentration of (sup 3)H in the reactor buiIding of Wolsung Heavy Water Reactor, a computer code for estimation of adsorption behavior was programmed based on an equation derived for analysis of water vapor adsorption, and a ba...

Science.gov (United States)

A certain model of one-dimensional detonation waves leads to a Stefan problem: the unknown f satisfies Burgers equations on the two sides of a moving discontinuity at which it is given (f, say) and the jump in it derivative (corresponding to the exothermi...

International Nuclear Information System (INIS)

The numerical calculation of oscillatory wavefunctions occurring in the theory of electron scattering from positive ions is considered, the aim being to develop methods for evaluating the oscillatory solutions using a logarithmic grid. Thus, the permitted step-size for the solution depends only upon the potential, enabling calculations at different energies to be performed using the same discretisation. Two similar generalisations of the W.K.B. transformation for second order ordinary differential equations are made and applied to the radial Dirac equations. Iterative schemes for the solution of the resulting non-linear amplitude equations are discussed, one for use in the asymptotic region and the other a Newton scheme for continuing the solution closer to the origin. Using these techniques a reliable and efficient program for calculating relativistic scattering phase shifts from ionic potentials has been written. ...

UK PubMed Central (United Kingdom)

Background. Detection of subjects with early chronic kidney disease (CKD) is important because some will progress up to stage 5 CKD, and most are at high risk of cardiovascular morbidity...Full Text Available

British Library Electronic Table of Contents (United Kingdom)

We study a rapidly convergent modification of a two-sided method for the approximate integration of a boundary-value problem with parameters in boundary conditions for a system of quasilinear second-order differential equations.

International Nuclear Information System (INIS)

The B test series from the course of ISP Nr. 43 was analysed. The boundary conditions measured include the initial temperature of the primary system, the front/slug injection flowrate and temperature, and the pressure drop across the core. Temperature data were collected at 185 thermocouple positions in the downcomer and 38 positions in the lower plenum. The frequency of data acquisition for code predictions was set to 2 Hz, which corresponds to the acquisition frequency of the two experimental setups. Calculations were performed using the FLUENT Computational Fluid Dynamics (CFD) code. This program is based on the finite volume method, The computational mesh was generated by the pre-processor - GAMBIT program. FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations, which can be solved numerically. This control volume technique consists of integrating the governing equations ...

CERN Document Server

The methods of statistical dynamics are applied to a fluid with 5 conserved fields (the mass, the energy, and the three components of momentum) moving in a given external potential. When the potential is zero, we recover a previously derived system of parabolic differential equations, called "corrections to fluid dynamics".

CERN Document Server

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, ...

UK PubMed Central (United Kingdom)

We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality...Full Text Available

Energy Technology Data Exchange (ETDEWEB)

It is urged that the lesson of gauge invariance in quantum electrodynamics implies the irrelevance of `Schwinger term` difficulties in current algebra. The divergence equations of Veltman form the basis of a gauge-variation formalism in which these questions are avoided. (author). 9 refs.

Energy Technology Data Exchange (ETDEWEB)

A new energy concept known as centrifugal potential energy was discussed. This new energy concept is capable of increasing the pressure, temperature and enthalpy of a fluid, without having to apply work or heat transfer to the fluid. It occurs through a change in the centrifugal potential energy of the flowing fluid in a rotating frame of reference or a centrifugal force field, where work is performed internally by the centrifugal weight of the fluid. This energy concept has resulted in new energy equations, such as the Rotational Frame Bernoulli's Equation for liquids and the Rotational Frame Steady-Flow Energy Equation for gases. Applications of these equations have been incorporated into the design of centrifugal field pumps and compressors. Rather than compressing a fluid with a physical load transfer, these devices can compress a fluid via the effect of centrifugal force applied to the ...

Science.gov (United States)

This paper describes the development of an interactive internet-based cost-estimating tool for commonly used urban storm runoff best management practices (BMP), including: retention and detention ponds, grassed swales, and constructed wetlands. The paper presents the cost data, c...

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A numerical model of multiphase air-water flow and contaminant transport in the unsaturated zone is presented. The multiphase flow equations are solved using the two-pressure, mixed form of the equations with a modified Picard linearization of the equations and a finite element spatial approximation. A volatile contaminant is assumed to be transported in either phase, or in both phases simultaneously. The contaminant partitions between phases with an equilibrium distribution given by Henry`s Law or via kinetic mass transfer. The transport equations are solved using a Galerkin finite element method with reduced integration to lump the resultant matrices. The numerical model is applied to published experimental studies to examine the behavior of the air phase and associated contaminant movement under water infiltration. The model is also used to evaluate a hypothetical design for a low-level radioactive ...

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A stable, accurate, and efficient implementation of MacCormack's explicit algorithm for the Parabolized Navier-Stokes equations is demonstrated. The familiar problem of decoding the conservative axial flux vector is solved, resulting in accurate, smooth dependent variable profiles through the viscous-layer sonic line. Source terms due to transformation of the parabolized governing equations into the computational plane and the equations into the computational plane and the resulting metric differencing have been identified and eliminated through inclusion of appropriate geometric conservation law terms. Test cases computed include two- and three-dimensional supersonic and hypersonic flow at laminar and turbulent Reynolds numbers. The computed results demonstrate very good agreement with experiment and with solutions of the full Navier-Stokes equations. Computational times required for the ...

Science.gov (United States)

Wood, R. A.; and Ogden, H. R.: The All-Beta Titanium Alloy (Ti-13V-llCr-3Al). DMIC Rept. 110 (ASTIA AD 214002), Battelle Mem. Inst., Apr. 17, 1959. 22. White ...

Science.gov (United States)

An exact solution method for the free vibration problem of thin circular cylindrical shells is presented. The differential equations of motion are solved directly with the use of simple Fourier series as the modal displacement functions. Stokes' transformation is exploited to obtain correct series expressions for the derivatives of the Fourier series. From this method an explicit expression of the exact frequency equation can be obtained for any kind of boundary conditions. The accuracy of the present method is checked against available data. The proposed method is then used to find the modal characteristics of the thermal liner of the Fast Test Reactor (FTR). The numerical results obtained are compared with finite element method solutions. (auth)

International Nuclear Information System (INIS)

In terms of Berezins's theory of symbols of operators, the integral formulation is suggested for the free differential algebra which gives rise to consistent equations of motion of interacting massless fields of all spins 0#<=#s<#infinity# in the frameworks of gravity. In the first nontrivial order of the expansion in powers of curvatures, Frobenius consistency conditions for higher-spin equations of motion are shown to reduce to the simple geometrical fast that there are two ways for splitting any quadrangle in two triangles. To clarify our construction, we illustrate how it works in the simplest case of pure gravity. (orig.).

CERN Document Server

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.

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Production decline-curve analysis is accepted for prediction of future performance of oil and gas wells and fields. One type of decline-curve analysis involves the hyperbolic-decline-curve equation. The challenge with this equation is to determine simultaneously three parameters. The new method creates a computer spreadsheet containing a set of production data. Then, the specific arrangement of cells and columns containing data and/or formulas allows for statistical fits of the data. Finally, setting-up the nonlinear solver allows for optimization of the three parameters by maximization of the square of the regression coefficient. Eight field cases demonstrated the repeatable and rapid curve-fitting of the method.

CERN Document Server

In symmetrical nuclear matter the solutions of pion dispersion equation are investigated in the complex plane of the pion frequency $\\omega$. There are three well-known branches of solutions on the physical sheet : sound, pion and isobar, at the matter density less than the critical one $\\rho <\\rho_c$. At the condition $\\omega^2_c\\leq0$ (in general case Re$ \\omega^2_c\\leq0$) takes place. This points out the instability of the ground state which is possibly related to the pion condensation.

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This paper presents a reverse time migration (RTM) method for the migration of shot records in tilted transversely isotropic (TTI) media. It is based on the tilted TI acoustic wave equation that was derived from the dispersion relation. The RTM is a full depth migration allowing for velocity to vary laterally as well as vertically and has no dip limitations. The wave equation is solved by a tenth-order finite difference scheme. Using 2D numerical models, we demonstrate that ignoring the tilt angle will introduce both lateral and vertical shifts in imaging. The shifts can be larger than 0.5 wavelength in the vertical direction and 1.5 wavelength in the lateral direction.

CERN Document Server

The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stock prices are in a certain correspondence with their velocity and interest rate behaviour. An analog of the Black-Scholes fundamental differential equation is derived, but, in contrast with the Black-Scholes model, this equation is hyperbolic. Explicit formulas for prices of European options are obtained using perfect and quantile hedging.

British Library Electronic Table of Contents (United Kingdom)

Isosteric heats and adsorption isotherms of methane on nanometer active carbon were measured at supercritical temperature (273-373 K) and pressure from 0 to 10 MPa. The measured data agreed well with Dubinin-Astakhov (DA) model at lower pressure but failed when pressure exceeded a special range. General Freundlich (GF) equation was used to modify the DA equation at high pressure and thus formed a combined bisection model GFDA. The adsorption mechanism of methane on nanometer active carbon was raised according to GFDA model and the heterogeneous energy distribution of the adsorbent was analyzed.

Science.gov (United States)

The entrainment flow rate distribution, the gas velocity profile, and the concentration profile of droplets across the channel cross section in fully developed region of a horizontal rectangular channel of 150mm width and 50mm height were measured. The concentration profile of droplets was expressed by a simple equation based on a constant diffusion coefficient model. From this equation the effects of gravity and turbulent diffusion of droplets on the concentration profile were evaluated. The characteristic mean settling velocity of a group of droplets with various diameters was derived, and using this value the mean diffusion coefficient of the group of droplets was obtained

International Nuclear Information System (INIS)

Bases of the algorithm for assessing the reinforcement status in reinforced concrete products by gamma-absorption method are presented. Analytical equations are obtained for estimation of error of the parameter characterizing the degree of reinforcement destruction. It is recommended to use high-energy Bremsstrahlung sources-betatrons of 4-10 MeV maximum energy for testing products of 500-600 mm thick. Linear radiation attenuation factor (LAF) of concrete in estimated equation is replaced by effective LAF of concrete, and LAF of reinforcement and corrosion materials - by differential LAF. Corresponding LAF of nonevident form in the algorithm is assessed by the results of processing of direct-shadow radiographs of defectometers

Energy Technology Data Exchange (ETDEWEB)

An energy control strategy (10) for a hybrid electric vehicle that controls an electric motor during bleed and charge modes of operation. The control strategy (10) establishes (12) a value of the power level at which the battery is to be charged. The power level is used to calculate (14) the torque to be commanded to the electric motor. The strategy (10) of the present invention identifies a transition region (22) for the electric motor's operation that is bounded by upper and lower speed limits. According to the present invention, the desired torque is calculated by applying equations to the regions before, during and after the transition region (22), the equations being a function of the power level and the predetermined limits and boundaries.

Science.gov (United States)

The present contribution deals with the thermophoresis particle deposition and thermal radiation effects on the flow, heat and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by means of the fourth-order Runge-Kutta method with a shooting technique. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are tabulated and discussed.

International Nuclear Information System (INIS)

A generalization of Faddeev's group cohomology applicable to diffeomorphism groups is presented. This cohomology is used to calculate the two cocycles associated with a projective representation of the diffeomorphism group on the circle. The group version of the n"3 term descends from a three dimensional Chern-Simons action based on the diffeomorphism group. The group version of the n term arises from an ambiguity in the descent equations of adding closed but not exact forms and is trivial only if its appropriately normalized coefficient is quantized to be an integer. Finally, a hamiltonian interpretation of global anomalies is suggested in the language of group cohomology. (orig.).

International Nuclear Information System (INIS)

Burnout data with low pressure Freon-113 for even- and odd- numbered peripheral rod clusters with relatively large spacings were used to derive equations in terms of dimensionless parameters suggested by Barnett. The equations which are for three different flow regimes for each rod geometry (even or odd) were found to predict burnout data with maximum RMS deviation being 3.8%. (author). 11 figs., 3 tabs., 15 refs.

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Diffusion of radon in a bed of activated charcoal is described by diffusion equations. An analytical solution of these equations is presented for the case of constant radon concentration in the atmosphere. The solutions are given separately for short term and long term exposure. An analytical form of the calibration constant f for long term exposure and constant radon concentration in air, was found. A numerical method and computer code based on the method of finite elements is developed for the case of variable radon concentration in air. This program simulates radon adsorption by the activated charcoal bed, enabling determination of sensitivity. The dependence of sensitivity on different parameters, such as temperature, thickness of the charcoal, etc. was studied using this program. (orig.) 10 refs.

CERN Document Server

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the "worm" algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.

International Nuclear Information System (INIS)

British Nuclear Fuels plc owns and operates the near-surface Drigg disposal facility for low level radioactive waste. The long-term performance of the site is modelled by a suite of computer codes called MONDRIAN. One of the modules of MONDRIAN deals with the transport of radionuclides through the environment, and this paper reports on the current status of this module (BIOS). We derive the basic set of working equations from first principles and show clearly how the approximate nature of the final equations is arrived at. This is done by an averaging process leading to compartments, in and out of which radionuclides, solids and water can flow. The equations allow radioactive decay chains and an arbitrary number of compartments. There is also the facility to deal with changes in the rate coefficients, thereby simulating different environmental states. It is also possible to include the creation of new compartments arising ...

Energy Technology Data Exchange (ETDEWEB)

The high energy limit of Quantum Chromodynamics is one of the most fascinating areas in the theory of strong interactions. Over a decade ago the HERA experiment at DESY in Hamburg provided strong evidence for the rise of the proton structure function at small values of the Bjorken variable x. This behavior can be explained as an increase of the gluon density of the proton with energy or correspondingly with smaller values of x. This increase can be attributed on the other hand to the large probability of gluon splitting in QCD. The natural framework for describing the gluon dynamics at small x is the Balitskii-Fadin-Kuraev-Lipatov formalism developed some 30 years ago. It predicts that the gluon density grows very fast with increasing energy, as a power with a large intercept. This increase has to be tamed in order to satisfy the unitarily bound. Over two decades ago, Gribov, Levin and Ryskin proposed the mechanism called the parton saturation, which slows down the fast rise of the ...

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For an electron storage ring the beam size evaluation including beam-beam interaction gives an example of such a problem. Another good example is finding the beam size for a nonlinear machine. The present work gives a way to solve some of these problems, at least in principle. The approach described here is an application of the well known Green's function method, which in this case is applied to the Fokker-Planck equation governing the distribution function in the phase space of particle motion. The new step made in this paper is to consider the particle motion in two degrees of freedom rather than in one dimension, a characteristic of all the previous work. This step seems to be necessary for an adequate description of the problem, at least for the class of problems which are considered below. This work consists of the formal solution of the Fokker-Planck equation in terms of its Green's function and describing the ...

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The microbial transport simulator (MTS) is a three-dimensional, three-phase, multiple-component numerical model that permits the study of the transport of microorganisms and nutrients in porous media. Microbial parameters incorporated into MTS include: Microbial growth and decay, microbial deposition, chemotaxis, diffusion, convective dispersion, tumbling, and nutrient consumption. Governing equations for microbial and nutrient transport are coupled with continuity and flow equations under conditions appropriate for a black oil reservoir. The model`s mathematical formulations and preparation procedures of data files for conducting simulations using MTS are described. A general background of microbial transport simulation is given in Section I and the governing equations, mechanisms, and numerical solutions of MTS are given in Section II. Explanations for preparing an input data file with reservoir and microbial transport ...

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The wavenumber-frequency spectral densities of turbulent wall pressure fluctuations are investigated over a rigid flat plate. Nonlinear Reynolds stress terms of the inhomogeneous Orr-Sommerfeld equation are regarded as a known forcing function. The forcing function is modeled after Bark{close_quote}s hydrodynamic bursting formulation. The inhomogeneous Orr-Sommerfeld equation is solved by the method of Eckhaus in terms of discrete homogeneous solutions. The method of Eckhaus is then extended and proved for the continuous Orr-Sommerfeld eigenfunctions. Turbulent wall pressure fluctuations in terms of wavenumber-frequency spectral densities are numerically computed and compared to the experimental results of Martin as well as to his transformation of Blake{close_quote}s data fitted to a modified Corcos model. The wavenumber-frequency spectral densities numerically computed from the discrete eigenfunctions compared well with Martin{close_quote}s ...

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This paper reports the results of an investigation into the vibration of functionally graded cylindrical shells with flowing fluid, embedded in an elastic medium, under mechanical and thermal loads. By considering rotary inertia, the first-order shear deformation theory (FSDT) and the fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived. Here, heat conduction equation along the thickness of the shell is applied to determine the temperature distribution and material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The equations of eigenvalue problem are obtained by using a modal expansion method. In numerical examples, effects of material composition, thermal loading, static axial loading, flow velocity, medium stiffness and shell geometry parameters on ...

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A stochastic-convective reactive (SCR) transport method is developed for one-dimensional steady transport in physically heterogeneous media with nonlinear degradation. The method is free of perturbation amplitude limitations and circumvents the difficulty of scale dependence of phenomenological parameters by avoiding volume-averaged specifications of diffusive/dispersive fluxes. The transport system is conceptualized as an ensemble of independent convective-reactive streamlines, each characterized by a randomized convective velocity (or travel time). Dispersive effects are treated as a component of the randomness in the streamline velocity ensemble, so no explicit expression for hydrodynamic dispersive flux is written in the streamline transport equation. The expected value of the transport over the stream tube ensemble is obtained as an average of solutions to the reactive convection equation according to the stream tube (travel time) ...

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A set of equations describing a stress-mediated evolution of the nonequilibrium dopant-defect system has been derived and analyzed. Together with coupled diffusion of dopant atoms and point defects, we consider the drift of all mobile species in different charge states, namely vacancies, self-interstitials, and pairs 'dopant atom-point defect', in the field of stress. It has been shown that stresses may affect the diffusion of dopant atoms mainly in two ways: (1) directly, due to the drift of the pairs in the field of stress; (2) indirectly, by the formation of nonuniform defect distribution due to the drift of point defects. On this basis, various features of doping processes, such as phenomena of 'uphill' impurity diffusion near the surface (within the framework of the first or second mechanisms) and the peculiarities of high concentration phosphorus diffusion (due to the second mechanism), can be explained. Numerical ...

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The performance of a 6 kW proton exchange membrane (PEM) electrolyzer was modeled using a semiempirical equation. Total cell voltage was represented as a sum of the Nernst voltage, activation overpotential and ohmic overpotential. A temperature and pressure dependent Nernst potential, derived from thermodynamic principles, was used to model the 20 cell PEM electrolyzer stack. The importance of including the temperature dependence of various model components is clearly demonstrated. The reversible potential without the pressure effect decreases with increasing temperature in a linear fashion. The exchange current densities at both the electrodes and the membrane conductivity were the coefficients of the semiempirical equation. An experimental system designed around a 6 kW PEM electrolyzer was used to obtain the current-voltage characteristics at different stack temperatures. A nonlinear curve fitting method was employed to determine the ...

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Based on the wave equation theory, the authors use finite difference method to derive wave-field extrapolation formula, by which both wavefield modeling and migration can be made. The migration program VSP MIG that was developed using P-wave equation may be used to migrate both surface seismic data and VSP data. Besides, it may be applied to the migrations of P-wave data and P-SV wave data, in which case the original velocity model should be modified properly. The migrated image times for P-wave and P-SV wave respectively are absolutely equal. The migrations of upgoing P-wave and upgoing P-SV wave which have been separated can offer migrated P-wave section and migrated S-wave section. Thus, one can get more information than from simultaneous migration of P-wave and S-wave data.

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This dissertation concerns a study of the utilization of sorghum biomass as the fuel for a methane production system. The objective of this research is to determine an optimal sorghum-methane production system based on anaerobic batch digestion technology. The system is described as the interaction of three components: estimation of available biomass, storage of biomass, and the gas production. Levelized costs are obtained for each component. The biomass supply is assumed to decay exponentially in quality with storage time. The gas production process is a batch type of digestion with an exponential production rate. Gas production is formulated for a fixed planning horizon (one year) as a function of the number of batches and the batch residence times. The cost equation is then described as a function of these gas production equations and their levelized costs. The structure of this resulting equation is exploited to obtain ...

CERN Document Server

We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond where spin effects first appear. Our method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian metric valid for general (continuous) fluids and represent pointlike compact objects with a delta-function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtonian spin effects, we use a different delta-function stress-energy tensor introduced by Bailey and Israel. In a future paper we will use the 2.5PN equations of motion for spinning bodies to derive the gravitational-wave luminosity and phase evolution of binary inspirals, which will be useful in constructing matched filters for signal analysis. The gravitational field derived here may help in posing initial data for numerical ...

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A numerical study of laminar flow and heat transfer in an array of stacked rectangular plates is presented. The array is placed in a uniform stream, and the plates are subjected to a constant surface heat flux. This flow configuration is relevant to a number of practical heat transfer devices with finned surfaces. The computations were performed using a finite volume solution of the steady, two-dimensional Navier-Stokes equations and energy equation. A numerical scheme that reduces numerical diffusion is used to discretize the equations. The dominant feature of the flow is the separation, and subsequent reattachment of, the boundary layer, which takes place at Reynolds numbers greater than about 75. The separation first occurs downstream of the leading edge of the plate; then as Re increases, the separation point moves upstream and remains fixed at the leading edge, and the reattachment length increases linearly with Re. ...

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This work deals with a study on estimation of energy consumption in eight readily defined unit operations of cashew nut processing. Data for analysis were collected from nine cashew nut mills stratified into small, medium and large categories to represent different mechanization levels. Series of equations were developed to easily compute requirements of electricity, fuel and labour for each of the unit operations. The computation of energy use was done using spreadsheet program on Microsoft Excel. The results of application test of the equations show that the total energy intensity in the cashew nut mills varied between 0.21 and 1.161MJ/kg. Electrical energy intensity varied between 0.0052 and 0.029MJ/kg, while thermal energy intensity varied from 0.085 to 1.064MJ/kg. The two identified energy intensive operations in cashew nut processing are cashew nut drying and cashew nut roasting, altogether accounting for over 85% of the total energy ...

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Plasma surface interactions in tokamaks are known to create significant quantities of dust, which settles onto surfaces and accumulates in the vacuum vessel. In ITER, a loss of vacuum accident may result in the release of dust which will be radioactive and/or toxic, and provides increased surface area for chemical reactions or dust explosion. A new method of analysis has been developed for modeling dust resuspension and transport in loss of vacuum accidents. The aerosol dynamic equation is solved via the user defined scalar (UDS) capability in the commercial CFD code Fluent. Fluent solves up to 50 generic transport equations for user defined scalars, and allows customization of terms in these equations through user defined functions (UDF). This allows calculation of diffusion coefficients based on local flow properties, inclusion of body forces such as gravity and thermophoresis in the convection term, and user defined ...

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Solid state nuclear track detectors (SSNTD) record radiation in the form of tracks. In the case of high track density, however, it is not always possible to distinguish each track separately. The track density might then be underestimated unless the loss of track number due to overlapping is compensated. An elaborated 'erosion' or curve fitting process is applied usually, for the separation of the overlapping tracks, to automatic track counting systems. This paper shows a much simpler correction method which was developed by the analogy of the correction equation for the dead time of GM counters. From a set of about 10 data obtained from high track density detectors, the equation for SSNTD can be determined by a least square fitting. Once the equation is found, true track density could be derived easily without any help of complex image processing or calculation, such as the erosion or curve fitting. This ...

CERN Document Server

We construct analytic models of incompressible, rigidly rotating stars in PN gravity and study their stability against nonaxisymmetric Jacobi-like bar modes. PN configurations are modeled by homogeneous triaxial ellipsoids and the metric is obtained as a solution of Einstein's equations in 3+1 ADM form. We use an approximate subset of the equations well-suited to numerical integration for strong field, 3D configurations in quasi--equilibrium. These equations are exact at PN order, and admit an analytic solution for homogeneous ellipsoids. In this paper we present this solution, as well as analytic functionals for the conserved global quantities, M, M_0 and J. By using a variational principle we construct sequences of axisymmetric equilibria of constant density and rest mass, i.e. the PN generalization of Maclaurin spheroids, which are compared to other PN and full relativistic sequences presented by previous authors. We ...

CERN Document Server

We propose to use alternative cosmic tracers to measure the dark energy equation of state and the matter content of the Universe [w(z) & \\Omega_m]. Our proposed method consists of two components: (a) tracing the Hubble relation using HII-like starburst galaxies, as an alternative to SNIa, which can be detected up to very large redshifts, z~4, and (b) measuring the clustering pattern of X-ray selected AGN at a median redshift of ~1. Each component of the method can in itself provide interesting constraints on the cosmological parameters, especially under our anticipation that we will reduce the corresponding random and systematic errors significantly. However, by joining their likelihood functions we will be able to put stringent cosmological constraints and break the known degeneracies between the dark energy equation of state (whether it is constant or variable) and the matter content of the universe and provide a powerful and alternative ...

Science.gov (United States)

In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady-state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah and the Wolcamp carbonate/sandstone aquifer of the Palo Duro Basin in the Texas Panhandle. Two performance measures are evaluated, local heads and velocity in the vicinity of potential high-level nuclear waste repositories. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Local velocity-related performance measures are more sensitive to hydraulic conductivities. The uncertainty in the performance measure is a function of the parameter sensitivity, parameter variance and the correlation between ...

International Nuclear Information System (INIS)

A nonlinear mathematical model is presented of a WWER-440 nuclear power plant horizontal steam generator. On the proposed model is based a computer program for investigating transients in steam generators during loss of coolant accidents. Processes taking place at the primary side of the steam generator are described by a set of partial differential equations while those at the secondary side of the steam generator are described by plain differential equations with the variables being complex time functions. The model takes account of the coolant as both a single- and two-phase medium, of changes in the direction of the primary coolant flow and of changes in the direction of heat transfer. Heat transfer through the wall is based on a simple model of heat transfer through a thin-walled tube and includes a correction for the heat resistance of the wall. (author).

Energy Technology Data Exchange (ETDEWEB)

This paper is an introduction course in modelling turbulent thermohydraulics, aimed at computational fluid dynamics users. No specific knowledge other than the Navier Stokes equations is required beforehand. Chapter I (which those who are not beginners can skip) provides basic ideas on turbulence physics and is taken up in a textbook prepared by the teaching team of the ENPC (Benque, Viollet). Chapter II describes turbulent viscosity type modelling and the 2k-{epsilon} two equations model. It provides details of the channel flow case and the boundary conditions. Chapter III describes the `standard` (R{sub ij}-{epsilon}) Reynolds tensions transport model and introduces more recent models called `feasible`. A second paper deals with heat transfer and the effects of gravity, and returns to the Reynolds stress transport model. (author). 37 refs.

Science.gov (United States)

We present a Poincare covariant Faddeev equation, which enables the simultaneous prediction of meson and baryon observables using the leading order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleon's dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q{sup 2} evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r{sub 1}{sup nu}>r{sub 1}{sup nd}. The proton electric-magnetic form factor ratio falls with increasing Q{sup 2}.

International Nuclear Information System (INIS)

Results of three-dimensional laminar and standard K-#epsilon# turbulent numerical simulations of natural convection cooling of ten cubic aluminum blocks mounted on an insulated plate, facing a shrouding wall, are presented. This geometry is chosen so that comparison with experimental results is possible. The considered problem is of great practical importance because it simulates the case of heated electronic chips, mounted on printed board assemblies, which are frequently encountered in electronic industry applications. The problem is mathematically modeled by the three-dimensional conservation differential equations of mass, momentum, energy and turbulent kinetic energy and dissipation (for the turbulent flow model). IN this paper, these equations are numerically solved by a finite volume method and the laminar and turbulent results are compared to the experimental results obtained with similar parameters.

International Nuclear Information System (INIS)

The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter C?0. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H. We found an excellent agreement between the exact solutions and asymptotic solutions when H is very small.

British Library Electronic Table of Contents (United Kingdom)

In this article, we studied the effects of variable viscosity and thermal conductivity on an unsteady two-dimensional laminar flow of a viscous incompressible conducting fluid past a semi-infinite vertical porous moving plate taking into account the effect of a magnetic field in the presence of variable suction. The fluid viscosity is assumed to vary as an inverse linear function of temperature but the thermal conductivity is assumed to vary as a linear function of temperature. It is assumed that the porous plate moves with a constant velocity in the direction of fluid flow, and the free stream velocity follows the exponentially increasing small perturbation law. The governing equations for the flow are transformed into a system of nonlinear ordinary differential equations by perturbation ...

British Library Electronic Table of Contents (United Kingdom)

The double diffusive convection in a horizontal couple stress fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameter, solute Rayleigh number, Lewis number, couple stress parameter, and Vadasz number on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the thermal anisotropy parameter, couple stress parameter, and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and fin...

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We consider Rashba spin-orbit effects on spin transport driven by an electric field in semiconductor quantum wells. We derive spin diffusion equations that are valid when the mean free path and the Rashba spin-orbit interaction vary on length scales larger than the mean free path in the weak spin-orbit coupling limit. From these general diffusion equations, we derive boundary conditions between regions of different spin-orbit couplings. We show that spin injection is feasible when the electric field is perpendicular to the boundary between two regions. When the electric field is parallel to the boundary, spin injection only occurs when the mean free path changes within the boundary, in agreement with the recent work by Tserkovnyak et al (Preprint cond-mat/0610190)

British Library Electronic Table of Contents (United Kingdom)

The literature regarding the free vibration analysis of Bernoulli?Euler and Timoshenko beams under various supporting conditions is plenty, but the free vibration analysis of Reddy?Bickford beams with variable cross-section on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded and semi-rigid connected Reddy?Bickford beam with variable cross-section on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the r...

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The performance of five well-known photosynthesis-light equations is compared by presenting a wide range of solutions in the form of dimensionless nomographs for the case where photosynthetically available radiation (PAR) reduces exponentially down the water column and is distributed sinusoidally through the photoperiod. These provide a simple means of calculating daily photosynthesis at any depth (e.g. at a benthic layer), or through a water column, avoiding the need to perform complex integrations. An examination is made of the accuracy of common approximate methods for calculating daily photosynthesis, assuming constant PAR. For optically deep water a modification is proposed to Talling's planimetric solution, to enable daily photosynthesis to be calculated more accurately, yet simply, over the whole range of possible PAR values. The errors induced by approximating the daily PAR distribution as a half-sinusoid are also reported. 13 refs., 9 figs., 5 ...

International Nuclear Information System (INIS)

A quantum mechanical analysis of the guided light in integrated photonics waveguides is presented. The analysis is made starting from one-dimensional (1D) guided vector modes by taking into account the modal orthonormalization property on a cross section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry in order to quantize the 1D vector modes and to derive the quantum momentum operator and the Heisenberg equations. The results provide a quantum-consistent formulation of the linear and nonlinear quantum light propagations as a function of forward and backward creation and annihilation operators in integrated photonics. As an illustration, an application to an integrated nonlinear directional coupler is given, that is, both the nonlinear momentum and the Heisenberg equations of the nonlinear coupler are derived.

British Library Electronic Table of Contents (United Kingdom)

A dense Pd-Ag membrane reactor (MR) with 100% hydrogen selectivity packed with either Rh/La2O3 or Rh/La2O3-SiO2 as catalysts was used to carry out the dry reforming of methane. The membrane reactor simulation was performed using a well-known reactor model. For this purpose, we employed the equations derived from complete kinetic studies of the dry reforming of methane reaction in connection with both catalysts. In addition, we developed the kinetic equation for the reverse water gas shift reaction (RWGS). The combination of detailed kinetic studies with the measured permeation flux for the Pd-Ag membrane allowed a complete comparison between experimental and simulated operation variables. The variables studied for both catalysts were methane conversion and hydrogen permeation as a function...

CERN Document Server

The problem of a spin 1 charged particle with electromagnetic polarizability, obeying a generalized 15-component quantum mechanical equation, is investigated in presence of the external Coulomb potential. With the use of the Wigner's functions techniques, separation of variables in the spherical tetrad basis is done and the 15-component radial system is given. It is shown that there exists a class of quantum states for which the additional characteristics, polarizability, does not manifest itself anyhow; at this the energy spectrum of the system coincides with the known spectrum of the scalar particle. For j=0 states, a 2-order differential equation is derived, it contains an additional potential term 1/r^{4}. In analogous approach wave functions the generalized particle are examined in presence of external Dirac monopole field. It is shown that there exists one special state with minimal conserved quantum number j_{min}. It this solution, ...

Science.gov (United States)

In this paper we study theoretically a pulsed corona discharge plasma in air at atmospheric pressure. A self consistent one-dimensional model, using a flux-corrected transport numerical scheme, is presented to achieve it. The charged particle kinetics in this model are described by one-dimensional continuity equations coupled with Poisson's equations. The spatio-temporal local field, charge density variations and the velocity profile of an ionizing front are calculated to describe the dynamical behavior of corona discharge plasmas. The simulation results of a wire-in-cylinder corona discharge plasma explain the physical mechanisms of discharge processes. These results may also be apply to obtain the optimizing parameters for designing the plasma reactor.

International Nuclear Information System (INIS)

Turbulent premixed methane-air combustion in a cylindrical chamber is numerically simulated considering radiation effect. Reaction rates are considered as minimum rates between Arrhenius rates and eddy break up rates. A five step reduced mechanism is used. Turbulent modeling is done via standard k-? model imposed by empirical inlet boundary conditions. Source terms of energy equation consist of reaction rates and radiation effects. The discrete ordinate method (DOM) is employed to solve the radiative transfer equation (RTE) and the weighted sum of gray gas model (WSGGM) is imposed to consider radiation effect of non-gray gases. The results indicate that in the case of turbulent combusting flows, the effect of radiation of gases can affect the temperature and species concentrations. The numerical results obtained considering radiation effect are closer to the experimental data than that of the case without radiation effect.

CERN Document Server

We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons - periodic imaginary-time solutions to time-dependent mean-field equations - that allows for a comparison with more familiar and used generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfils the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions of energy conservation and the velocity-momentum relations. In the adiabatic limit the instanton method reduces to the time-odd ATDHF equation, with collective mass including the time-odd Thouless-Valatin term, while the GCM mass completely ignores velocity-momentum relations. This implies that GCM inertia generally overestimates instanton-related decay ...

Energy Technology Data Exchange (ETDEWEB)

A set of nomographs to estimate the levelized energy cost for photovoltaic systems are presented. These are designed to assist system designers, analysts, and planners in estimating the effects of research and development and system-design optimization on the delivered cost of energy. The nomographs are based on a refined version of the energy cost estimation equation that appears in the National Photovoltaics Program Five-Year Research Plan. The nomographs have been prepared to emphasize technologies with the potential of producing low-cost energy (<$0.40/kWh levelized in nominal terms or $0.17/kWh in 1982 dollars), and thus primarily apply to far-term or advanced intermediate photovoltaic technologies. Separate sets of nomographs are presented to encompass both flat-plate and concentrator technologies. To supplement the nomographs, a set of tabular solutions of the energy cost equation are included as an appendix.

CERN Document Server

In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumour and immune cells is based on the generic Michaelis-Menten kinetics describing interaction and competition between the tumour and the immune system. The appropriate phenomenological equation modeling cell-mediated immune surveillance against cancer is of the predator-prey form and within a given choice of parameters exhibits bistability. Under the influence of spontaneous weak fluctuations, the model may be analyzed in terms of a stochastic differential equation bearing the form of an overdamped Langevin-like dynamics in the external quasi-potential represented by a double well. We analyze properties of the system within the range of parameters for which the potential wells are of the same depth and when the additional perturbation describing a periodic treatment is insufficient to overcome ...

British Library Electronic Table of Contents (United Kingdom)

The aim of this work is the development and experimental validation of a detailed dynamic fuel cell model using the gPROMS modeling environment. The model is oriented towards optimization and control and it relies on material and energy balances as well as electrochemical equations including semi-empirical equations. For the experimental validation of the model a fully automated and integrated hydrogen fuel cell testing unit was used. The predictive power of the model has been compared with the data obtained during load change experiments. A sensitivity analysis has been employed to reveal the most critical empirical model parameters that should be estimated using a systematic estimation procedure. Model predictions are in good agreement with experimental data under a wide range of operati...

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This thesis deals with the reduced-order modeling of electrical machines and interconnected power systems in the medium time scale using integral manifold techniques. First, an improved model for power system stabilizer design that captures the damping due to the amortisseur windings while retaining the simplicity of the DeMello-Concordia model is presented. Second, time scales of the regulated synchronous machine are analyzed using the linearized models, and the well-known effects of the high-gain regulator on the system are explained. A reduced-order model that captures the damping due to the power-system stabilizer is presented. Third, speed-damping terms are obtained in the swing equation in a multimachine environment by approximating the integral manifold associated with fast damper windings. This provides a theoretical basis for the practice of adding cross-damping terms to the swing equation to account for damping present in the system. ...

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Analytical and numerical methods have been used in this investigation to model the behavior of geothermal systems under exploitation. The work is divided into three parts: (1) development of a numerical code, (2) theoretical studies of geothermal systems, and (3) field applications. A new single-phase three-dimensional simulator, capable of solving heat and mass flow problems in a saturated, heterogeneous porous or fractured medium has been developed. The simulator uses the integrated finite difference method for formulating the governing equations and an efficient sparse solver for the solution of the linearized equations. In the theoretical studies, various reservoir engineering problems have been examined. These include (a) well-test analysis, (b) exploitation strategies, (c) injection into fractured rocks, and (d) fault-charged geothermal reservoirs.

CERN Document Server

This paper presents three non-linear asymptotic observers corresponding to three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of invariant observers, i.e, symmetry-preserving observers. We consider an observer to consist in a copy of the system equation and a correction term, and we give a constructive method (based on the Cartan moving-frame method) to find all the symmetry-preserving correction terms. They rely on an invariant frame (a classical notion) and on an invariant output-error, a less standard notion precisely defined here. For each example, the convergence analysis relies also on symmetries consideration with a key use of invariant state-errors. For the non-holonomic car and the inertial navigation system, the invariant state-errors is shown to obey an autonomous differential ...

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In the process of backward Raman amplification (BRA), the leading layers of the seed laser pulse can shadow the rear layers, thus weakening the effective seeding power and affecting parameters of output pulses in BRA. We study this effect numerically and also analytically by approximating the pumped pulse by the ''*-pulse'' manifold of self-similar solutions. We determine how the pumped pulse projection moves within the *-pulse manifold, and describe quantitatively the effective seeding power evolution. Our results extend the quantitative theory of BRA to regimes where the effective seeding power varies substantially during the amplification. These results might be of broader interest, since the basic equations, are general equations for resonant 3-wave interactions.

Energy Technology Data Exchange (ETDEWEB)

The standard Friedmann-Robertson-Walker (FRW) big bang model of the universe requires special initial conditions: the early universe is highly homogeneous and isotropic even though there exist causally disconnected regions (horizon problem). A plane symmetric (anisotropic) solution of field equations in a generalized theory of gravitation predicts the beginning of the universe as a vacuum instability at a specific fundamental time (which can be associated with the Planck time (tsub(p))), after which matter is created as the universe begins to expand. At a time t=tsub(c) there is a singular expansion, the anisotropy vanishes, and the physical horizon becomes infinite. Thereafter the solution of the field equations goes over into the FRW model. Thus the special initial conditions of the FRW model at the big bang singularity t=tsub(c) are predicted by the theory.

International Nuclear Information System (INIS)

We develop a continuum description for the axial segregation of granular materials in a long rotating drum based on the dynamics of the thin near-surface granular flow coupled to bulk flow. The equations of motion are reduced to the one-dimensional system for two local variables only, the concentration difference and the dynamic angle of repose, or the average slope of the free surface. The parameters of the system are established from comparison with experimental data. The resulting system describes both initial transient traveling wave dynamics and the formation of quasi-stationary bands of segregated materials. A long-term evolution proceeds through slow logarithmic coarsening of the band structure which is analogous to the spinoidal decomposition described by the Cahn-Hilliard equation. copyright 1999 The American Physical Society

CERN Document Server

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. AMR coalescences of neutron stars can now be simulated with sufficient resolution covering the neutron stars while having the computational domain extend to the local wave zone. We show an AMR simulation carried out with a workstation having an accuracy equivalent to that of a 1025^3 regular uni-grid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.

British Library Electronic Table of Contents (United Kingdom)

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption ...

International Nuclear Information System (INIS)

We present a new relativistic bound-state formalism for two interacting Fermi-Dirac particles. The kernel of the integral equation for the bound-state system is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. The method is illustrated through calculations of the hyperfine and fine splittings of positronium up to order #alpha#"5. Our calculations of the one-loop contributions are carried out in the explicitly covariant Feynman gauge. We also present new results for the hyperfine and fine splittings in positronium to order #alpha#"5 for arbitrary principal quantum number n, which are easily obtained owing to the virtue of conceptual and calculational simplicity of our formalism. In addition, we present the one-loop renormalization scheme in our formalism. (author).

Energy Technology Data Exchange (ETDEWEB)

Using a quasi-static approach valid for Stefan numbers less than one, we derive approximate equations governing the movement of a phase change front for materials which generate internal heat. These models are applied for both constant surface temperature and constant surface heat flux boundary conditions, in cylindrical, spherical, plane wall and semi-infinite geometries. Exact solutions with the constant surface temperature condition are obtained for the steady-state solidification thickness using the cylinder, sphere, and plane wall geometries which show that the thickness depends on the inverse square root of the internal heat generation. Under constant surface heat flux conditions, closed form equations can be obtained for the three geometries. In the case of the semi-infinite wall, we show that for constant temperature and constant heat flux out of the wall conditions, the solidification layer grows then remelts. (orig.)

British Library Electronic Table of Contents (United Kingdom)

The heating of water layer using microwave oven with a rectangular waveguide has been studied both numerically and experimentally. The mathematical model is validated with the experimental data. The transient Maxwell's equations are solved by using the Finite Difference Time Domain (FDTD) method to describe the electromagnetic field inside the waveguide and sample. The temperature profile and velocity field within sample are determined by the solutions of the momentum, energy and Maxwell's equations. In this study, the effects of physical parameters, e.g. microwave power level, placement of sample inside the waveguide, volume of sample, are studied. The distribution of electric field, temperature profile and velocity field are presented in details. The results show good agreement between s...

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Three geothermal direct heat applications were examined to derive a set of cost estimates from which one could determine the effect of changes in system parameters (temperature, flow, load, etc.) on the cost of heat. For each application, a set of resource characteristics and system inputs were chosen to best represent a site specific baseline condition. The baseline estimated cost of heat was calculated along with other cost estimates representing optimistic and pessimistic conditions, bracketing the range any input variable might reasonably take. Regression equations based upon these cost estimates were developed for each application to quantitatively relate changes in cost to changes in the input variables. These three equations and their accompanying nomographs serve as easily understandable planning tools for direct heat geothermal energy projects.

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The ASFIT (Anisotropic Source-Flux Iteration Technique) code was first developed in India about 1970 to solve the radiation transport equation represented in the form of coupled integral equations separating the spatial and energy-angular transmissions. The ASFIT code uses a nodal structure in the wavelength [lambda] domain in Compton units (CU) rather than in the energy domain. The ASFIT-VARI code is the latest version available from the Radiation Shielding Information Center. It incorporates variable dimensioning and has been adapted for use on MS-DOS personal computers using the Ryan-McFarland or Microsoft Version 5.0 FORTRAN compilers. While earlier versions used point cross sections (well suited for gamma-ray transport), the present version also allows multigroup cross sections for neutron and coupled neutron-gamma-ray transport.

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The FVM-LES-acoustic analogy method (FVM-LES-AAM), which is a hybrid prediction technique for the acoustical property computation, is presented and performed in this paper. The FVM-LES-AAM was developed by combining the finite volume method (FVM), the large eddy simulation (LES), and the Ffowcs Williams-Hawkings analogy algorithm (FWH-AA). To predict the acoustical properties of induction cookers, the FVM is used for discretizing the calculation field and building numerical equations, and the LES and FWH-AA are performed for computing the sound sources and predicting the far-field sound, respectively. Using the FVM with the unstructured grids method to discretize the control equation of Navier-Stokes was introduced for illuminating the above numerical simulation procedure. To prove the FVM...

International Nuclear Information System (INIS)

Counter rotating longitudinal vortices produced by winglet in a channel are known to enhance heat transfer. In the present investigation the flow structure and heat-transfer enhancement by a winglet pair of non-zero thickness has been studied. A delta winglet pair type vortex generator is placed in a hydrodynamically developed and thermally developing laminar channel flow. Computations are done by solving the unsteady, three-dimensional, incompressible Navier-Strokes equations and energy equation using a modified Marker-and-Cell (MAC) method. The flow structure is complex and consists of main, corner and induced vortices. It is observed that as compared to a channel without winglets, the heat transfer is enhanced by 33% when single winglet is used and by 67% when a winglet pair is employed. Effects of thickness of the winglets and Reynolds number on the heat transfer augmentation are presented.

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The GASPAR module utilized in MAXIGASP and POPGASP has been verified by hand calculations. The program operates as documented by the NRC [Eckerman et. al. 1980]. Equations used in the code to calculate downwind deposition rates, concentrations in air, on ground surfaces, and in vegetables, meat, and milk are provided in this report.

Science.gov (United States)

We solve an R -linear problem for a multiple-connected circular domain in a class of doubly periodic functions in analytic form by a method of functional equations. This problem models transport properties of two-dimensional composite materials made from a collection of disks embedded in an otherwise uniform host.

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A Bianchi type-IX cosmological model has been found as a solution of Einstien's vacuum field equations with a cosmological constant. The solution represents a rotating generalziation fo the de Sitter universe. This universe shows a transition to exponential expansion and the vorticity begins to decay exponentially at the grand-unified-theory time. The point of time for this transition is independent of the magnitude of the vorticity. During the Guth inflationary era the vorticity decays by a factor of the order 10 US.

International Nuclear Information System (INIS)

We present a general procedure to construct the first law of thermodynamics on the apparent horizon and illustrate its validity by examining it in some extended gravity theories. Applying this procedure, we can describe the thermodynamics on the apparent horizon in Randall-Sundrum braneworld imbedded in a nontrivial bulk. We discuss the mass-like function which was used to link Friedmann equation to the first law of thermodynamics and obtain its special case which gives the generalized Misner-Sharp mass in Lovelock gravity.

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Equations are derived to calculate the work required for the isentropic compression of a 2-phase fuel-air mixture. Methanol evaporation during compression substantially reduces compression work and improves cycle efficiency and maximum power. Effects of evaporative cooling in the intake manifold are calculated. Energy d. of methanol and gasoline fuel-air charges are compared. The phase equilibrium and evaporation rate are causes of the poor cold-starting performance of methanol.

International Nuclear Information System (INIS)

Relative densities and relative massic heat capacities have been measured for aqueous solutions of Y(ClO_4)_3, Yb(ClO_4)_3, Dy(ClO_4)_3, and Sm(ClO_4)_3 at T=(288.15,298.15,313.15, and 328.15) K and p=0.1 MPa. These measurements were made in the concentration range 0.01624#<=#m/(mol#centre dot#kg"-"1)#<=#0.41822 using a Sodev 02D Vibrating Tube Densimeter and a Picker Microflow Calorimeter, respectively. To counter the potential effects of hydrolysis, aqueous solutions of the investigated salts were acidified with perchloric acid. After correcting for the presence of the acid, the measured properties were used to calculate apparent molar volumes and apparent molar heat capacities for solutions of the perchlorate salts in water. The calculated apparent molar properties were modeled at each investigated temperature using Pitzer ion interaction equations to produce estimates of apparent molar volumes and heat capacities at infinite dilution. In addition, the ...

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Using the Relativistic Mean Field Theory (RMF) it is shown that different proton fraction which is directly connected with the neutron excess and with the asymmetry of the system affects proto-neutron stars parameters and changes their composition. The obtained form of the equation of state allows to construct the mass-radius relations and shows that the increasing asymmetry creates more compact stars. The inclusion of {delta} meson together with nonlinear vector meson interaction terms and magnetic field make this effect even stronger.

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This paper gives a Coulomb gas representation for level kN = 1 supersymmetric SU(2) Kac-Moody algebra in terms of three free scalar superfields. It is clarified how this representation reduces to a Coulomb gas representation for the corresponding bosonic SU(2) Kac-Moody algebra and the free fermionic algebra. The primary superfields and the correlation functions, which satisfy the supersymmetric Knizhnik-Zamolodchikov equation, are also discussed.

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The Thomsen and Frandsen (1983) cosmological test employing the observed correlation between elliptical galaxy surface brightness and scale size in order to avoid problems due to dynamical evolution is presently extended to make use of arbitrary galaxy samples. The explicit dependence on stellar evolution is also demonstrated. On the assumption that this evolution is calculable, an equation for the deceleration parameter entirely in terms of observables is derived. The test is applied to two available samples. 25 references.

Science.gov (United States)

A flutter-motion equation is presently derived for a 2D composite sandwich panel considering the total lateral displacement of the plate as the sum of the displacement due to bending of the plate, and that which is due to shear deformation at the core. The effects of core thickness and stacking sequence of the faces on the flutter boundary of the plate are discussed; it is shown that the sandwich panel greatly improves the flutter boundary over that of a composite laminate panel, provided it has sufficient core thickness.

International Nuclear Information System (INIS)

Etching of SiO_2 rods has been obtained with a dc torch with argon as the process gas in an air environment at atmospheric pressure; the high temperature of the plasma jet causes vaporization of the exposed area. The apparatus and torch operative parameters have been set up to obtain a depth etch rate of up to 0.6 mm min"-"1 corresponding to 0.826 g min"-"1. An enthalpy probe has been employed to monitor the plasma conditions before the thermal plasma etching process and from the experimental etch rate a surface rod temperature of T_s_u_r = 2057 K has been derived. Etching has been obtained with uniformity over the entire exposed area with peak to peak differences below 1%. The plasma to rod heat transfer has been simulated using a commercial CFD code Fluent (copyright). The model consists of a non-steady two-dimensional simulation for a compressible turbulent fluid, with an adapted grid calculation. Boundary conditions have been set out using the enthalpy probe plasma jet map. In ...

Science.gov (United States)

The authors have determined quantitative characteristics for oxide films forming on (111) surfaces of cadmium telluride single crystals on anodic oxidation in 0.1 M KOH: the constants in the Guenterschulze-Betz equation and the film growth constant, which is 2.4 nm/V, from which the activation energy for cadmium telluride electrooxidation has been calculated.