Algebraic resolution of the Burgers equation with a forcing term
Indian Academy of Sciences (India)
2017-04-07
Apr 7, 2017 ... stochastic processes, dispersive water waves, gas dyna- mics, heat conduction ... as the adhesion model [14], vehicular traffic [13], the study of directed polymers in ... ing to note that Burgers equation also appears naturally.
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
International Nuclear Information System (INIS)
Hoang, Viet Ha
2012-01-01
This paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes’ formula and the well posedness of the posterior measure are studied. The abstract theory is then applied to Burgers and Hamilton–Jacobi equations on a semi-infinite time interval with forcing functions which are white noise in time. Inference is made on the white noise forcing, assuming the Wiener measure as the prior. (paper)
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.
A systematic literature review of Burgers' equation with recent ...
Indian Academy of Sciences (India)
A systematic literature review of Burgers' equation with recent advances ... Research Article Volume 90 Issue 6 June 2018 Article ID 69 ... Burgers' equation is well documented in the literature, a detailed literature survey indicates that gaps still ...
Classification and Recursion Operators of Dark Burgers' Equation
Chen, Mei-Dan; Li, Biao
2018-01-01
With the help of symbolic computation, two types of complete scalar classification for dark Burgers' equations are derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark Burgers' systems; so some special equations including symmetry equation and dual symmetry equation are obtained by selecting the free parameter. Furthermore, two kinds of recursion operators for these dark Burgers' equations are constructed by two direct assumption methods.
Exact solitary waves of the Korteveg - de Vries - Burgers equation
Kudryashov, N. A.
2004-01-01
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor ... It is to observe the layer behavior of the solution for smaller values of ε leading to singular ...... Burger equation, momentum gas equation and heat equation.
A systematic literature review of Burgers' equation with recent advances
Bonkile, Mayur P.; Awasthi, Ashish; Lakshmi, C.; Mukundan, Vijitha; Aswin, V. S.
2018-06-01
Even if numerical simulation of the Burgers' equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers' equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective-diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers' equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers' equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers' equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers' equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.
A discrete model of a modified Burgers' partial differential equation
Mickens, R. E.; Shoosmith, J. N.
1990-01-01
A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.
Numerical solution of the one-dimensional Burgers' equation ...
Indian Academy of Sciences (India)
Burgers' equation; exponential finite difference method; implicit exponential finite difference method ... prescribed functions of the variables. Pramana – J. ... explicit exponential finite difference method was originally developed by Bhattacharya.
Analytical Approach to Space- and Time-Fractional Burgers Equations
International Nuclear Information System (INIS)
Yıldırım, Ahmet; Mohyud-Din, Syed Tauseef
2010-01-01
A scheme is developed to study numerical solution of the space- and time-fractional Burgers equations under initial conditions by the homotopy analysis method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed
Level crossing analysis of Burgers equation in 1 + 1 dimensions
International Nuclear Information System (INIS)
Movahed, M Sadegh; Bahraminasab, A; Rezazadeh, H; Masoudi, A A
2006-01-01
We investigate the average frequency of positive slope ν + α , crossing the velocity field u(x) - u-bar = α in the Burgers equation. The level crossing analysis in the inviscid limit and the total number of positive crossings of the velocity field before the creation of singularities are given. The main goal of this paper is to show that this quantity, ν + α , is a good measure for the fluctuations of velocity fields in the Burgers turbulence
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...
On a stochastic Burgers equation with Dirichlet boundary conditions
Directory of Open Access Journals (Sweden)
Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Convergence of a random walk method for the Burgers equation
International Nuclear Information System (INIS)
Roberts, S.
1985-10-01
In this paper we consider a random walk algorithm for the solution of Burgers' equation. The algorithm uses the method of fractional steps. The non-linear advection term of the equation is solved by advecting ''fluid'' particles in a velocity field induced by the particles. The diffusion term of the equation is approximated by adding an appropriate random perturbation to the positions of the particles. Though the algorithm is inefficient as a method for solving Burgers' equation, it does model a similar method, the random vortex method, which has been used extensively to solve the incompressible Navier-Stokes equations. The purpose of this paper is to demonstrate the strong convergence of our random walk method and so provide a model for the proof of convergence for more complex random walk algorithms; for instance, the random vortex method without boundaries
Cole's ansatz and extensions of Burgers' equation
International Nuclear Information System (INIS)
Tasso, H.
1976-01-01
A sequence of nonlinear partial differential equations is constructed. It contains all equation whose solutions can be obtained from applying the Cole-Hopf transformation to linear partial differential equations. An exemple is usub(t) = (u 3 )sub(x) + 3/2(u 2 )sub(xx) + usub(xxx). (orig.) [de
A lattice Boltzmann model for the Burgers-Fisher equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.
Solution of the Burgers Equation in the Time Domain
Directory of Open Access Journals (Sweden)
M. Bednařík
2002-01-01
Full Text Available This paper deals with a theoretical description of the propagation of a finite amplitude acoustic waves. The theory based on the homogeneous Burgers equation of the second order of accuracy is presented here. This equation takes into account both nonlinear effects and dissipation. The method for solving this equation, using the well-known Cole-Hopf transformation, is presented. Two methods for numerical solution of these equations in the time domain are presented. The first is based on the simple Simpson method, which is suitable for smaller Goldberg numbers. The second uses the more advanced saddle point method, and is appropriate for large Goldberg numbers.
Distributed Approximating Functional Approach to Burgers' Equation ...
African Journals Online (AJOL)
This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. In addition, the presented scheme has numerically stable behavior. After demonstrating the convergence and accuracy of the ...
Koopman decomposition of Burgers' equation: What can we learn?
Page, Jacob; Kerswell, Rich
2017-11-01
Burgers' equation is a well known 1D model of the Navier-Stokes equations and admits a selection of equilibria and travelling wave solutions. A series of Burgers' trajectories are examined with Dynamic Mode Decomposition (DMD) to probe the capability of the method to extract coherent structures from ``run-down'' simulations. The performance of the method depends critically on the choice of observable. We use the Cole-Hopf transformation to derive an observable which has linear, autonomous dynamics and for which the DMD modes overlap exactly with Koopman modes. This observable can accurately predict the flow evolution beyond the time window of the data used in the DMD, and in that sense outperforms other observables motivated by the nonlinearity in the governing equation. The linearizing observable also allows us to make informed decisions about often ambiguous choices in nonlinear problems, such as rank truncation and snapshot spacing. A number of rules of thumb for connecting DMD with the Koopman operator for nonlinear PDEs are distilled from the results. Related problems in low Reynolds number fluid turbulence are also discussed.
Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation
Directory of Open Access Journals (Sweden)
Hongwei Yang
2012-01-01
Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.
HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation
Directory of Open Access Journals (Sweden)
Shu-Li Mei
2013-01-01
Full Text Available Based on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a nonlinear matrix ordinary differential equation. In order to obtain the analytical solution of the system of ODEs, the homotopy analysis method (HAM proposed by Shijun Liao was developed to solve the system of ODEs by combining the precise integration method (PIM which can be employed to get the analytical solution of linear system of ODEs. The numerical experiences show that HAM is not sensitive to the time step, and so the arithmetic error is mainly derived from the discrete in physical space.
Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation
International Nuclear Information System (INIS)
Deng Xijun; Han Libo; Li Xi
2009-01-01
In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)
Hyperbolic white noise functional solutions of Wick-type stochastic compound KdV-Burgers equations
International Nuclear Information System (INIS)
Han Xiu; Xie Yingchao
2009-01-01
Variable coefficient and Wick-type stochastic compound KdV-Burgers equations are investigated. By using white noise analysis, Hermite transform and the hyperbolic function method, we obtain a number of Wick versions of hyperbolic white noise functional solutions and hyperbolic function solutions for Wick-type stochastic and variable coefficient compound KdV-Burgers equations, respectively.
Directory of Open Access Journals (Sweden)
Imtiaz Wasim
2018-01-01
Full Text Available In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.
On numerical solution of Burgers' equation by homotopy analysis method
International Nuclear Information System (INIS)
Inc, Mustafa
2008-01-01
In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions
Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus
2014-01-01
Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.
Non-perturbative analytical solutions of the space- and time-fractional Burgers equations
International Nuclear Information System (INIS)
Momani, Shaher
2006-01-01
Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0 < α, β ≤ 1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed
International Nuclear Information System (INIS)
Wang Qi; Chen Yong; Zhang Hongqing
2005-01-01
In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation
A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
Sudao, Bilige; Wang, Xiaomin
2015-01-01
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation
International Nuclear Information System (INIS)
Wu Guocheng
2011-01-01
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
International Nuclear Information System (INIS)
Chen Huaitang; Zhang Hongqing
2004-01-01
A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation
Zhu, C
2003-01-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
International Nuclear Information System (INIS)
Zhu, Changjiang; Duan, Renjun
2003-01-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation
New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method
Directory of Open Access Journals (Sweden)
L.K. Ravi
2017-03-01
Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.
On "new travelling wave solutions" of the KdV and the KdV-Burgers equations
Kudryashov, Nikolai A.
The Korteweg-de Vries and the Korteweg-de Vries-Burgers equations are considered. Using the travelling wave the general solutions of these equations are presented. "New travelling wave solutions" of the KdV and the KdV-Burgers equations by Wazzan [Wazzan L Commun Nonlinear Sci Numer Simulat
New exact solutions of the KdV-Burgers-Kuramoto equation
International Nuclear Information System (INIS)
Zhang Sheng
2006-01-01
A generalized F-expansion method is proposed and applied to the KdV-Burgers-Kuramoto equation. As a result, many new and more general exact travelling wave solutions are obtained including combined non-degenerate Jacobi elliptic function solutions, solitary wave solutions and trigonometric function solutions. The method can be applied to other nonlinear partial differential equations in mathematical physics
EXPONENTIAL ERGODICITY FOR STOCHASTIC BURGERS AND 2D NAVIER-STOKES EQUATIONS
Goldys, B
2004-01-01
It is shown that transition measures of the stochastic Navier-Stokes equation in dimension 2 converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.
International Nuclear Information System (INIS)
Wang Baodong; Song Lina; Zhang Hongqing
2007-01-01
In this paper, we present a new elliptic equation rational expansion method to uniformly construct a series of exact solutions for nonlinear partial differential equations. As an application of the method, we choose the (2 + 1)-dimensional Burgers equation to illustrate the method and successfully obtain some new and more general solutions
Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
A regularization of the Burgers equation using a filtered convective velocity
International Nuclear Information System (INIS)
Norgard, Greg; Mohseni, Kamran
2008-01-01
This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations
Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations
Abdulwahhab, Muhammad Alim
2016-10-01
Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.
Adib, Arash; Poorveis, Davood; Mehraban, Farid
2018-03-01
In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.
International Nuclear Information System (INIS)
Zhang Liang; Zhang Lifeng; Li Chongyin
2008-01-01
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions
Davies, I M; Zhao, H
2004-01-01
We study the inviscid limit, $\\mu\\to 0$, of the stochastic viscous Burgers equation, for the velocity field $v^{\\mu}(x,t)$, $t>0$, $x\\in\\mathbb R^d$,\\frac{\\partial{v^{\\mu}}}{\\partial{t}} + (v^{\\mu}\\cdot\
A note on Burgers' equation with time delay: Instability via finite-time blow-up
International Nuclear Information System (INIS)
Jordan, P.M.
2008-01-01
Burgers' equation with time delay is considered. Using the Cole-Hopf transformation, the exact solution of this nonlinear partial differential equation (PDE) is determined in the context of a (seemingly) well-posed initial-boundary value problem (IBVP) involving homogeneous Dirichlet data. The solution obtained, however, is shown to exhibit a delay-induced instability, suffering blow-up in finite-time
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
International Nuclear Information System (INIS)
Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.
2007-01-01
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple
Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations
International Nuclear Information System (INIS)
Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.
2011-01-01
The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)
Exact solutions of Fisher and Burgers equations with finite transport memory
International Nuclear Information System (INIS)
Kar, Sandip; Banik, Suman Kumar; Ray, Deb Shankar
2003-01-01
The Fisher and Burgers equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect
Exact solutions of Fisher and Burgers equations with finite transport memory
Kar, S; Ray, D S
2003-01-01
The Fisher and Burgers equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect.
International Nuclear Information System (INIS)
Ma Hongcai; Ge Dongjie; Yu Yaodong
2008-01-01
Based on the Bäcklund method and the multilinear variable separation approach (MLVSA), this paper nds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+1)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution). (general)
A systematic literature review of Burgers' equation with recent ...
Indian Academy of Sciences (India)
Mayur P Bonkile
2018-04-30
Apr 30, 2018 ... are prescribed functions of variables depending upon the specific conditions for ...... A semi-implicit finite-difference method was used to find the numerical ... ordinary differential equation solver to classical explicit and implicit ...
Darboux transformations for the time-dependent nonhomogeneous Burgers equation in (1+1) dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Manuel Carballo Jimenez, Juan
2009-01-01
We extend the formalism of nth order Darboux transformations to the time-dependent nonhomogeneous Burgers equation (NBE) in (1+1) dimensions. Similar to the Schroedinger case, our Darboux transformation retains the form of the NBE, while changing the nonhomogeneous term. The transformed solution of the NBE and the corresponding transformed nonhomogeneity are given in closed form. Furthermore, properties of the transformation are discussed and an application is given.
A Marker Method for the Solution of the Damped Burgers' Equation
International Nuclear Information System (INIS)
Jerome L.V. Lewandowski
2005-01-01
A new method for the solution of the damped Burgers equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations
Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers
Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru
2018-06-01
The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.
Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity
International Nuclear Information System (INIS)
Yepez, Jeffrey
2006-01-01
Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory
On the Boussinesq-Burgers equations driven by dynamic boundary conditions
Zhu, Neng; Liu, Zhengrong; Zhao, Kun
2018-02-01
We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2015-01-01
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Numerical analysis of the Burgers' equation in the presence of uncertainty
International Nuclear Information System (INIS)
Pettersson, Per; Iaccarino, Gianluca; Nordstroem, Jan
2009-01-01
The Burgers' equation with uncertain initial and boundary conditions is investigated using a polynomial chaos (PC) expansion approach where the solution is represented as a truncated series of stochastic, orthogonal polynomials. The analysis of well-posedness for the system resulting after Galerkin projection is presented and follows the pattern of the corresponding deterministic Burgers equation. The numerical discretization is based on spatial derivative operators satisfying the summation by parts property and weak boundary conditions to ensure stability. Similarly to the deterministic case, the explicit time step for the hyperbolic stochastic problem is proportional to the inverse of the largest eigenvalue of the system matrix. The time step naturally decreases compared to the deterministic case since the spectral radius of the continuous problem grows with the number of polynomial chaos coefficients. An estimate of the eigenvalues is provided. A characteristic analysis of the truncated PC system is presented and gives a qualitative description of the development of the system over time for different initial and boundary conditions. It is shown that a precise statistical characterization of the input uncertainty is required and partial information, e.g. the expected values and the variance, are not sufficient to obtain a solution. An analytical solution is derived and the coefficients of the infinite PC expansion are shown to be smooth, while the corresponding coefficients of the truncated expansion are discontinuous.
The KdV—Burgers equation in a modified speed gradient continuum model
International Nuclear Information System (INIS)
Lai Ling-Ling; Ge Hong-Xia; Cheng Rong-Jun; Li Zhi-Peng
2013-01-01
Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micro-macro linkage (Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull. 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405). In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries—Burgers (KdV—Burgers) equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis
International Nuclear Information System (INIS)
Zhang Weiguo; Dong Chunyan; Fan Engui
2006-01-01
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.
International Nuclear Information System (INIS)
Kraenkel, R.A.; Pereira, J.G.; Manna, M.A.
1991-01-01
The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)
Existence of solutions to Burgers equations in domains that can be transformed into rectangles
Directory of Open Access Journals (Sweden)
Yassine Benia
2016-06-01
Full Text Available This work is concerned with Burgers equation $\\partial _{t}u+u\\partial_x u-\\partial _x^2u=f$ (with Dirichlet boundary conditions in the non rectangular domain $\\Omega =\\{(t,x\\in R^2;\\ 0
International Nuclear Information System (INIS)
Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing
2009-01-01
In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.
Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2016-03-01
Full Text Available Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.
Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations
Emad A.-B. Abdel-Salam; Gamal F. Hassan
2016-01-01
Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.
International Nuclear Information System (INIS)
Neate, A D; Truman, A
2005-01-01
The inviscid limit of the Burgers equation, with body forces white noise in time, is discussed in terms of the level surfaces of the minimizing Hamilton-Jacobi function and the classical mechanical caustic and their algebraic pre-images under the classical mechanical flow map. The problem is analysed in terms of a reduced (one-dimensional) action function using a circle of ideas due to Arnol'd, Cayley and Klein. We characterize those parts of the caustic which are singular, and give an explicit expression for the cusp density on caustics and level surfaces. By considering the double points of level surfaces we find an explicit formula for the Maxwell set in the two-dimensional polynomial case, and we extend this to higher dimensions using a double discriminant of the reduced action, solving a long-standing problem for Hamiltonian dynamical systems. When the pre-level surface touches the pre-caustic, the geometry (number of cusps) on the level surface changes infinitely rapidly causing 'real turbulence'. Using an idea of Klein, it is shown that the geometry (number of swallowtails) on the caustic also changes infinitely rapidly when the real part of the pre-caustic touches its complex counterpart, causing 'complex turbulence'. These are both inherently stochastic in nature, and we determine their intermittence in terms of the recurrent behaviour of two processes
Waqas, M.; Hayat, T.; Shehzad, S. A.; Alsaedi, A.
2018-03-01
A mathematical model is formulated to characterize the non-Fourier and Fick's double diffusive models of heat and mass in moving flow of modified Burger's liquid. Temperature-dependent conductivity of liquid is taken into account. The concept of stratification is utilized to govern the equations of energy and mass species. The idea of boundary layer theory is employed to obtain the mathematical model of considered physical problem. The obtained partial differential system is converted into ordinary ones with the help of relevant variables. The homotopic concept lead to the convergent solutions of governing expressions. Convergence is attained and acceptable values are certified by expressing the so called ℏ -curves and numerical benchmark. Several graphs are made for different values of physical constraints to explore the mechanism of heat and mass transportation. We explored that the liquid temperature and concentration are retard for the larger thermal/concentration relaxation time constraint.
Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method
Directory of Open Access Journals (Sweden)
Muhammad Shakeel
2014-01-01
Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.
International Nuclear Information System (INIS)
Estevez, P G; Kuru, S; Negro, J; Nieto, L M
2006-01-01
The travelling wave solutions of the two-dimensional Korteweg-de Vries-Burgers and Kadomtsev-Petviashvili equations are studied from two complementary points of view. The first one is an adaptation of the factorization technique that provides particular as well as general solutions. The second one applies the Painleve analysis to both equations, throwing light on some aspects of the first method and giving an explanation to some restriction on the coefficients, as well as the relation between factorizations and integrals of motion
MODELLING SOLUTIONS TO THE KdV-BURGERS EQUATION IN THE CASE OF NONHOMOGENEOUS DISSIPATIVE MEDIA
Directory of Open Access Journals (Sweden)
V. Samokhin Alexey
2017-01-01
Full Text Available The behavior of the soliton type solutions to the KdV-Burgers equation is studied numerically in the case of non- homogeneous dissipative media. A soliton moves from left to right and it does not change its form. The solitons with great- er amplitude are narrower and move faster. The aim of the presented research is to study the behavior of the soliton that, while moving in nondissipative medium encounters a barrier (finite or infinite with finite constant dissipation; one may imagine an impulse of light meeting on its way a partially absorbing layer. The modelling included the case of a finite dis- sipative layer similar to a wave passing through the air-glass-air as well as a wave passing from a nondissipative layer into a dissipative one (similar to the passage of light from air to water. The present paper is a continuation of the authors’ pub- lications. New results include a numerical model of the wave’s behavior for different types of the media non-homogeneity. The dissipation predictably results in reducing the soliton’s amplitude, but some new effects occur in the case of finite piecewise constant barrier on the soliton path: after the wave leaves the dissipative barrier it retains, on the whole, a soliton form yet some small and rapidly decreasing oscillations arises in front of the soliton. These oscillations are getting larger and spread as the soliton is moving of the barrier; the distance between the soliton and the oscillation grows. That is, the oscillations are faster than the soliton. The modelling used the Maple software PDETools packet; these activities were time and resources consuming.
International Nuclear Information System (INIS)
Feng Zhaosheng
2003-01-01
In this paper, we study the two-dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analysing an equivalent two-dimensional autonomous system, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded travelling wave solution. Then by using a direct method, a travelling solitary wave solution to the 2D-BKdV equation is expressed explicitly, which appears to be more efficient than the existing methods proposed in the literature. At the end of the paper, the asymptotic behaviour of the proper solutions of the 2D-BKdV equation is established by applying the qualitative theory of differential equations
Directory of Open Access Journals (Sweden)
Suheel Abdullah Malik
Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul
2015-01-01
In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.
Directory of Open Access Journals (Sweden)
Sunday O. Edeki
2018-03-01
Full Text Available In this study, approximate solutions of a system of time-fractional coupled Burger equations were obtained by means of a local fractional operator (LFO in the sense of the Caputo derivative. The LFO technique was built on the basis of the standard differential transform method (DTM. Illustrative examples used in demonstrating the effectiveness and robustness of the proposed method show that the solution method is very efficient and reliable as – unlike the variational iteration method – it does not depend on any process of identifying Lagrange multipliers, even while still maintaining accuracy.
Hashimoto, Itsuko
2016-01-01
We investigate the large-time behavior of the radially symmetric solution for Burgers equation on the exterior of a small ball in multi-dimensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to $0$ or negative, the asymptotic stability is the same as that for the viscous conservation law. In the present paper, it is proved that if the boundary data i...
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
The generalized (G′/G)-expansion method; Burgers equation; Fisher's equation; ... the travelling wave solutions plays an important role in nonlinear sciences. ... Burgers, Fisher, Huxley equations and combined forms of these equations will ...
The forced nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain
Directory of Open Access Journals (Sweden)
Masood Khan
Full Text Available The present paper reports a theoretical study of the dynamics of an electroosmotic flow (EOF in cylindrical domain. The Cauchy momentum equation is first simplified by incorporating the electrostatic body force in the electric double layer and the generalized Burgers fluid constitutive model. The electric potential distribution is given by the linearized Poisson–Boltzmann equation. After solving the linearized Poisson–Boltzmann equation, the Cauchy momentum equation with electrostatic body force is solved analytically by using the temporal Fourier and finite Hankel transforms. The effects of important involved parameters are examined and presented graphically. The results obtained reveal that the magnitude of velocity increases with increase of the Debye–Huckel and electrokinetic parameters. Further, it is shown that the results presented for generalized Burgers fluid are quite general so that results for the Burgers, Oldroyd-B, Maxwell and Newtonian fluids can be obtained as limiting cases. Keywords: Generalized Burgers fluid, Electroosmotic flow, Fourier and Hankel transform
International Nuclear Information System (INIS)
Keanini, R.G.
2011-01-01
Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the
DEFF Research Database (Denmark)
Rytter, Mikkel
2016-01-01
Based on a number of ‘burger episodes’ during ten days of itikaf at a Sufi lodge in Pakistan, this article discusses the difficulties of religious self-cultivation among young Muslim pilgrims from Denmark. The focus on food and eating is not only used to discuss how religious brotherhoods and spi...... and spiritual kinship are created and maintained, but also becomes a prism to discuss emic conceptualizations of the nafs, the lower self, as well as how the jihad of dedicated Sufi Muslims is tested by fatal attractions of various kinds – in this case, in the guise of tasty burgers....
Energy Technology Data Exchange (ETDEWEB)
Ge, Hong-Xia [Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211 (China); Lai, Ling-Ling [Faculty of Science, Ningbo University, Ningbo 315211 (China); Zheng, Peng-Jun [Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211 (China); Cheng, Rong-Jun, E-mail: chengrongjun76@126.com [Ningbo Institute of Technology, Zhejiang University, Ningbo 315100 (China)
2013-12-13
A new continuum traffic flow model is proposed based on an improved car-following model, which takes the driver's forecast effect into consideration. The backward travel problem is overcome by our model and the neutral stability condition of the new model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves and the Korteweg–de Vries–Burgers (KdV–Burgers) equation is derived to describe the traffic flow near the neutral stability line. The corresponding solution for traffic density wave is also derived. Finally, the numerical results show that our model can not only reproduce the evolution of small perturbation, but also improve the stability of traffic flow.
International Nuclear Information System (INIS)
He, Y B; Tang, X H
2016-01-01
In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)
Exploring Capabilities within ForTrilinos by Solving the 3D Burgers Equation
Directory of Open Access Journals (Sweden)
Karla Morris
2012-01-01
Full Text Available We present the first three-dimensional, partial differential equation solver to be built atop the recently released, open-source ForTrilinos package (http://trilinos.sandia.gov/packages/fortrilinos. ForTrilinos currently provides portable, object-oriented Fortran 2003 interfaces to the C++ packages Epetra, AztecOO and Pliris in the Trilinos library and framework [ACM Trans. Math. Softw.31(3 (2005, 397–423]. Epetra provides distributed matrix and vector storage and basic linear algebra calculations. Pliris provides direct solvers for dense linear systems. AztecOO provides iterative sparse linear solvers. We demonstrate how to build a parallel application that encapsulates the Message Passing Interface (MPI without requiring the user to make direct calls to MPI except for startup and shutdown. The presented example demonstrates the level of effort required to set up a high-order, finite-difference solution on a Cartesian grid. The example employs an abstract data type (ADT calculus [Sci. Program.16(4 (2008, 329–339] that empowers programmers to write serial code that lower-level abstractions resolve into distributed-memory, parallel implementations. The ADT calculus uses compilable Fortran constructs that resemble the mathematical formulation of the partial differential equation of interest.
International Nuclear Information System (INIS)
Yan Zhenya
2002-01-01
In this paper, an auto-Baecklund transformation is presented for the generalized Burgers equation: u t +u xy + αuu y +αu x ∂ -1 x u y =0 (α is constant) by using an ansatz and symbolic computation. Particularly, this equation is transformed into a (1+2)-dimensional generalized heat equation ω t + ω xy =0 by the Cole-Hopf transformation. This shows that this equation is C-integrable. Abundant types of new soliton-like solutions are obtained by virtue of the obtained transformation. These solutions contain n-soliton-like solutions, shock wave solutions and singular soliton-like solutions, which may be of important significance in explaining some physical phenomena. The approach can also be extended to other types of nonlinear partial differential equations in mathematical physics
International Nuclear Information System (INIS)
Shah, Asif; Saeed, R
2011-01-01
The ion-acoustic shock waves are studied in electron-positron-ion plasma. The plasma system is composed of three components, specifically relativistic adiabatic ions, kappa distributed electrons and positrons. The Korteweg-de Vries-Burger equation is derived, solved analytically. The effects of plasma parameters on the shock strength and steepness are investigated. The numerical results are presented graphically for illustration. The results may have importance in non-thermal and relativistic plasmas of pulsar magnetosphere (Arons 2009 Astrophys. Space Sci. Library 357 373; Blasi and Amato arXiv:1007.4745V1 [astro-Ph.HE]).
OSCILLATION CRITERIA FOR FORCED SUPERLINEAR DIFFERENCE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using Riccati transformation techniques,some oscillation criteria for the forced second-order superlinear difference equations are established.These criteria are dis- crete analogues of the criteria for differential equations proposed by Yan.
Generalized Lorentz-Force equations
International Nuclear Information System (INIS)
Yamaleev, R.M.
2001-01-01
Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles
expansion method for the Burgers, Burgers–Huxley and modified
Indian Academy of Sciences (India)
expansion method; Burgers equation; Burgers–Huxley equation; modified. Burgers–KdV equation .... Substituting the solution set (12) and the corresponding solutions of (4) into (8), we have ..... During the past several years, many have done.
Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.
1978-01-01
Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
Generalized Cole–Hopf transformations for generalized Burgers ...
Indian Academy of Sciences (India)
2015-10-15
Oct 15, 2015 ... Cole–Hopf transformations; Burgers equation; invariance analysis. ... was to generate nonlinear parabolic equations from a linear parabolic equation via a ..... BMV acknowledges the financial support to attend the NMI Workshop ... [16] P J Olver, Applications of Lie Groups to differential equations, Graduate ...
Collapse in a forced three-dimensional nonlinear Schrodinger equation
DEFF Research Database (Denmark)
Lushnikov, P.M.; Saffman, M.
2000-01-01
We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation.......We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation....
Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space
International Nuclear Information System (INIS)
Rodriguez D, R.
2007-01-01
In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)
Forced oscillation of hyperbolic equations with mixed nonlinearities
Directory of Open Access Journals (Sweden)
Yutaka Shoukaku
2012-04-01
Full Text Available In this paper, we consider the mixed nonlinear hyperbolic equations with forcing term via Riccati inequality. Some sufficient conditions for the oscillation are derived by using Young inequality and integral averaging method.
Modelling equation of knee force during instep kicking using ...
African Journals Online (AJOL)
This paper presents the biomechanics analysis of the football players, to obtain the equation that relates with the variables and to get the force model equation when the kicking was made. The subjects delivered instep kicking by using the dominant's leg where one subjects using right and left leg. 2 Dimensional analysis ...
Generalized force in classical field theory. [Euler-Lagrange equations
Energy Technology Data Exchange (ETDEWEB)
Krause, J [Universidad Central de Venezuela, Caracas
1976-02-01
The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.
Randomly forced CGL equation stationary measures and the inviscid limit
Kuksin, S
2003-01-01
We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable~$x$. Assuming that $\\dim x\\le4$, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schr\\"odinger equation.
The Kadomtsev endash Petviashvili equation under rapid forcing
International Nuclear Information System (INIS)
Moroz, I.M.
1997-01-01
We consider the initial value problem for the forced Kadomtsev endash Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data. copyright 1997 American Institute of Physics
Solutions of Navier-Stokes Equation with Coriolis Force
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Sunggeun Lee
2017-01-01
Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.
Classical and Quantum Burgers Fluids: A Challenge for Group Analysis
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Philip Broadbridge
2015-10-01
Full Text Available The most general second order irrotational vector field evolution equation is constructed, that can be transformed to a single equation for the Cole–Hopf potential. The exact solution to the radial Burgers equation, with constant mass influx through a spherical supply surface, is constructed. The complex linear Schrödinger equation is equivalent to an integrable system of two coupled real vector equations of Burgers type. The first velocity field is the particle current divided by particle probability density. The second vector field gives a complex valued correction to the velocity that results in the correct quantum mechanical correction to the kinetic energy density of the Madelung fluid. It is proposed how to use symmetry analysis to systematically search for other constrained potential systems that generate a closed system of vector component evolution equations with constraints other than irrotationality.
Oscillation criteria for first-order forced nonlinear difference equations
Grace Said R; Agarwal Ravi P; Smith Tim
2006-01-01
Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 85; Issue 1. Solitary wave and periodic wave solutions for Burgers, Fisher, Huxley and combined forms of these equations by the (′/)-expansion method. Jalil Manafian Mehrdad Lakestani. Volume 85 Issue 1 July 2015 pp 31-52 ...
Michael, Manesh; Willington, Neethu T.; Jayakumar, Neethu; Sebastian, Sijo; Sreekala, G.; Venugopal, Chandu
2016-12-01
We investigate the existence of ion-acoustic shock waves in a five component cometary plasma consisting of positively and negatively charged oxygen ions, kappa described hydrogen ions, hot solar electrons, and slightly colder cometary electrons. The KdVB equation has been derived for the system, and its solution plotted for different kappa values, oxygen ion densities, as well as the temperature ratios for the ions. It is found that the amplitude of the shock wave decreases with increasing kappa values. The strength of the shock profile decreases with increasing temperatures of the positively charged oxygen ions and densities of negatively charged oxygen ions.
Force-free thin flux tubes: Basic equations and stability
International Nuclear Information System (INIS)
Zhugzhda, Y.D.
1996-01-01
The thin flux tube approximation is considered for a straight, symmetrical, force-free, rigidly rotating flux tube. The derived set of equations describes tube, body sausage, and Alfveacute charn wave modes and is valid for any values of Β. The linear waves and instabilities of force-free flux tubes are considered. The comparison of approximate and exact solutions for an untwisted, nonrotating flux tube is performed. It is shown that the approximate and exact dispersion equations coincides, except the 20% discrepancy of sausage frequencies. An effective cross section is proposed to introduce the removal of this discrepancy. It makes the derived approximation correct for the force-free thin flux tube dynamics, except the detailed structure of radial eigenfunction. The dispersion of Alfveacute charn torsional waves in a force-free tubes appears. The valve effect of one directional propagation of waves in rotating twisted tube is revealed. The current and rotational sausage instabilities of a force-free, thin flux tube are considered. copyright 1996 American Institute of Physics
Bifurcation of forced periodic oscillations for equations with Preisach hysteresis
International Nuclear Information System (INIS)
Krasnosel'skii, A; Rachinskii, D
2005-01-01
We study oscillations in resonant systems under periodic forcing. The systems depend on a scalar parameter and have the form of simple pendulum type equations with ferromagnetic friction represented by the Preisach hysteresis nonlinearity. If for some parameter value the period of free oscillations of the principal linear part of the system coincides with the period of the forcing term, then one may expect the existence of unbounded branches of periodic solutions for nearby parameter values. We present conditions for the existence and nonexistence of such branches and estimates of their number
DEFF Research Database (Denmark)
Rytter, Mikkel
2013-01-01
Based on a number of burger incidents during ten days of itikaf at a Sufi astana (lodge) in Pakistan, this article discusses religious self-cultivation among Muslim pilgrims from Denmark. The focus on food and eating is not only used to discuss how religious brotherhoods and spiritual kinship...
Mathematical modeling of fish burger baking using fractional calculus
Directory of Open Access Journals (Sweden)
Bainy Eduarda M.
2017-01-01
Full Text Available Tilapia (Oreochromis sp. is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.
PHYSICOCHEMICAL, MICROBIOLOGICAL QUALITY AND OXIDATIVE STABILITY IN SPICED LAMB MEAT BURGERS
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Almudena Cózar
2013-12-01
Full Text Available The effect of adding two powdered spices (rosemary and thyme on the pH, colour coordinates, Cooking yield (CY Cooking loss (CL, Diameter Reduction (DR, Shear Force (SF, microbiological levels and lipid oxidation (LO in two types of lamb burgers (L= leg meat; LNB= leg+neck+breast meat was assessed over a six day period. Both spices increased stability during the storage period, LO values being six times lower than those of the non-spiced control group at 6 days. L samples showed higher CY, lower CL and DR than LNB burgers, with significant differences at 6 d (P < 0.001. The length of storage only affected (P < 0.01 these parameters in L burgers. In general, SF was higher in LNB than in L burgers but did not vary with time. The colour coordinates showed lower values in L than in LNB samples. The formulation type affected TVC and Pseudomonas spp.
Mathematical modeling and exact solutions to rotating flows of a Burgers' fluid
International Nuclear Information System (INIS)
Hayat, T.
2005-12-01
The aim of this study is to provide the modeling and exact analytic solutions for hydromagnetic oscillatory rotating flows of an incompressible Burgers' fluid bounded by a plate. The governing time-dependent equation for the Burgers' fluid is different than those from the Navier-Stokes' equation. The entire system is assumed to rotate around an axis normal to the plate. The governing equations for this investigation are solved analytically for two physical problems. The solutions for the three cases, when the two times angular velocity is greater than the frequency of oscillation or it is smaller than the frequency or it is equal to the frequency (resonant case), are discussed in second problem. In Burgers' fluid, it is also found that hydromagnetic solution in the resonant case satisfies the boundary condition at infinity. Moreover, the obtained analytical results reduce to several previously published results as the special cases. (author)
Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra
2016-01-01
In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.
Bainy, Eduarda Molardi; Bertan, Larissa Canhadas; Corazza, Marcos Lucio; Lenzi, Marcelo Kaminski
2015-08-01
The influence of two common cooking methods, grilling and baking, on chemical composition, water retention, fat retention, cooking yield, diameter reduction, expressible water, color and mechanical texture of tilapia (Oreochromis niloticus) fish burgers was investigated. Texture analyses were performed using a Warner-Bratzler test. The fish burger had a softer texture with a lower shear force than other meat products reported in the literature. There were no significant differences in proximate composition, diameter reduction, fat retention and expressible water between the grilled and oven-baked fish burgers. Cooking methods did not affect the cooking times and cooking rates. Warner-Bratzler parameters and color were significantly influenced by the cooking method. Grilling contributed to a shear force and work of shearing increase due to the lower cooking yield and water retention. Raw burgers had the highest L* (69.13 ± 0.96) and lowest b* (17.50 ± 0.75) values. Results indicated that baking yielded a product with better cooking characteristics, such as a desired softer texture with lower shear values (4.01 ± 0.54) and increased water retention (95.82 ± 0.77). Additionally, the baked fish burgers were lighter (higher L*) and less red (lower a*) than the grilled ones.
Asymptotic behavior of solutions of forced fractional differential equations
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Said Grace
2016-09-01
where $y(t=\\left( a(tx^{\\prime }(t\\right ^{\\prime }$, $c_{0}=\\frac{y(c}{\\Gamma (1}=y(c$, and $c_{0}$ is a real constant. The technique used in obtaining their results will apply to related fractional differential equations with Caputo derivatives of any order. Examples illustrate the results obtained in this paper.
Directory of Open Access Journals (Sweden)
Luning Shi
2014-01-01
Full Text Available A prestress force identification method for externally prestressed concrete uniform beam based on the frequency equation and the measured frequencies is developed. For the purpose of the prestress force identification accuracy, we first look for the appropriate method to solve the free vibration equation of externally prestressed concrete beam and then combine the measured frequencies with frequency equation to identify the prestress force. To obtain the exact solution of the free vibration equation of multispan externally prestressed concrete beam, an analytical model of externally prestressed concrete beam is set up based on the Bernoulli-Euler beam theory and the function relation between prestress variation and vibration displacement is built. The multispan externally prestressed concrete beam is taken as the multiple single-span beams which must meet the bending moment and rotation angle boundary conditions, the free vibration equation is solved using sublevel simultaneous method and the semi-analytical solution of the free vibration equation which considered the influence of prestress on section rigidity and beam length is obtained. Taking simply supported concrete beam and two-span concrete beam with external tendons as examples, frequency function curves are obtained with the measured frequencies into it and the prestress force can be identified using the abscissa of the crosspoint of frequency functions. Identification value of the prestress force is in good agreement with the test results. The method can accurately identify prestress force of externally prestressed concrete beam and trace the trend of effective prestress force.
Directory of Open Access Journals (Sweden)
Waqar Azeem Khan
Full Text Available The present paper deals with the analysis of melting heat and mass transfer characteristics in the stagnation point flow of an incompressible generalized Burgers fluid over a stretching sheet in the presence of non-linear radiative heat flux. A uniform magnetic field is applied normal to the flow direction. The governing equations in dimensional form are reduced to a system of dimensionless expressions by implementation of suitable similarity transformations. The resulting dimensionless problem governing the generalized Burgers is solved analytically by using the homotopy analysis method (HAM. The effects of different flow parameters like the ratio parameter, magnetic parameter, Prandtl number, melting parameter, radiation parameter, temperature ratio parameter and Schmidt number on the velocity, heat and mass transfer characteristics are computed and presented graphically. Moreover, useful discussions in detail are carried out with the help of plotted graphs and tables. Keywords: Generalized Burgers fluid, Non-linear radiative flow, Magnetic field, Melting heat transfer
Moyal noncommutative integrability and the Burgers-KdV mapping
International Nuclear Information System (INIS)
Sedra, M.B.
2005-12-01
The Moyal momentum algebra, is once again used to discuss some important aspects of NC integrable models and 2d conformal field theories. Among the results presented, we set up algebraic structures and makes useful convention notations leading to extract non trivial properties of the Moyal momentum algebra. We study also the Lax pair building mechanism for particular examples namely, the noncommutative KdV and Burgers systems. We show in a crucial step that these two systems are mapped to each other through the following crucial mapping ∂ t 2 → ∂ t 3 ≡ ∂ t 2 ∂ x + α∂ x 3 . This makes a strong constraint on the NC Burgers system which corresponds to linearizing its associated differential equation. From the CFT's point of view, this constraint equation is nothing but the analogue of the conservation law of the conformal current. We believe that the considered mapping might help to bring new insights towards understanding the integrability of noncommutative 2d-systems. (author)
Relativistic equation of the orbit of a particle in a arbitrary central force field
International Nuclear Information System (INIS)
Aaron, Francisc D.
2005-01-01
The equation of the orbit of a relativistic particle moving in an arbitrary central force field is derived. Straightforward generalizations of well-known first and second order differential equations are given. It is pointed out that the relativistic equation of the orbit has the same form as in the non-relativistic case, the only changes consisting in the appearance of additional terms proportional to 1/c 2 in both potential and total energies. (author)
Transient flows of a Burgers' fluid
International Nuclear Information System (INIS)
Khan, M.
2005-12-01
An analysis is performed to develop the analytical solutions for some unsteady magnetohydrodynamic (MHD) flows of a Burgers' fluid between two plates. A uniform magnetic field is applied transversely to the fluid motion. The exact solutions are given for three problems. Results for the velocity fields are discussed and compared with the flows of Oldroyd-B, Maxwell, second grade and Newtonian fluids. (author)
Swan Song for the Burger Court.
Hayman, Robert L., Jr.; Ramarui, Cornelis O.
1986-01-01
Reviews a collection of decisions rendered by the Burger Court during its waning months. The decisions involve (1) criminal procedures, (2) racial bias in jury selection, (3) search and seizure, and (4) the exclusion of jurors who have reservations about the death penalty. (JDH)
Copepod behavior response to Burgers' vortex treatments mimicking turbulent eddies
Elmi, D.; Webster, D. R.; Fields, D. M.
2017-11-01
Copepods detect hydrodynamic cues in the water by their mechanosensory setae. We expect that copepods sense the flow structure of turbulent eddies in order to evoke behavioral responses that lead to population-scale distribution patterns. In this study, the copepods' response to the Burgers' vortex is examined. The Burgers' vortex is a steady-state solution of three-dimensional Navier-Stokes equations that allows us to mimic turbulent vortices at the appropriate scale and eliminate the stochastic nature of turbulence. We generate vortices in the laboratory oriented in the horizontal and vertical directions each with four intensity levels. The objective of including vortex orientation as a parameter in the study is to quantify directional responses that lead to vertical population distribution patterns. The four intensity levels correspond to target vortex characteristics of eddies corresponding to the typical dissipative vortices in isotropic turbulence with mean turbulent dissipation rates in the range of 0.002 to 0.25 cm2/s3. These vortices mimic the characteristics of eddies that copepods most likely encounter in coastal zones. We hypothesize that the response of copepods to hydrodynamic features depends on their sensory architecture and relative orientation with respect to gravity. Tomo-PIV is used to quantify the vortex circulation and axial strain rate for each vortex treatment. Three-dimensional trajectories of the copepod species Calanus finmarchicus are analyzed to examine their swimming kinematics in and around the vortex to quantify the hydrodynamic cues that trigger their behavior.
Qualitative improvement of rabbit burgers using Zingiber officinale Roscoe powder
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S. Mancini
2017-12-01
Full Text Available The object of this study was to evaluate the effect of Zingiber officinale powder on physical-chemical traits, microbiological growth and sensory properties of rabbit burger. Raw burgers (only meat and meat added with 1 and 2% w/w ginger powder were stored at 4°C for 1, 4 and 7 d and then cooked. Ginger modified the colour of both raw and cooked burgers, leading to more yellow hue and reducing lightness. Aspect of burgers were affected by ginger powder addition, leading to a noticeable difference between the samples. During storage time, the highest modifications were recorded for control samples, followed by burgers with added ginger. Sensory evaluation highlighted that ginger enhanced the juiciness of the burgers; moreover, burgers with ginger powder presented a significant delay in microbial growth. Ginger powder might be considered as a potential ingredient in rabbit meat products to increase their quality and extend their shelf-life.
Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.
1982-01-01
Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.
Coupled force-balance and particle-occupation rate equations for high-field electron transport
International Nuclear Information System (INIS)
Lei, X. L.
2008-01-01
It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field
Johnson, Kennita A.; Vormohr, Hannah R.; Doinikov, Alexander A.; Bouakaz, Ayache; Shields, C. Wyatt; López, Gabriel P.; Dayton, Paul A.
2016-05-01
Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.
Effect of disjoining pressure in a thin film equation with non-uniform forcing
MOULTON, D. E.; LEGA, J.
2013-01-01
We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations
The centripetal force law and the equation of motion for a particle on a curved hypersurface
International Nuclear Information System (INIS)
Hu, L.D.; Lian, D.K.; Liu, Q.H.
2016-01-01
It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable. (orig.)
Tripathi, D; Anwar Bég, O
2014-02-01
A mathematical study of the peristaltic flow of complex rheological viscoelastic fluids using the generalized fractional Burgers' model through a non-uniform channel is presented. This model is designed to study the movement of chyme and undigested chyme (biophysical waste materials) through the small intestine to the large intestine. To simulate blockages and impedance of debris generated by cell shedding, infections, adhesions on the wall and undigested material, a drag force porous media model is utilized. This effectively mimicks resistance to chyme percolation generated by solid matrix particles in the regime. The conduit geometry is mathematically simulated as a sinusoidal propagation with linear increment in shape of the bolus along the length of channel. A modified Darcy-Brinkman model is employed to simulate the generalized flows through isotropic, homogenous porous media, a simplified but physically robust approximation to actual clinical situations. To model the rheological properties of chyme, a viscoelastic Burgers' fluid formulation is adopted. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. Numerical and approximate analytical solutions are obtained with two semi-numerical techniques, namely the homotopy perturbation method and the variational iteration method. Visualization of the results is achieved with Mathematica software. The influence of the dominant hydromechanical and geometric parameters such as fractional viscoelastic parameters, wave number, non-uniformity constant, permeability parameter, and material constants on the peristaltic flow characteristics are depicted graphically. Copyright © 2013 Elsevier Inc. All rights reserved.
A study of wave forces on an offshore platform by direct CFD and Morison equation
Directory of Open Access Journals (Sweden)
Zhang D.
2015-01-01
The next step is the presentation of 3D multiphase RANS simulation of the wind-turbine platform in single-harmonic regular waves. Simulation results from full 3D simulation will be compared to the results from Morison’s equation. We are motivated by the challenges of a floating platform which has complex underwater geometry (e.g. tethered semi-submersible. In cases like this, our hypothesis is that Morison’s equation will result in inaccurate prediction of forces, due to the limitations of 2D coefficients of simple geometries, and that 3D multiphase RANS CFD will be required to generate reliable predictions of platform loads and motions.
Ergodicity for the Randomly Forced 2D Navier-Stokes Equations
International Nuclear Information System (INIS)
Kuksin, Sergei; Shirikyan, Armen
2001-01-01
We study space-periodic 2D Navier-Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N 0 coefficients (where N 0 is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties
Prediction equations of forced oscillation technique: the insidious role of collinearity.
Narchi, Hassib; AlBlooshi, Afaf
2018-03-27
Many studies have reported reference data for forced oscillation technique (FOT) in healthy children. The prediction equation of FOT parameters were derived from a multivariable regression model examining the effect of age, gender, weight and height on each parameter. As many of these variables are likely to be correlated, collinearity might have affected the accuracy of the model, potentially resulting in misleading, erroneous or difficult to interpret conclusions.The aim of this work was: To review all FOT publications in children since 2005 to analyze whether collinearity was considered in the construction of the published prediction equations. Then to compare these prediction equations with our own study. And to analyse, in our study, how collinearity between the explanatory variables might affect the predicted equations if it was not considered in the model. The results showed that none of the ten reviewed studies had stated whether collinearity was checked for. Half of the reports had also included in their equations variables which are physiologically correlated, such as age, weight and height. The predicted resistance varied by up to 28% amongst these studies. And in our study, multicollinearity was identified between the explanatory variables initially considered for the regression model (age, weight and height). Ignoring it would have resulted in inaccuracies in the coefficients of the equation, their signs (positive or negative), their 95% confidence intervals, their significance level and the model goodness of fit. In Conclusion with inaccurately constructed and improperly reported models, understanding the results and reproducing the models for future research might be compromised.
Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing
Directory of Open Access Journals (Sweden)
Lianbing She
2018-01-01
Full Text Available This paper deals with pullback dynamics for the weakly damped Schrödinger equation with time-dependent forcing. An increasing, bounded, and pullback absorbing set is obtained if the forcing and its time-derivative are backward uniformly integrable. Also, we obtain the forward absorption, which is only used to deduce the backward compact-decay decomposition according to high and low frequencies. Based on a new existence theorem of a backward compact pullback attractor, we show that the nonautonomous Schrödinger equation has a pullback attractor which is compact in the past. The method of energy, high-low frequency decomposition, Sobolev embedding, and interpolation are quite involved in calculating a priori pullback or forward bound.
Burgers vector content of an interfacial ledge
Bonnet, R.; Loubradou, M.; Pénisson, J. M.
1992-07-01
A new way of investigating the elastic field around a ledge of a faceted interface is proposed for crystalline materials. The length and/or angular misfits along two adjacent facets are accommodated by slightly deforming the atomic structural units with an appropriate distribution of translation dislocations. The Burgers vector content of the ledge is not defined as usual from a circuit crossing the interface twice, a method which proves to be sometimes misleading. An example treats, at the atomic scale, an unusual ledge of the interface TiAl/Ti3Al.
Inzicht in beslisgedrag maakt dat meer burgers meedoen
Kerstholt, J.H.
2014-01-01
Participatiesamenleving Inzicht in beslisgedrag maakt dat meer burgers meedoen Waar was de bank van de dode buurvrouw? De sekte van de burgerkracht Al het werk is zingevend, ook het vrijwillige De ondernemende burger rukt op, schort het oordeel even op Blij met het luide debat over de
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Babajanova, Gulmira; Matrasulov, Jasur; Nakamura, Katsuhiro
2018-04-01
With use of the scheme of fast forward which realizes quasistatic or adiabatic dynamics in shortened timescale, we investigate a thermally isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size L =L (t ) . In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity (L ˙) and acceleration (L ̈) of L besides rapidly changing state variables like effective temperature (T ) and L itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of L and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number (N ) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
International Nuclear Information System (INIS)
Zheng, Lin; Zheng, Song; Zhai, Qinglan
2016-01-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Energy Technology Data Exchange (ETDEWEB)
Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)
2016-02-05
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
Construction of alternative Hamiltonian structures for field equations
Energy Technology Data Exchange (ETDEWEB)
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Aydogmus, F., E-mail: fatma.aydogmus@gmail.com [Istanbul University, Department of Physics, Faculty of Science (Turkey)
2015-02-15
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.
Effect of disjoining pressure in a thin film equation with non-uniform forcing
MOULTON, D. E.
2013-08-02
We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations and analytical considerations. The disjoining pressure has a regularizing influence on the evolution of the system and appears to select a single steady-state solution for fixed height boundary conditions; this is in contrast with the existence of a continuum of locally attracting solutions that exist in the absence of disjoining pressure for the same boundary conditions. We numerically implement matched asymptotic expansions to construct equilibrium solutions and also investigate how they behave as the disjoining pressure is sent to zero. Finally, we consider the effect of the competition between forcing and disjoining pressure on the coarsening dynamics of the thin film for fixed contact angle boundary conditions. Copyright © Cambridge University Press 2013.
International Nuclear Information System (INIS)
Itasse, Maxime; Brazier, Jean-Philippe; Léon, Olivier; Casalis, Grégoire
2015-01-01
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m 1 , n 1 ), (m 2 , n 2 ), such that the difference in azimuth and in frequency matches the desired “target” mode (m 1 − m 2 , n 1 − n 2 ). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes
Analytical equation of state with three-body forces: Application to noble gases
International Nuclear Information System (INIS)
Río, Fernando del; Díaz-Herrera, Enrique; Guzmán, Orlando; Moreno-Razo, José Antonio; Ramos, J. Eloy
2013-01-01
We developed an explicit equation of state (EOS) for small non polar molecules by means of an effective two-body potential. The average effect of three-body forces was incorporated as a perturbation, which results in rescaled values for the parameters of the two-body potential. These values replace the original ones in the EOS corresponding to the two-body interaction. We applied this procedure to the heavier noble gases and used a modified Kihara function with an effective Axilrod-Teller-Muto (ATM) term to represent the two- and three-body forces. We also performed molecular dynamics simulations with two- and three-body forces. There was good agreement between predicted, simulated, and experimental thermodynamic properties of neon, argon, krypton, and xenon, up to twice the critical density and up to five times the critical temperature. In order to achieve 1% accuracy of the pressure at liquid densities, the EOS must incorporate the effect of ATM forces. The ATM factor in the rescaled two-body energy is most important at temperatures around and lower than the critical one. Nonetheless, the rescaling of two-body diameter cannot be neglected at liquid-like densities even at high temperature. This methodology can be extended straightforwardly to deal with other two- and three-body potentials. It could also be used for other nonpolar substances where a spherical two-body potential is still a reasonable coarse-grain approximation
Energy Technology Data Exchange (ETDEWEB)
Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)
2015-08-15
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
2011-06-01
STRATEGIC IMPLICATIONS OF US FIGHTER FORCE REDUCTIONS: AIR-TO-AIR COMBAT MODELING USING LANCHESTER ...TO-AIR COMBAT MODELING USING LANCHESTER EQUATIONS GRADUATE RESEARCH PAPER Presented to the Faculty Department of Operational Sciences...MODELING USING LANCHESTER EQUATIONS Ronald E. Gilbert, BS, MBA Major, USAF Approved
Directory of Open Access Journals (Sweden)
Zhang Sheng
2015-01-01
Full Text Available In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.
Civic crowdfunding is niet alleen een speeltje van zelfredzame burgers
de Graaf, Frank Jan; Bakker, Ezrah
2017-01-01
De opkomst van civic crowdfunding biedt mogelijkheden voor gemeentelijke overheden die burgerinitiatieven willen stimuleren. Maar slaat civic crowdfunding vooral aan bij een beperkte groep relatief hoogopgeleide burgers? De Hogeschool van Amsterdam onderzoekt dit.
Fish burger enriched by olive oil industrial by-product.
Cedola, Annamaria; Cardinali, Angela; Del Nobile, Matteo Alessandro; Conte, Amalia
2017-07-01
Oil industry produces large volume of waste, which represents a disposal and a potential environmental pollution problem. Nevertheless, they are also promising sources of compounds that can be recovered and used as valuable substances. The aim of this work is to exploit solid olive by-products, in particular dry olive paste flour (DOPF) coming from Coratina cultivar, to enrich fish burger and enhance the quality characteristics. In particular, the addition of olive by-products leads to an increase of the phenolic content and the antioxidant activity; however, it also provokes a deterioration of sensory quality. Therefore, to balance quality and sensory characteristics of fish burgers, three subsequent phases have been carried out: first, the quality of DOPF in terms of phenolic compounds content and antioxidant activity has been assessed; afterward, DOPF has been properly added to fish burgers and, finally, the formulation of the enriched fish burgers has been optimized in order to improve the sensory quality. Results suggested that the enriched burgers with 10% DOPF showed considerable amounts of polyphenols and antioxidant activity, even though they are not very acceptable from the sensory point of view. Pre-treating DOPF by hydration/extraction with milk, significantly improved the burger sensory quality by reducing the concentration of bitter components.
Qualitative improvement of low meat beef burger using Aloe vera.
Soltanizadeh, Nafiseh; Ghiasi-Esfahani, Hossein
2015-01-01
Low meat beef burgers have found their niche in the food markets in developing countries because of their lower price. However, these burgers still lack an acceptable quality. This study investigates the effects of different concentrations of Aloe vera on the quality of this food product. For this purpose, beef burgers were produced with 0%, 1%, 3%, and 5% Aloe vera and the changes in their cooking parameters, lipid oxidation, texture, and appeal to consumers over 7days of refrigerated storage were evaluated. Results indicate that Aloe vera contributed to some extent to decreased cooking loss and diameter reduction in the burgers. Increased concentrations of Aloe vera led to improvements in the water absorption and texture of the burgers as well as their lipid stability. However, a concentration level of 3% led to the most acceptability of the product to the panelists. Finally, it was found that Aloe vera acts as a hydrocolloid and improves the quality of burgers. Copyright © 2014 Elsevier Ltd. All rights reserved.
Chenciner bubbles and torus break-up in a periodically forced delay differential equation
Keane, A.; Krauskopf, B.
2018-06-01
We study a generic model for the interaction of negative delayed feedback and periodic forcing that was first introduced by Ghil et al (2008 Nonlinear Process. Geophys. 15 417–33) in the context of the El Niño Southern Oscillation climate system. This model takes the form of a delay differential equation and has been shown in previous work to be capable of producing complicated dynamics, which is organised by resonances between the external forcing and dynamics induced by feedback. For certain parameter values, we observe in simulations the sudden disappearance of (two-frequency dynamics on) tori. This can be explained by the folding of invariant tori and their associated resonance tongues. It is known that two smooth tori cannot simply meet and merge; they must actually break up in complicated bifurcation scenarios that are organised within so-called resonance bubbles first studied by Chenciner. We identify and analyse such a Chenciner bubble in order to understand the dynamics at folds of tori. We conduct a bifurcation analysis of the Chenciner bubble by means of continuation software and dedicated simulations, whereby some bifurcations involve tori and are detected in appropriate two-dimensional projections associated with Poincaré sections. We find close agreement between the observed bifurcation structure in the Chenciner bubble and a previously suggested theoretical picture. As far as we are aware, this is the first time the bifurcation structure associated with a Chenciner bubble has been analysed in a delay differential equation and, in fact, for a flow rather than an explicit map. Following our analysis, we briefly discuss the possible role of folding tori and Chenciner bubbles in the context of tipping.
Li, DaLei; Lou, Yu-Qing; Esimbek, Jarken
2018-01-01
We study self-similar hydrodynamics of spherical symmetry using a general polytropic (GP) equation of state and derive the GP dynamic Lane-Emden equation (LEE) with a radial inertial force. In reference to Lou & Cao, we solve the GP dynamic LEE for both polytropic index γ = 1 + 1/n and the isothermal case n → +∞; our formalism is more general than the conventional polytropic model with n = 3 or γ = 4/3 of Goldreich & Weber. For proper boundary conditions, we obtain an exact constant solution for arbitrary n and analytic variable solutions for n = 0 and n = 1, respectively. Series expansion solutions are derived near the origin with the explicit recursion formulae for the series coefficients for both the GP and isothermal cases. By extensive numerical explorations, we find that there is no zero density at a finite radius for n ≥ 5. For 0 ≤ n 0 for monotonically decreasing density from the origin and vanishing at a finite radius for c being less than a critical value Ccr. As astrophysical applications, we invoke our solutions of the GP dynamic LEE with central finite boundary conditions to fit the molecular cloud core Barnard 68 in contrast to the static isothermal Bonnor-Ebert sphere by Alves et al. Our GP dynamic model fits appear to be sensibly consistent with several more observations and diagnostics for density, temperature and gas pressure profiles.
Coupled energy-drift and force-balance equations for high-field hot-carrier transport
International Nuclear Information System (INIS)
Huang, Danhong; Alsing, P.M.; Apostolova, T.; Cardimona, D.A.
2005-01-01
Coupled energy-drift and force-balance equations that contain a frictional force for the center-of-mass motion of electrons are derived for hot-electron transport under a strong dc electric field. The frictional force is found to be related to the net rate of phonon emission, which takes away the momentum of a phonon from an electron during each phonon-emission event. The net rate of phonon emission is determined by the Boltzmann scattering equation, which depends on the distribution of electrons interacting with phonons. The work done by the frictional force is included into the energy-drift equation for the electron-relative scattering motion and is found to increase the thermal energy of the electrons. The importance of the hot-electron effect in the energy-drift term under a strong dc field is demonstrated in reducing the field-dependent drift velocity and mobility. The Doppler shift in the energy conservation of scattering electrons interacting with impurities and phonons is found to lead to an anisotropic distribution of electrons in the momentum space along the field direction. The importance of this anisotropic distribution is demonstrated through a comparison with the isotropic energy-balance equation, from which we find that defining a state-independent electron temperature becomes impossible. To the leading order, the energy-drift equation is linearized with a distribution function by expanding it into a Fokker-Planck-type equation, along with the expansions of both the force-balance equation and the Boltzmann scattering equation for hot phonons
Rachid, Hassan
2015-12-01
In the present study,we investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Burgers' model in an inclined tube. We suppose that the viscosity is variable in the radial direction. This analysis has been carried out under low Reynolds number and long-wavelength approximations. An analytical solution to the problem is obtained using a fractional calculus approach. Figures are plotted to show the effects of angle of inclination, Reynolds number, Froude number, material constants, fractional parameters, parameter of viscosity and amplitude ratio on the pressure gradient, pressure rise, friction force, axial velocity and on the mechanical efficiency.
Differential-algebraic solutions of the heat equation
Buchstaber, Victor M.; Netay, Elena Yu.
2014-01-01
In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation.
Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee
In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.
On the non-intrusive evaluation of fluid forces with the momentum equation approach
International Nuclear Information System (INIS)
David, L; Jardin, T; Farcy, A
2009-01-01
The aim of this paper is to discuss the advantages and difficulties linked with the experimental application of the momentum equation approach as a non-intrusive way to predict the unsteady loads experienced by an airfoil in motion. First, in order to evaluate the influence of the varying parameters relative to the calculation of the corresponding drag and lift coefficients, numerical flow fields obtained by means of DNS are used. The comprehension of the impact of the spatial and temporal resolutions, velocity accuracy or third velocity component on the estimation of forces allows us to quantify the accuracy of the approach and helps in specifying the parameters setting which could lead to a consistent experimental application. In a second step, the approach is applied to experimental flow fields measured through the use of time resolved particle image velocimetry (TR-PIV). A low Reynolds number flow around an impulsively started airfoil is considered. The loads and vorticity flow fields are correlated and compared with those obtained by DNS
Force-balance and differential equation for the ground-state electron density in atoms and molecules
International Nuclear Information System (INIS)
Amovilli, C.; March, N.H.; Gal, T.; Nagy, A.
2000-01-01
Holas and March (1995) established a force-balance equation from the many-electron Schroedinger equation. Here, the authors propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example they present the simple case of two-electron systems with different external potentials but with weak electron-electron Coulomb repulsion λe 2 /r 12 . In this case first-order Rayleigh-Schroedinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix γ(r,rprime) in terms of its diagonal density ρ(r) and the density corresponding to λ = 0. This result allows the force-balance equation to be written as a third-order linear, differential homogeneous equation for the ground-state electron density ρ(r). The example of the two-electron Hookean atom is treated: For this case one can also transcend the first-order RS perturbation theory and get exact results for discrete choices of force constants (external potential)
Xiong, Yuan
2014-04-28
Spurious current emerging in the vicinity of phase interfaces is a well-known disadvantage of the lattice Boltzmann equation (LBE) for two-phase flows. Previous analysis shows that this unphysical phenomenon comes from the force imbalance at discrete level inherited in LBE (Guo et al 2011 Phys. Rev. E 83 036707). Based on the analysis of the LBE free of checkerboard effects, in this work we further show that the force imbalance is caused by the different discretization stencils: the implicit one from the streaming process and the explicit one from the discretization of the force term. Particularly, the total contribution includes two parts, one from the difference between the intrinsically discretized density (or ideal gas pressure) gradient and the explicit ones in the force term, and the other from the explicit discretized chemical potential gradients in the intrinsically discretized force term. The former contribution is a special feature of LBE which was not realized previously.
Directory of Open Access Journals (Sweden)
D. K. Lian
2017-12-01
Full Text Available In classical mechanics, a nonrelativistic particle constrained on an N − 1 curved hypersurface embedded in N flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is ”driven” by not only the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.
FORCED OSCILLATIONS OF SECOND ORDER SUPER-LINEAR DIFFERENTIAL EQUATION WITH IMPULSES
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
Rosemary as natural antioxidant to prevent oxidation in chicken burgers
Directory of Open Access Journals (Sweden)
Daiane PEREIRA
Full Text Available Abstract Rosemary (Rosmarinus officinalis is known for their sensory characteristics and antioxidant properties, mainly due to the presence of several phenolic compounds. The aim of this work, was determine the antioxidant activity and apply the Rosemary lyophilized extract (RLE in chicken burger, for assess their ability to reduce the lipid oxidation. Total antioxidant capacity and phenolic compounds profile were analyzed by colorimetric tests and liquid chromatography analysis, respectively. Thiobarbituric acid reactive substances assay was used to evaluate the ability of the RLE to prevent lipid peroxidation in chicken burger stored at 4 °C. Three treatments of chicken burgers were prepared (T1 – control, without addition of synthetic antioxidant BHT: butylated hydroxytoluene or RLE, T2 – with addition of BHT, and T3 – experimental, containing RLE. The high contents of total phenolic compounds (40.91 mg GAE g-1: Gallic Acid Equivalent and total flavonoids (24.26 mg QE g-1: Quercetin Equivalents were found in RLE. Rutin was the major phenolic compound identified in the RLE. The RLE showed strong antioxidant capacity and inhibited 48.29% of lipid oxidation (21 days of storage in comparison to the control (T1, with low production of malonaldehyde, which has potential to be used in chicken burgers.
Improving pork burgers quality using Zingiber officinale Roscoe powder (ginger).
Mancini, Simone; Paci, Gisella; Fratini, Filippo; Torracca, Beatrice; Nuvoloni, Roberta; Dal Bosco, Alessandro; Roscini, Valentina; Preziuso, Giovanna
2017-07-01
Pork burgers were evaluated for physical-chemical characteristics, fatty acids profile, lipid oxidation, antioxidant capacity, microbiological growth and sensory evaluation during storage time of seven days at 4°C as function of three formulations as only meat (control, B) and meat added with ginger powder at the percentage of 1 and 2% (BG1 and BG2). BG1 and BG2 were less redness than control ones with incremented yellow hue. These modifications in color parameters did not modify sensory characteristics of burgers. PUFA were incremented (both PUFAω3 and PUFAω6) by the addition of ginger. Furthermore, BG1 and BG2 burgers showed to be less sensitive to lipid oxidation and to possess an increase in antioxidant capacity. Microbial growth evaluation of total aerobic count and Pseudomonas spp. showed that ginger powder delayed in time the bacterial contamination. Results highlighted that the presence of ginger led to an enhanced shelf life and health characteristics of burgers (increasing peroxidisability, ratio hypocholesterolemic/hypercholesterolemic and ratio ω3/ω6; reducing atherogenicity and thrombogenicity). Copyright © 2017 Elsevier Ltd. All rights reserved.
A novel method of evaluating the lift force on the bluff body based on Noca’s flux equation
International Nuclear Information System (INIS)
Sui Xiang-Kun; Jiang Nan
2015-01-01
The influence of experimental error on lift force evaluated by Noca’s flux equation is studied based on adding errors into the direct numerical simulation data for flow past cylinder at Re = 100. As Noca suggested using the low-pass filter to get rid of the high-frequency noise in the evaluated lift force, we verify that his method is inapplicable for dealing with the dataset of 1% experimental error, although the precision is acceptable in practice. To overcome this defect, a novel method is proposed in this paper. The average of the lift forces calculated by using multiple control volume is taken as the evaluation before applying the low-pass filter. The method is applied to an experimental data for flow past a cylinder at approximately Re = 900 to verify its validation. The results show that it improves much better on evaluating the lift forces. (paper)
New exact solutions of Einstein's field equations: gravitational force can also be repulsive!
International Nuclear Information System (INIS)
Dietz, W.
1988-01-01
This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given
The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on $\\beta$-plane
Kuksin, Sergei; Maiocchi, Alberto
2014-01-01
We consider the 2d quasigeostrophic equation on the $\\beta$-plane for the stream function $\\psi$, with dissipation and a random force: $$ (*)\\qquad (-\\Delta +K)\\psi_t - \\rho J(\\psi, \\Delta\\psi) -\\beta\\psi_x= \\langle \\text{random force}\\rangle -\\kappa\\Delta^2\\psi +\\Delta\\psi, $$ where $\\psi=\\psi(t,x,y), \\ x\\in\\mathbb{R}/2\\pi L\\mathbb{Z}, \\ y\\in \\mathbb{R}/2\\pi \\mathbb{Z}$. For typical values of the horizontal period $L$ we prove that the law of the action-vector of a solution for $(*)$ (formed...
Oscillating flow of a Burgers' fluid in a pipe
International Nuclear Information System (INIS)
Khan, M.; Asghar, S.; Hayat, T.
2005-12-01
An analysis is made to see the influences of Hall current on the flow of a Burgers' fluid. The velocity field corresponding to flow in a pipe is determined. The closed form analytical solutions for several Newtonian and non-Newtonian fluid models can be obtained from the present analysis as the limiting cases. The purpose of this work is twofold. Firstly, to investigate the oscillating flow in a pipe using Burgers? fluid model. Secondly, to see the effects of Hall current on the velocity field. The flow in a pipe is induced due to imposition of an oscillating pressure gradient. An exact analytical solution to the governing problem is given using the Fourier transform technique. The obtained expression for the velocity field shows that there are pronounced effects of Hall and rheological parameters. The considered fluid model is a viscoelastic model and has been used to characterize food products such as cheese, soil, asphalt and asphalt mixes etc. (author)
The Burgers/squirt-flow seismic model of the crust and mantle
Carcione, José M.; Poletto, Flavio; Farina, Biancamaria
2018-01-01
Part of the crust shows generally brittle behaviour while areas of high temperature and/or high pore pressure, including the mantle, may present ductile behaviour. For instance, the potential heat source of geothermal fields, overpressured formations and molten rocks. Seismic waves can be used to detect these conditions on the basis of reflection and transmission events. Basically, from the elastic-plastic point of view the seismic properties (seismic velocity, quality factor and density) depend on effective pressure and temperature. Confining and pore pressures have opposite effects on these properties, and high temperatures may induce a similar behaviour by partial melting. In order to model these effects, we consider a poro-viscoelastic model based on the Burgers mechanical element and the squirt-flow model to represent the properties of the rock frame to describe ductility in which deformation takes place by shear plastic flow, and to model local and global fluid flow effects. The Burgers element allows us to model the effects of the steady-state creep flow on the dry-rock frame. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. Effective pressure effects are taken into account in the dry-rock moduli by using exponential functions whose parameters are obtained by fitting experimental data as a function of confining pressure. Since fluid effects are important, the density and bulk modulus of the saturating fluids (water at sub- and supercritical conditions) are modeled by using the equations provided by the NIST website. The squirt-flow model has a single free parameter represented by the aspect ratio of the grain contacts. The theory generalizes a preceding theory based on Gassmann (low-frequency) moduli to the more general case of the presence of local (squirt) flow and global (Biot) flow, which contribute with
Nanobioprobe for the Determination of Pork Adulteration in Burger Formulations
Directory of Open Access Journals (Sweden)
M. E. Ali
2012-01-01
Full Text Available We report the development of a swine-specific hybrid nanobioprobe through a covalent integration of a fluorophore-labeled 27-nucleotide AluI-fragment of swine cytochrome b gene to a 3 nm gold nanoparticle for the determination of pork adulteration in processed meat products. We tested the probe to estimate adulterated pork in ready-to-eat pork-spiked beef burgers. The probe quantitatively detected 1–100% spiked pork in burger formulations with ≥90% accuracy. A plot of observed fluorescence against the known concentration of AluI-digested pork DNA targets generated a concave curve, demonstrating a power relationship (y=2.956x0.509 with a regression coefficient (R2 of 0.986. No cross-species detection was found in a standard set of pork, beef, chicken, mutton, and chevon burgers. The method is suitable for the determination of very short-length nucleic acid targets which cannot be estimated by conventional and real-time PCR but are essential for the determination of microRNA in biodiagnostics and degraded DNA in forensic testing and food analysis.
Nanobioprobe for the Determination of Pork Adulteration in Burger Formulations
International Nuclear Information System (INIS)
Ali, M.E.; Hashim, U.K.; Foo, L.; Mustafa, S.; Che Man, Y.B.
2012-01-01
We report the development of a swine-specific hybrid nanobioprobe through a covalent integration of a fluorophore-labeled 27-nucleotide AluI-fragment of swine cytochrome b gene to a 3 nm gold nanoparticle for the determination of pork adulteration in processed meat products. We tested the probe to estimate adulterated pork in ready-to-eat pork-spiked beef burgers. The probe quantitatively detected 1-100% spiked pork in burger formulations with ≥90% accuracy. A plot of observed fluorescence against the known concentration of AluI-digested pork DNA targets generated a concave curve, demonstrating a power relationship (y=2.956x 0.509 ) with a regression coefficient (R 2 ) of 0.986. No cross-species detection was found in a standard set of pork, beef, chicken, mutton, and chevon burgers. The method is suitable for the determination of very short-length nucleic acid targets which cannot be estimated by conventional and real-time PCR but are essential for the determination of micro RNA in bio diagnostics and degraded DNA in forensic testing and food analysis.
The Gassmann-Burgers Model to Simulate Seismic Waves at the Earth Crust And Mantle
Carcione, José M.; Poletto, Flavio; Farina, Biancamaria; Craglietto, Aronne
2017-03-01
The upper part of the crust shows generally brittle behaviour while deeper zones, including the mantle, may present ductile behaviour, depending on the pressure-temperature conditions; moreover, some parts are melted. Seismic waves can be used to detect these conditions on the basis of reflection and transmission events. Basically, from the elastic-plastic point of view the seismic properties (seismic velocity and density) depend on effective pressure and temperature. Confining and pore pressures have opposite effects on these properties, such that very small effective pressures (the presence of overpressured fluids) may substantially decrease the P- and S-wave velocities, mainly the latter, by opening of cracks and weakening of grain contacts. Similarly, high temperatures induce the same effect by partial melting. To model these effects, we consider a poro-viscoelastic model based on Gassmann equations and Burgers mechanical model to represent the properties of the rock frame and describe ductility in which deformation takes place by shear plastic flow. The Burgers elements allow us to model the effects of seismic attenuation, velocity dispersion and steady-state creep flow, respectively. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. Effective pressure effects are taken into account in the dry-rock moduli using exponential functions whose parameters are obtained by fitting experimental data as a function of confining pressure. Since fluid effects are important, the density and bulk modulus of the saturating fluids (water and steam) are modeled using the equations provided by the NIST website, including supercritical behaviour. The theory allows us to obtain the phase velocity and quality factor as a function of depth and geological pressure and temperature as well as time frequency. We then obtain the PS and SH
Dias, Clenilda F; Carvalho-Santos, Vagson L
2012-01-01
The Euler-Lagrange equations (EL) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of EL to study one-dimensional motions under the action of a constant force. From using the definition of partial derivative, we have proposed two operators, here called \\textit{mean delta operators}, which may be used to solve the EL in a simplest way. We have applied this simplification to solve three simple mechanical problems under th...
Travelling wave solutions for some time-delayed equations through factorizations
International Nuclear Information System (INIS)
Fahmy, E.S.
2008-01-01
In this work, we use factorization method to find explicit particular travelling wave solutions for the following important nonlinear second-order partial differential equations: The generalized time-delayed Burgers-Huxley, time-delayed convective Fishers, and the generalized time-delayed Burgers-Fisher. Using the particular solutions for these equations we find the general solutions, two-parameter solution, as special cases
Burger King in Portugal : to lead or to follow?
Patrone, Sara Saraiva
2012-01-01
In 2001, the Burger King (BK) brand, managed by Ibersol group entered the growing fast food Portuguese market. Marginally higher prices along with the fact of having entered the market 10 years after its most direct competitor (McDonald´s), led BK to a sub leader position. Although being recognized as offering superior quality products when compared to McDonald´s, BK´s growth margins in the Portuguese market have been decreasing since 2007. The company´s uncertainty situation, offers the p...
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
If you build it, will they eat it? Consumer preferences for plant-based and cultured meat burgers.
Slade, Peter
2018-06-01
In a hypothetical choice experiment consumers were given the option of purchasing burgers that were made from beef, plant-based protein, or cultured meat. Willingness to purchase plant-based and cultured meat burgers is linked to age, sex, views of other food technologies, and attitudes towards the environment and agriculture. Although consumers were told that all burgers tasted the same, there was a marked preference for beef burgers. A mixed-logit model predicts that, if prices were equal, 65% of consumers would purchase the beef burger, 21% would purchase the plant-based burger, 11% would purchase the cultured meat burger, and 4% would make no purchase. Preferences for plant-based and cultured meat burgers are found to be highly, but not perfectly, correlated. Copyright © 2018 Elsevier Ltd. All rights reserved.
Laplace's equation and Faraday's lines of force
Energy Technology Data Exchange (ETDEWEB)
Narasimhan, T.N.
2007-06-01
Boundary-value problems involve two dependent variables: a potential function, and a stream function. They can be approached in two mutually independent ways. The first, introduced by Laplace, involves spatial gradients at a point. Inspired by Faraday, Maxwell introduced the other, visualizing the flow domain as a collection of flow tubes and isopotential surfaces. Boundary-value problems intrinsically entail coupled treatment (or, equivalently, optimization) of potential and stream functions Historically, potential theory avoided the cumbersome optimization task through ingenious techniques such as conformal mapping and Green's functions. Laplace's point-based approach, and Maxwell's global approach, each provides its own unique insights into boundary-value problems. Commonly, Laplace's equation is solved either algebraically, or with approximate numerical methods. Maxwell's geometry-based approach opens up novel possibilities of direct optimization, providing an independent logical basis for numerical models, rather than treating them as approximate solvers of the differential equation. Whereas points, gradients, and Darcy's law are central to posing problems on the basis of Laplace's approach, flow tubes, potential differences, and the mathematical form of Ohm's law are central to posing them in natural coordinates oriented along flow paths. Besides being of philosophical interest, optimization algorithms can provide advantages that complement the power of classical numerical models. In the spirit of Maxwell, who eloquently spoke for a balance between abstract mathematical symbolism and observable attributes of concrete objects, this paper is an examination of the central ideas of the two approaches, and a reflection on how Maxwell's integral visualization may be practically put to use in a world of digital computers.
Müller, Erich A; Jackson, George
2014-01-01
A description of fluid systems with molecular-based algebraic equations of state (EoSs) and by direct molecular simulation is common practice in chemical engineering and the physical sciences, but the two approaches are rarely closely coupled. The key for an integrated representation is through a well-defined force field and Hamiltonian at the molecular level. In developing coarse-grained intermolecular potential functions for the fluid state, one typically starts with a detailed, bottom-up quantum-mechanical or atomic-level description and then integrates out the unwanted degrees of freedom using a variety of techniques; an iterative heuristic simulation procedure is then used to refine the parameters of the model. By contrast, with a top-down technique, one can use an accurate EoS to link the macroscopic properties of the fluid and the force-field parameters. We discuss the latest developments in a top-down representation of fluids, with a particular focus on a group-contribution formulation of the statistical associating fluid theory (SAFT-γ). The accurate SAFT-γ EoS is used to estimate the parameters of the Mie force field, which can then be used with confidence in direct molecular simulations to obtain thermodynamic, structural, interfacial, and dynamical properties that are otherwise inaccessible from the EoS. This is exemplified for several prototypical fluids and mixtures, including carbon dioxide, hydrocarbons, perfluorohydrocarbons, and aqueous surfactants.
Alst, S.
2011-01-01
De overheid voert een actief beleid om burgers op te roepen tot (zelf)redzaam gedrag in rampsituaties. Hierdoor bestaat de mogelijkheid dat burgers schade toebrengen aan zichzelf of anderen. Tevens kunnen zich situaties voordoen waarbij hulpverleningsdiensten schade toebrengen aan derden. Er zijn
Energy Technology Data Exchange (ETDEWEB)
Kaizl, Mira
2010-07-15
At Waghaeusel in the German state of Baden-Wuerttemberg, the local solar provider Wirsol Solar AG constructed a restaurant building for the Burger King GmbH. The building consumes comparably little energy and has a solar roof for photovoltaic power generation. Burger King hopes for good money and a clean image, while Wirsol Solar is hoping for new projects in Europe and in the USA. (orig.)
Bioactive compounds from orange epicarp to enrich fish burgers.
Spinelli, Sara; Lecce, Lucia; Likyova, Desislava; Del Nobile, Matteo Alessandro; Conte, Amalia
2018-05-01
The orange industry produces considerable amounts of by-products, traditionally used for animal feed or fuel production. Most of these by-products could be used as functional ingredients. To assess the potential food application of orange epicarp, different percentages of micro-encapsulated orange extract were added to fresh fish burgers. Then, an in vitro digestion was also carried out, before and after micro-encapsulation, to measure the bio-accessibility of the active compounds. A significant increase of bio-accessibility of bioactive compounds has been observed in the orange epicarp extract after micro-encapsulation by spray-drying. From the sensory point of view, the fish sample enriched with 50 g kg -1 micro-encapsulated extract was the most comparable to the control burger, even if it showed a higher phenolic, flavonoid and carotenoid bio-accessibility. Orange epicarp may be used as a food additive to enhance the health content of food products. The micro-encapsulation is a valid technique to protect the bioactive compounds and increase their bio-accessibility. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.
Nuclear equation of state for core-collapse supernova simulations with realistic nuclear forces
Energy Technology Data Exchange (ETDEWEB)
Togashi, H., E-mail: hajime.togashi@riken.jp [Nishina Center for Accelerator-Based Science, Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Nakazato, K. [Faculty of Arts and Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395 (Japan); Takehara, Y.; Yamamuro, S.; Suzuki, H. [Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510 (Japan); Takano, M. [Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Department of Pure and Applied Physics, Graduate School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)
2017-05-15
A new table of the nuclear equation of state (EOS) based on realistic nuclear potentials is constructed for core-collapse supernova numerical simulations. Adopting the EOS of uniform nuclear matter constructed by two of the present authors with the cluster variational method starting from the Argonne v18 and Urbana IX nuclear potentials, the Thomas–Fermi calculation is performed to obtain the minimized free energy of a Wigner–Seitz cell in non-uniform nuclear matter. As a preparation for the Thomas–Fermi calculation, the EOS of uniform nuclear matter is modified so as to remove the effects of deuteron cluster formation in uniform matter at low densities. Mixing of alpha particles is also taken into account following the procedure used by Shen et al. (1998, 2011). The critical densities with respect to the phase transition from non-uniform to uniform phase with the present EOS are slightly higher than those with the Shen EOS at small proton fractions. The critical temperature with respect to the liquid–gas phase transition decreases with the proton fraction in a more gradual manner than in the Shen EOS. Furthermore, the mass and proton numbers of nuclides appearing in non-uniform nuclear matter with small proton fractions are larger than those of the Shen EOS. These results are consequences of the fact that the density derivative coefficient of the symmetry energy of our EOS is smaller than that of the Shen EOS.
Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
International Nuclear Information System (INIS)
Ebaid, A.
2007-01-01
Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method
Dias, Clenilda F.; Araújo, Maria A. S.; Carvalho-Santos, Vagson L.
2018-01-01
The Euler-Lagrange equations (ELE) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of ELE to study one-dimensional motions under the action of a constant force. From the use of the definition of partial derivative, we have proposed two operators, here called mean delta operators, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three simple mechanical problems in which the particle is under the action of the gravitational field: a free fall body, the Atwood’s machine and the inclined plan. The proposed simplification can be used to introduce the lagrangian formalism in teaching classical mechanics in introductory physics courses.
Karavashkin, S B
2002-01-01
We analyse the exact analytical solutions for 1D elastic lumped lines under action of an external force inclined to the line axis. We show that in this case an inclined wave being described by an implicit function propagates along the line. We extend this conclusion both to free vibrations and to distributed lines. We prove that the presented solution in the form of implicit function is a generalizing for the wave equation. When taken into consideration exactly, the dynamical processes pattern leads to the conclusion that the divergence of a vector in dynamical fields is not zero but proportional to the scalar product of the partial derivative of the given vector with respect to time into the wave propagation direction vector.
Classification of solutions of the forced periodic nonlinear Schrödinger equation
International Nuclear Information System (INIS)
Shlizerman, Eli; Rom-Kedar, Vered
2010-01-01
The integrable structure of the periodic one-dimensional nonlinear Schrödinger equation is utilized to gain insights regarding the perturbed near-integrable dynamics. After recalling the known results regarding the structure and stability of the unperturbed standing and travelling waves solutions, two new stability results are presented: (1) it is shown numerically that the stability of the 'outer' (cnoidal) unperturbed solutions depends on their power (the L 2 norm): they undergo a finite sequence of Hamiltonian–Hopf bifurcations as their power is increased. (2) another proof that the 'inner'(dnoidal) unperturbed solutions with multiplicity ≥2 are linearly unstable is presented. Then, to study the global phase-space structure, an energy–momentum bifurcation diagram (PDE-EMBD) that consists of projections of the unperturbed standing and travelling waves solutions to the energy–power plane and includes information regarding their linear stability is constructed. The PDE-EMBD helps us to classify the behaviour near the plane wave solutions: the diagram demonstrates that below some known threshold amplitude, precisely three distinct observable chaotic mechanisms arise: homoclinic chaos, homoclinic resonance and, for some parameter values, parabolic-resonance. Moreover, it appears that the dynamics of the PDE chaotic solutions that exhibit the parabolic-resonance instability may be qualitatively predicted: these exhibit the same dynamics as a recently derived parabolic-resonance low-dimensional normal form. In particular, these solutions undergo adiabatic chaos: they follow the level lines of an adiabatic invariant till they reach the separatrix set at which the adiabatic invariant undergoes essentially random jumps
Simulation of seismic waves in the brittle-ductile transition (BDT) using a Burgers model
Poletto, Flavio; Farina, Biancamaria; Carcione, José Maria
2014-05-01
The seismic characterization of the brittle-ductile transition (BDT) in the Earth's crust is of great importance for the study of high-enthalpy geothermal fields in the proximity of magmatic zones. It is well known that the BDT can be viewed as the transition between zones with viscoelastic and plastic behavior, i.e., the transition between the upper, cooler, brittle crustal zone, and the deeper ductile zone. Depending on stress and temperature conditions, the BDT behavior is basically determined by the viscosity of the crustal rocks, which acts as a key factor. In situ shear stress and temperature are related to shear viscosity and steady-state creep flow through the Arrhenius equation, and deviatory stress by octahedral stress criterion. We present a numerical approach to simulate the propagation of P-S and SH seismic waves in a 2D model of the heterogeneous Earth's crust. The full-waveform simulation code is based on a Burgers mechanical model (Carcione, 2007), which enables us to describe both the seismic attenuation effects and the steady-state creep flow (Carcione and Poletto, 2013; Carcione et al. 2013). The differential equations of motion are calculated for the Burgers model, and recast in the velocity-stress formulation. Equations are solved in the time domain using memory variables. The approach uses a direct method based on the Runge-Kutta technique, and the Fourier pseudo-spectral methods, for time integration and for spatial derivation, respectively. In this simulation we assume isotropic models. To test the code, the signals generated by the full-waveform simulation algorithm are compared with success to analytic solutions obtained with different shear viscosities. Moreover, synthetic results are calculated to simulate surface and VSP seismograms in a realistic rheological model with a dramatic temperature change, to study the observability of BDT by seismic reflection methods. The medium corresponds to a selected rheology of the Iceland scenario
Directory of Open Access Journals (Sweden)
Ilyas Khan
Full Text Available The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the flow. The equations governing the flow are modeled and then solved using the Laplace transform technique. The expressions of velocity field and tangential stress are developed when the relaxation time satisfies the condition γ = λ²/4 or γ> λ²/4. The obtained closed form solutions are presented in the form of simple or multiple integrals in terms of Bessel functions and terms with only Bessel functions. The numerical integration is performed and the graphical results are displayed for the involved flow parameters. It is found that the velocity decreases whereas the shear stress increases when the Hartmann number is increased. The solutions corresponding to the Stokes' first problem for hydrodynamic Burgers' fluids are obtained as limiting cases of the present solutions. Similar solutions for Stokes' second problem of hydrodynamic Burgers' fluids and those for Newtonian and Oldroyd-B fluids can also be obtained as limiting cases of these solutions.
Pamadi, Bandu N.; Toniolo, Matthew D.; Tartabini, Paul V.; Roithmayr, Carlos M.; Albertson, Cindy W.; Karlgaard, Christopher D.
2016-01-01
The objective of this report is to develop and implement a physics based method for analysis and simulation of multi-body dynamics including launch vehicle stage separation. The constraint force equation (CFE) methodology discussed in this report provides such a framework for modeling constraint forces and moments acting at joints when the vehicles are still connected. Several stand-alone test cases involving various types of joints were developed to validate the CFE methodology. The results were compared with ADAMS(Registered Trademark) and Autolev, two different industry standard benchmark codes for multi-body dynamic analysis and simulations. However, these two codes are not designed for aerospace flight trajectory simulations. After this validation exercise, the CFE algorithm was implemented in Program to Optimize Simulated Trajectories II (POST2) to provide a capability to simulate end-to-end trajectories of launch vehicles including stage separation. The POST2/CFE methodology was applied to the STS-1 Space Shuttle solid rocket booster (SRB) separation and Hyper-X Research Vehicle (HXRV) separation from the Pegasus booster as a further test and validation for its application to launch vehicle stage separation problems. Finally, to demonstrate end-to-end simulation capability, POST2/CFE was applied to the ascent, orbit insertion, and booster return of a reusable two-stage-to-orbit (TSTO) vehicle concept. With these validation exercises, POST2/CFE software can be used for performing conceptual level end-to-end simulations, including launch vehicle stage separation, for problems similar to those discussed in this report.
Quasi-exact solutions of nonlinear differential equations
Kudryashov, Nikolay A.; Kochanov, Mark B.
2014-01-01
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.
Evaluation of oxidative stability of lamb burger with Origanum vulgare extract.
Fernandes, R P P; Trindade, M A; Tonin, F G; Pugine, S M P; Lima, C G; Lorenzo, J M; de Melo, M P
2017-10-15
The objective was to evaluate replacement of sodium erythorbate with a natural antioxidant (oregano extract) on physicochemical and sensory stability of lamb burgers, and determine the appropriate amount. Five treatments were prepared, including control (without antioxidant), sodium erythorbate, and three concentrations of oregano extract (13.32, 17.79 and 24.01mL/kg), based on antioxidant capacity determined using the Folin-Ciocalteu, 2,2-diphenyl-1-picrylhydrazyl (DPPH) and ferric reducing antioxidant power (FRAP) methods, respectively. Burgers containing oregano extract, at the concentration determined by FRAP method, had higher oxidative stability, evidenced by an 80% reduction (Pextract did not impair (P>0.05) consumers' sensory acceptance of the lamb burgers. Under the conditions tested, addition of 24mL/kg of oregano extract could be recommended as a natural antioxidant in lamb burgers. Copyright © 2017 Elsevier Ltd. All rights reserved.
The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations
International Nuclear Information System (INIS)
Liu Chunping; Liu Xiaoping
2004-01-01
First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions
International Nuclear Information System (INIS)
Tawfik, S.S.; El kabbani, H.M.; Sallam, M.H.; Attia, A.I.
2007-01-01
Meat industry in Egypt has a great economic potential, but till now it has not received adequate attention. Beef burgers were prepared (50 g, 1 cm thick steaks) and aerobically packaged into polyethylene pages then divided into control, cooking and gamma-irradiated (3 and 4 kGy) groups. Samples stored at (5±degree c) and periodically judged after 5, 10, 15, 20,25 and 30 days. The results showed that irradiation increased the shelf life of stored cooked beef burger, as compared to control samples. In addition, the dose of 3 kGy is considered the most adequate for irradiation of this meat product because it obtained the same results reflected by 4 kGy. The microbiological, chemical and sensorial testing for stored cooking and irradiated beef burger steaks were examined according an experimental design presented conditions that were adequate for human consumption of this product during the refrigeration storage periods. For the non-irradiated beef burger samples, bacterial contamination was the main limiting factor with respect to the shelf life, whereas for the irradiated beef burger samples this factor was lipid oxidation. Conclusion: The cooking before food irradiation may be of practical efficacy in enhancing the technical effectiveness and feasibility of irradiation of a variety of meat products. Recommendation: The necessity for a proper preservation method for marketing the processing beef burger steaks in each of its numerous retail markets should be established central irradiation units for processing and packing before distribution in these retail markets
A procedure to construct exact solutions of nonlinear fractional differential equations.
Güner, Özkan; Cevikel, Adem C
2014-01-01
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.
Little, C L; Gillespie, I A; Mitchell, R T
2001-12-01
During May and June 1999 a microbiological study of ready-to-eat burgers purchased anonymously from burger outlets (combined take-away and burger restaurants, take-away-only fixed premises, mobile vendors, temporary stalls and other burger outlets) was undertaken. The intention was to determine the microbiological quality of ready-to-eat burgers as purchased by customers of take-away premises and to ascertain, where information was available, whether the Chief Medical Officer's advice on cooking burgers was being followed. Examination of 3,128 ready-to-eat burgers found that 2,868 (92%) were of acceptable quality and 260 (8%) were of unsatisfactory quality. Unsatisfactory results were mostly due to high aerobic colony counts (ACCs). Salmonella spp., Campylobacter spp. and Escherichia coli O157 were not detected in any of the samples examined. Acceptable microbiological quality of ready-to-eat burgers was associated with outlets, such as combined take-away and burger restaurants and in particular national franchise outlets, which had management food hygiene training and hazard analysis in place. Poor microbiological quality was associated with undercooking and local outlets as indicated by Local Authority Inspectors' Consumers at Risk scores.
Polygons of differential equations for finding exact solutions
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given
International Nuclear Information System (INIS)
Huang, Danhong; Apostolova, T.; Alsing, P.M.; Cardimona, D.A.
2004-01-01
The dynamics of a many-electron system under both dc and infrared fields is separated into a center-of-mass and a relative motion. The first-order force-balance equation is employed for the slow center-of-mass motion of electrons, and the Fokker-Planck equation is used for the ultrafast relative scattering motion of degenerate electrons. This approach allows us to include the anisotropic energy-relaxation process which has been neglected in the energy-balance equation in the past. It also leads us to include the anisotropic coupling to the incident infrared field with different polarizations. Based on this model, the transport of electrons is explored under strong dc and infrared fields by going beyond the relaxation-time approximation. The anisotropic dependence of the electron distribution function on the parallel and perpendicular kinetic energies of electrons is displayed with respect to the dc field direction, and the effect of anisotropic coupling to an incident infrared field with polarizations parallel and perpendicular to the applied dc electric field is shown. The heating of electrons is more accurately described beyond the energy-balance equation with the inclusion of an anisotropic coupling to the infrared field. The drift velocity of electrons is found to increase with the amplitude of the infrared field due to a suppressed momentum-relaxation process (or frictional force) under parallel polarization but decreases with the amplitude due to an enhanced momentum-relaxation process under perpendicular polarization
Feedback control for unsteady flow and its application to the stochastic Burgers equation
Choi, Haecheon; Temam, Roger; Moin, Parviz; Kim, John
1993-01-01
The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.
Complex solutions for generalised fitzhughnagumo equation
International Nuclear Information System (INIS)
Neirameh, A.
2014-01-01
During present investigation, a direct algebraic method on complex solutions of nonlinear partial differential equation is developed and tested in the case of generalized Burgers-Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction-diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even in the case of a small number of grid points. This method is a very reliable, simple, small computation costs, flexible, and convenient alternative method. (author)
Martín de Vicente, Carlos; de Mir Messa, Inés; Rovira Amigo, Sandra; Torrent Vernetta, Alba; Gartner, Silvia; Iglesias Serrano, Ignacio; Carrascosa Lezcano, Antonio; Moreno Galdó, Antonio
2018-01-01
Recent publication of multi-ethnic spirometry reference equations for subjects aged from 3-95 years aim to avoid age-related discontinuities and provide a worldwide standard for interpreting spirometric test results. To assess the agreement of the Global Lung Function Initiative (GLI-2012) and All ages (FEV 0.5 ) reference equations with the Spanish preschool lung function data. To verify the appropriateness of these reference values for clinical use in Spanish preschool children. Spirometric measurements were obtained from children aged 3 to 6 years attending 10 randomly selected schools in Barcelona (Spain). Stanojevic's quality control criteria were applied. Z-scores were calculated for the spirometry outcomes based on the GLI equations. If the z-score (mean) of each parameter was close to 0, with a maximum variance of ± 0.5 from the mean and a standard deviation of 1, the GLI-2012 equations would be applicable in our population. Of 543 children recruited, 405 (74.6%) were 'healthy', and of these, 380 were Caucasians. Of these 380, 81.6% (169 females, 141 males) performed technically acceptable and reproducible maneuvers to assess FEVt, and 69.5% achieved a clear end-expiratory plateau. Z-scores for FVC, FEV 1 , FEV 1 /FVC, FEV 0.75 , FEV 0.75 /FVC, FEV 0.5 , FEF 75 and FEF 25-75 all fell within ± 0.5, except for FEV 1 /FVC (0.53 z-scores). GLI equations are appropriate for Spanish preschool children. These data provide further evidence to support widespread application of the GLI reference equations. Copyright © 2017 SEPAR. Publicado por Elsevier España, S.L.U. All rights reserved.
Nonlocal symmetry generators and explicit solutions of some partial differential equations
International Nuclear Information System (INIS)
Qin Maochang
2007-01-01
The nonlocal symmetry of a partial differential equation is studied in this paper. The partial differential equation written as a conservation law can be transformed into an equivalent system by introducing a suitable potential. The nonlocal symmetry group generators of original partial differential equations can be obtained through their equivalent system. Further, new explicit solutions can be constructed from the newly obtained symmetry generators. The Burgers equation is chosen as an example; many new valuable explicit solutions and nonlocal symmetry generators are presented
Dissociated Structure of Dislocation Loops with Burgers Vector alpha in Electron-Irradiated Cu-Ni
DEFF Research Database (Denmark)
Bilde-Sørensen, Jørgen; Leffers, Torben; Barlow, P.
1977-01-01
The rectangular dislocation loops with total Burgers vector a100 which are formed in Cu-Ni alloys during 1 MeV electron irradiation at elevated temperatures have been examined by weak-beam electron microscopy. The loop edges were found to take up a Hirth-lock configuration, dissociating into two ...
Measurement and assessment of aflatoxin B1 and its producing molds in Iranian sausages and burgers
Directory of Open Access Journals (Sweden)
Siavash Maktabi
2016-09-01
Full Text Available Abstract Introduction: Aflatoxin B1 (AFB1 is one of the most well-known hepatocarcinogens in humans. Contamination of raw materials, used in the production of sausages and burgers, with aflatoxin producing molds can lead to increased level of aflatoxin in the final products and can impose hazards to human health. Unfortunately, aflatoxin is resistant to heating and freezing processes, etc. and can remain in these products untile consumption. Methods: During a six-month period, 45 sausage and 53 burger samples from valid brands across the country were randomly purchased from the stores. The samples were analyzed for AFB1 by ELISA technique. Meanwhile, the number of molds was calculated and aflatoxin producing molds were identified by direct and slide culture methods. Results: The findings showed that 2 susage samples (4.9% and 3 burger samples (6.3% were contaminated with >1 ng/g aflatoxin. Moreover, 4 burger samples (8.9% contaminated with mold included aspergillus flavus, aspergillus niger, mucor, and penicillium while, none of the susage samples showed mold contamination. Conclusion: The Iranian meat products had a relative aflatoxin B1 contamination during the study period, but the contamination rate was low and in allowable range. Standard hygienic preparation and packaging of meat products molds is recommended to reduce fungal contamination, especially aflatoxin-producing molds.
Directory of Open Access Journals (Sweden)
George L. Karakostas
2006-08-01
Full Text Available We provide sufficient conditions for the existence of positive solutions of a three-point boundary value problem concerning a second order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning introduced in [19]. By writing the damping term as a difference of two factors one can extract more information on the solutions. (For instance, in an application, given in the last section, we can give the exact value of the norm of the solution.
Xiong, Yuan; Guo, Zhaoli
2014-01-01
at discrete level inherited in LBE (Guo et al 2011 Phys. Rev. E 83 036707). Based on the analysis of the LBE free of checkerboard effects, in this work we further show that the force imbalance is caused by the different discretization stencils: the implicit
Saitoh, K.; Magnanimo, Vanessa; Luding, Stefan
2016-01-01
Mechanical responses of soft particle packings to quasi-static deformations are determined by the microscopic restructuring of force-chain networks, where complex non-affine displacements of constituent particles cause the irreversible macroscopic behavior. Recently, we have proposed a master
International Nuclear Information System (INIS)
Geloni, G.; Yurkov, M.V.
2003-10-01
As a consequence of motions driven by external forces, self-fields originate within an electron bunch, which are different from the static case. In the case of magnetic external forces acting on an ultrarelativistic beam, the longitudinal self-interactions are responsible for CSR (coherent synchrotron radiation)-related phenomena, which have been studied extensively. On the other hand, transverse self-interactions are present too. At the time being, several existing theoretical analysis of transverse dynamics rely on the so-called cancellation effect, which has been around for more than ten years. In this paper we explain why in our view such an effect is not of practical nor of theoretical importance. (orig.)
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
It is shown that the (′/)-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations. ... Mehrdad Lakestani1. Department of Applied Mathematics, Faculty of Mathematics Science, University of Tabriz, Tabriz, Iran ...
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
Energy Technology Data Exchange (ETDEWEB)
Burda, Zdzislaw, E-mail: zdzislaw.burda@agh.edu.pl [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, PL-30059 Kraków (Poland); Grela, Jacek, E-mail: jacekgrela@gmail.com [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Nowak, Maciej A., E-mail: nowak@th.if.uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Tarnowski, Wojciech, E-mail: wojciech.tarnowski@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Warchoł, Piotr, E-mail: piotr.warchol@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland)
2015-08-15
Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size N and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large N limit is completely determined by the coevolution of the spectral density and a certain eigenvector correlation function. This coevolution is best visible in an electrostatic potential of a quaternionic argument built of two complex variables, the first of which governs standard spectral properties while the second unravels the hidden dynamics of eigenvector correlation function. We obtain general formulas for the spectral density and the eigenvector correlation function for large N and for any initial conditions. We exemplify our studies by solving three examples, and we verify the analytic form of our solutions with numerical simulations.
International Nuclear Information System (INIS)
Gelles, D.S.; Shibayama, T.
1998-01-01
A procedure for determining the Burgers vector anisotropy in irradiated ferritic steels allowing identification of all a and all a/2 dislocations in a region of interest is applied to a pressurized tube specimen of JLF-1 irradiated at 430 C to 14.3 x 10 22 n/cm 2 (E > 0.1 MeV) or 61 dpa. Analysis of micrographs indicates large anisotropy in Burgers vector populations develop during irradiation creep
Unsteady analytical solutions to the Poisson–Nernst–Planck equations
International Nuclear Information System (INIS)
Schönke, Johannes
2012-01-01
It is shown that the Poisson–Nernst–Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unsteady exact solutions for one and multidimensional cases are presented. Besides new mathematical insights which these first known unsteady solutions give, they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code. (paper)
International Nuclear Information System (INIS)
MATTAR, Z.A.; ABDELDAIEM, M.H.
2008-01-01
This investigation was carried out to extend the shelf-life of chicken burger using ethanol extract of propolis (EEP) at different concentrations (1 and 2%) as individual treatment using gamma irradiation at doses of 1.5, 3 and 4.5 kGy as individual treatment and combined treatments. The untreated and treated samples of chicken burger were divided into three groups, the first was control, the second group was chicken burger samples treated with 1% EEP then irradiated at doses of 1.5, 3 and 4.5 kGy and the third group was chicken burger samples treated with 2 % EEP then irradiated at doses of 1.5, 3 and 4.5 kGy. The effects of these treatments on the microbiological, chemical and sensory characteristics of chicken burger samples were studied post-treatment and during cold storage (4±1 0 C). The results showed that concentrations of EEP at 1 and 2% reduced the total bacterial count, lactic acid bacteria, Enterobacteriaceae total mold and yeast count, Staphylococcus aureus, Enterococccus faecalis and Bacillus cereus, and the growth of Salmonella spp, was not detected in all treated samples. Also, shelf-life periods were increased up to 27 days for chicken burger treated by 2% EEP and gamma radiation at dose of 4.5 kGy and these combined treatment were more effective as antimicrobial, consequently may be useful as natural food preservative
Exact solutions for nonlinear evolution equations using Exp-function method
International Nuclear Information System (INIS)
Bekir, Ahmet; Boz, Ahmet
2008-01-01
In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions
Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.
2015-01-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256
Assessment of value creation in private equity: the acquisition of Burger King by 3G Capital
Hoene, Daniel Jobst Elmar
2016-01-01
This thesis elaborates the creation of value in private equity and in particular analyzes value creation in 3G Capital’s acquisition of Burger King. In this sense, a specific model is applied that composes value creation into several drivers, in order to answer the question of how value creation can be addressed in private equity investments. Although previous research by Achleitner et al. (2010) introduced a specific model that addresses value creation in private equity, the r...
On exact solutions for oscillatory flows in a generalized Burgers fluid with slip condition
Energy Technology Data Exchange (ETDEWEB)
Hayat, Tasawar [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan); Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Najam, Saher [Theoretical Plasma Physics Div., PINSTECH, P.O. Nilore, Islamabad (Pakistan); Sajid, Muhammad; Mesloub, Said [Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Ayub, Muhammad [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan)
2010-05-15
An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency. (orig.)
Espina, Laura; García-Gonzalo, Diego; Pagán, Rafael
2014-08-01
Despite the vast body of available literature on the possibilities of essential oils (EOs) as food preservatives or functional ingredients, the sensory impact of their addition to foods has barely been approached. This work focuses on the hedonic taste acceptance of 3 food products (tomato juice, vegetable soup, and poultry burgers) when they are incorporated with potentially antimicrobial concentrations (20 to 200 μL/L) of 6 selected EOs (lemon, pennyroyal mint, thyme, and rosemary) and individual compounds (carvacrol, p-cymene). Although addition of 20 μL/L of pennyroyal mint or lemon EO did not change the taste acceptance of tomato juice, higher concentrations of these compounds or any concentration of the other 4 compounds did. In vegetable soup, the tolerance limit for rosemary EO, thyme EO, carvacrol, or p-cymene was 20 μL/L, while the addition of 200 μL/L of lemon EO was accepted. Tolerance limits in poultry burgers were established in 20 μL/L for carvacrol and thyme EOs, 100 μL/L for pennyroyal mint EO and p-cymene, and 200 μL/L for lemon and rosemary EOs. Moreover, incorporation of pennyroyal mint EO to tomato juice or poultry burgers, and enrichment of vegetable soup with lemon EO, could contribute to the development of food products with an improved sensory appeal. © 2014 Institute of Food Technologists®
Directory of Open Access Journals (Sweden)
Harun URAN
2017-10-01
Full Text Available Abstract Transglutaminases are enzymes that catalyze the cross-linking between peptides or proteins. They play an important role in heat stability, gel-formation capability, water-holding capacity, emulsification and nutritional properties of proteins. They are preferred in the use of a variety of meat products due to the binding properties. In this study the effect of transglutaminase on the quality characteristics of chicken burgers were investigated. The enzyme was added at 5 different concentrations (0.2%, 0.4%, 0.6%, 0.8% and 1% and the other treatments applied in burger production were followed. After the product was formed, it was left in the cold for a while and then analyses were carried out. According to the results, the enzyme contribution did not cause changes in the nutritional items (ash, fat, protein of the product groups. However, there was a significant decrease in the cooking loss and a significant increase in the texture values in the groups in which the enzyme amount was increased. Although the texture of the products have been increased, the transglutaminase treatment did not effect sensory parameters of burgers compared to the control samples. Scanning Electron Microscopy (SEM images also supported to the texture values of samples with the increase of cross-linking in microstructure.
My 2030s. Citizens about the Biobased Economy; My 2030s. Burgers over de Biobased Economy
Energy Technology Data Exchange (ETDEWEB)
Van den Berg, N.; Hulshof, M.; Van der Veen, M.
2013-02-15
My 2030s is the first qualitative study of the needs and concerns of citizens about the Biobased Economy, an economy in which fossil fuels are largely substituted by vegetable alternatives. This final report describes the reason and purpose of My 2030s, the course of the public debates and the results of research into ideas of citizens on the Biobased Economy The report concludes with recommendations on how the stakeholders can actively involve citizens in one of the major transitions of the next century [Dutch] My 2030s is het eerste kwalitatieve onderzoek naar de wensen en zorgen van burgers over de Biobased Economy, een economie waarin fossiele grondstoffen grotendeels zijn vervangen door plantaardige alternatieven. Dit eindrapport beschrijft de aanleiding en opzet van My 2030s, het verloop van de publieksdebatten en de resultaten van het onderzoek naar denkbeelden van burgers over de Biobased Economy. Het rapport eindigt met aanbevelingen over hoe de stakeholders burgers actief kunnen betrekken bij een van de belangrijkste transities van de komende eeuw.
Mancini, Simone; Preziuso, Giovanna; Dal Bosco, Alessandro; Roscini, Valentina; Szendrő, Zsolt; Fratini, Filippo; Paci, Gisella
2015-12-01
The objective of this study was to evaluate the effect of Curcuma longa powder and ascorbic acid on some quality traits of rabbit burgers. The burgers (burgers control with no additives; burgers with 3.5 g of turmeric powder/100g meat; burgers with 0.1g of ascorbic acid/100g meat) were analyzed at Days 0 and 7 for pH, color, drip loss, cooking loss, fatty acid profile, TBARS, antioxidant capacity (ABTS, DPPH and FRAP) and microbial growth. The addition of turmeric powder modified the meat color, produced an antioxidant capacity similar to ascorbic acid and determined a lower cooking loss than other formulations. Turmeric powder might be considered as a useful natural antioxidant, increasing the quality and extending the shelf life of rabbit burgers. Copyright © 2015 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2014-09-01
Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.
Optimal moving grids for time-dependent partial differential equations
Wathen, A. J.
1992-01-01
Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.
Directory of Open Access Journals (Sweden)
S Fathi
2014-05-01
Full Text Available Consolidated fish burger is a new product which is a combination of common Kilka (Clupeonellacultriventriscaspia and Silver carp (Hypophthalmichthys molitrix minced with flavors, fillers, vegetables and tofu dressing. Consolidated fish burger is produced in order to boost the nutritional value and to reduce the cost of end product. This study aimed to investigate the variations in the composition of consolidated burger during 4 months of storage at -18 °C. For this purpose, 4 types of burgers with a combination of a various percentages of Kilka and Silver carp were produced. The chemical composition by means of total protein, fat, moisture and ash contents were evaluated during preparation (zero phase and 4 months of storage. Results showed that at zero-phase protein% and moisture% in raw Silver carp was higher, whereas fat% and ash% in Kilka was found higher. Protein content in all groups was decreased during 4 months of storage. The decreasing rate was more rapid in control group as well as treatment 3. Fat percentage was dropped during the storage period and the decreasing trend in treatment 2 was found higher. In the case of moisture, the percentage was declined in all groups and in treatment 1, in particular. Considering the results, it was concluded that freezing could significantly decrease the nutritional value of the consolidated Burgers.
Formulation and shelf-life of fish burgers served to preschool children
Directory of Open Access Journals (Sweden)
Giorgio Smaldone
2017-03-01
Full Text Available Consumer is very careful about healthiness; in this context nutritionists often highlight the importance of fish for human nutrition because of their protein and fatty acid composition. In order to stimulate utilisation and consumption of fish species by unusual target groups such as children, the aim of this research was to formulate and to evaluate shelf-life and nutritional values of fish preparations stored in modified atmosphere packaging (MAP. Fish species used for trail were Trachurus trachurus and Oncorhynchus mykiss fished and farmed in Basilicata region respectively. Fish burgers were made with different ingredients of plant and animal origin and packed in air (control and in MAP and stored at refrigeration atemperature. Sensory, physicalchemical analysis as pH, aw, total volatile nitrogen (TVN, trimetilammine (TMA, thiobarbituric acid (TBA, free fatty acids (FFA and microbiological analysis like aerobic plate count, Enterobacteriaceae, Escherichia coli, Pseudomonas spp., sulphite-reducing clostridia, Staphylococci, Salmonella spp. and Listeria monocytogenes were performed at intervals of 0°, 1°, 2°, 5°, 8°, 15°, 22°, day from production. Results showed that fish burgers stored in MAP had a longer shelf-life; protein degradation indexes and spoilage bacterial species showed lower values in the samples packaged in MAP compared with the control. The formulation of the fish burger meets the approval of the target consumers. The mixing of natural ingredients has made possible both the enhancement of the organoleptic characteristics with an excellent balance of nutritional values. The diversification of fish preparations, besides enhancing the fish production of marginal areas would add value to a product with potential and remarkable profit margins.
Detection of Antibiotic Resistant Listeria spp. in Beef Burgers Distributed in Ahvaz City, Iran
Directory of Open Access Journals (Sweden)
Maktabi
2016-03-01
Full Text Available Background Listeria spp. are able to be survive in many foods during frozen storage. One particular species, Listeria monocytogenes, is one of the most important food-borne pathogens globally. The antimicrobial resistance of pathogenic microorganisms is a worldwide public health concern because of increasing global trade and travel. Objectives The aim of this study was to evaluate the occurrence and antibiotic resistance of Listeria spp. in the Iranian beef burgers distributed in Ahvaz city. Materials and Methods During a five-month period, 150 frozen burgers were purchased from local markets in Ahvaz city, and tested for presence of Listeria spp. The experimental procedure consisted of a one-step enrichment in Listeria enrichment broth, followed by plating on Oxford agar. Suspected colonies were subjected to subsequent biochemical tests and a polymerase chain reaction (PCR assay. The susceptibility of the isolates to various antibiotics was investigated using the Kirby-Bauer disk diffusion method, and the results were analyzed via the chi-square test and Fisher’s exact test using SPSS 16.0 software. Results Out of 150 samples, only two were contaminated with Listeria innocua, and the statistical analysis showed no significant differences in the prevalence of Listeria between companies (P > 0.05. One of the isolates was resistant to tetracycline and the other to co-trimoxazole. Both of the isolates showed an intermediate susceptibility to chloramphenicol; however, they were sensitive to the other tested antibiotics. Conclusions L. innocua is not a pathogen, but the presence of the bacterium could be an indicator of probable contamination with L. monocytogenes. Moreover, there is a potential risk to public health from the consumption of raw or undercooked burgers, which may increase the possibility of the acquisition of resistance to antibiotics.
Consumer-orientated development of hybrid beef burger and sausage analogues.
Neville, Michelle; Tarrega, Amparo; Hewson, Louise; Foster, Tim
2017-07-01
Hybrid meat analogues, whereby a proportion of meat has been partially replaced by more sustainable protein sources, have been proposed to provide a means for more sustainable diets in the future. Consumer testing was conducted to determine consumer acceptability of different formulations of Hybrid beef burgers and pork sausages in comparison with both meat and meat-free commercial products. Acceptability data were generated using the 9-point hedonic scale. Check-all-that-apply (CATA) questioning was used to determine the sensory attributes perceived in each product as well as information on the attributes of consumers' ideal products. It was identified that Hybrid products were generally well liked among consumers and no significant differences in consumer acceptability (p > .05) were identified between Hybrid and full meat products, whereas meat-free products were found to be less accepted. However, Hybrid sausages received higher acceptability scores (6.00-6.51) than Hybrid burgers (5.84-5.92) suggesting that format may have a large impact on consumer acceptability of Hybrid products. Correspondence Analysis (CA) indicated that Hybrid products were grouped with meat products in their sensory attributes. Penalty analysis found that a "meaty flavor" was the largest factor driving consumer acceptability in both burgers and sausages. Cluster analysis of consumer acceptability data identified key differences in overall acceptability between different consumer groups (consumers who only eat meat products and consumers who eat both meat and meat-free products). The Hybrid concept was found to bridge the acceptability gap between meat and meat-free products; however, further product reformulation is required to optimize consumer acceptability.
Directory of Open Access Journals (Sweden)
Kongkarn Kijroongrojana
2009-11-01
Full Text Available A battered shrimp burger, as a new value-added shrimp product, was developed by increasing the juiciness of a frozen battered shrimp burger using a mixture of hydrocolloids. The formulations of hydrocolloid mixtures containing modified tapioca starch (MTS, sodium alginate (AL, and iota-carrageenan (CA were optimized. Juiciness measurements were defined and analyzed by 13 trained panelists. Texture Profile Analysis (TPA as well as moisture and fat contents of the products were analyzed. The mixture of MTS and AL had an impact on moisture content and juiciness scores, while CA influenced the hardness. The product made using the optimized formulation (0.3% MTS + 0.7% AL had a higher moisture content andjuiciness scores (p0.05. However, higher springiness and gumminess were found in the control burger (p0.05.
Class of unconditionally stable second-order implicit schemes for hyperbolic and parabolic equations
International Nuclear Information System (INIS)
Lui, H.C.
The linearized Burgers equation is considered as a model u/sub t/ tau/sub x/ = bu/sub xx/, where the subscripts t and x denote the derivatives of the function u with respect to time t and space x; a and b are constants (b greater than or equal to 0). Numerical schemes for solving the equation are described that are second-order accurate, unconditionally stable, and dissipative of higher order. (U.S.)
Directory of Open Access Journals (Sweden)
S. Mancini
2016-06-01
Full Text Available The aim of this study was to evaluate the effects of turmeric powder and ascorbic acid on lipid oxidation and antioxidant capacity in cooked rabbit burgers. The burgers were derived from 3 different formulations (C, control, with no additives; Tu with 3.5% of turmeric powder and AA with 0.1% of ascorbic acid and were stored at 4°C for 0 and 7 d and cooked. The lipid oxidation (thiobarbituric acid reactive substances [TBARS] and antioxidant capacity (2,2-azinobis-[3 ethylbenzothiazoline-6-sulfonic acid] {ABTS}, 1,1-diphenyl-2-pircydrazyl [DPPH] and ferric reducing ability [FRAP] were evaluated. A significant interaction between storage time and formulation (P<0.001 was observed for DPPH, FRAP and TBARS in cooked burgers. At day 0 and day 7, the DPPH value was higher in Tu and AA compared to C burgers. At day 0, C showed a lower level of FRAP than the Tu and AA burgers. At day 7, the FRAP values tended to decrease but remained significantly higher in Tu and AA compared to C burgers. Lipid oxidation at day 0 in Tu and AA showed lower TBARS values compared to C burgers. The addition of 3.5% turmeric powder in rabbit burgers exerts an antioxidant effect during storage and it seems more effective in controlling lipid oxidation than ascorbic acid after cooking.
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Monjurul Haq
2013-12-01
Full Text Available Fish burger was produced from grass carp (Ctenophygodon idella to assess the feasibility of value addition to this low priced fish in Bangladesh. Different food additives (25% mashed potato, 2% NaCl, 2% soybean oil, 2% spices and 0.6% sugar were used to enhance the consumer’s acceptance of the fishery product. Consumers' acceptance of the fish burger was determined by sensory evaluation based on its color, flavor, softness or firmness (S/F, chewy/ rubbery (C/R using 10 point scoring system by a group of 10 untrained judges (20-50 years old. The results were found as follows: color (7.25±1.15, flavor (6.67±1.17, S/F (8.47±1.20 and C/R (7.83±1.23. Evaluation of proximate composition showed that the moisture and protein contents in grass carp mince were 79.15 ± 1.16 % and 18.01±0.44 % respectively which were higher than that of fish burger, 69.46 ± 0.89 % and 16.42 ± 0.57 %, respectively. Lipid (6.64±0.15 % and ash (2.98±0.09 % contents in fish burger were also higher than fish mince. The pH of fish mince and fish burger was 6.8±0.11 and 6.6±0.05 respectively. Therefore, from simple cost-profit analysis, it can be assumed that business of fish burger in Bangladesh has a very good prospect and it would be profitable.
Solutions of hyperbolic equations with the CIP-BS method
International Nuclear Information System (INIS)
Utsumi, Takayuki; Koga, James; Yamagiwa, Mitsuru; Yabe, Takashi; Aoki, Takayuki
2004-01-01
In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve general hyperbolic equations efficiently. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution owing to the constraints from the spatial derivatives of the master equations. Then, introducing scalar products, the linear and nonlinear partial differential equations are uniquely reduced to the ordinary differential equations for values and spatial derivatives at the grid points. The method gives stable, less diffusive, and accurate results. It is successfully applied to the continuity equation, the Burgers equation, the Korteweg-de Vries equation, and one-dimensional shock tube problems. (author)
Darboux transformations and linear parabolic partial differential equations
International Nuclear Information System (INIS)
Arrigo, Daniel J.; Hickling, Fred
2002-01-01
Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor
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Hadi Hashemi Gahruie
2017-01-01
Full Text Available In this study, the oxidative stability of beef burgers incorporated with Shirazi thyme, cinnamon, and rosemary extracts was compared with that of BHT-incorporated and antioxidant-free samples. The chemical composition, TBARS, metmyoglobin, pH, color, and microbial and sensory characteristics were evaluated during storage at −18°C for 2 months. The results indicated that Shirazi thyme and cinnamon extracts did not change the colorimetric properties significantly (P BHT > Shirazi thyme > rosemary > control. Finally, the results showed that these plant extracts can be utilized as an alternative to synthetic antioxidants in formulation of burgers.
Stephens, Neil; Ruivenkamp, Martin
2016-01-01
In vitro meat, also known as cultured meat, involves growing cells into muscle tissue to be eaten as food. The technology had its most high profile moment in 2013 when a cultured burger was cooked and tasted in a press conference. Images of the burger featured in the international media and were circulated across the internet. These images – literally marks on a two-dimension surface - do important work in establishing what in vitro meat is and what it can do. A combination of visual semiotic...
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2016-01-01
modulus. Three different approaches have been used and compared for calibrating the Burger's contact model. Values of the dynamic modulus and phase angle of asphalt mixtures were predicted by conducting DE simulation under dynamic strain control loading. The excellent agreement between the predicted......In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional discrete element method. Combined with Burger's model, three contact models were used for the construction of constitutive asphalt mixture model with viscoelastic properties...
Cooper, J D; Bird, S M
2002-01-01
The most likely human exposure to bovine spongiform encephalopathy (BSE) is dietary, through beef mechanically recovered meat (MRM) and head meat used in burgers, sausages and other meat products. The majority, reportedly 90% of beef MRM and 80% of head meat, was used in burgers. To enable quantification of UK dietary exposure to BSE, we quantified bovine carcass meat consumed as burgers, sausages and other meat products by birth cohort, gender and calendar period (1980-1989, 1990-1996). Synthesis of dietary data (cross-sectional National Dietary and Nutrition Surveys, and serial National Food Surveys and Realeat Surveys) to simulate weekly consumption by one-thousandth of the UK population in each year from 1980 to 1996. In 1980-1989, the highest number of consumers (per 7 days) of all three food groups was in the 1940-1969 birth cohort - averaging 3.7 million male consumers of burgers, 2.6 million of sausages and 8.5 million of other meat products. The post-1969 birth cohort had the next highest number of consumers of burgers (1.8 million males). In 1990-1996, consumer numbers declined for the two older cohorts, most strikingly for burgers (down to 2.5 million males in the 1940-1969 cohort). The 1940-1969 cohort retained the highest number of consumers of sausages and other meat products, and second place for burgers. Male consumption was higher, even in the pre-1940 birth cohort where, for demographic reasons, female consumers outnumbered males. In the post-1969 birth cohort, female consumption of bovine carcass meat weight as burgers increased from 68 tonnes in 1980-1989 to 81 tonnes in 1990-1996, and male consumption increased more markedly (by 41%) from 84 tonnes to 119 tonnes; and similarly for other meat products. Properly marshalled age-group and gender-specific consumption data contribute to a clearer understanding of the demography of those who were at risk of dietary exposure to BSE and of when their exposure intensity was greatest. Other countries may
International Nuclear Information System (INIS)
Furusawa, S; Togashi, H; Nagakura, H; Sumiyoshi, K; Yamada, S; Suzuki, H; Takano, M
2017-01-01
We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two- and three-body nuclear forces. We have extended the liquid drop model of heavy nuclei, utilizing the mass formula that accounts for the dependences of bulk, surface, Coulomb and shell energies on density and/or temperature. As for light nuclei, we employ a quantum-theoretical mass evaluation, which incorporates the Pauli- and self-energy shifts. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOSs, which covers a wide range of density, temperature and proton fraction that supernova simulations normally encounter. We make comparisons with the FYSS EOS, which is based on the same formulation for the nuclear ensemble but adopts the relativistic mean field theory with the TM1 parameter set for uniform nuclear matter. The new EOS is softer than the FYSS EOS around and above nuclear saturation densities. We find that neutron-rich nuclei with small mass numbers are more abundant in the new EOS than in the FYSS EOS because of the larger saturation densities and smaller symmetry energy of nuclei in the former. We apply the two EOSs to 1D supernova simulations and find that the new EOS gives lower electron fractions and higher temperatures in the collapse phase owing to the smaller symmetry energy. As a result, the inner core has smaller masses for the new EOS. It is more compact, on the other hand, due to the softness of the new EOS and bounces at higher densities. It turns out that the shock wave generated by core bounce is a bit stronger initially in the simulation with the new EOS. The ensuing outward propagations of the shock wave in the outer core are very similar in the two simulations, which
Dislocation Loops with a Burgers Vector Produced by 1 MeV Electron Irradiation in FCC Copper-Nickel
DEFF Research Database (Denmark)
Leffers, Torben; Barlow, P.
1975-01-01
Dislocation loops with Burgers vector a are formed in Cu-Ni alloys during 1 MeV electron irradiation in a high-voltage electron microscope at 350°-400°C. The dislocation loops are of interstitial type and pure edge in character with line vectors. Some of the loops are seen to dissociate into loop...
Dommering, E.
2008-01-01
De Abu Ghraib-foto's markeren een nieuw mediatijdperk, waarin de burgers actieve deelnemers in de media zijn geworden. In zijn afscheidscollege gaat Egbert Dommering in op de ontwikkeling van deze publieksparticipatie vanaf het moment van het afschaffen van overheidscensuur in de achttiende eeuw tot
Stephens, Neil; Ruivenkamp, Martin
2016-07-02
In vitro meat (IVM), also known as cultured meat, involves growing cells into muscle tissue to be eaten as food. The technology had its most high-profile moment in 2013 when a cultured burger was cooked and tasted in a press conference. Images of the burger featured in the international media and were circulated across the Internet. These images-literally marks on a two-dimensional surface-do important work in establishing what IVM is and what it can do. A combination of visual semiotics and narrative analysis shows that images of IVM afford readings of their story that are co-created by the viewer. Before the cultured burger, during 2011, images of IVM fell into four distinct categories: cell images, tissue images, flowcharts, and meat in a dish images. The narrative infrastructure of each image type affords different interpretations of what IVM can accomplish and what it is. The 2013 cultured burger images both draw upon and depart from these image types in an attempt to present IVM as a normal food stuff, and as 'matter in place' when placed on the plate. The analysis of individual images and the collection of images about a certain object or subject-known as the imagescape-is a productive approach to understanding the ontology and promise of IVM and is applicable to other areas of social life.
Directory of Open Access Journals (Sweden)
Manoela A. Pires
2017-01-01
Full Text Available The present study aimed to evaluate the effect of natural extracts (rosemary and green tea extracts in frozen storage of chicken burgers. Chicken burger treatments were prepared as follows: control (CON, 20 mg BHA/kg (BHA20, 10 mg green tea extract/kg (GT10, 38 mg green tea extract/kg (GT38, 18.6 mg rosemary extract/kg (RO18, and 480 mg rosemary extract/kg (RO480. Analysis of physicochemical parameters, color, TBAR index, and sensory acceptance were performed at 0, 30, 60, and 120 days of storage at −18°C in burgers packaged in LDPE plastic bags. The addition of natural antioxidants did not affect (p>0.05 the color and physicochemical parameters of the chicken burgers. After 120 days at −18°C, the RO480 sample showed a TBAR index similar (p>0.05 to BHA20 (0.423 and 0.369 mg, resp.. Sensory acceptance did not differ (p>0.05 among the treatments throughout the storage period (p>0.05.
Integrable discretization s of derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tsuchida, Takayuki
2002-01-01
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)
Using plukenetia volubilis (sacha inchi to improve the nutritional components of burger
Directory of Open Access Journals (Sweden)
Daniela Baldeón Clavijo
2015-06-01
Full Text Available (Received: 2015/03/18 - Accepted: 2015/05/27Three levels of paste Plukenetia volubilis (Sacha Inchi consisting of 10, 15% and 20% were evaluated to replace the weight percent lard conventionally used to improve the nutritional quality of the common hamburger, compared with a reference group. The experimental units were 10 burgers, weighing 100 g. each and a total of 120 were analyzed in a completely randomized design with three replications. The research was conducted in the Universidad Estatal Amazónica and bromatológics and microbiological analyzes to determine the quality of the raw material and products are made in laboratory of the Faculty of Chemical Sciences of the Universidad Central del Ecuador. As supplements sensory tests and studies Benefit / Cost performed. The results show the variation of 10% pulp Sacha Inchi as the most recommended for use in industry.
Copepods' Response to Burgers' Vortex: Deconstructing Interactions of Copepods with Turbulence.
Webster, D R; Young, D L; Yen, J
2015-10-01
This study examined the behavioral response of two marine copepods, Acartia tonsa and Temora longicornis, to a Burgers' vortex intended to mimic the characteristics of a turbulent vortex that a copepod is likely to encounter in the coastal or near-surface zone. Behavioral assays of copepods were conducted for two vortices that correspond to turbulent conditions with mean dissipation rates of turbulence of 0.009 and 0.096 cm(2) s(-3) (denoted turbulence level 2 and level 3, respectively). In particular, the Burgers' vortex parameters (i.e., circulation and rate of axial strain rate) were specified to match a vortex corresponding to the median rate of dissipation due to viscosity for each target level of turbulence. Three-dimensional trajectories were quantified for analysis of swimming kinematics and response to hydrodynamic cues. Acartia tonsa did not significantly respond to the vortex corresponding to turbulence level 2. In contrast, A. tonsa significantly altered their swimming behavior in the turbulence-level-3 vortex, including increased relative speed of swimming, angle of alignment of the trajectory with the axis of the vortex, ratio of net-to-gross displacement, and acceleration during escape, along with decreased turn frequency (relative to stagnant control conditions). Further, the location of A. tonsa escapes was preferentially in the core of the stronger vortex, indicating that the hydrodynamic cue triggering the distinctive escape behavior was vorticity. In contrast, T. longicornis did not reveal a behavioral response to either the turbulence level 2 or the level 3 vortex. © The Author 2015. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved. For permissions please email: journals.permissions@oup.com.
Entropy viscosity method applied to Euler equations
International Nuclear Information System (INIS)
Delchini, M. O.; Ragusa, J. C.; Berry, R. A.
2013-01-01
The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)
Structural stability and chaotic solutions of perturbed Benjamin-Ono equations
International Nuclear Information System (INIS)
Birnir, B.; Morrison, P.J.
1986-11-01
A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is very sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform
Selfinteraction force in a theory of gravitation with higher derivatives
International Nuclear Information System (INIS)
Jankiewicz, C.
1981-01-01
Approximate equations of motion are derived from gravitational field equations with higher derivatives. The approximation takes into account the selfinteraction force. The selfinteraction force coincides with the analogous force resulting from the Einstein field equations. (author)
Hossain, M A Motalib; Ali, Md Eaqub; Hamid, Sharifah Bee Abd; Hossain, S M Azad; Asing; Nizar, Nina Naquiah Ahmad; Uddin, Mohammad Nasir; Ali, Lokman; Asaduzzaman, Md; Akanda, Md Jahurul Haque
2017-06-01
Replacement of beef by buffalo and vice versa is frequent in global markets, but their authentication is challenging in processed foods due to the fragmentation of most biomarkers including DNA. The shortening of target sequences through use of two target sites might ameliorate assay reliability because it is highly unlikely that both targets will be lost during food processing. For the first time, we report a tetraplex polymerase chain reaction (PCR) assay targeting two different DNA regions in beef (106 and 120-bp) and buffalo (90 and 138-bp) mitochondrial genes to discriminate beef and buffalo in processed foods. All targets were stable under boiling, autoclaving and microwave cooking conditions. A survey in Malaysian markets revealed 71% beef curries contained buffalo but there was no buffalo in beef burgers. The assay detected down to 0.01ng DNA and 1% meat in admixed and burger products. Copyright © 2016 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Stam, T.; Diependaal, F.; Van ' t Hull, C.
2013-06-15
In the Solar Vision it is explained how the Amsterdam municipality plans to enable its citizens and businesses to realize their own solar energy project. The Solar Vision is prepared based on input from residents, businesses and institutions [Dutch] In de zonvisie staat hoe de gemeente Amsterdam haar burgers en bedrijven in staat wil stellen om hun eigen zonne-energieproject te realiseren. De zonvisie is mede opgesteld op basis van input van bewoners, bedrijven en instellingen.
International Nuclear Information System (INIS)
Trindade, Reginaldo Almeida da
2007-01-01
Radiation processing has been employed in some countries as a mean of treatment to assure microbiological safety of meat and meat products, avoiding the occurrence of food-borne disease. The ionizing radiation may cause some undesirable changes on chemistry composition of food and the lipid oxidation is one of the main reactions. In meat products processing industry, the lipid composition is directly related to nutritional and sensory quality of the product. For preventing oxidation, use of antioxidants which can be synthetic or natural, has been practically applied in some products. Currently, most attention has been given to natural antioxidants from herbs and spices like rosemary and oregano. The aim this study was to assess the antioxidant effects of either rosemary and oregano extract in beef burgers submitted to irradiation in 60 Co source with dose 6, 7 e 8 kGy, electron beams with dose 3,5 e 7 kGy and storage under freeze along 0, 45 e 90 days. The results showed that rosemary extract has the major antioxidant effects when it is used on heterogeneous food matrix like beef burger, but oregano extract was better efficient to delay lipid oxidation along storage time when it is used in synergism with rosemary and/or BHT/BHA. Although to have occurred changes in the fatty acids composition it was not possible to demonstrate a straight dependence of irradiation dose and/or storage time. Sensory analysis showed that between the samples prepared with natural antioxidants, the beef burger prepared with oregano has received better scores by panelists. Irradiated beef burger prepared with rosemary has received better scores when compared to non-irradiated one. The use of spices with antioxidant activity to avoid the oxidative damage in foods that contain fats in their formulation is thought to be promising to application in food facilities. (author)
de Gouvêa, Ana Al; Oliveira, Ronaldo L; Leão, André G; Assis, Dallyson Yc; Bezerra, Leilson R; Nascimento Júnior, Nilton G; Trajano, Jaqueline S; Pereira, Elzania S
2016-08-01
Licuri cake is a biodiesel byproduct and has been tested as an alternative feed additive for use in cattle production. This study analyzed the color, sensory and chemical attributes of burger meat from bovines. Thirty-two young Nellore bulls were used, housed in individual pens and distributed in a randomized experimental design with four treatments: no addition or the addition of 7, 14 or 21% (w/w) licuri cake in the dry matter of the diet. Interactions between the licuri cake level and the physicochemical variables (P > 0.05) were observed. Additionally, an interaction was observed between the licuri cake level and the burger beef color parameter lightness index (L*) (P = 0.0305). The L* value was positively and linearly correlated with the proportion of licuri cake in the diet of young bulls. The level of inclusion of licuri cake did not affect (P > 0.05) the sensory characteristics; the variables were graded between 6 and 7, indicating good overall acceptance. Up to 21% (w/w) licuri cake can be included in the diet of young bulls without negatively impacting on beef burger quality. © 2015 Society of Chemical Industry. © 2015 Society of Chemical Industry.
Groiss, Heiko; Glaser, Martin; Marzegalli, Anna; Isa, Fabio; Isella, Giovanni; Miglio, Leo; Schäffler, Friedrich
2015-06-01
By transmission electron microscopy with extended Burgers vector analyses, we demonstrate the edge and screw character of vertical dislocations (VDs) in novel SiGe heterostructures. The investigated pillar-shaped Ge epilayers on prepatterned Si(001) substrates are an attempt to avoid the high defect densities of lattice mismatched heteroepitaxy. The Ge pillars are almost completely strain-relaxed and essentially defect-free, except for the rather unexpected VDs. We investigated both pillar-shaped and unstructured Ge epilayers grown either by molecular beam epitaxy or by chemical vapor deposition to derive a general picture of the underlying dislocation mechanisms. For the Burgers vector analysis we used a combination of dark field imaging and large-angle convergent beam electron diffraction (LACBED). With LACBED simulations we identify ideally suited zeroth and second order Laue zone Bragg lines for an unambiguous determination of the three-dimensional Burgers vectors. By analyzing dislocation reactions we confirm the origin of the observed types of VDs, which can be efficiently distinguished by LACBED. The screw type VDs are formed by a reaction of perfect 60° dislocations, whereas the edge types are sessile dislocations that can be formed by cross-slips and climbing processes. The understanding of these origins allows us to suggest strategies to avoid VDs.
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
The E-assessment burger: Supporting the Before and After in E-Assessment Systems
Directory of Open Access Journals (Sweden)
Anne Adams
2015-08-01
Full Text Available This paper describes a threshold concept-driven e-assessment system that supports teachers in writing effective formative multiple-choice questions, creating quizzes tailored to students’ learning pathways. The system, which has been co-designed with teachers, acts as the ‘bun’ on either side of an ‘e-assessment burger’ pedagogically scaffolding quiz creation (the top of the bun, integrating the quiz within personalized learning trajectories (the burger and feeding the results back to the learners and teachers to guide the direction of future learning pathways (the bottom of the bun. The evaluation with 26 students in 3 subjects across two schools identified that supporting the before and after e-assessment empowers a shift in teachers’ encouragement for student ownership of assessment, guiding their learning pathways. Teachers also provide insights into how the system scaffolding and visualisations inspired changes to sequencing learning and teaching practices. In conclusion the changing role of assessment within a school ecosystem is debated.
International Nuclear Information System (INIS)
Inada, Fumio; Yoneda, Kimitoshi; Yasuo, Akira; Nishihara, Takashi
2000-01-01
In the circular tube bundle immersed in the crossflow, the exciting force induced by the turbulence and periodically discharged vortices becomes large, and it is necessary to confirm a long-term integrity to the flow induced vibration. In this report, the local fluid exciting force and the correlation length in the direction of tube axis were measured. The exciting force acting on the first row was smaller than that inside the tube bundle, and the exciting force was almost saturated at the third row. As for vortex induced vibration, there could be an influence when a dimensionless frequency was 0.4 or less. When vortex induced vibration did not affect the vibration, a correlation composed of a correlation length and power spectrum density of the local fluid exciting force were proposed, with which we could estimate the amplitude of the vibration. A computer program to estimate the vibration amplitude and maximum stress was made using the flow velocity distribution and the mode of vibration. (author)
Selani, Miriam M; Shirado, Giovanna A N; Margiotta, Gregório B; Rasera, Mariana L; Marabesi, Amanda C; Piedade, Sonia M S; Contreras-Castillo, Carmen J; Canniatti-Brazaca, Solange G
2016-05-01
The effect of freeze-dried pineapple by-product and canola oil as fat replacers on the oxidative stability, cholesterol content and fatty acid profile of low-fat beef burgers was evaluated. Five treatments were performed: conventional (CN, 20% fat) and four low-fat formulations (10% fat): control (CT), pineapple by-product (PA), canola oil (CO), and pineapple by-product and canola oil (PC). Low-fat cooked burgers showed a mean cholesterol content reduction of 9.15% compared to the CN. Canola oil addition improved the fatty acid profile of the burgers, with increase in the polyunsaturated/saturated fatty acids ratio and decrease in the n-6/n-3 ratio, in the atherogenic and thrombogenic indexes. The oxidative stability of the burgers was affected by the vegetable oil addition. However, at the end of the storage time (120 days), malonaldehyde values of CO and PC were lower than the threshold for the consumer's acceptance. Canola oil, in combination with pineapple by-product, can be considered promising fat replacers in the development of healthier burgers. Copyright © 2016 Elsevier Ltd. All rights reserved.
López-Vargas, Jairo H; Fernández-López, Juana; Pérez-Álvarez, José Ángel; Viuda-Martos, Manuel
2014-06-01
The aim of this work determined the technological, nutritional and sensory characteristics of pork burgers, added with different concentrations (2.5 and 5%) of passion fruit albedo (PFA) co-product, obtained from passion fruit juice processing. The addition of PFA on pork burgers improves their nutritional value (higher fiber content). In raw and cooked burger, all textural parameters, except springiness and cohesiveness, were affected by the incorporation of PFA. PFA addition was found to be effective improving the cooking yield, moisture retention and fat retention. The raw and cooked pork burgers added with PFA had lower TBA values and lower counts of aerobic mesophilic bacteria and enterobacteria than the control samples. No Escherichia coli and molds were found in the samples. The overall acceptability scores showed that the most appreciated sample was the one containing 2.5% PFA. According to the results obtained, 2.5 and 5% of PFA addition can be recommended in pork burger production as a new dietary fiber source. Copyright © 2014 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
C. Aquilani
2018-03-01
Full Text Available The most beneficial omega-3 PUFAs to human health, EPA and DHA fatty acids, are typically present in fish products, but extraneous to meat. Therefore, Cinta Senese pork burgers were added with microencapsulated (M and bulk fish oil (F and subjected to three storage conditions: no storage (T0, chilled (T5 and frozen storage (T30. The physico-chemical and sensory attributes of raw and cooked burgers were investigated. After storage and cooking, EPA and DHA were better preserved in M burgers than in F samples, which showed the highest TBAR values at T0 and T5, while M samples presented scores similar to the control. Panelists observed differences mainly in greasy appearance, odor intensity and cooked meat odor and flavor. The M group showed the best scores at T5 with respect to the control and F burgers. So, fish oil microencapsulation was an effective method to prevent EPA and DHA oxidation while respecting burger quality characteristics.
Selani, Miriam M; Shirado, Giovanna A N; Margiotta, Gregório B; Saldaña, Erick; Spada, Fernanda P; Piedade, Sonia M S; Contreras-Castillo, Carmen J; Canniatti-Brazaca, Solange G
2016-02-01
Pineapple byproduct and canola oil were evaluated as fat replacers on physicochemical and sensory characteristics of low-fat burgers. Five treatments were performed: conventional (CN, 20% fat) and four low-fat formulations (10% fat): control (CT), pineapple byproduct (PA), canola oil (CO), pineapple byproduct and canola oil (PC). Higher water and fat retention and lower cooking loss and diameter reduction were found in burgers with byproduct addition. In raw burgers, byproduct incorporation reduced L*, a*, and C* values, but these alterations were masked after cooking, leading to products similar to CN. Low-fat treatments were harder, chewier, and more cohesive than full-fat burgers. However, in Warner Bratzler shear measurements, PA and PC were as tender as CN. In QDA, no difference was found between CN and PC. Pineapple byproducts along with canola oil are promising fat replacers in beef burgers. In order to increase the feasibility of use of pineapple byproduct in the meat industry, alternative processes of byproduct preparation should be evaluated in future studies. Copyright © 2015 Elsevier Ltd. All rights reserved.
left-angle 100 right-angle Burgers vector in single phase γ' material verified by image simulation
International Nuclear Information System (INIS)
Link, T.; Knobloch, C.; Glatzel, U.
1998-01-01
The deformation mechanisms of Ni 3 Al, an ordered L1 2 or γ' phase, is under intense research since Westbrook showed the increase of its hardness with temperature in 1957. The super dislocations of this ordered phase normally have Burgers vectors rvec b = a left-angle 110 right-angle, disassociated in either two a/2 left-angle 110 right-angle or two rvec b = a/3 left-angle 112 right-angle, depending on deformation temperature and rate. Recent observations in [111] oriented γ' specimens suggest that additional dislocations with the shorter Burgers vector rvec b = a left-angle 100 right-angle might be active. Dislocations with rvec b = a left-angle 110 right-angle on cube glide planes have a Schmidt factor of 0.47 and on octahedral planes of 0.27. Dislocations with rvec b = a left-angle 100 right-angle have a Schmidt factor of 0.47 for {110} glide planes and 0.33 for cube glide planes. The a left-angle 100 right-angle Burgers vector is the shortest of all complete dislocations of the L1 2 structure and creates no planar fault like antiphase boundaries or stacking faults. Due to the [111] oriented stress axis, which is used in this contribution, plastic deformation by a left-angle 100 right-angle dislocations as well as cube glide planes for left-angle 110 right-angle dislocations is encouraged. These dislocations could be reaction products, but will soon after contribute to deformation
Forced solitary Rossby waves under the influence of slowly varying topography with time
International Nuclear Information System (INIS)
Yang Hong-Wei; Yin Bao-Shu; Yang De-Zhou; Xu Zhen-Hua
2011-01-01
By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg—de Vries (KdV)—Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves. (general)
Nonlinear second- and first-sound wave equations in 3He-4He mixtures
International Nuclear Information System (INIS)
Mohazzab, Masoud; Mulders, Norbert
2000-01-01
We derive nonlinear Burgers equations for first and second sound in mixtures of 3 He- 4 He, using a reductive perturbation method and obtain expressions for the nonlinear and dissipation coefficients. We further find a diffusion equation for a coupled temperature-concentration mode. The amplitude of first (second) sound generated from second (first) sound in mixtures is also derived. Our derivation includes the dependence of thermodynamical quantities on temperature, pressure, and 3 He concentration, and is valid up to a first order in terms of the isobaric expansion coefficient. We show that close to the λ line the nonlinearity of second sound in mixtures is enhanced as compared with pure 4 He
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Wheeler, J; Mariani, E; Piazolo, S; Prior, D J; Trimby, P; Drury, M R
2009-03-01
The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
International Nuclear Information System (INIS)
Wei, Guang-Mei
2006-01-01
Generalized two-dimensional variable-coefficient Burgers model is of current value in fluid mechanics, acoustics and cosmic-ray astrophysics. In this paper, Painleve analysis leads to the constraints on the variable coefficients for such a model to pass the Painleve test and to an auto-Baecklund transformation. Moreover, four transformations from this model are constructed, to the standard two-dimensional and one-dimensional Burgers models with the relevant constraints on the variable coefficients via symbolic computation. By virtue of the given transformations the properties and solutions of this model can be obtained from those of the standard two-dimensional and one-dimensional ones
Lorentz Covariance of Langevin Equation
International Nuclear Information System (INIS)
Koide, T.; Denicol, G.S.; Kodama, T.
2008-01-01
Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)
Nonlinear and linear wave equations for propagation in media with frequency power law losses
Szabo, Thomas L.
2003-10-01
The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Ebert, Marcelo R
2018-01-01
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes...
The aims of the current study were to investigate the presence of carcinogenic and mutagenic heterocyclic aromatic amines (HAAs) in chicken burgers (CBs) and chicken nuggets (CNs) purchased from fast food restaurants and the effects of green tea extract addition (GTE) to the covering material as wel...
Paredes-Madrid, Leonel; Matute, Arnaldo; Bareño, Jorge O; Parra Vargas, Carlos A; Gutierrez Velásquez, Elkin I
2017-11-21
Force Sensing Resistors (FSRs) are manufactured by sandwiching a Conductive Polymer Composite (CPC) between metal electrodes. The piezoresistive property of FSRs has been exploited to perform stress and strain measurements, but the rheological property of polymers has undermined the repeatability of measurements causing creep in the electrical resistance of FSRs. With the aim of understanding the creep phenomenon, the drift response of thirty two specimens of FSRs was studied using a statistical approach. Similarly, a theoretical model for the creep response was developed by combining the Burger's rheological model with the equations for the quantum tunneling conduction through thin insulating films. The proposed model and the experimental observations showed that the sourcing voltage has a strong influence on the creep response; this observation-and the corresponding model-is an important contribution that has not been previously accounted. The phenomenon of sensitivity degradation was also studied. It was found that sensitivity degradation is a voltage-related phenomenon that can be avoided by choosing an appropriate sourcing voltage in the driving circuit. The models and experimental observations from this study are key aspects to enhance the repeatability of measurements and the accuracy of FSRs.
Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations
Müller, Ingo
2008-12-01
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Spiecker, E
2002-01-01
A transmission electron microscopy method is described which allows us to determine the Burgers vectors (BVs) of a large number of interfacial misfit dislocations (MDs) in mismatched heterostructures. The method combines large-area plan-view thinning of the sample for creating a strongly bent electron transparent foil with the analysis of the splitting and displacement of bend contours at their crossings with the MDs. The BV analysis is demonstrated for 60 deg. MDs in a low-mismatched SiGe/Si(001) heterostructure. Crossings of various bend contours with the MDs are analysed with respect to their information content for the BV analysis. In future applications the method may be used for analysing such a large number of MDs that a quantitative comparison with x-ray diffraction experiments, especially with data on diffusely scattered x-rays originating from the strain fields around the dislocations, becomes possible.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Lattice Boltzmann model for high-order nonlinear partial differential equations
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
Lattice Boltzmann model for high-order nonlinear partial differential equations.
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
International Nuclear Information System (INIS)
Liu Hongzhun; Pan Zuliang; Li Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
Pomeau, Yves; Piasecki, Jarosław
2017-11-01
The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
DEFF Research Database (Denmark)
Bialynicki-Birula, I; Cirone, M.A.; Dahl, Jens Peder
2002-01-01
We present Heisenberg's equation of motion for the radial variable of a free non-relativistic particle in D dimensions. The resulting radial force consists of three contributions: (i) the quantum fictitious force which is either attractive or repulsive depending on the number of dimensions, (ii......) a singular quantum force located at the origin, and (iii) the centrifugal force associated with non-vanishing angular momentum. Moreover, we use Heisenberg's uncertainty relation to introduce a lower bound for the kinetic energy of an ensemble of neutral particles. This bound is quadratic in the number...... of atoms and can be traced back to the repulsive quantum fictitious potential. All three forces arise for a free particle: "Force without force"....
International Nuclear Information System (INIS)
Trindade, R.A.; Lima, A.; Andrade-Wartha, E.R.; Oliveira e Silva, A.M.; Mancini-Filho, J.; Villavicencio, A.L.C.H.
2009-01-01
The effect of addition of rosemary and oregano extracts on the sensory quality of irradiated beef burger was investigated. Batches of beef burgers were prepared with 400 ppm of rosemary or oregano extract and a group prepared with 200 ppm of synthetic butyl-hydroxytoluene (BHT)/butyl-hydroxy-anisol (BHA) was used as a control. Half of each formulation was irradiated at the maximum dose allowed for frozen meat (7 kGy). Samples were kept under frozen conditions (-20 deg. C) during the whole storage period, including during irradiation. Two analyses were performed after 20 and 90 days to verify the influence of the addition of the different types of antioxidants and the effect of irradiation and storage time on the acceptance of the product. Thirty-three and thirty-four untrained panelists were invited to participate in the first and second test, respectively. A structured hedonic scale ranging from 1 to 9 points was used in both analyses. BHT/BHA formulation obtained the highest score (6.73) and regarding the natural antioxidants, oregano received better acceptance (6.36). Irradiated samples formulated with oregano received a lower score, 6.03 in the first test and 5.06 in the second one, compared to the non-irradiated sample (6.36 and 5.79). In the second test (90 days), the sample formulated with BHT/BHA and which was irradiated received a higher score (6.59) when compared to the non-irradiated one (5.85). In both tests, the irradiated samples formulated with rosemary extract obtained a better score compared to the non-irradiated one, the scores being 5.00-3.82 and 5.00-3.76 in the first and second test, respectively. Our results allowed us to conclude that the natural antioxidants, rosemary and oregano extracts, present a good alternative for replacing synthetic additives in food industries, and that the irradiation process, in some cases, may help to enhance the sensory quality of food
Trindade, R. A.; Lima, A.; Andrade-Wartha, E. R.; Oliveira e Silva, A. M.; Mancini-Filho, J.; Villavicencio, A. L. C. H.
2009-04-01
The effect of addition of rosemary and oregano extracts on the sensory quality of irradiated beef burger was investigated. Batches of beef burgers were prepared with 400 ppm of rosemary or oregano extract and a group prepared with 200 ppm of synthetic butyl-hydroxytoluene (BHT)/butyl-hydroxy-anisol (BHA) was used as a control. Half of each formulation was irradiated at the maximum dose allowed for frozen meat (7 kGy). Samples were kept under frozen conditions (-20 °C) during the whole storage period, including during irradiation. Two analyses were performed after 20 and 90 days to verify the influence of the addition of the different types of antioxidants and the effect of irradiation and storage time on the acceptance of the product. Thirty-three and thirty-four untrained panelists were invited to participate in the first and second test, respectively. A structured hedonic scale ranging from 1 to 9 points was used in both analyses. BHT/BHA formulation obtained the highest score (6.73) and regarding the natural antioxidants, oregano received better acceptance (6.36). Irradiated samples formulated with oregano received a lower score, 6.03 in the first test and 5.06 in the second one, compared to the non-irradiated sample (6.36 and 5.79). In the second test (90 days), the sample formulated with BHT/BHA and which was irradiated received a higher score (6.59) when compared to the non-irradiated one (5.85). In both tests, the irradiated samples formulated with rosemary extract obtained a better score compared to the non-irradiated one, the scores being 5.00-3.82 and 5.00-3.76 in the first and second test, respectively. Our results allowed us to conclude that the natural antioxidants, rosemary and oregano extracts, present a good alternative for replacing synthetic additives in food industries, and that the irradiation process, in some cases, may help to enhance the sensory quality of food.
DEFF Research Database (Denmark)
Hesthaven, Jan
1997-01-01
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...
Smooth, cusped, and discontinuous traveling waves in the periodic fluid resonance equation
Kruse, Matthew Thomas
The principal motivation for this dissertation is to extend the study of small amplitude high frequency wave propagation in solutions for hyperbolic conservation laws begun by A. Majda and R. Rosales in 1984. It was then that Majda and Rosales obtained equations governing the leading order wave amplitudes of resonantly interacting weakly nonlinear high frequency wave trains in the compressible Euler equations. The equations were obtained through systematic application of multiple scales and result in a pair of nonlinear acoustic wave equations coupled through a convolution operator. The extended solutions satisfy a pair of inviscid Burgers' equations coupled via a spatial convolution operator. Since then, many mathematicians have used this technique to extend the time validity of solutions to systems of equations other than the Euler equations and have arrived at similar nonlinear non-local systems. This work attempts to look at some of the basic features of the linear and nonlinear coupled and decoupled non- local equations, offering some analytic solutions and numerical insight into the phenomena associated with these equations. We do so by examining a single non-local linear equation, and then a single equation coupling a Burgers' nonlinearity with a linear convolution operator. The linear case is completely solvable. Analytic solutions are provided along with numerical results showing the fundamental properties of the linear non- local equations. In the nonlinear case some analytic solutions, including steady state profiles and traveling wave solutions, are provided along with a battery of numerical simulations. Evidence indicates the existence of attractors for solutions of the single equation with a single mode kernel. Provided resonant interaction takes place, the profile of the attractor is uniquely dependent on the kernel alone. Hamiltonian equations are obtained for both the linear and nonlinear equations with the condition that the resonant kernel must
International Nuclear Information System (INIS)
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
Self-force on dislocation segments in anisotropic crystals
International Nuclear Information System (INIS)
Fitzgerald, S P; Aubry, S
2010-01-01
A dislocation segment in a crystal experiences a 'self-force', by virtue of the orientation dependence of its elastic energy. If the crystal is elastically isotropic, this force is manifested as a couple acting to rotate the segment toward the lower energy of the pure screw orientation (i.e. acting to align the dislocation line with its Burgers vector). If the crystal is anisotropic, there are additional contributions to the couple, arising from the more complex energy landscape of the lattice itself. These effects can strongly influence the dynamic evolution of dislocation networks, and via their governing role in dislocation multiplication phenomena, control plastic flow in metals. In this paper we develop a model for dislocation self-forces in a general anisotropic crystal, and briefly consider the technologically important example of α-iron, which becomes increasingly anisotropic as the temperature approaches that of the α-γ phase transition at 912 0 C.
Directory of Open Access Journals (Sweden)
E Harlia
2010-01-01
Full Text Available The aims of animal husbandry improvements are to increase both the quality and the quantity of livestock production and to ensure the safety of the product. It is necessarry for consumers to pay attention to the food safety of livestock product because it is related to human's health. The research was conducted to determine the food safety of livestock product condition by detecting heavy metal residues on several food products from livestock like meatball, corned beef, burger’s beef, and sausages. This research was explored by using survey's method and purposive technique sampling, then the resulted data were descriptively analyzed. The observed variables were heavy metal contents such as Plumbum (Pb and Cadmium (Cd in which being measured by using AAS (Atomic Absorption Spectrophotometri . The result showed that in general, heavy metal residue of Pb from several livestock products (meatball, corned beef, beef burger, and sausages were smaller than Maximum Residue Limit (MRL, while the Cd’s residue was partly over the MRL concentration, therefore further action has to be taken as it affects the human's health. (Animal Production 12(1: 50-54 (2010 Key words : food safety, MRL, heavy metal Pb, Cd.
San, O.
2016-01-01
The idea of spatial filtering is central in approximate deconvolution large-eddy simulation (AD-LES) of turbulent flows. The need for low-pass filters naturally arises in the approximate deconvolution approach which is based solely on mathematical approximations by employing repeated filtering operators. Two families of low-pass spatial filters are studied in this paper: the Butterworth filters and the Padé filters. With a selection of various filtering parameters, variants of the AD-LES are systematically applied to the decaying Burgers turbulence problem, which is a standard prototype for more complex turbulent flows. Comparing with the direct numerical simulations, it is shown that all forms of the AD-LES approaches predict significantly better results than the under-resolved simulations at the same grid resolution. However, the results highly depend on the selection of the filtering procedure and the filter design. It is concluded that a complete attenuation for the smallest scales is crucial to prevent energy accumulation at the grid cut-off.
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Velivelli, A. C.; Bryden, K. M.
2006-03-01
Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.
Unsteady Stokes equations: Some complete general solutions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes flow in the absence of body forces is derived. Keywords. Complete ...
DEFF Research Database (Denmark)
Engell-Nørregård, Morten Pol; Erleben, Kenny
We present a method for simulating the active contraction of deformable models, usable for interactive animation of soft deformable objects. We present a novel physical principle as the governing equation for the coupling between the low dimensional 1D activation force model and the higher...
International Nuclear Information System (INIS)
Sutton, C.
1989-01-01
Inside the atom, particles interact through two forces which are never felt in the everyday world. But they may hold the key to the Universe. These ideas on subatomic forces are discussed with respect to the strong force, the electromagnetic force and the electroweak force. (author)
Directory of Open Access Journals (Sweden)
A. A. Hemeda
2013-01-01
Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.
Some aspects of equations of state
International Nuclear Information System (INIS)
Frisch, H.L.
1979-02-01
Some elementary properties of the equation of state of molecules repulsing each other as point centers of force are developed briefly. An inequality for the Lennard--Jones gas is presented. The scaled particle theory equation of state of hard spheres is also reviewed briefly. Means of possibly applying these concepts to represent thermodynamic data on model detonating gases are suggested
DEFF Research Database (Denmark)
Csiszár, Gábor; Pantleon, Karen; Alimadadi, Hossein
2012-01-01
distribution are determined by high-resolution X-ray diffraction line profile analysis. The substructure parameters are correlated with the strength of the films by using the combined Taylor and Hall-Petch relations. The convolutional multiple whole profile method is used to obtain the substructure parameters......Nanocrystalline Ni thin films have been produced by direct current electrodeposition with different additives and current density in order to obtain 〈100〉, 〈111〉 and 〈211〉 major fiber textures. The dislocation density, the Burgers vector population and the coherently scattering domain size...
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Picone-type inequalities for nonlinear elliptic equations and their applications
Directory of Open Access Journals (Sweden)
Takaŝi Kusano
2001-01-01
Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.
Gravity as Quantum Entanglement Force
Lee, Jae-Weon; Kim, Hyeong-Chan; Lee, Jungjai
2010-01-01
We conjecture that the total quantum entanglement of matter and vacuum in the universe tends to increase with time, like entropy, and that an effective force is associated with this tendency. We also suggest that gravity and dark energy are types of quantum entanglement forces, similar to Verlinde's entropic force, and give holographic dark energy with an equation of state comparable to current observational data. This connection between quantum entanglement and gravity could give some new in...
Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood
2018-06-01
Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.
Packing force data correlations
International Nuclear Information System (INIS)
Heiman, S.M.
1994-01-01
One of the issues facing valve maintenance personnel today deals with an appropriate methodology for installing and setting valve packing that will minimize leak rates, yet ensure functionality of the the valve under all anticipated operating conditions. Several variables can affect a valve packing's ability to seal, such as packing bolt torque, stem finish, and lubrication. Stem frictional force can be an excellent overall indicator of some of the underlying conditions that affect the sealing characteristics of the packing and the best parameter to use when adjusting the packing. This paper addresses stem friction forces, analytically derives the equations related to these forces, presents a methodology for measuring these forces on valve stems, and attempts to correlate the data directly to the underlying variables
Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas
International Nuclear Information System (INIS)
Masood, W.; Rizvi, H.
2011-01-01
Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the small amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.
Exact results for the Boltzmann equation and Smoluchowski's coagulation equation
International Nuclear Information System (INIS)
Hendriks, E.M.
1983-01-01
Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)
African Journals Online (AJOL)
Owner
23 Jul 2008 ... In this novel memory and the importance of remembering is contemplated. ... process, often brings a sense of loss, but also contributes finding a way ... gemoeid met herinnering, met die wal gooi teen die verbygaan van tyd.
DEFF Research Database (Denmark)
Knakkergård, Martin
2010-01-01
Frank Zappas konceptalbum og filmmanuskript Uncle Meat fra 1969 kan på flere måder ses som en nøgle til hans kunst, hans samfundsopfattelse og hans livsforståelse. Allerede titlen synes at dække over et på samme tid humoristisk og aparte, ja, nærmest makabert dramatisk univers, og den lange...... programnote – præambel – støtter dette indtryk med sit skin af mytologi og karikeret science-fiction. I sit konkrete materiale fremstår Uncle Meat både tekstligt og musikalsk som en tætført pastiche sat kalejdoskopisk sammen af unikke brokker af især rock, jazz, musique concrète, pop, electronic og neoklassik......, som i forening med tekster, baseret på et til tider absurd billedsprog, fremstiller menneskelig fremmedgørelse, fornedrelse og tingsliggørelse. Artiklen her er en aftegning af Uncle Meats univers stykket sammen af deskriptive analyser af et udvalg af værkets nøgle- og hovedelementer med henblik på...
Directory of Open Access Journals (Sweden)
N.C.F. van Sas
2002-01-01
Full Text Available 1800N.C.F. van Sas'1800. Blueprints for a society' argues the case for the primacy of culture in late 18th-century Dutch society. Drawing upon the work of a generation of dix-huitiémistes it presents an impressive and highly readable overview of the Dutch Enlightenment. Unfortunately, this cultural vantage-point also results in a rather one-sided, if not positively unhistorical reading of this period which — by all accounts so far — was highly charged with politics. In fact, an opportunity is missed to connect the Enlightened civil society of the 1760s and 1770s with the revolutionary developments of the 1780s and 1790s.
Generalized equations of gravitational field
International Nuclear Information System (INIS)
Stanyukovich, K.P.; Borisova, L.B.
1985-01-01
Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Integrodifferential equation approach. Pt. 1
International Nuclear Information System (INIS)
Oehm, W.; Sofianos, S.A.; Fiedeldey, H.; South Africa Univ., Pretoria. Dept. of Physics); Fabre de la Ripelle, M.; South Africa Univ., Pretoria. Dept. of Physics)
1990-02-01
A single integrodifferential equation in two variables, valid for A nucleons interacting by pure Wigner forces, which has previously only been solved in the extreme and uncoupled adiabatic approximations is now solved exactly for three- and four-nucleon systems. The results are in good agreement with the values obtained for the binding energies by means of an empirical interpolation formula. This validates all our previous conclusions, in particular that the omission of higher (than two) order correlations in our four-body equation only produces a rather small underbinding. The integrodifferential equation approach (IDEA) is here also extended to spin-dependent forces of the Malfliet-Tjon type, resulting in two coupled integrodifferential equations in two variables. The exact solution and the interpolated adiabatic approximation are again in good agreement. The inclusion of the hypercentral part of the two-body interaction in the definition of the Faddeev-type components again leads to substantial improvement for fully local potentials, acting in all partial waves. (orig.)
Occupational Outlook Quarterly, 2012
2012-01-01
The labor force is the number of people ages 16 or older who are either working or looking for work. It does not include active-duty military personnel or the institutionalized population, such as prison inmates. Determining the size of the labor force is a way of determining how big the economy can get. The size of the labor force depends on two…
Towards information-optimal simulation of partial differential equations.
Leike, Reimar H; Enßlin, Torsten A
2018-03-01
Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.
Gale, David; And Others
Four units make up the contents of this document. The first examines applications of finite mathematics to business and economies. The user is expected to learn the method of optimization in optimal assignment problems. The second module presents applications of difference equations to economics and social sciences, and shows how to: 1) interpret…
Guiding-center equations for electrons in ultraintense laser fields
International Nuclear Information System (INIS)
Moore, J.E.; Fisch, N.J.
1994-01-01
The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation
Buhmann, Stefan Yoshi
2012-01-01
In this book, a modern unified theory of dispersion forces on atoms and bodies is presented which covers a broad range of advanced aspects and scenarios. Macroscopic quantum electrodynamics is shown to provide a powerful framework for dispersion forces which allows for discussing general properties like their non-additivity and the relation between microscopic and macroscopic interactions. It is demonstrated how the general results can be used to obtain dispersion forces on atoms in the presence of bodies of various shapes and materials. Starting with a brief recapitulation of volume I, this volume II deals especially with bodies of irregular shapes, universal scaling laws, dynamical forces on excited atoms, enhanced forces in cavity quantum electrodynamics, non-equilibrium forces in thermal environments and quantum friction. The book gives both the specialist and those new to the field a thorough overview over recent results in the field. It provides a toolbox for studying dispersion forces in various contex...
Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen
2018-06-01
In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.
Numerical solution of modified differential equations based on symmetry preservation.
Ozbenli, Ersin; Vedula, Prakash
2017-12-01
In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.
Rizwan Khan, Mohammad; Naushad, Mu; Abdullah Alothman, Zeid
2017-05-10
Heterocyclic amines (HCAs) are formed by cooking protein-rich foods, for instance, meat and fish, and are listed as possible human carcinogens. In the present study, the presence of five potential HCAs (IQ, MeIQ, MeIQx, 4,8-DiMeIQx, and PhIP) in cooked camel meat burgers was analyzed for the first time. The analysis was performed in home-cooked and fast-food burger samples containing food additives. The applied cooking technique for the home-cooked samples was pan frying for a controlled cooking time and temperature. In the control cooked meat samples (samples that contained no food additives), the concentrations of MeIQx, 4,8-DiMeIQx, and PhIP ranged from 2.47 ng/g to 4.89 ng/g, whereas IQ and MeIQ were found to be below the limit of quantification. The concentrations contents of MeIQx, 4,8-DiMeIQx, and PhIP in the home-cooked and fast-food samples ranged from 1.52 ng/g to 2.13 ng/g and 1.85 ng/g to 3.46 ng/g, respectively. IQ and MeIQ were not detected in either type of sample. In comparison to the control samples, the home-cooked and fast-food samples produced lower levels of HCAs. Such observations could result from the existence of antioxidants in incorporated food additives, which induce pro-oxidative effects with the successive formation and/or scavenging of free radicals.
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Nonlinear stability of source defects in the complex Ginzburg–Landau equation
International Nuclear Information System (INIS)
Beck, Margaret; Nguyen, Toan T; Sandstede, Björn; Zumbrun, Kevin
2014-01-01
In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction–diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg–Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for Green's function, which allow one to close a nonlinear iteration scheme. (paper)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2015-04-01
This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.
A new formulation of equations of compressible fluids by analogy with Maxwell's equations
International Nuclear Information System (INIS)
Kambe, Tsutomu
2010-01-01
A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.
1982-01-01
The different forces, together with a pictorial analogy of how the exchange of particles works. The table lists the relative strength of the couplings, the quanta associated with the force fields and the bodies or phenomena in which they have a dominant role.
Occupational Outlook Quarterly, 2010
2010-01-01
The labor force is the number of people aged 16 or older who are either working or looking for work. It does not include active-duty military personnel or institutionalized people, such as prison inmates. Quantifying this total supply of labor is a way of determining how big the economy can get. Labor force participation rates vary significantly…
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
Directory of Open Access Journals (Sweden)
Vladimir P. Gerdt
2006-05-01
Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.
Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation
Chang, Xiangke; Szmigielski, Jacek
2018-02-01
Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem, the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds, as well as Toda-like sorting property.
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Solitons in a random force field
International Nuclear Information System (INIS)
Bass, F.G.; Konotop, V.V.; Sinitsyn, Y.A.
1985-01-01
We study the dynamics of a soliton of the sine-Gordon equation in a random force field in the adiabatic approximation. We obtain an Einstein-Fokker equation and find the distribution function for the soliton parameters which we use to evaluate its statistical characteristics. We derive an equation for the averaged functions of the soliton parameters. We determine the limits of applicability of the delta-correlated in time random field approximation
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Mathieu's Equation and its Generalizations: Overview of Stability Charts and their Features
DEFF Research Database (Denmark)
Kovacic, Ivana; Rand, Richard H.; Sah, Si Mohamed
2018-01-01
This work is concerned with Mathieu's equation - a classical differential equation, which has the form of a linear second-order ordinary differential equation with Cosine-type periodic forcing of the stiffness coefficient, and its different generalizations/extensions. These extensions include...... and features, and how it differs from that of the classical Mathieu's equation....
Quantization of Equations of Motion
Directory of Open Access Journals (Sweden)
D. Kochan
2007-01-01
Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail.
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Magnus force in superfluids and superconductors
International Nuclear Information System (INIS)
Sonin, E.B.
1997-01-01
The forces on the vortex, transverse to its velocity, are considered. In addition to the superfluid Magnus force from the condensate (superfluid component), there are transverse forces from thermal quasiparticles and external fields violating the Galilean invariance. The forces between quasiparticles and the vortex originate from interference of quasiparticles with trajectories on the left and on the right from the vortex like similar forces for electrons interacting with the thin magnetic-flux tube (the Aharonov-Bohm effect). These forces are derived for phonons from the equations of superfluid hydrodynamics, and for BCS quasiparticles from the Bogolyubov endash de Gennes equations. The effect of external fields breaking Galilean invariance is analyzed for vortices in the two-dimensional Josephson junction array. The symmetry analysis of the classical equations for the array shows that the total transverse force on the vortex vanishes. Therefore the Hall effect which is linear in the transverse force is absent also. This means that the Magnus force from the superfluid component exactly cancels with the transverse force from the external fields. The results of other approaches are also brought together for discussion. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Holinde, K.
1990-01-01
In this paper the present status of the meson theory of nuclear forces is reviewed. After some introductory remarks about the relevance of the meson exchange concept in the era of QCD and the empirical features of the NN interaction, the exciting history of nuclear forces is briefly outlined. In the main part, the author gives the basic physical ideas and sketch the derivation of the one-boson-exchange model of the nuclear force, in the Feynman approach. Secondly we describe, in a qualitative way, various necessary extensions, leading to the Bonn model of the N interaction. Finally, points to some interesting pen questions connected with the extended quark structure of the hadrons, which are topics of current research activity
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Forced vibrations of rotating circular cylindrical shells
International Nuclear Information System (INIS)
Igawa, Hirotaka; Maruyama, Yoshiyuki; Endo, Mitsuru
1995-01-01
Forced vibrations of rotating circular cylindrical shells are investigated. Basic equations, including the effect of initial stress due to rotation, are formulated by the finite-element method. The characteristic relations for finite elements are derived from the energy principle by considering the finite strain. The equations of motion can be separated into quasi-static and dynamic ones, i.e., the equations in the steady rotating state and those in the vibration state. Radial concentrated impulses are considered as the external dynamic force. The transient responses of circular cylindrical shells are numerically calculated under various boundary conditions and rotating speeds. (author)
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
An equation of movement for supporting a drilling machine
Energy Technology Data Exchange (ETDEWEB)
Totev, Sl
1982-01-01
Support of a drilling machine is examined and an equation of movement is written. The equation has an invariant form and may be used for theoretical study of support in order to determine the forces and to study the stability and endurance of the elements as a whole.
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
Ponderomotive force near cyclotron resonance
Energy Technology Data Exchange (ETDEWEB)
Kono, Mitsuo; Sanuki, Heiji
1987-01-01
The ponderomotive force, which is involved in the excitation of macroscopic behaviors of plasma caused by wave motion, plays an important role in various non-linear wave motion phenomena. In the present study, equations for the pondermotive force for plasma in a uniform magnetic field is derived using a renormalization theory which is based on the Vlasov equation. It is shown that the pondermotive force, which diverges at the cyclotron resonence point according to adiabatic approximation, can be expressed by a non-divergent equation by taking into account the instability of the cyclotron orbit due to high-order scattering caused by a wave. This is related with chaotic particle behaviors near cyclotron resonance, where the pondermotive force is small and the diffusion process prevails. It is assumed here that the amplitude of the high-frequency electric field is not large and that the broadening of cyclotron levels is smaller than the distance between the levels. A global chaos will be created if the amplitude of the electric field becomes greater to allow the broadening to exceed the distance between the levels. (Nogami, K.).
SU(6) symmetry and the quark forces
International Nuclear Information System (INIS)
Bartnik, E.A.; Namyslowski, J.M.
1984-01-01
The short distance forces between 3 valence quarks in the proton are investigated in perturbative QCD formulated on the light cone. These forces are the driving terms in the Brodsky-Lepage type evolution equation for the partially decomposed distribution amplitudes. The one-gluon exchange force, which is the lowest order force in the running coupling constant αsub(s) retains the SU(6) symmetry, while the αsub(s) 2 -order force, corresponding to one Coulomb gluon and one transverse gluon, breaks the SU(6) symmetry. The latter force contributes to the deviation from 1/2 of the d/u ratio for the proton, observed experimentally. In the kinematical domain of one fast quark, the αsub(s) 2 -order force gives the leading (1-x) 3 behaviour of the deep inelastic structure function F 2 (x), in contrast to the αsub(s)-order force, which gives (1-x) 5 , for xapprox.=1. (orig.)
Chekroun, Mickaël D; Wang, Shouhong
2015-01-01
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Langevin equation with the deterministic algebraically correlated noise
International Nuclear Information System (INIS)
Ploszajczak, M.; Srokowski, T.
1995-01-01
Stochastic differential equations with the deterministic, algebraically correlated noise are solved for a few model problems. The chaotic force with both exponential and algebraic temporal correlations is generated by the adjoined extended Sinai billiard with periodic boundary conditions. The correspondence between the autocorrelation function for the chaotic force and both the survival probability and the asymptotic energy distribution of escaping particles is found. (author)
Obtention of an empirical equation for annular channels
International Nuclear Information System (INIS)
Diaz H, C.; Salinas R, G.A.
1996-01-01
Using a trial circuit, the experimental heat transfer coefficient is determined, in forced convection at one phase only within an annular channel in which water flows ascendantly and for this reason an empirical equation is determined. This work tries to contribute to the understanding of the forced convection phenomena in non tubular geometries like the annular channels. (Author)
Manca, V.; Salibra, A.; Scollo, Giuseppe
1990-01-01
Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Energy Technology Data Exchange (ETDEWEB)
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1994-01-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation
African Journals Online (AJOL)
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
M. Hazewinkel (Michiel)
1995-01-01
textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an
The generalized Fermat equation
Beukers, F.
2006-01-01
This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Numerical integration of the Langevin equation: Monte Carlo simulation
International Nuclear Information System (INIS)
Ermak, D.L.; Buckholz, H.
1980-01-01
Monte Carlo simulation techniques are derived for solving the ordinary Langevin equation of motion for a Brownian particle in the presence of an external force. These methods allow considerable freedom in selecting the size of the time step, which is restricted only by the rate of change in the external force. This approach is extended to the generalized Langevin equation which uses a memory function in the friction force term. General simulation techniques are derived which are independent of the form of the memory function. A special method requiring less storage space is presented for the case of the exponential memory function
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Supersymmetric quasipotential equations
International Nuclear Information System (INIS)
Zaikov, R.P.
1981-01-01
A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru
Local instant conservation equations
International Nuclear Information System (INIS)
Delaje, Dzh.
1984-01-01
Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Turbulence modification by periodically modulated scale-depending forcing
Kuczaj, Arkadiusz K.; Geurts, Bernardus J.; Lohse, Detlef; van de Water, W.
2006-01-01
The response of turbulent flow to time-modulated forcing is studied by direct numerical simulation of the Navier-Stokes equations. The forcing is modulated via periodic energy input variations at a frequency $\\omega$. Such forcing of the large-scales is shown to yield a response maximum at
Turbulence modification by periodically modulated scale-dependent forcing
Kuczaj, A.K.; Geurts, B.J.; Lohse, D.; Water, van de W.
2006-01-01
The response of turbulent flow to time-modulated forcing is studied by direct numerical simulation of the Navier-Stokes equations. The forcing is modulated via periodic energy input variations at a frequency !. Such forcing of the large-scales is shown to yield a response maximum at frequencies in
Turbulence modification by periodically modulated scale-dependent forcing
Kuczaj, A.K.; Geurts, B.J.; Lohse, D.; Water, van de W.
2008-01-01
The response of turbulent flow to time-modulated forcing is studied by direct numerical simulation of the Navier–Stokes equations. The forcing is modulated via periodic energy-input variations at a frequency ¿. Harmonically modulated forcing of the large scales is shown to yield a response maximum
Turbulence modification by periodically modulated scale-dependent forcing
Kuczaj, Arkadiusz K.; Geurts, Bernardus J.; Lohse, Detlef; van de Water, W.
2008-01-01
The response of turbulent flow to time-modulated forcing is studied by direct numerical simulation of the Navier–Stokes equations. The forcing is modulated via periodic energy-input variations at a frequency x. Harmonically modulated forcing of the large scales is shown to yield a response maximum
Evaluation of peak power prediction equations in male basketball players.
Duncan, Michael J; Lyons, Mark; Nevill, Alan M
2008-07-01
This study compared peak power estimated using 4 commonly used regression equations with actual peak power derived from force platform data in a group of adolescent basketball players. Twenty-five elite junior male basketball players (age, 16.5 +/- 0.5 years; mass, 74.2 +/- 11.8 kg; height, 181.8 +/- 8.1 cm) volunteered to participate in the study. Actual peak power was determined using a countermovement vertical jump on a force platform. Estimated peak power was determined using countermovement jump height and body mass. All 4 prediction equations were significantly related to actual peak power (all p jump prediction equations, 12% for the Canavan and Vescovi equation, and 6% for the Sayers countermovement jump equation. In all cases peak power was underestimated.
Evolution of wave turbulence under "gusty" forcing.
Annenkov, S Y; Shrira, V I
2011-09-09
We consider nonlinear evolution of a random wave field under gusty forcing, fluctuating around a constant mean. Here the classical wave turbulence theory that assumes a proximity to stationarity is not applicable. We show by direct numerical simulation that the self-similarity of wave field evolution survives under fluctuating forcing. The wave field statistical characteristics averaged over fluctuations of forcing evolve as if there were a certain constant "effective wind." The results justify the use of the kinetic equations with forcing averaged over gusts as a good first approximation.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Nonlinear differential equations
International Nuclear Information System (INIS)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
Equations of radiation hydrodynamics
International Nuclear Information System (INIS)
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
Quantum linear Boltzmann equation
International Nuclear Information System (INIS)
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Covariant field equations in supergravity
Energy Technology Data Exchange (ETDEWEB)
Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2017-12-15
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Covariant field equations in supergravity
International Nuclear Information System (INIS)
Vanhecke, Bram; Proeyen, Antoine van
2017-01-01
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A derivation of the beam equation
International Nuclear Information System (INIS)
Duque, Daniel
2016-01-01
The Euler–Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig of their undergraduate studies. We explain how this equation may be deduced, beginning with an approximate expression for the energy, from which the forces and finally the equation itself may be obtained. The description is begun at the level of small ‘particles’, and the continuum level is taken later on. However, when a computational solution is sought, the description turns back to the discrete level again. We first consider the easier case of a string under tension, and then focus on the beam. Numerical solutions for several loads are obtained. (paper)
A derivation of the beam equation
Duque, Daniel
2016-01-01
The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig of their undergraduate studies. We explain how this equation may be deduced, beginning with an approximate expression for the energy, from which the forces and finally the equation itself may be obtained. The description is begun at the level of small ‘particles’, and the continuum level is taken later on. However, when a computational solution is sought, the description turns back to the discrete level again. We first consider the easier case of a string under tension, and then focus on the beam. Numerical solutions for several loads are obtained.
Differential Equation over Banach Algebra
Kleyn, Aleks
2018-01-01
In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.
Marciuc, Daly; Solschi, Viorel
2017-04-01
Understanding the Coriolis effect is essential for explaining the movement of air masses and ocean currents. The lesson we propose aims to familiarize students with the manifestation of the Coriolis effect. Students are guided to build, using the GeoGebra software, a simulation of the motion of a body, related to a rotating reference system. The mathematical expression of the Coriolis force is deduced, for particular cases, and the Foucault's pendulum is presented and explained. Students have the opportunity to deepen the subject, by developing materials related to topics such as: • Global Wind Pattern • Ocean Currents • Coriolis Effect in Long Range Shooting • Finding the latitude with a Foucault Pendulum
International Nuclear Information System (INIS)
Panek, Richard
2010-01-01
Astronomers have compiled evidence that what we always thought of as the actual universe- all the planets, stars, galaxies and matter in space -represents a mere 4% of what's out there. The rest is dark: 23% is called dark matter, 73% dark energy. Scientists have ideas about what dark matter is, but hardly any understanding about dark energy. This has led to rethinking traditional physics and cosmology. Assuming the existence of dark matter and that the law of gravitation is universal, two teams of astrophysicists, from Lawrence Berkeley National Laboratory and the Australian National University, analysed the universe's growth and to their surprise both concluded that the universe expansion is not slowing but speeding up. If the dominant force of evolution isn't gravity what is it?
Magnetic monopoles, Galilean invariance, and Maxwell's equations
International Nuclear Information System (INIS)
Crawford, F.S.
1992-01-01
Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, ''as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities v much-lt c are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
BCS equations in the continuum
International Nuclear Information System (INIS)
Sandulescu, N.; Liotta, R. J.; Wyss, R.
1998-01-01
The properties of nuclei close to the drip line are significantly influenced by the continuum part of the single-particle spectrum. The main role is played by the resonant states which are largely confined in the region of nuclear potential and therefore stronger coupled with the bound states in an excitation process. Resonant states are also important in the nuclei beyond the drip line. In this case the decay properties of the nucleus can be directly related to the widths of the narrow resonances occupied by the unbound nucleons. The aim of this work is to propose an alternative for evaluating the effect of the resonant part of single-particle spectrum on the pairing correlations calculated within the BCS approximation. We estimated the role of resonances in the case of the isotope 170 Sn. The Resonant-BCS (RBCS) equations are solved for the case of a seniority force. The BCS approximation based on a seniority force cannot be applied in the case of a nucleus immersed in a box if all discrete states simulating the continuum are considered. In such a case the pairing correlations will increase with the number of states in the box. In our case one can still apply a seniority force with RBCS because the effect of the continuum appears here through a finite number of physical resonances, well defined by the given mean field. Because these resonances have a spatial distribution concentrated within the region of the nuclear potential, one expects that the localization probability of nucleons, far out from the nuclear surface, to be small. The gap obtained taking correctly the contribution of resonances, according to RBCS equations, is about 1.3 MeV, while pairing gap calculated only with the bound single-particle spectrum has the value Δ = 1.10 MeV. If we introduce also the resonant states, neglecting completely their widths, the gap will increase to the value Δ = 1.880 MeV. Therefore, one cannot estimate properly the pairing correlations by supplementing the spectrum
Transversal light forces in semiconductors
Lindberg, M
2003-01-01
The transversal light force is a well established effect in atomic and molecular systems that are exposed to spatially inhomogeneous light fields. In this paper it is shown theoretically that in an excited semiconductor, containing an electron-hole plasma or excitons, a similar light force exists, if the semiconductor is exposed to an ultrashort spatially inhomogeneous light field. The analysis is based on the equations of motion for the Wigner distribution functions of charge carrier populations and interband polarizations. The results show that, while the light force on the electron-hole plasma or the excitons does exist, its effects on the kinetic behaviour of the electron-hole plasma or the excitons are different compared to the situation in an atomic or molecular system. A detailed analysis presented here traces this difference back to the principal differences between atoms and molecules on the one hand and electron-hole plasmas or excitons on the other hand.
Transport equation solving methods
International Nuclear Information System (INIS)
Granjean, P.M.
1984-06-01
This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations
Wagenmaker, Timothy Roger
This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of
New Formulation of the Governing Equations for Analyzing Outrigger Structures
International Nuclear Information System (INIS)
Er, G.-K.
2010-01-01
In this paper, an easily comprehensible solution procedure is proposed for the analysis of outrigger-braced structures. The idea is based on the compatibility of the columns' axial deformation. The unknowns are selected to be the axial forces in the columns. The resulted governing equations and the equations for the optimum analysis of the outrigger locations are different from the conventional ones, but numerical analysis shows that the results obtained with the new equations are same as those obtained with conventional equations. The relations between the new equations and the conventional ones are also figured out. The new procedure of formulating the governing equations can be easily extended to more complicated cases of outrigger-braced structures.
Generalization of the Dirac’s Equation and Sea
DEFF Research Database (Denmark)
Javadi, Hossein; Forouzbakhsh, Farshid; Daei Kasmaei, Hamed
2016-01-01
Newton's second law is motion equation in classic mechanics that does not say anything about the nature of force. The equivalent formulations and their extensions such as Lagrangian and Hamiltonian do not explain about mechanism of converting Potential energy to Kinetic energy and Vice versa....... In quantum mechanics, Schrodinger equation is similar to Newton's second law in classic mechanics. Quantum mechanics is also extension of Newtonian mechanics to atomic and subatomic scales and relativistic mechanics is extension of Newtonian mechanics to high velocities near to velocity of light too....... Schrodinger equation is not a relativistic equation, because it is not invariant under Lorentz transformations. Dirac expanded The Schrodinger equation by presenting Dirac Sea and founded relativistic quantum mechanics. In this paper by reconsidering the Dirac Sea and his equation, the structure of photon...
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Iteration of adjoint equations
International Nuclear Information System (INIS)
Lewins, J.D.
1994-01-01
Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Speranza, B; Bevilacqua, A; Mastromatteo, M; Sinigaglia, M; Corbo, M R
2010-08-01
The objective of the current study was to examine the interactions between Pseudomonas putida and Escherichia coli O157:H7 in coculture studies on fish-burgers packed in air and under different modified atmospheres (30 : 40 : 30 O(2) : CO(2) : N(2), 5 : 95 O(2) : CO(2) and 50 : 50 O(2) : CO(2)), throughout the storage at 8 degrees C. The lag-exponential model was applied to describe the microbial growth. To give a quantitative measure of the occurring microbial interactions, two simple parameters were developed: the combined interaction index (CII) and the partial interaction index (PII). Under air, the interaction was significant (P exponential growth phase (CII, 1.72), whereas under the modified atmospheres, the interactions were highly significant (P exponential and in the stationary phase (CII ranged from 0.33 to 1.18). PII values for E. coli O157:H7 were lower than those calculated for Ps. putida. The interactions occurring into the system affected both E. coli O157:H7 and pseudomonads subpopulations. The packaging atmosphere resulted in a key element. The article provides some useful information on the interactions occurring between E. coli O157:H7 and Ps. putida on fish-burgers. The proposed index describes successfully the competitive growth of both micro-organisms, giving also a quantitative measure of a qualitative phenomenon.
Analysis of wave equation in electromagnetic field by Proca equation
International Nuclear Information System (INIS)
Pamungkas, Oky Rio; Soeparmi; Cari
2017-01-01
This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Forced vibration analysis of a Timoshenko cracked beam using a continuous model for the crack
Mahdi Heydari; Alireza Ebrahimi; Mehdi Behzad
2014-01-01
In this paper, forced flexural vibration of a cracked beam is studied by using a continuous bilinear model for the displacement field. The effects of shear deformation and rotary inertia are considered in the model. The governing equation of motion for the beam is obtained using the Hamilton principle and based on the proposed displacement field. The equation of motion is given for a general force distribution. Then, the equation of motion has been solved for a concentrated force to present a...
Attractors of the periodically forced Rayleigh system
Directory of Open Access Journals (Sweden)
Petre Bazavan
2011-07-01
Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.
Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series
Gnoffo, Peter A.
2015-01-01
Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.
Indian Academy of Sciences (India)
The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Indian Academy of Sciences (India)
research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
African Journals Online (AJOL)
Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.
Indian Academy of Sciences (India)
However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...
Guiding center drift equations
International Nuclear Information System (INIS)
Boozer, A.H.
1979-03-01
The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Quantum equations from Brownian motions
International Nuclear Information System (INIS)
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
International Nuclear Information System (INIS)
Li Juan; Xu Tao; Zhang Haiqiang; Gao Yitian; Tian Bo
2008-01-01
In this paper, the cylindrical Kadomtsev-Petviashvili (KP) equation arising from dusty plasmas and Bose-Einstein condensates is investigated by the decomposition method. Through the nonlinearization of a single Lax pair, this equation is decomposed into a generalized variable-coefficient Burgers equation and its third-order extension, and then a series of analytic soliton-like solutions are obtained. Furthermore, with the aid of symbolic computation, a symmetry potential constraint in terms of the squared eigenfunctions is proposed to nonlinearize two symmetry Lax pairs into the first two variable-coefficient 2N-coupled soliton systems in the same hierarchy. Based on the Lax representation for these two decomposed soliton systems, a Darboux transformation is constructed to iteratively generate the multi-soliton-like solutions. Via the obtained analytic soliton-like solutions, the graphical analysis is devoted to the one-parabola soliton structure, compressive and rarefactive soliton resonance phenomena occurring in dusty plasmas and Bose-Einstein condensates
On generalized fractional vibration equation
International Nuclear Information System (INIS)
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-01-01
Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.
Erfgoedconstructies in landschapspraktijken van burgers
Braaksma, Patricia
2017-01-01
Decisions to cut down monumental trees or demolish historic buildings can always count on civilian protests. Every year, the Dutch tradition of Zwarte Piet (‘Black Pete’) is heavily debated, the protests almost a tradition themselves. There are regular reports about concerned people
Null controllability of a cascade system of Schrodinger equations
Directory of Open Access Journals (Sweden)
Marcos Lopez-Garcia
2016-03-01
Full Text Available This article presents a control problem for a cascade system of two linear N-dimensional Schrodinger equations. We address the problem of null controllability by means of a control supported in a region not satisfying the classical geometrical control condition. The proof is based on the application of a Carleman estimate with degenerate weights to each one of the equations and a careful analysis of the system in order to prove null controllability with only one control force.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
equateIRT: An R Package for IRT Test Equating
Directory of Open Access Journals (Sweden)
Michela Battauz
2015-12-01
Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.
R5FORCE: a program to compute fluid induced forces using hydrodynamic output from the RELAP5 code
International Nuclear Information System (INIS)
Watkins, J.C.
1983-01-01
This paper describes the computer code R5FORCE, a postprocessor to the RELAP5/MOD1 thermal-hydraulics code. R5FORCE computes piping hydraulic force/time histories that can be input into various structural analysis computer codes. R5FORCE solves the momentum conservation equation using the pressure and wall shear force terms rather than the pressure and fluid acceleration terms; eliminating potential instabilities associated with computing the time derivative in the fluid acceleration term. The updates to REALP5 required to generate the input data to R5FORCE are also discussed
Force AOR Travel Info News prevnext Slide show 76,410 pounds of food delivered to Haiti 12th Air Force the French Air Force, Colombian Air Force, Pakistan Air Force, Belgian Air Force, Brazilian Air Force
Breit, Dominic; Hofmanová, Martina
2018-01-01
The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences.
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Flavored quantum Boltzmann equations
International Nuclear Information System (INIS)
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Causal electromagnetic interaction equations
International Nuclear Information System (INIS)
Zinoviev, Yury M.
2011-01-01
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Equations of multiparticle dynamics
International Nuclear Information System (INIS)
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Electroweak evolution equations
International Nuclear Information System (INIS)
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
The incompressible non-relativistic Navier-Stokes equation from gravity
International Nuclear Information System (INIS)
Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.
2009-01-01
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Fractional Bhatnagar-Gross-Krook kinetic equation
Goychuk, Igor
2017-11-01
The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.
Langevin equation with the deterministic algebraically correlated noise
Energy Technology Data Exchange (ETDEWEB)
Ploszajczak, M. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France); Srokowski, T. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)]|[Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
Stochastic differential equations with the deterministic, algebraically correlated noise are solved for a few model problems. The chaotic force with both exponential and algebraic temporal correlations is generated by the adjoined extended Sinai billiard with periodic boundary conditions. The correspondence between the autocorrelation function for the chaotic force and both the survival probability and the asymptotic energy distribution of escaping particles is found. (author). 58 refs.
An Alternative Stability Equation For Rock Armoured Rubble Mound Breakwaters
DEFF Research Database (Denmark)
Hald, Tue; Burcharth, H. F.
2000-01-01
Rubble mound breakwaters are by far the most common type of breakwater, the importance of which is clearly reflected in the vast amount of published research. Especially, the hydraulic stability of the main armour layer has been studied in order to obtain reliable design equations. It should...... equations and model test results still exists. When turning toward prototype the situation is even worse. With the objective to reduce some of the variability an alternative approach based on force considerations is presented. The paper will describe a new stability equation for rock armoured slopes derived...
The propagation of travelling waves for stochastic generalized KPP equations
International Nuclear Information System (INIS)
Elworthy, K.D.; Zhao, H.Z.
1993-09-01
We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, milk, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the appendix J.G. Gaines illustrates these different regimes by computer simulations. (author). 27 refs, 13 figs
Moment equation approach to neoclassical transport theory
International Nuclear Information System (INIS)
Hirshman, S.P.
1978-01-01
The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory unifies the numerous complex expressions for the transport coefficients, previously obtained by solving the Fokker--Planck equation, and elucidates their physical basis. In the large aspect ratio limit, the continuous transition in the scaling of the diffusion coefficient throughout various collisionality regimes is shown to depend on the ratio of parallel viscosity coefficients of the plasma species. Comparison of the present results with the kinetic theory expressions for the neoclassical fluxes determines the parallel viscosity coefficients for a multispecies plasma in the long-mean-free-path regime
The Lorentz-Dirac equation in light of quantum theory
International Nuclear Information System (INIS)
Nikishov, A.I.
1996-01-01
To high accuracy, an electron in ultrarelativistic motion 'sees' an external field in its rest frame as a crossed field (E=H, E·H=0). In this case, quantum expressions allow the introduction of a local intensity of the radiation, which determines the radiative term of the force of radiative reaction. For γ=(1-v2)-1/2>> 1 this term is much larger than the mass term, i.e., the term with xd3do. Under these conditions, the reduced Lorentz-Dirac equation, which is obtained from the full Lorentz-Dirac equation by eliminating the terms xd3do and xe on the right side using the equation of motion without taking into account the force of radiative reaction, is equivalent to good accuracy to the original Lorentz-Dirac equation. Exact solutions to the reduced Lorentz-Dirac equation are obtained for a constant field and the field of a plane wave. For γ∼1 a local expression for the radiative term cannot be obtained quantitatively from the quantum expressions. In this case the mass (Lorentz-Dirac) terms in the original and reduced Lorentz-Dirac equations are not small compared to the radiative term. The predictions of these equations, which depend appreciably on the mass terms, are therefore less reliable
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...
African Journals Online (AJOL)
eobe
plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
On the Eikonal equation in the pedestrian flow problem
Felcman, J.; Kubera, P.
2017-07-01
We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.
Directory of Open Access Journals (Sweden)
Mervan Pašić
2014-01-01
Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.
System modelling of a lateral force microscope
International Nuclear Information System (INIS)
Michal, Guillaume; Lu, Cheng; Kiet Tieu, A
2008-01-01
To quantitatively analyse lateral force microscope measurements one needs to develop a model able to relate the photodiode signal to the force acting on the tip apex. In this paper we focus on the modelling of the interaction between the cantilever and the optical chain. The laser beam is discretized by a set of rays which propagates in the system. The analytical equation of a single ray's position on the optical sensor is presented as a function of the reflection's state on top of the cantilever. We use a finite element analysis on the cantilever to connect the optical model with the force acting on the tip apex. A first-order approximation of the constitutive equations are derived along with a definition of the system's crosstalk. Finally, the model is used to analytically simulate the 'wedge method' in the presence of crosstalk in 2D. The analysis shows how the torsion loop and torsion offset signals are affected by the crosstalk.
Auxiliary equation method for solving nonlinear partial differential equations
International Nuclear Information System (INIS)
Sirendaoreji,; Jiong, Sun
2003-01-01
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
Stefanescu, Dan Mihai
2011-01-01
Part I introduces the basic ""Principles and Methods of Force Measurement"" acording to a classification into a dozen of force transducers types: resistive, inductive, capacitive, piezoelectric, electromagnetic, electrodynamic, magnetoelastic, galvanomagnetic (Hall-effect), vibrating wires, (micro)resonators, acoustic and gyroscopic. Two special chapters refer to force balance techniques and to combined methods in force measurement. Part II discusses the ""(Strain Gauge) Force Transducers Components"", evolving from the classical force transducer to the digital / intelligent one, with the inco
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
dimensional Jaulent–Miodek equations
Indian Academy of Sciences (India)
(2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...
Equationally Noetherian property of Ershov algebras
Dvorzhetskiy, Yuriy
2014-01-01
This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
International Nuclear Information System (INIS)
Tsuchida, Takayuki; Wolf, Thomas
2005-01-01
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
Energy Technology Data Exchange (ETDEWEB)
Tsuchida, Takayuki [Department of Physics, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337 (Japan); Wolf, Thomas [Department of Mathematics, Brock University, St Catharines, ON L2S 3A1 (Canada)
2005-09-02
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.