Motivated by the numerical investigations of Laval, Dubrulle & Nazarenko (1999), we develop a quasilinear theory of the 2D Euler equation and derive an integro-differentialequation for the evolution of the coarse-grained vorticity. This equation respects all the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel (as well as in an infinite domain). The explicit energy is not rigorously conserved as it is partly transfered into fine-grained fluctuations but the total energy is conserved. We prove a H-theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.
Displacements per atom (DPA) is a widely used damage unit for displacement damage in nuclear materials. Calculating the DPA for SiC irradiated in a particular facility requires a knowledge of the neutron spectrum as well as specific information about displacement damage in that material. In recent years significant improvements in displacement damage information for SiC have been generated, especially the energy required to displace an atom in an irradiation event and the models used to describe electronic and nuclear stopping. Using this information, numerical solutions for the displacement functions in SiC have been determined from coupled integro-differentialequations for displacements in polyatomic materials and applied in calculations of spectral-averaged displacement cross sections for SiC. This procedure has been used to generate spectrally averaged displacement cross sections for SiC in a number of reactors used for radiation damage ...
Displacements per atom (DPA) is a widely used damage unit for displacement damage in nuclear materials. Calculating the DPA for SiC irradiated in a particular facility requires a knowledge of the neutron spectrum as well as specific information about displacement damage in that material. In recent years significant improvements in displacement damage information for SiC have been generated, especially the energy required to displace an atom in an irradiation event and the models used to describe electronic and nuclear stopping. Using this information, numerical solutions for the displacement functions in SiC have been determined from coupled integro-differentialequations for displacements in polyatomic materials and applied in calculations of spectral-averaged displacement cross sections for SiC. This procedure has been used to generate spectrally averaged displacement cross sections for SiC in a number of reactors used for radiation damage ...
... Abstract : The purpose of this study was to evaluate the tooling cost estimating equation of the DAPCA III model and determine if more accurate ...
... Abstract : The purpose of this paper is to introduce strapdown inertial navigation error equations based on a quaternion relation between body-fixed ...
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...
Abstract The available surface equation of state for pure pulmonary surfactant monolayers is generalised to binary mixture monolayers by introducing a group of parameters, i(i-=-1-4) in the form of $x_{r}^{\\beta _{i} } $ to express the influence of the components in new mixing rules and a new factor, I $\\left[ { = \\left( {\\prod\\limits_{i = 1}^{4} {\\beta _{i} } } \\right)^{{\\raise0.5ex\\hbox{$\\scriptstyle 1$}\\kern-0.1em/\\kern-0.15em\\lower0.25ex\\hbox{$\\scriptstyle {4}$}}} } \\right]$, is defined to represent the interaction intensity between two different components. The ---A isotherms getting by the surface equations of state agree with the experimental data for protein-lipid binary monolayers, and the average deviation is about 11.41%. The result shows the order of the interaction intensity b...
Abstract in english This paper presents an HP-Adaptive Procedure with Hierarchical formulation for the Boundary Element Method in 2-D Elasticity problems. Firstly, H, P and HP formulations are defined. Then, the hierarchical concept, which allows a substantial reduction in the dimension of equation system, is introduced. The error estimator used is based on the residual computation over each node inside an element. Finally, the HP strategy is defined and applied to two examples.
Abstract in english Numerical solutions for the effects of radiation on a MHD convective heat transfer past a semi-infinite porous plate with a magnetic field are obtained. 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 magnetic field acts perpendicular to the porous surface which absorbs the fluid with a suction velocity varying with time. The gov (more) erning equations for the flow are transformed into a system of nonlinear ordinary differential equations by perturbation technique and then are solved numerically by using the shooting method. The effects of the various parameters on the velocity, temperature profiles as well as the surface skin-friction and surface heat transfer are illustrated graphically.
Abstract: In many biological processes heterogeneity within clonal cell populations is an important issue. One of the most striking examples is a population of cancer cells in which after a common, identical death signal some cells die whereas others survive. The reason for this heterogeneity is intrinsic and extrinsic noise. In this paper we present a mechanistic multi-scale modeling framework for cell populations, in which the dynamics of every individual cell is captured by a parameter dependent stochastic differential equation (SDE). Heterogeneity among individual cells is accounted for by differences in parameter values, modeling extrinsic influences. Based on the statistical properties of the extrinsic noise and the SDE model for the individual cell, a partial differential equation (...
English abstract: In the "Intuitive Quantum Physics" course, we use graphical interpretations of mathematical equations and qualitative reasoning to develop and teach a simplified model of quantum physics. Our course contains three units: Wave physics, Development of a conceptual toolbox, and quantum physics. It also contains three key themes: wave-particle duality, the Schroedinger equation, and tunneling of quantum particles. Students learn most new material in lab-tutorials in which students work in small groups (3 to 3 people) on specially designed worksheets. Lecture reinforces the lab-tutorial content and focuses more on issues about the nature of science. Data show that students are able to learn some of the most difficult concepts in the course, and also that students learn to believe that there is a conceptually accessible structure to the physics in the course. German abstract: Im Kurs ...
Available in abstract form only. Full text of publication follows: In this study. simulation of carbon dioxide absorption by Sodium Hydroxide solution in a packed bed has been investigated. At first, mass and energy balances were applied around a differential height of the bed. So, the governing equations were obtained. Surface renewal theory by Danckwerts was used to represent the mass transfer operation Finally, by changing the operating parameters like solvent temperature, inlet gas composition pressure and height of the bed, the effect of these parameters on the absorption and the composition of carbon dioxide in exit stream have been investigated. (authors)
Abstract: The recent National Academy of Sciences report on forensic sciences states that the study of fire patterns and debris in arson fires is in need of additional work and eventual standardization. We discuss a recently introduced method that can provide predicted evaporation patterns for ignitable liquids as a function of temperature. The method is a complex fluid analysis protocol, the advanced distillation curve approach, featuring a composition explicit data channel for each distillate fraction (for qualitative, quantitative, and trace analysis), low uncertainty temperature measurements that are thermodynamic state points that can be modeled with an equation of state, consistency with a century of historical data, and an assessment of the energy content of each distillate fraction...
Abstract A large number of massive stars are known to rotate rapidly, resulting in a significant distortion and variation in surface temperature from the pole to the equator. Radiatively driven mass-loss is temperature-dependent, so rapid rotation produces a variation in the mass-loss and angular momentum loss rates across the surface of the star, which is expected to affect the evolution of rapidly rotating massive stars. In this work, we use zero-age main-sequence (ZAMS) stellar models to investigate the two-dimensional effects of rotation on stellar mass-loss, using two common prescriptions for radiatively driven mass-loss. The associated loss of angular momentum from these models is also considered. Using 2D stellar models, which give the variation in surface parameters as a function o...
Abstract in english A mathematical model has been developed for describing the dynamic operation of the N-formylmorpholine extractive distillation column and the corresponding solvent recovery column in the benzene extraction plant. The NRTL equation was used to calculate the equilibrium and thermodynamic properties of the mixtures. The validity of the model in terms of temperature, pressure and split fraction was examined using actual plant data at steady-state conditions. Comparison betwee (more) n model results and plant data shows good consistency. In order to improve the control of the process and selection of the optimal control strategy, the model was used to find the optimum values of the constants of the controllers with Nelder-Mead algorithm during unsteady-state operation by minimizing the deviation from steady-state conditions. The outcome of this study could be used by operators and engineers to increase the productivity of the ...
In order to alleviate the inefficiencies caused by the interaction of the logic and functional sides, integrated languages may take advantage of \\emph{demand} information -- i.e. knowing in advance which computations are needed and, to which extent, in a particular context. This work studies \\emph{demand analysis} -- which is closely related to \\emph{backwards strictness analysis} -- in a semantic framework of \\emph{partial predicates}, which in turn are constructive realizations of ideals in a domain. This will allow us to give a concise, unified presentation of demand analysis, to relate it to other analyses based on abstract interpretation or strictness logics, some hints for the implementation, and, more important, to prove the soundness of our analysis based on \\emph{demand equations}. There are also some innovative results. One of them is that a set constraint-based analysis has been derived in a stepwise manner using ideas taken ...
Conference abstract book contains seven sections: Plenary-4 abstracts; Chemical-9 abstracts; Radiation-7 abstracts; Ultra Low Doses and Medicine-6 abstracts; Biomedical-11 abstracts; Risk Assessment-5 abstracts and Poster Sessions-25 abstracts. Each abstract was provided by the author/presenter participating in the conference.
Research highlights: {yields} Mathematical model represents a power system which consists of synchronous machine connected to infinite bus through transmission line. {yields} Power system stabilizer was designed based on optimal pole shifting controller. {yields} The system performances was tested through load disturbances at different operating conditions. {yields} The system performance with the proposed optimal pole shifting controller is compared with the conventional pole placement controller. {yields} The digital simulation results indicated that the proposed controller has a superior performance. -- Abstract: Power system stabilizer based on optimal pole shifting is proposed. An approach for shifting the real parts of the open-loop poles to any desired positions while preserving the imaginary parts is presented. In each step of this approach, it is required to solve a first-order or a second-order linear matrix Lyapunov equation for ...
Research highlights: ? Mathematical model represents a power system which consists of synchronous machine connected to infinite bus through transmission line. ? Power system stabilizer was designed based on optimal pole shifting controller. ? The system performances was tested through load disturbances at different operating conditions. ? The system performance with the proposed optimal pole shifting controller is compared with the conventional pole placement controller. ? The digital simulation results indicated that the proposed controller has a superior performance. -- Abstract: Power system stabilizer based on optimal pole shifting is proposed. An approach for shifting the real parts of the open-loop poles to any desired positions while preserving the imaginary parts is presented. In each step of this approach, it is required to solve a first-order or a second-order linear matrix Lyapunov equation for shifting one real pole or two complex ...
The quaternionic formalism for subluminal field equations (Maxwell's equations) and its interrelationship with complex superluminal Lorentz transformations have been given and it has been shown that the quaternionic forms of relativistic equations describe tachyons.
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...
1 - Description of program or function: T-HEMP3D (Transportable HEMP3D) is a derivative of the STEALTH three-dimensional thermodynamics code developed by Science Applications, Inc. Changes were made primarily in three areas: material specification, coordinate generation, and the addition of sliding surface boundary conditions. STEALTH itself is based entirely on the HEMP3D code written at LLNL. HEMP3D solves problems in solid mechanics involving dynamic plasticity and time-dependent material behavior and problems in gas dynamics. 2 - Method of solution: The equations of motion, conservation equations, and constitutive relations for stresses, strains, hydrostatic pressure, the von Mises yield condition, and artificial viscosity are solved by finite difference methods following the format of the HEMP code (NESC Abstract 775). The physical object is divided into zones defined by 8 grid points. The grid (i,j,k) moves with the ...
A one-dimensional tachyon Klein-Gordon equation is reduced to a nonrelativistic-tachyon equation of motion. The interpretation of this reduced equation leads to the following conclusions: 1) tachyons can be localized in time instead of in space as compared with bradyons, 2) space representation and momentum representation of bradyonic quantum equation of motion are replaced by time representation and energy representation in tachyon quantum equation of motion and 3) with the aid of these results, it has been found that the solutions of the tachyon Klein-Gordon equation of motion form a complete set. (author).
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.
We obtain the radial Dirac equations for the Plebanski metric and transform these equations into one-dimensional wave equations. Finally we conclude with the result that the electron and the neutrino fields are not superradiant.
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.
We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations.
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 ...
The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.
A general theorem on the GBDT version of the B\\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and inverse problems for Dirac-type systems, including systems with singularities, and for the system auxiliary to the $N$-wave equation are reviewed. New results on explicit construction of the wave functions for radial Dirac equation are obtained.
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.
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)
A method for transforming the Euler and Navier-Stokes equations and a complete system of fluid dynamics equations in three dimensions to a closed system on any moving surface is proposed. As a result, for an arbitrary geometric configuration, the dimension of the equations is reduced by one, which makes them convenient for numerical simulation. The general principles of the method are described, and verifying examples are presented.
The time-dependent probability distribution of neutrons, precursors and detectrons in a space-independent, low-power, multiplying assembly with a source is developed in the multigroup approximation as forward and backward Kolmogorov equations. The relationship between these as adjoint equations is made explicit in a tensor notation and the equations developed in the generating-function formalism. (author).
This book contains the abstracts of all the presentations made either in oral or poster form, at the VII International Symposium on Photosynthetic Prokaryotes.
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 ...
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.
The top quark antiquark production system in the dilepton decay channel is described by a set of equations which is nonlinear in the unknown neutrino momenta. Its most precise and least time consuming solution is of major importance for measurements of top quark properties like the top quark mass and tt spin correlations. The initial system of equations can be transformed into two polynomial equations with two unknowns by means of elementary algebraic operations. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation is solved analytically.
Research highlights: ? We model power oscillations in boiling water reactors using a lumped parameter model. ? The nature and amplitudes of oscillations is obtained using a nonlinear analysis. ? The method of multiple scales has been used for the analytical treatment. ? Fuel temperature coefficient of reactivity determines the nature of oscillations. ? The presented systematic method of analysis useful for reduced order reactor models. - Abstract: In this paper, we perform a parametric study of the nonlinear dynamics of a reduced order model for boiling water reactors (BWR) near the Hopf bifurcation point using the method of multiple scales (MMS). Analysis has been performed for general values of the parameters, but the results are demonstrated for parameter values of the model corresponding to the advanced heavy water reactor (AHWR). The neutronics of the AHWR is modeled using point reactor kinetic equations while a one-node lumped parameter ...
This progress report consists of an article, the abstract of which follows, and apparently the references and vita from a proposal. A review of perturbation diagnostics applied to microwave resonant cavity discharges is presented. The classical microwave perturbation technique examines the shift in the resonant frequency and cavity quality factor of the resonant cavity caused by low electron density discharges. However, modifications presented here allow the analysis to be applied to discharges with electron densities beyond the limit predicted by perturbation theory. An {open_quote}exact{close_quote} perturbation analysis is presented which models the discharge as a separate dielectric, thereby removing the restrictions on electron density imposed by the classical technique. The {open_quote}exact{close_quote} method also uses measurements of the shifts in the resonant conditions of the cavity. Thirdly, an electromagnetic analysis is presented which uses a ...
Biosorption is presented as an alternative choice to traditional physicochemical means for removing toxic metals from groundwater and wastewaters. Removal of lead (Pb) from solutions was studied using Escherichia coli (parental) and Vitreoscilla hemoglobin (VHb)-expressing E. coli (transformed) cells. Pb biosorption was increased in bacterial hemoglobin-expressing E. coli cells grown in Luria broth B containing different concentrations of Pb{sup 2+}. The maximum Pb{sup 2+} biosorption of transformed and parental cells was determined to be 612 and 370 {mu}g Pb/g biomass, respectively. The inhibitory effect of Pb{sup 2+} on the parental strain was determined at 10 ppm. However, in transformed cells, Pb{sup 2+} was lethal at 100 ppm. The optimum aeration required for the transformed cells was lower than that for the parental strain on a growth yield basis. A linear correlation was established between the biosorption and uptake amounts. The biosorption process was analyzed using ...
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 ...
The interfacial area transport equation dynamically models two-phase flow regime transitions and predicts continuous changes of the interfacial area concentration along the flow field. It replaces the flow regime-dependent correlations for the interfacial area concentration in thermal-hydraulic system analysis. In the present study, detailed formulation of the interfacial area transport equation is presented along with its evaluation results based on the detailed benchmark experiments. In view of model evaluation, the equation is simplified into one-dimensional steady state one-group interfacial area transport equation. The prediction made by model agrees well with the experimental data obtained in round pipes of various diameters. The framework for the two-group transport equation and the necessary constitutive relations are also presented in view of bubble transport of various ...
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 ...
An analysis is made of the manner in which the process of primordial black-hole formation and the subsequent accretion of gas depend on the equation of state. On the assumption that the process is spherically symmetric, the problem is solved numerically.
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 ...
The static thermodynamic 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 15%LiF-58%NaF-27%BeF_2, over the temperature range of 873.15K to 1073.15K at one atmosphere pressure, is described using Peng-Robinson equation modified by us. And 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 thermodynamic properties such as the enthalpy, entropy and heat capacity at constant pressure are estimated by the residual function method and the fugacity coefficient method respectively. The density calculated by Peng-Robinson equation is in highly agreement with the experimental data, and the enthalpy, ...
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 ...
We extend Winger's work on the wave equations for integer-spin particles to the spinorial case. A recent suggestion that the neutrino might be a fermionic tachyon is examined. We point out that a four-component Dirac equation cannot describe fermionic tachyon. (orig.).
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.
Allometric equations are often used to extrapolate traits in animals for which only body mass estimates are known, such as dinosaurs. One important decision can be whether these equations should be...Full Text Available
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
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.
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.
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.
the progressive simplification of composite sandwich panels. The equations ... The thermal and structural behavior of composite sandwich panels with a ...
In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric $\\delta (r-r_{0})$-potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of $r_{0}$ can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem.
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.
Sandia National Laboratories maintains several libraries of equation of state tables, in a modified Sesame format, for use in hydrocode calculations and other applications. This report discusses one of those libraries, the seslan file, which contains 78 tables from the Los Alamos equation of state library. Minor changes have been made to these tables, making them more convenient for code users and reducing numerical difficulties that occasionally arise in hydrocode calculations.
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.
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
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.
The aim of this paper is to illustrate the validity and efficiency of iterative methods for solving large linear systems arising from the finite element discretization of the equation governing conduction-controlled solidification processes. Starting from the basic enthalpy equation, two alternative formulations are obtained and fixed-grid finite element discretizations are developed. These discretizations yield a set of nonlinear equations that are linearized using the Newton-Raphson scheme. The linearized equations are used as a basis for evaluating different iterative methods of the conjugated gradient type. Symmetric scaling and incomplete factorization preconditioning of the linear equations are used to improve the convergence properties of the iterative methods. Vectorization and parallelization are also employed to make full use of the CRAY-2 supercomputer. The results ...
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.).
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.).
The molten salt reactor (MSR), which is one of the generation IV reactors, can meet the demand of transmutation and breeding. The thermodynamic properties of the molten salt system like LiF-NaF-BeF2 influence the design and construction of the fuel salt and coolant in the MSR for the new generation. In this paper, the equation of state of the ternary system 15%LiF-58%NaF-27%BeF2, over the temperature range from 873.15 to 1 073.15 K at one atmosphere pressure, is described using a modified Peng-Robinson (PR) equation. The densities of the ternary system and its components are estimated by this equation directly, and compared with the experimental data. Based on the equation of state, the other thermodynamic properties such as the enthalpy, entropy and heat capacity at constant pressure are ...
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 ...
Separate abstracts were prepared for 60 papers in this volume of conference proceedings. None other papers in the proceedings were previously abstracted for EDB. Also included in the proceedings but not indexed separately are six workshop summaries and a session introduction. (LEW)
The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...
The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...
Biomass Abstracts - Cumulative Indexes is an annual publication prepared by the Information Technology Group of the Institute for Industrial Research and Standards. This book indexes compiled biomass publications by corporate author, author and subject. (DT)
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 ...
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 ...
Real-time mission-oriented embedded systems are much more difficult to design than ordinary software systems. They require highly reliable and efficient implementations to satisfy mission and time constraints imposed by the applications. The Ada language was designed to facilitate real-time-system software development. However, for many programmers the size and complexity of Ada itself are of concern. In the assertive programming paradigm, computations are specified as sets of assertions about properties of the solution, and not as a sequence of procedural steps. Solving procedures are automatically generated from the assertive description. Real-time programming for mission-oriented systems is supported by equational languages in which assertions are expressed as algebraic equations. Programs written in equational languages are concise, free from implementation details, and easily amenable to verification and parallel ...
Abstract: HARVEST was designed as a strategic research and planning tool, allowing assessment of the spatial pattern consequences of broad timber management ...
... Title : Refining the Magnetic Forming Capability. ... Abstract : The purpose of this project was to refine the in-house magnetic forming capability. ...