Institute of Scientific and Technical Information of China (English)
Shu-hai ZHANG; Xiao-gang DENG; Mei-liang MAO; Chi-Wang SHU
2013-01-01
The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X.and Zhang H.(2000),J.Comput.Phys.165,22-44 and Zhang S.,Jiang S.and Shu C.-W.(2008),J.Comput.Phys.227,7294-7321] is studied through numerical tests.Like most other shock capturing schemes,WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level.In this paper,the techniques studied in [Zhang S.and Shu.C.-W.(2007),J.Sci.Comput.31,273-305 and Zhang S.,Jiang S and Shu.C.-W.(2011),J.Sci.Comput.47,216-238],to improve the convergence to steady state solutions for WENO schemes,are generalized to the WCNS.Detailed numerical studies in one and two dimensional cases are performed.Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS.The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.
Inverse solution technique of steady-state responses for local nonlinear structures
Wang, Xing; Guan, Xin; Zheng, Gangtie
2016-03-01
An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude-frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Lin, Zhi; Zhang, Qinghai
2017-09-01
We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1990-01-01
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1991-01-01
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
Rips, Simon; Wilson-Rae, Ignacio; Hartmann, Michael J
2011-01-01
We propose a scheme to prepare nanomechanical oscillators in non-classical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser driven resonances of an optical cavity. By lowering the resonant frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables preparation of the nanomechanical oscillator in a single phonon Fock state. Our scheme can for example be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.
Steady-state solution methods for open quantum optical systems
Nation, P. D.
2015-01-01
We discuss the numerical solution methods available when solving for the steady-state density matrix of a time-independent open quantum optical system, where the system operators are expressed in a suitable basis representation as sparse matrices. In particular, we focus on the difficulties posed by the non-Hermitian structure of the Lindblad super operator, and the numerical techniques designed to mitigate these pitfalls. In addition, we introduce a doubly iterative inverse-power method that...
Institute of Scientific and Technical Information of China (English)
王自东; 胡汉起
1997-01-01
The nonlinear dynamics equations of the time dependence of the perturbation amplitude of the solid/ liquid interface during unidirectional solidification of a dilute binary alloy are established. The solutions to these equations are obtained, and the condition of the initial steady state growth of the cellular and dendritic structure after the planar solid/liquid interface bifurcates (mGc> G) with the increase of the growth rate is given. The condition of the steady state growth of fine cellular and dendritic structure in the beginning after the coarse dendrites bifurcate ( mGc<Γw2 + G) under the rapid solidification is obtained. The relationship of the steady state cell and dendrite tip radius, the perturbation amplitude and wavelength at the solid/liquid interface is presented.
STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING
Institute of Scientific and Technical Information of China (English)
吴俊; 陈立群
2004-01-01
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
Halász, Adám M; Lai, Hong-Jian; McCabe Pryor, Meghan; Radhakrishnan, Krishnan; Edwards, Jeremy S
2013-01-01
True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.
Steady-state solution methods for open quantum optical systems
Nation, P D
2015-01-01
We discuss the numerical solution methods available when solving for the steady-state density matrix of a time-independent open quantum optical system, where the system operators are expressed in a suitable basis representation as sparse matrices. In particular, we focus on the difficulties posed by the non-Hermitian structure of the Lindblad super operator, and the numerical techniques designed to mitigate these pitfalls. In addition, we introduce a doubly iterative inverse-power method that can give reduced memory and runtime requirements in situations where other iterative methods are limited due to poor bandwidth and profile reduction. The relevant methods are demonstrated on several prototypical quantum optical systems where it is found that iterative methods based on iLU factorization using reverse Cuthill-Mckee ordering tend to outperform other solution techniques in terms of both memory consumption and runtime as the size of the underlying Hilbert space increases. For eigenvalue solving, Krylov iterat...
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
Steady State Solution for the Weakly Damped Forced Korteweg—de Vries Equation
Institute of Scientific and Technical Information of China (English)
BolingGUO; GuoguangLIN
1998-01-01
The existence and uniqueness of steady state solution for the weakly damped forced KdV equation with a periodic boundary value problems are proved.It is obtained that the every solution of the weakly damped forced KdV equations converges to the steady state soluton as time t→∞。
Analysis of steady-state and dynamical radially-symmetric problems of nonlinear viscoelasticity
Stepanov, Alexey B.
This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics. The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). We first treat the radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend critically on the material properties of the bodies, physically reasonable refined descriptions of which are given and examined here with great care, and on the nature of boundary conditions. he treatment here, giving new and sharp results, employs several different mathematical tools, ranging from phase-plane analysis to the mathematically more sophisticated direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. We then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model
Lou, Yuan; Tao, Youshan; Winkler, Michael
2017-05-01
In this paper we study the Shigesada-Kawasaki-Teramoto model for two competing species with triangular cross-diffusion. We determine explicit parameter ranges within which the model exclusively possesses constant steady state solutions.
Lunin, Andrei; Grudiev, Alexej
2011-01-01
Analytical solutions are derived for transient and steady state gradient distributions in the travelling wave accelerating structures with arbitrary variation of parameters over the structure length. The results of both the unloaded and beam loaded cases are presented.
Zheng, Zhenzhen; Chou, Ching-Shan; Yi, Tau-Mu; Nie, Qing
2011-10-01
Cell polarization, in which substances previously uniformly distributed become asymmetric due to external or/and internal stimulation, is a fundamental process underlying cell mobility, cell division, and other polarized functions. The yeast cell S. cerevisiae has been a model system to study cell polarization. During mating, yeast cells sense shallow external spatial gradients and respond by creating steeper internal gradients of protein aligned with the external cue. The complex spatial dynamics during yeast mating polarization consists of positive feedback, degradation, global negative feedback control, and cooperative effects in protein synthesis. Understanding such complex regulations and interactions is critical to studying many important characteristics in cell polarization including signal amplification, tracking dynamic signals, and potential trade-off between achieving both objectives in a robust fashion. In this paper, we study some of these questions by analyzing several models with different spatial complexity: two compartments, three compartments, and continuum in space. The step-wise approach allows detailed characterization of properties of the steady state of the system, providing more insights for biological regulations during cell polarization. For cases without membrane diffusion, our study reveals that increasing the number of spatial compartments results in an increase in the number of steady-state solutions, in particular, the number of stable steady-state solutions, with the continuum models possessing infinitely many steady-state solutions. Through both analysis and simulations, we find that stronger positive feedback, reduced diffusion, and a shallower ligand gradient all result in more steady-state solutions, although most of these are not optimally aligned with the gradient. We explore in the different settings the relationship between the number of steady-state solutions and the extent and accuracy of the polarization. Taken together
Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.
Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong
2014-02-01
We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.
Arbitrary Steady-State Solutions with the K-epsilon Model
Rumsey, Christopher L.; Pettersson Reif, B. A.; Gatski, Thomas B.
2006-01-01
Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com
2007-07-15
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.
Institute of Scientific and Technical Information of China (English)
李博江; 胡钋; 习山; 康基伟; 李洪江; 王战胜
2013-01-01
In this paper ,A method of computing steady-state responses of the nonlinear discrete systems to multiple input fre-quencies is presented by applying Picard Iteration Principle and knowledge of matrix theory and the general solutions of the nonlinear discrete systems to multiple input frequencies is given .By way of this algorithm ,the steady-state responses of a nonlinear discrete system to the multiple input frequencies can be obtained by solving steady-state responses of the same linear discrete systems to dif-ferent multiple input .In this paper ,Lipschitz which can guarantee that there is a sole steady-state response of a nonlinear discrete system is presented through rigorous mathematical derivation and proof .The judging method is also presented to judge whether a nonlinear discrete system meet Lipschitz or not .Programs are developed using the MATLAB language based on the presented solu-tion and plenty of typical examples are simulated to compute responses using these programs .Numerous computing results indicate that the method presented in the paper is correct and convergence is fast .%本文应用picard迭代原理和矩阵论中范数的理论提出了一种计算非线性离散系统多频输入稳态响应的方法，并给出了非线性离散系统多频输入稳态响应的通解。这种方法将一个非线性离散系统多频输入稳态响应计算问题化成计算同一个线性离散系统在不同输入下稳态响应的问题。文章用数学推导证明给出了多频输入的非线性离散系统存在唯一稳态响应的李普希次条件，并给出了判断一个非线性离散系统是否满足规定的李普希次条件的判定方法。基于所构建的求解方法，运用MATLAB语言编制了算法程序，对典型实例进行了仿真计算。大量仿真结果表明，本文提出的方法是正确的，且收敛速度较快。
Iterative solutions to the steady-state density matrix for optomechanical systems
Nation, P. D.; Johansson, J. R.; Blencowe, M. P.; Rimberg, A. J.
2015-01-01
We present a sparse matrix permutation from graph theory that gives stable incomplete lower-upper preconditioners necessary for iterative solutions to the steady-state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse and is the only method found to be stable at large Hilbert space dimensions. This allows for steady-state solutions to otherwise intractable quantum optomechanical systems.
Iterative solutions to the steady state density matrix for optomechanical systems
Nation, P D; Blencowe, M P; Rimberg, A J
2014-01-01
We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Chen, Zhi-Min
2016-10-01
It is shown that the non-homogeneous dissipative quasi-geostrophic equation ∂θ∂t+uṡ∇θ+κ(-Δ)αθ=sinx2, u=(-∂x2, ∂x1)(-Δ)-β/2θ with α =0 and β >1 losses stability at a critical value {κc}>0 and this instability gives rise to a circle of steady-state solutions.
Transient and Steady-State Analysis of Nonlinear RF and Microwave Circuits
Directory of Open Access Journals (Sweden)
Zhu Lei(Lana
2006-01-01
Full Text Available This paper offers a review of simulation methods currently available for the transient and steady-state analysis of nonlinear RF and microwave circuits. The most general method continues to be the time-marching approach used in Spice, but more recent methods based on multiple time dimensions are particularly effective for RF and microwave circuits. We derive nodal formulations for the most widely used multiple time dimension methods. We put special emphasis on methods for the analysis of oscillators based in the warped multitime partial differential equations (WaMPDE approach. Case studies of a Colpitts oscillator and a voltage controlled Clapp-Gouriet oscillator are presented and discussed. The accuracy of the amplitude and phase of these methods is investigated. It is shown that the exploitation of frequency-domain latency reduces the computational effort.
Signatures of nonlinear optomechanics and engineering of nonclassical mechanical steady states
Borkje, Kjetil
2013-03-01
Motivated by recent improvements in coupling strength between light and mechanical motion, we study the strong coupling regime of cavity optomechanics theoretically. We focus on the regime where the optomechanical coupling rate is still small compared to the mechanical resonance frequency, but where the mechanically induced Kerr nonlinearity is significant. The response of the system to an optical drive is characterized. The average photon number in the cavity as a function of drive detuning can feature several peaks due to multi-photon transitions. Furthermore, we show that by optically driving the system at multiple frequencies, multi-photon transitions can facilitate the engineering of nonclassical steady states of the mechanical oscillator. The author acknowledges financial support from The Danish Council for Independent Research under the Sapere Aude program.
A multi-level solution algorithm for steady-state Markov chains
Horton, Graham; Leutenegger, Scott T.
1993-01-01
A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.
Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
Camporeale, E; MacDonald, E A
2015-01-01
We study the steady-state expansion of a collisionless, electrostatic, quasi-neutral plasma plume into vacuum, with a fluid model. We analyze approximate semi-analytical solutions, that can be used in lieu of much more expensive numerical solutions. In particular, we focus on the earlier studies presented in Parks and Katz (1979), Korsun and Tverdokhlebova (1997), and Ashkenazy and Fruchtman (2001). By calculating the error with respect to the numerical solution, we can judge the range of validity for each solution. Moreover, we introduce a generalization of earlier models that has a wider range of applicability, in terms of plasma injection profiles. We conclude by showing a straightforward way to extend the discussed solutions to the case of a plasma plume injected with non-null azimuthal velocity.
Self-regulating genes. Exact steady state solution by using Poisson representation
Sugár, István; Simon, István
2014-09-01
Systems biology studies the structure and behavior of complex gene regulatory networks. One of its aims is to develop a quantitative understanding of the modular components that constitute such networks. The self-regulating gene is a type of auto regulatory genetic modules which appears in over 40% of known transcription factors in E. coli. In this work, using the technique of Poisson Representation, we are able to provide exact steady state solutions for this feedback model. By using the methods of synthetic biology (P.E.M. Purnick and Weiss, R., Nature Reviews, Molecular Cell Biology, 2009, 10: 410-422) one can build the system itself from modules like this.
Highly enhanced steady-state optomechanical entanglement via cross-Kerr nonlinearity
Chakraborty, Subhadeep
2016-01-01
We study steady-state optomechanical entanglement in presence of an additional cross-Kerr coupling between the optical and mechanical mode. We find that a significant enhancement of the steady-state entanglement can be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature.
Leray, Sarah; Engdahl, Nicholas B.; Massoudieh, Arash; Bresciani, Etienne; McCallum, James
2016-12-01
This review presents the physical mechanisms generating residence time distributions (RTDs) in hydrologic systems with a focus on steady-state analytical solutions. Steady-state approximations of the RTD in hydrologic systems have seen widespread use over the last half-century because they provide a convenient, simplified modeling framework for a wide range of problems. The concept of an RTD is useful anytime that characterization of the timescales of flow and transport in hydrologic systems is important, which includes topics like water quality, water resource management, contaminant transport, and ecosystem preservation. Analytical solutions are often adopted as a model of the RTD and a broad spectrum of models from many disciplines has been applied. Although these solutions are typically reduced in dimensionality and limited in complexity, their ease of use makes them preferred tools, specifically for the interpretation of tracer data. Our review begins with the mechanistic basis for the governing equations, highlighting the physics for generating a RTD, and a catalog of analytical solutions follows. This catalog explains the geometry, boundary conditions and physical aspects of the hydrologic systems, as well as the sampling conditions, that altogether give rise to specific RTDs. The similarities between models are noted, as are the appropriate conditions for their applicability. The presentation of simple solutions is followed by a presentation of more complicated analytical models for RTDs, including serial and parallel combinations, lagged systems, and non-Fickian models. The conditions for the appropriate use of analytical solutions are discussed, and we close with some thoughts on potential applications, alternative approaches, and future directions for modeling hydrologic residence time.
The transverse magnetic field effect on steady-state solutions of the Bursian diode
Energy Technology Data Exchange (ETDEWEB)
Pramanik, Sourav; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Ender, A. Ya.; Kuznetsov, V. I. [Ioffe Institute, St. Petersburg 194021 (Russian Federation)
2015-04-15
A study of steady-states of a planar vacuum diode driven by a cold electron beam (the Bursian diode) under an external transverse magnetic field is presented. The regime of no electrons turned around by a magnetic field only is under the consideration. The emitter electric field is evaluated as a characteristic function for the existence of solutions depending on the diode length, the applied voltage, and the magnetic field strength. At certain conditions, it is shown that a region of non-unique solutions exists in the Bursian diode when the magnetic field is absent. An expression for the maximum current transmitted through the diode is derived. The external magnetic field is put forth to control fast electronic switches based on the Bursian diode.
Exact solution to the steady-state dynamics of a periodically modulated resonator
Directory of Open Access Journals (Sweden)
Momchil Minkov
2017-07-01
Full Text Available We provide an analytic solution to the coupled-mode equations describing the steady-state of a single periodically modulated optical resonator driven by a monochromatic input. The phenomenology of this system was qualitatively understood only in the adiabatic limit, i.e., for low modulation speed. However, both in and out of this regime, we find highly non-trivial effects for specific parameters of the modulation. For example, we show complete suppression of the transmission even with zero detuning between the input and the static resonator frequency. We also demonstrate the possibility for complete, lossless frequency conversion of the input into the sideband frequencies, as well as for optimizing the transmitted signal towards a given target temporal waveform. The analytic results are validated by first-principle simulations.
Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes
Zhu, Yajun; Zhong, Chengwen; Xu, Kun
2016-06-01
This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.
Gor, G Yu
2009-01-01
The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the non-steady profiles of dissolved gases around the bubble. We show that the necessary condition for the self-similar regime of bubble growth is the constant, steady-state composition of the bubble. The equation for the steady-state composition is obtained. We reveal the dependence of the steady-state composition on the solubility laws of the bubble components. Besides, the universal, independent from the solubility laws, expressions for the steady-state composition are obtained for the case of strong supersaturations, which are typical for the homogeneous nucleation of a bubble.
Joannin, Colas; Chouvion, Benjamin; Thouverez, Fabrice; Ousty, Jean-Philippe; Mbaye, Moustapha
2017-01-01
This paper presents an extension to classic component mode synthesis methods to compute the steady-state forced response of nonlinear and dissipative structures. The procedure makes use of the nonlinear complex modes of each substructure, computed by means of a modified harmonic balance method, in order to build a reduced-order model easily solved by standard iterative solvers. The proposed method is applied to a mistuned cyclic structure subjected to dry friction forces, and proves particularly suitable for the study of such systems with high modal density and non-conservative nonlinearities.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The generalized Smoluchovski equation with reinforced source is analysed. The asymptotic expression of the size distribution of cluster Cm(t) is obtained by seeking the steady-state solution and post-gel solution of the generalized Smoluchovski equation with reinforced source. The result can be verified by Friedlander's experiment.
Cosmic ray heating in cool core clusters I: diversity of steady state solutions
Jacob, Svenja
2016-01-01
The absence of large cooling flows in cool core clusters appears to require self-regulated energy feedback by active galactic nuclei (AGNs) but the exact heating mechanism has not yet been identified. Here, we analyse whether a combination of cosmic ray (CR) heating and thermal conduction can offset radiative cooling. To this end, we compile a large sample of 39 cool core clusters and determine steady state solutions of the hydrodynamic equations that are coupled to the CR energy equation. We find stable solutions that match the observed density and temperature profiles for all our clusters well. Radiative cooling is balanced by CR heating in the cluster centres and by thermal conduction on larger scales, thus demonstrating the relevance of both heating mechanisms. Our mass deposition rates vary by three orders of magnitude and are linearly correlated to the observed star formation rates. Clusters with large mass deposition rates show larger cooling radii and require a larger radial extent of the CR injection...
Larsen, Jon S.; Santos, Ilmar F.
2015-06-01
The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristics, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections and rotor movements are simultaneously solved, considering foil stiffness and damping coefficients estimated using a structural model, previously described and validated against experiments.
Two-lane traffic-flow model with an exact steady-state solution.
Kanai, Masahiro
2010-12-01
We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence, we have an exact flow-density diagram for two-lane traffic. In addition, we introduce two parameters that indicate, respectively, driver's driving-lane preference and passing-lane priority. Due to the additional parameters, the model shows a deviation of the density ratio for driving-lane use and a biased lane efficiency in flow. Then, a mean-field approach explicitly describes the asymmetric flow by the hop rates, the driving-lane preference, and the passing-lane priority. Meanwhile, the simulation results are in good agreement with an observational data, and we thus estimate these parameters. We conclude that the proposed model successfully produces two-lane traffic flow particularly with the driving-lane preference and the passing-lane priority.
Pan, Li-Hua; Hou, Peng-Fei; Chen, Jia-Yun
2016-08-01
The 2D steady-state solutions regarding the expressions of stress and strain for fluid-saturated, orthotropic, poroelastic plane are derived in this paper. For this object, the general solutions of the corresponding governing equation are first obtained and expressed in harmonic functions. Based on these compact general solutions, the suitable harmonic functions with undetermined constants for line fluid source in the interior of infinite poroelastic body and a line fluid source on the surface of semi-infinite poroelastic body are presented, respectively. The fundamental solutions can be obtained by substituting these functions into the general solution, and the undetermined constants can be obtained by the continuous conditions, equilibrium conditions and boundary conditions.
Nonlinear Steady-State Vibration Analysis of a Beam with Breathing Cracks
Kamiya, Keisuke; Yoshinaga, Terumitsu
This paper presents a method for analysis of steady-state vibration of a beam with breathing cracks, which open and close during vibration. There are several papers treating problems of vibration analysis of a beam with breathing cracks. However, due to their treatments of the condition which determines the switch between the open and closed states of the crack, it is difficult for one to obtain steady-state vibration efficiently by methods such as the incremental harmonic balance method. Since opening and closing of a breathing crack depends on the sign of the bending moment, or the curvature, of the beam, the key point to this problem is explicit treatment of the bending moment. The mixed variational principle allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper a governing equation of a beam with breathing cracks is derived by a finite element procedure based on the mixed variational principle. Then, the derived governing equations are solved by combining the iteration method and the harmonic balance method. Finally, examples of analysis by the presented method are given.
Elman, Howard C.; Forstall, Virginia
2017-04-01
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem at significantly lower cost, producing an accurate estimate of the solution. For nonlinear problems, however, standard methods do not achieve the desired cost savings. Empirical interpolation methods represent a modification of this methodology used for cases of nonlinear operators or nonaffine parameter dependence. These methods identify points in the discretization necessary for representing the nonlinear component of the reduced model accurately, and they incur online computational costs that are independent of the spatial dimension $N$. We will show that empirical interpolation methods can be used to significantly reduce the costs of solving parameterized versions of the Navier-Stokes equations, and that iterative solution methods can be used in place of direct methods to further reduce the costs of solving the algebraic systems arising from reduced-order models.
New analytical solution for solving steady-state heat conduction problems with singularities
Directory of Open Access Journals (Sweden)
Laraqi Najib
2013-01-01
Full Text Available A problem of steady-state heat conduction which presents singularities is solved in this paper by using the conformal mapping method. The principle of this method is based on the Schwarz-Christoffel transformation. The considered problem is a semi-infinite medium with two different isothermal surfaces separated by an adiabatic annular disc. We show that the thermal resistance can be determined without solving the governing equations. We determine a simple and exact expression that provides the thermal resistance as a function of the ratio of annular disc radii.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the steady-state solution for the case of the large Schmidt number, in terms of the multiple variable expansion method. The changes of the temperature and concentration fields, the morphology of the interface, the normalization parameter and the Peclet number of the system induced by uniform external flow are derived. The results show that, compared with the system of dendritic growth from undercooled pure melt, the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface. Nevertheless, the shape of the interface still remains nearly a paraboloid.
Institute of Scientific and Technical Information of China (English)
CHEN MingWen; WANG ZiDong; XU JianJun
2009-01-01
The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered.By neglecting the interface energy,interface kinetics and buoyancy effects in the system,we obtaine the steady-state solution for the case of the large Schmidt number,in terms of the multiple variable expansion method.The changes of thtemperature and concentration fields,the morphology of the interface,the normalization parameter and the Peclet number of the system induced by uniform external flow are derived.The results show that,compared with the system of dendritic growth from undercooled pure melt,the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface.Nevertheless,the shape of the interface still remains nearly a paraboloid.
Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki
2009-02-01
Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.
Intrator, T.; Hershkowitz, N.; Chan, C.
1984-01-01
Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.
Zech, Alraune; Attinger, Sabine
2016-05-01
A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
Mellor, Andrew; Zia, R K P
2016-01-01
We introduce an heterogeneous nonlinear $q$-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type $q_1$ or $q_2$. While here zealots never change their opinion, a $q_i$-susceptible voter ($i=1,2$) consults a group of $q_i$ neighbors at each time step, and adopts their opinion if all group members agree. We show that this model violates the detailed balance whenever $q_1 \
On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow.
Sanz-Prat, Alicia; Lu, Chuanhe; Finkel, Michael; Cirpka, Olaf A
2015-01-01
conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized.
Institute of Scientific and Technical Information of China (English)
Li Yeping
2008-01-01
A one-dimensional stationary nonisentropic hydrodynamic model for semicon-ductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron tempera-ture, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.
Directory of Open Access Journals (Sweden)
Yulong Ying
2015-01-01
Full Text Available In the lifespan of a gas turbine engine, abrupt faults and performance degradation of its gas-path components may happen; however the performance degradation is not easily foreseeable when the level of degradation is small. Gas path analysis (GPA method has been widely applied to monitor gas turbine engine health status as it can easily obtain the magnitudes of the detected component faults. However, when the number of components within engine is large or/and the measurement noise level is high, the smearing effect may be strong and the degraded components may not be recognized. In order to improve diagnostic effect, a nonlinear steady-state model based gas turbine health status estimation approach with improved particle swarm optimization algorithm (PSO-GPA has been proposed in this study. The proposed approach has been tested in ten test cases where the degradation of a model three-shaft marine engine has been analyzed. These case studies have shown that the approach can accurately search and isolate the degraded components and further quantify the degradation for major gas-path components. Compared with the typical GPA method, the approach has shown better measurement noise immunity and diagnostic accuracy.
Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method
Directory of Open Access Journals (Sweden)
Bahadir A. R.
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.
Hall, A J; Minchin, P E H
2013-12-01
A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.
Asymptotic Steady State Solution to a Bow Shock with an Infinite Mach Number
Yalinewich, Almog
2015-01-01
The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force and expected spectra are calculated for such shock, both in case of an optically thin and thick media. Finally, relations to astrophysical bow shocks and other analytic works on oblique shocks are discussed.
Steady State Analysis of Towed Marine Cables
Institute of Scientific and Technical Information of China (English)
WANG Fei; HUANG Guo-liang; DENG De-heng
2008-01-01
Efficient numerical schemes were presented for the steady state solutions of towed marine cables. For most of towed systems, the steady state problem can be resolved into two-point boundary-value problem, or initial value problem in some special cases where the initial values are available directly. A new technique was proposed and attempted to solve the two-point boundary-value problem rather than the conventional shooting method due to its algorithm complexity and low efficiency. First, the boundary conditions are transformed into a set of nonlinear governing equations about the initial values, then bisection method is employed to solve these nonlinear equations with the aid of 4th order Runge-Kutta method. In common sense, non-uniform (sheared) current is assumed, which varies in magnitude and direction with depth. The schemes are validated through the DE Zoysa's example, then several numerical examples are also presented to illustrate the numerical schemes.
Foose, Gary J
2010-01-01
New adaptations of analytical equations for predicting the impact of solute transport through composite landfill liners on groundwater quality for steady-state conditions are presented. Analytical equations are developed for evaluating average concentration and mass flow rate in an underlying aquifer resulting from diffusion of volatile organic compounds (VOCs) through intact composite liners and transport of inorganic constituents through defects in composite liners. The equations are applied to evaluate the effectiveness and equivalency of composite liners having either a 0.6 m-thick compacted soil liner or a 6.5 mm-thick geosynthetic clay liner (GCL) overlying an intermediate attenuation layer and an aquifer having horizontal flow. Example analyses for designing composite liners meeting particular performance criteria are also provided. The analytical equations are relatively simple to apply and can be used for preliminary design and analysis, to evaluate experimental results, and to possibly verify more complex numerical models for evaluating the impact of landfills on groundwater quality if consistency of the assumptions of the analytical equations and the more complex numerical models can be specified.
Tseitlin, Mark; Eaton, Gareth R; Eaton, Sandra S
2013-12-01
Rapid-scan EPR has been shown to improve the signal-to-noise ratio relative to conventional continuous wave spectroscopy. Equations are derived for the steady-state solution to the Bloch equations as a Fourier expansion in the harmonics of the scan frequency. This simulation method is about two orders of magnitude faster than time-domain numerical integration.
Cosmogenic 22Na as a steady-state tracer of solute transport and water age in first-order catchments
Kaste, James M.; Lauer, Nancy E.; Spaetzel, Alana B.; Goydan, Claire
2016-12-01
Naturally-occurring cosmogenic 22Na (T1/2 = 2.6 yr) is a potentially powerful tracer of solute and water movement in catchments. However, due to its low abundance in precipitation (∼10-20 molL-1), there are only a handful of datasets documenting cosmogenic 22Na atmospheric fluxes and concentrations in surface waters. Here we present the first record of cosmogenic 22Na fallout to North America and test its use as a radiometric tracer of water age in three small catchments in the Eastern United States. We show that 22Na deposition to southeastern Virginia, USA during 2012-2014 was 187 ± 10 mBqm-2yr-1 and that flux is largely additive with precipitation amounts. Our measurements of fallout combined with previous 22Na deposition data from other regions indicate that approximately 77% of the variability in the annual global 22Na atmospheric flux is controlled by precipitation. Export of 22Na in drainage waters from three first-order forested catchments ranged from 12.5 to 174 mBq m-2 yr-1 and can be explained by a flux-based radioactive decay model, indicating that the watersheds are in steady-state with respect to cosmogenic 22Na on annual timescales. We conclude that in temperate climates with no systematic changes in rainfall amounts at the annual timescale, 22Na may be useful for quantifying the recharge age of relatively young (<20 yr) surface waters and groundwaters and for tracing solute transport at the watershed scale.
Directory of Open Access Journals (Sweden)
Xiaohong Tian
2014-01-01
Full Text Available A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
Directory of Open Access Journals (Sweden)
J. Xia
2012-04-01
Full Text Available The spin-up of land models to steady state of coupled carbon-nitrogen processes is computationally so costly that it becomes a~bottleneck issue for global analysis. In this study, we introduced a semi-analytical solution (SAS for the spin-up issue. SAS is fundamentally based on the analytic solution to a set of equations that describe carbon transfers within ecosystems over time. SAS is implemented by three steps: (1 having an initial spin-up with prior pool-size values until net primary productivity (NPP reaches steady state, (2 calculating quasi steady-state pool sizes by letting fluxes of the equations equal zero, and (3 having a final spin-up to meet the criterion of steady state. Step 2 is enabled by averaged time-varying variables over one period of repeated driving forcings. SAS was applied to both site-level and global scale spin-up of the Australian Community Atmosphere Biosphere Land Exchange (CABLE model. For the carbon-cycle-only simulations, SAS saved 95.7% and 92.4% of computational time for site-level and global spin-up, respectively, in comparison with the traditional method. For the carbon-nitrogen-coupled simulations, SAS reduced computational cost by 84.5% and 86.6% for site-level and global spin-up, respectively. The estimated steady-state pool sizes represent the ecosystem carbon storage capacity, which was 12.1 kg C m^{−2} with the coupled carbon-nitrogen global model, 14.6% lower than that with the carbon-only model. The nitrogen down-regulation in modeled carbon storage is partly due to the 4.6% decrease in carbon influx (i.e., net primary productivity and partly due to the 10.5% reduction in residence times. This steady-state analysis accelerated by the SAS method can facilitate comparative studies of structural differences in determining the ecosystem carbon storage capacity among biogeochemical models. Overall, the computational efficiency of SAS potentially permits many global analyses that are impossible
Pérez-Molina, Manuel; Pérez-Polo, Manuel F.
2014-10-01
This paper analyzes a controlled servomechanism with feedback and a cubic nonlinearity by means of the Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations, from which steady-state, self-oscillating and chaotic behaviors will be investigated using the center manifold theorem. The system controller is formed by a Proportional plus Integral plus Derivative action (PID) that allows to stabilize and drive to a prescribed set point a body connected to the shaft of a DC motor. The Bogdanov-Takens bifurcation is analyzed through the second Lyapunov stability method and the harmonic-balance method, whereas the first Lyapunov value is used for the Andronov-Poincaré-Hopf bifurcation. On the basis of the results deduced from the bifurcation analysis, we show a procedure to select the parameters of the PID controller so that an arbitrary steady-state position of the servomechanism can be reached even in presence of noise. We also show how chaotic behavior can be obtained by applying a harmonical external torque to the device in self-oscillating regime. The advantage of achieving chaotic behavior is that it can be used so that the system reaches a set point inside a strange attractor with a small control effort. The analytical calculations have been verified through detailed numerical simulations.
Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido
2011-01-28
Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristi...
Cha, Chae Young; Noma, Akinori
2012-08-21
The cell volume continuously changes in response to varying physiological conditions, and mechanisms underlying volume regulation have been investigated in both experimental and theoretical studies. Here, general formulations concerning cell volume change are presented in the context of developing a comprehensive cell model which takes Ca(2+) dynamics into account. Explicit formulas for charge conservation and steady-state volumes of the cytosol and endoplasmic reticulum (ER) are derived in terms of membrane potential, amount of ions, Ca(2+)-bound buffer molecules, and initial cellular conditions. The formulations were applied to a ventricular myocyte model which has plasma-membrane Ca(2+) currents with dynamic gating mechanisms, Ca(2+)-buffering reactions with diffusive and non-diffusive buffer proteins, and Ca(2+) uptake into or release from the sarcoplasmic reticulum (SR) accompanied by compensatory cationic or anionic currents through the SR membrane. Time-dependent volume changes in cardiac myocytes induced by varying extracellular osmolarity or by action potential generation were successfully simulated by the novel formulations. Through application of bifurcation analysis, the existence and uniqueness of steady-state solutions of the cell volume were validated, and contributions of individual ion channels and transporters to the steady-state volume were systematically analyzed. The new formulas are consistent with previous fundamental theory derived from simple models of minimum compositions. The new formulations may be useful for examination of the relationship between cell function and volume change in other cell types.
Jentsch, V.
1984-03-01
The steady state proton flux in the earth's radiation belt is analyzed in detail based on a first-order partial differential equation which is equivalent to the radial diffusion equation with charge exchange and energy degradation included. It is found that for the most part of invariant space, the diffusion flux is directed inward. However, it is directed outward in a narrow L range centered on L about two, when charge exchange and energy loss are of comparable importance. Radial diffusion and losses strongly modify the proton flux's spectral shape, with the spectra exponentially decreasing at the outer boundary, becoming flat around L = 3.5, and assuming large positive gradients further downward. Proton fluxes gain anisotropy in the course of diffusion; the diffusion coefficient governs both the magnitude and the shape of the proton flux. External effects are important in the diffusion-dominated zone, but are relatively unimportant in the loss-dominated region.
Tyree, M T; Christy, A L; Ferrier, J M
1974-10-01
A simple steady state iterative solution of Münch pressure-flow in unbranched sieve tubes containing only water and sucrose is derived. The iterative equations can be solved on a programmable desk calculator. Solutions are presented for steady state transport with specific mass transfer rates up to 1.5 x 10(-5) mole second(-1) centimeters(-2) (= 18.5 grams hour(-1) centimeters(-2)) over distances in excess of 50 meters. The calculations clearly indicate that a Münch pressure-flow system can operate over long distances provided (a) the sieve tube is surrounded by a semipermeable membrane; (b) sugars are actively loaded in one region and unloaded at another; (c) the sieve pores are unblocked so that the sieve tube hydraulic conductivity is high (around 4 centimeters(2) second(-1) bar(-1)); (d) the sugar concentration is kept high (around one molar in the source region); and (e) the average sap velocity is kept low (around 20-50 centimeters hour(-1)). The dimensions of sieve cells in several species of plants are reviewed and sieve tube hydraulic conductivities are calculated; the values range from 0.2 to 20 centimeters(2) second(-1) bar(-1). For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes must be about 5 x 10(-7) centimeters second(-1) bar(-1) or greater.
A Least-Squares Solution to Nonlinear Steady-State Multi-Dimensional IHCP
Institute of Scientific and Technical Information of China (English)
无
1996-01-01
In this paper,the least-squares method is used to solve the Inverse Heat Conduction Probles(IHCP) to determine the space-wise variation of the unknown boundary condition on the inner surface of a helically coied tube with fluid flow inside,electrical heating and insulation outside.The sensitivity coefficient is analyzed to give a rational distribution of the thermocouples.The results demonstrate that the method effectively extracts information about the unknown boundary condition for the heat conduction problem from the experimental measurements.The results also show that the least-squares method conerges very quickly.
DEFF Research Database (Denmark)
Koestel, J. K.; Nørgaard, Trine; Loung, N. M.
2013-01-01
It is known that solute transport through soil is heterogeneous at all spatial scales. However, little data are available to allow quantification of these heterogeneities at the field scale or larger. In this study, we investigated the spatial patterns of soil properties, hydrologic state variabl...
Exact solution of the problem of steady-state MHD flow for the case of slow sphere rotation
Energy Technology Data Exchange (ETDEWEB)
Antimirov, M.Ya.
1979-01-01
A nonconducting sphere rotates in a conducting liquid at a constant angular velocity about a specified axis in a homogeneous external magnetic field, directed along the axis of rotation. Spherical coordinates are used in the derivation of the system of equations in a Stokes approximation. The solution of the linear system of equations for the velocity field and the induced magnetic field is obtained in the form of series containing Bessel functions and Legendre polynomials. The expression which is derived relating the moment of rotation, L, to the moment of rotation in the absence of the field, L/sub O/, and the Hartmann number Ha is L/sub O/(5/63)Ha, which is less than half the value (L/sub O/Ha/6) from earlier literature, where Ha tends to infinity. At small values of Ha, the same approximate formulas are obtained as in the earlier literature and the qualitative agreement is the same (L increases linearly with Ha). An exact solution could not be derived for the case of finite conductivity, and the previous approximate solution when Ha tends to infinity yields results which are only qualitatively true. Quantitatively accurate results for this case can apparently be obtained by employing a Wenzel-Kramers-Brillouin approximation for the system of equations derived in this paper. 3 references.
Directory of Open Access Journals (Sweden)
X. Gong
2014-06-01
Full Text Available A bell-shape vertical profile of chlorophyll a (Chl a concentration, conventionally referred as Subsurface Chlorophyll Maximum (SCM phenomenon, has frequently been observed in stratified oceans and lakes. This profile is assumed to be a general Gaussian distribution in this study. By substituting the general Gaussian function into ecosystem dynamical equations, the steady-state solutions for SCM characteristics (i.e. SCM layer depth, thickness, and intensity in various scenarios are derived. These solutions indicate that: (1 The maximum in Chl a concentrations occurs at or below the depth with the maximum in growth rates of phytoplankton locating at the transition from nutrient limitation to light limitation, and the depth of SCM layer deepens logarithmically with an increase in surface light intensity; (2 The shape of SCM layer (thickness and intensity is mainly influenced by nutrient supply, but independence of surface light intensity; (3 The intensity of SCM layer is proportional to the diffusive flux of nutrient from below, getting stronger as a result of this layer being shrank by a higher light attenuation coefficient or a larger sinking velocity of phytoplankton. The analytical solutions can be useful to estimate environmental parameters difficultly obtained from on-site observations.
Multiple steady state phenomenon in martensitic transformation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Based on the basic facts that the martensitic transformation is a physical phenomenon which occurs in non-equilibrium conditions and there exists the feedback mechanism in the martensitic transformation, the dynamical processes of the isothermal and athermal martensitic transformations were analyzed by using nonlinear theory and a bifurcation theory model was established. It is shown that a multiple steady state phenomenon can take place as austenite is cooled, and the transitions of the steady state temperature between the branches of stable steady states can be considered the transformation from austenite to martensite. This model can estimate the starting temperature of the martensitic transformation and explain some experimental features of the martensitic transformation such as the effects of cooling rate, fluctuation and austenitic grain size on the martensitic transformation.
Pramanik, Sourav; Kuznetsov, V. I.; Bakaleinikov, L. A.; Chakrabarti, Nikhil
2016-08-01
A comprehensive study on the steady states of a planar vacuum diode driven by a cold relativistic electron beam in the presence of an external transverse magnetic field is presented. The regimes, where no electrons are turned around by the external magnetic field and where they are reflected back to the emitter by the magnetic field, are both considered in a generalized way. The problem is solved by two methods: with the Euler and the Lagrange formulation. Taking non-relativistic limit, the solutions are compared with the similar ones which were obtained for the Bursian diode with a non-relativistic electron beam in previous work [Pramanik et al., Phys. Plasmas 22, 112108 (2015)]. It is shown that, at a moderate value of the relativistic factor of the injected beam, the region of the ambiguous solutions located to the right of the SCL bifurcation point (space charge limit) in the non-relativistic regime disappears. In addition, the dependencies of the characteristic bifurcation points and the transmitted current on the Larmor frequency as well as on the relativistic factor are explored.
Energy Technology Data Exchange (ETDEWEB)
Droseros, Nikolaos; Seintis, Kostas [Department of Physics, University of Patras, 26500 Patras (Greece); Fakis, Mihalis, E-mail: fakis@upatras.gr [Department of Physics, University of Patras, 26500 Patras (Greece); Gardelis, Spiros; Nassiopoulou, Androula G. [NCSR Demokritos INN, Terma Patriarchou Grigoriou, Aghia Paraskevi, 15310 Athens (Greece)
2015-11-15
The photoluminescence properties of CuInS{sub 2}/ZnS quantum dots (QDs) dispersed in solutions of different concentrations and solvent polarity and deposited as solid films on quartz substrates by drop-casting and spin-coating are studied. Both steady state and time-resolved photoluminescence spectroscopy have been used. The CuInS{sub 2}/ZnS QDs in solutions exhibit a red-shift of their absorption and photoluminescence spectra by increasing concentration and solvent polarity. In addition, they exhibit a three-exponential decay with time constants 1–3, 20–40 and 200–300 ns, depending on solvent, concentration and detection wavelength. In films, a red-shifted photoluminescence spectrum is observed for films made by drop-casting compared to those prepared by spin-coating. The time-resolved photoluminescence decays in films, apart from the three mechanisms observed in solutions, also exhibit a fast decay component of <1 ns, which is more pronounced in the spin coated films and especially at long emission wavelengths. The time resolved photoluminescence spectra in the drop-casted films experience a larger transient red-shift than in the spin-coated ones, indicative of a possible energy transfer among adjacent QDs. In general, it is shown that the chemical environment and the presence of defects play a central role in the recombination processes. - Highlights: • The photoluminescence (PL) properties CuInS2/ZnS quantum dots (QDs) are studied. • A red-shifted PL spectrum is observed in concentrated QD solutions and thick films. • Three-decay times of 1–3, 20–40 and 200–300 ns are observed in QD solutions. • An additional fast decay time of <1 ns is observed in QD films.
Institute of Scientific and Technical Information of China (English)
XU Dongying; REN Jiaoyan; LIAO Zhengfu; WANG Hui; ZHAO Mouming; LI Guangji
2011-01-01
The interactions of 4-aminosalicylic acid (4-ASA) and surfactants in aqueous solutions were investigated by using UV-Vis spectra and steady-state fluorescence spectroscopy.The results showed that the strongest peak at UV-vis spectra of 4-ASA aqueous solution in the presence of cationic surfactant and cetyltrimethyl ammonium bromide (CTAB) appeared at 206 nm and took.a red shift from 206 nm to 221 nm with the increase of 4-ASA concentrations from 0.8× 10-5 to 4.4× 10-4 mol/L.Similarly,the strongest peak at UV-vis spectra of 4-ASA aqueous solution in the presence of nonionic surfactant and polyvinylpyrrolidone (PVP)appeared at 206 nm and took a red shift from 206 nm to 219 nm with the increase of 4-ASA concentrations from 0.8× 10-5 to 4.4x 10-4 mol/L.However,the similar phenomena did not appeared in the presence of anion surfactant,sodium dodecyl sulfate (SDS),the UV-vis spectra of 4-ASA aqueous solution remained the same peak position and the peak value increased with the 4-ASA concentration increase.The results could be attributed to the electrostatic attraction between 4-ASA and CTAB or PVP,as well as the electrostatic repulsion between 4-ASA and SDS.Furthermore,the value of critical micelle concentration (CMC) of surfactants in the presence of 4-ASA was determined with Fluorescence method.The first and second CMC of CTAB was 1.2×10-4 M and 2.4x10-4 M,respectively.The first and second CMC of PVP was 1.2×10 4 M and 2.8x 10 4 M.SDS realized the multiple micellizations to form multiple CMC.
DEFF Research Database (Denmark)
Bauer, R.; Danielsen, E.; Hemmingsen, L.;
1997-01-01
restricted coordination geometry occurs for the steady-state peptide intermediates of Bz-Gly-L-Phe and Bz-Gly-L-Phe in solution, suggesting that substrate binding locks the structure in a rigid conformation. The results further indicate that the peptide intermediate has a six-coordinated metal coordination...... geometry with an OH- ligand at the solvent site and a carbonyl oxygen at an additional ligand site. In marked contrast, conformational rigidity is not induced by the inhibitor/poor substrate Gly-L-Tyr nor by the products of high turnover substrates, Bz-Gly, Bz-Gly-Gly, and L-Phe. These results...... are consistent with an intact scissile peptide bond in the enzyme-substrate complex of Bz-Gly-L-Phe and Bz-Gly-Gly-L-Phe. A single nuclear quadrupole interaction (NQI) is observed for the crystalline state of the enzyme between pH 5.7 and pH 9.4. This NQI agrees with calculations based on the metal coordination...
Coexistence Steady States in a Predator-Prey Model
Walker, Christoph
2010-01-01
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence steady states bifurcates from the marginal steady state with no prey. A similar result is obtained when the fertility of the prey varies.
一类糖酵解模型正平衡解的存在性分析%Existence Analysis of the Positive Steady-State Solutions for a Glycolysis Model
Institute of Scientific and Technical Information of China (English)
魏美华; 吴建华
2011-01-01
This paper deals with a representative glycolysis model in biochemical reaction. We study the non-existence of non-constant positive steady-state solutions by using a priori estimates. A necessary condition for the existence of non-constant positive steady-state solutions is obtained. On the basis of Turing instability of constant steady-state solutions, the degree theory is combined with a priori estimates to give a sufficient condition for the existence of non-constant positive steady-state solutions.%研究生化反应中具有代表性的一类糖酵解模型．运用先验估计讨论非常数正平衡解的不存在性，得到非常数正平衡解存在的必要条件．在常数平衡解Turing不稳定的基础上，利用度理论方法和解的先验估计，进一步给出非常数正平衡解存在的充分条件．
Einstein's steady-state cosmology
O'Raifeartaigh, Cormac
2014-09-01
Last year, a team of Irish scientists discovered an unpublished manuscript by Einstein in which he attempted to construct a "steady-state" model of the universe. Cormac O'Raifeartaigh describes the excitement of finding this previously unknown work.
二次型CSTR模型和SG模型的恒稳定解的degree%Degree of Steady-state Solutions of Quadratic CSTR Model and SG Model
Institute of Scientific and Technical Information of China (English)
廉进国; 孙炯
2006-01-01
Two systems of nonlinear ordinary differential equations are studied,which are quadratic CSTR model and SG model.Strictly positive invariant regions are found for these models.It is shown that for each model,there exists only one steady-state solution in invariant region and its degree equals 1.These establish a foundation for studying the patterns of the extended quadratic CSTR model and SG model.%研究了两个非线性常微分方程系统二次型CSTR模型和SG模型.证明了这两个模型分别存在一个严格的正不变区域且它们在各自的正不变区域内只有一个恒稳定解,这个恒稳定解的Degree是1.这为研究推广的二次型CSTR模型和SG模型解的存在性奠定了基础.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.
Constrained optimal steady-state control for isolated traffic intersections
Institute of Scientific and Technical Information of China (English)
Jack HADDAD; David MAHALEL; Ilya IOSLOVICH; Per-Olof GUTMAN
2014-01-01
The steady-state or cyclic control problem for a simplified isolated traffic intersection is considered. The optimization problem for the green-red switching sequence is formulated with the help of a discrete-event max-plus model. Two steady-state control problems are formulated: optimal steady-state with green duration constraints, and optimal steady-state control with lost time. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the steady-state control problems can be solved analytically. The structure of constrained optimal steady-state traffic control is revealed, and the effect of the lost time on the optimal solution is illustrated.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Steady-State Process Modelling
DEFF Research Database (Denmark)
2011-01-01
illustrate the “equation oriented” approach as well as the “sequential modular” approach to solving complex flowsheets for steady state applications. The applications include the Williams-Otto plant, the hydrodealkylation (HDA) of toluene, conversion of ethylene to ethanol and a bio-ethanol process.......This chapter covers the basic principles of steady state modelling and simulation using a number of case studies. Two principal approaches are illustrated that develop the unit operation models from first principles as well as through application of standard flowsheet simulators. The approaches...
Energy Technology Data Exchange (ETDEWEB)
Pramanik, Sourav; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Kuznetsov, V. I. [Ioffe Institute, 194021 St. Petersburg (Russian Federation)
2015-11-15
The properties of a steady-state planar vacuum diode driven by a cold electron beam have been investigated in the presence of an external transverse magnetic field, employing both the Eulerian and the Lagrangian formalism. With the help of a numerical scheme, the features of the steady-state solutions have been explored in the Eulerian frame, particularly for the case that corresponds to the potential distributions with a virtual cathode. However, exact analytical formulae for the potential and velocity profiles within the inter-electrode region have been derived with the Lagrangian description. In contrast to the previous work [Phys. Plasmas 22, 042110 (2015)], here we have emphasized the situation when electrons are reflected back to the emitter by the magnetic field. Both partial and complete reflection of the electrons due to the magnetic field have been taken into account. Using the emitter electric field as a characteristic parameter, steady-state solutions have been evaluated for specific values of diode length, applied voltage, and magnetic field strength. It has been shown that, due to the inclusion of the magnetic field, a new region of non-unique solutions appears. An external magnetic field seems to have a profound effect in controlling fast electronic switches based on the Bursian diode.
Relativistic Hydrodynamics and Non-Equilibrium Steady States
Spillane, Michael
2015-01-01
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.
Steady states of the parametric rotator and pendulum
Energy Technology Data Exchange (ETDEWEB)
Bouzas, Antonio O, E-mail: abouzas@fis.mda.cinvestav.m [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2010-11-15
We discuss several steady-state rotation and oscillation modes of the planar parametric rotator and pendulum with damping. We consider a general elliptic trajectory of the suspension point for both rotator and pendulum, for the latter at an arbitrary angle with gravity, with linear and circular trajectories as particular cases. We treat the damped, nonlinear equation of motion of the parametric rotator and pendulum perturbatively for small parametric excitation and damping, although our perturbative approach can be extended to other regimes as well. Our treatment involves only ordinary second-order differential equations with constant coefficients, and provides numerically accurate perturbative solutions in terms of elementary functions. Some of the steady-state rotation and oscillation modes studied here have not been discussed in the previous literature. Other well-known ones, such as parametric resonance and the inverted pendulum, are extended to elliptic parametric excitation tilted with respect to gravity. The results presented here should be accessible to advanced undergraduates, and of interest to graduate students and specialists in the field of nonlinear mechanics.
Steady-State Process Modelling
DEFF Research Database (Denmark)
2011-01-01
This chapter covers the basic principles of steady state modelling and simulation using a number of case studies. Two principal approaches are illustrated that develop the unit operation models from first principles as well as through application of standard flowsheet simulators. The approaches i...
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Yan-Chao, She; Ting-Ting, Luo; Wei-Xi, Zhang; Mao-Wu, Ran; Deng-Long, Wang
2016-01-01
The linear optical properties and Kerr nonlinear optical response in a four-level loop configuration GaAs/AlGaAs semiconductor quantum dot are analytically studied with the phonon-assisted transition (PAT). It is shown that the changes among a single electromagnetically induced transparency (EIT) window, a double EIT window and the amplification of the probe field in the absorption curves can be controlled by varying the strength of PAT κ. Meanwhile, double switching from the anomalous dispersion regime to the normal dispersion regime can likely be achieved by increasing the Rabi energy of the external optical control field. Furthermore, we demonstrate that the group velocity of the probe field can be practically regulated by varying the PAT and the intensity of the optical control field. In the nonlinear case, it is shown that the large SPM and XPM can be achieved as linear absorption vanishes simultaneously, and the PAT can suppress both third-order self-Kerr and the cross-Kerr nonlinear effect of the QD. Our study is much more practical than its atomic counterpart due to its flexible design and the controllable interference strength, and may provide some new possibilities for technological applications. Project supported by the National Natural Science Foundation of China (Grant No. 61367003), the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 12A140), and the Scientific Research Fund of Guizhou Provincial Education Department, China (Grant Nos. KY[2015]384 and KY[2015]446).
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Ferraro, N. M.; Jardin, S. C.
2009-11-01
M3D- C1 is an implicit, high-order finite element code for the solution of the time-dependent nonlinear two-fluid magnetohydrodynamic equations [S.C. Jardin, J. Breslau, N. Ferraro, A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions, J. Comp. Phys. 226 (2) (2007) 2146-2174]. This code has now been extended to allow computations in toroidal geometry. Improvements to the spatial integration and time-stepping algorithms are discussed. Steady-states of a resistive two-fluid model, self-consistently including flows, anisotropic viscosity (including gyroviscosity) and heat flux, are calculated for diverted plasmas in geometries typical of the National Spherical Torus Experiment (NSTX) [M. Ono et al., Exploration of spherical torus physics in the NSTX device, Nucl. Fusion 40 (3Y) (2000) 557-561]. These states are found by time-integrating the dynamical equations until the steady-state is reached, and are therefore stationary or statistically steady on both magnetohydrodynamic and transport time-scales. Resistively driven cross-surface flows are found to be in close agreement with Pfirsch-Schlüter theory. Poloidally varying toroidal flows are in agreement with comparable calculations [A.Y. Aydemir, Shear flows at the tokamak edge and their interaction with edge-localized modes, Phys. Plasmas 14]. New effects on core toroidal rotation due to gyroviscosity and a local particle source are observed.
Energy repartition in the nonequilibrium steady state
Yan, Peng; Bauer, Gerrit E. W.; Zhang, Huaiwu
2017-01-01
The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are applicable to other thermodynamic systems such as Newtonian liquids, elastic solids, and Josephson junctions.
Multimode optical fibers: steady state mode exciter.
Ikeda, M; Sugimura, A; Ikegami, T
1976-09-01
The steady state mode power distribution of the multimode graded index fiber was measured. A simple and effective steady state mode exciter was fabricated by an etching technique. Its insertion loss was 0.5 dB for an injection laser. Deviation in transmission characteristics of multimode graded index fibers can be avoided by using the steady state mode exciter.
Padma, S; Hariharan, G
2016-06-01
In this paper, we have developed an efficient wavelet based approximation method to biofilm model under steady state arising in enzyme kinetics. Chebyshev wavelet based approximation method is successfully introduced in solving nonlinear steady state biofilm reaction model. To the best of our knowledge, until now there is no rigorous wavelet based solution has been addressed for the proposed model. Analytical solutions for substrate concentration have been derived for all values of the parameters δ and SL. The power of the manageable method is confirmed. Some numerical examples are presented to demonstrate the validity and applicability of the wavelet method. Moreover the use of Chebyshev wavelets is found to be simple, efficient, flexible, convenient, small computation costs and computationally attractive.
Non-Markovianity assisted Steady State Entanglement
Huelga, Susana F; Plenio, Martin B
2011-01-01
We analyze the dependence of steady state entanglement in a dimer system with a coherent exchange interaction and subject to local dephasing on the degree of Markovianity of the system-environment interaction. We demonstrate that non-Markovianity of the system-environment interaction is an essential resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations results in separable steady states. This result illustrates possible mechanisms leading to long lived entanglement in purely decohering local environments. A feasible experimental demonstration of this non-Markovianity assisted steady state entanglement using a system of trapped ions is presented.
Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems
Directory of Open Access Journals (Sweden)
Plasser René
2014-12-01
Full Text Available An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.
Quantum quasi-steady states in current transport
D'Agosta, Roberto; Zwolak, Michael; di Ventra, Massimiliano
2007-03-01
We investigate quasi-steady state solutions to transport in quantum systems by finding states which at some time minimize the change in density throughout all space and have a given current density flowing from one part of the system to another [1]. Contrary to classical dynamics, in a quantum mechanical system there are many states with a given energy and particle number which satisfy this minimization criterion. Taking as an example spinless fermions on a one-dimensional lattice, we explicitly show the phase space of a class of quasi-steady states. We also discuss the possibility of coherent and incoherent mixing of these steady state solutions leading to a new type of noise in quantum transport. [1] M. Di Ventra and T.N. Todorov J. Phys. Cond. Matt. 16, 8025 (2004).
Yousfi, Ammar; Mechergui, Mohammed
2016-04-01
The seepage face is an important feature of the drainage process when recharge occurs to a permeable region with lateral outlets. Examples of the formation of a seepage face above the downstream water level include agricultural land drained by ditches. Flow problem to these drains has been investigated extensively by many researchers (e.g. Rubin, 1968; Hornberger et al. 1969; Verma and Brutsaert, 1970; Gureghian and Youngs, 1975; Vauclin et al., 1975; Skaggs and Tang, 1976; Youngs, 1990; Gureghian, 1981; Dere, 2000; Rushton and Youngs, 2010; Youngs, 2012; Castro-Orgaz et al., 2012) and may be tackled either using variably saturated flow models, or the complete 2-D solution of Laplace equation, or using the Dupuit-Forchheimer approximation; the most widely accepted methods to obtain analytical solutions for unconfined drainage problems. However, the investigation reported by Clement et al. (1996) suggest that accounting for the seepage face alone, as in the fully saturated flow model, does not improve the discharge estimate because of disregarding flow the unsaturated zone flow contribution. This assumption can induce errors in the location of the water table surface and results in an underestimation of the seepage face and the net discharge (e.g. Skaggs and Tang, 1976; Vauclin et al., 1979; Clement et al., 1996). The importance of the flow in the unsaturated zone has been highlighted by many authors on the basis of laboratory experiments and/or numerical experimentations (e.g. Rubin, 1968; Verma and Brutsaert, 1970; Todsen, 1973; Vauclin et al., 1979; Ahmad et al., 1993; Anguela, 2004; Luthin and Day, 1955; Shamsai and Narasimhan, 1991; Wise et al., 1994; Clement et al., 1996; Boufadel et al., 1999; Romano et al., 1999; Kao et al., 2001; Kao, 2002). These studies demonstrate the failure of fully saturated flow models and suggested that the error made when using these models not only depends on soil properties but also on the infiltration rate as reported by Kao et
Le Hardy, D.; Favennec, Y.; Rousseau, B.
2016-08-01
The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline-Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way.
Steady-state probability density function in wave turbulence under large volume limit
Institute of Scientific and Technical Information of China (English)
Yeontaek Choia; Sang Gyu Job
2011-01-01
We investigate the possibility for two-mode probability density function (PDF) to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state two- or higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.
Ho, Pang-Yen; Chuang, Guo-Syong; Chao, An-Chong; Li, Hsing-Ya
2005-05-01
The capacity of complex biochemical reaction networks (consisting of 11 coupled non-linear ordinary differential equations) to show multiple steady states, was investigated. The system involved esterification of ethanol and oleic acid by lipase in an isothermal continuous stirred tank reactor (CSTR). The Deficiency One Algorithm and the Subnetwork Analysis were applied to determine the steady state multiplicity. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability, hysteresis and bifurcation are discussed. Moreover, the capacity of steady state multiplicity is extended to the family of the studied reaction networks.
Stable MIMO Constrained Predictive Control with Steady state Objective Optimization
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A two-stage multi-objective optimization model-predictive control algorithms(MPC) strategy is pre sented. A domain MPC controller with input constraints is used to increase freedom for steady-state objective and enhance stabilization of the controller. A steady-state objective optimization algorithm oriented to transient process is adopted to realize optimization of objectives else than dynamic control. It is proved that .the stabilization for both dynamic control and steady-state objective optimization can be guaranteed. The theoretical results are demonstrated and discussed using a distillation tower as the model. Theoretical analysis and simulation results show that this control strategy is efficient and provides a good strategic solution to practical process control.
Institute of Scientific and Technical Information of China (English)
李生虎; 朱婷涵; 华玉婷
2014-01-01
In view of the need of a boundary condition to obtain the unique solution for the steady-state constraints of permanent magnet synchronous generators (PMSGs) that are a set of indeterminate equations with the reactive power output of the machine-side converter unfixed,steady-state solutions based on the stator current/voltage orientations are proposed.Because of inconsistency with the reactive power balance of the machine-side-converter,the solutions under two orientations are different. Further consideration of the power dispatch by adj usting the rotor speed or the pitch angle,steady-state solutions to PMSG are proposed.The numerical results show that:(1) the stator current orientation yields less active loss and higher efficiency,but absorbs more reactive power;(2)with increased wind speed,the PMSG absorbs more reactive power,the efficiency decreases with stator current orientation,but increases with stator voltage orientation;(3) active power dispatch may be realized by changing the rotor speed or the pitch angle,while the efficiency is different,and adj usting the pitch angle yields better convergence than adj usting the rotor speed.%针对直驱永磁同步发电机(PMSG)机侧变流器无功功率未知时,PMSG 稳态约束为不定方程组,需要补充边界条件才能得到唯一解的问题,文中建立了基于定子电流或定子电压定向约束的稳态求解算法。发现由于定向约束不能反映机侧无功平衡,两种定向下计算结果不一致。进一步考虑有功调度,在两种定向约束下分别采用转速调节或桨距角调节,建立 PMSG 稳态解算法。计算结果证实：定子电流定向时发电机有功损耗更小,机电能量转换效率更高,但是吸收无功功率更多；随风速增加,吸收无功功率增加,定子电流定向时发电机能量转换效率下降,定子电压定向时效率增加；转速偏离最优转速或增加桨距角,都可实现对PMSG的有功调度,但机电能量转换效率
Plasticity, Fracture and Friction in Steady-State Plate Cutting
DEFF Research Database (Denmark)
Simonsen, Bo Cerup; Wierzbicki, Tomasz
1997-01-01
A closed form solution to the problem of steady-state wedge cutting through a ductile metal plate is presented. The considered problem is an idealization of a ship bottom raking process, i.e. a continuous cutting damage of a ship bottom by a hard knife-like rock in a grounding event. A new...
Non-Markovianity-assisted steady state entanglement.
Huelga, Susana F; Rivas, Ángel; Plenio, Martin B
2012-04-20
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.
Institute of Scientific and Technical Information of China (English)
无
1998-01-01
The Landau-Lifshitz equation of the ferromagnetic spin chain with Gilbert damping term is considered.which is described by δS/δt=S×ΔS-λS×（S×ΔS），All spatial nonhomogenuos steady-state solutions.which are the form S=R1 cos(lr)+ R2 sin(lr)Al∈R,wherer |R1|=|R2|=1 and R1⊥R2,are proposed,Moreover the instability of the spatial nonhomogenuos steady-state solutions Sl(r)(l≠0) is investigated.Every perturbation of the spatial nonhomogenuos steady-state tends to a spatial homogeneous steady-state as t→∞.Thus the hetercolinic orbits,which connect the spatial nonhomogenuos steady-state and the spatial homogeneous steady-state,are exist.Filially numerical experiments are provided.
Qualitative Analysis on a Reaction-Diffusion Prey Predator Model and the Corresponding Steady-States
Institute of Scientific and Technical Information of China (English)
Qunyi BIE; Rui PENG
2009-01-01
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived.
NON-CONSTANT POSITIVE STEADY-STATES OF A PREDATOR-PREY-MUTUALIST MODEL
Institute of Scientific and Technical Information of China (English)
CHEN WENYAN; WANG MINGXIN
2004-01-01
In this paper, the authors deal with the non-constant positive steady-states of a predator-prey-mutualist model with homogeneous Neumann boundary condition. They first give a priori estimates (positive upper and lower bounds) of positive steady-states,and then study the non-existence, the global existence and bifurcation of non-constant positive steady-states as some parameters are varied. Finally the asymptotic behavior of such solutions as d3 →∞ is discussed.
Institute of Scientific and Technical Information of China (English)
林启荣; 刘正兴; 李红云
2001-01-01
Based on the linear piezoelectric constitutive relations hip and compressible and non-viscous fluid dynamic equation, the steady-state solution to cylindrical fluid containers with piezoelectric layers is derived. D ue to the complexity of the fluid-solid interaction and electric-mechanical co upling, only the displacement, stress and fluid pressure of axisymmetrical fl uid-solid interaction intelligent structure under periodic stimulation are disc ussed. The results obtained are useful in studying noise control.%基于线性压电理论和可压缩无粘流场运动方程，推导出无限长带压电圆柱体流固耦合稳态解．由于流固耦合与力电耦合的复杂性，文中只考虑轴对称问题，研究了流固耦合智能结构在不同电压作用下位移、应力、流体压力的分布情况，为振动噪声控制奠定基础．
Steady state HNG combustion modeling
Energy Technology Data Exchange (ETDEWEB)
Louwers, J.; Gadiot, G.M.H.J.L. [TNO Prins Maurits Lab., Rijswijk (Netherlands); Brewster, M.Q. [Univ. of Illinois, Urbana, IL (United States); Son, S.F. [Los Alamos National Lab., NM (United States); Parr, T.; Hanson-Parr, D. [Naval Air Warfare Center, China Lake, CA (United States)
1998-04-01
Two simplified modeling approaches are used to model the combustion of Hydrazinium Nitroformate (HNF, N{sub 2}H{sub 5}-C(NO{sub 2}){sub 3}). The condensed phase is treated by high activation energy asymptotics. The gas phase is treated by two limit cases: the classical high activation energy, and the recently introduced low activation energy approach. This results in simplification of the gas phase energy equation, making an (approximate) analytical solution possible. The results of both models are compared with experimental results of HNF combustion. It is shown that the low activation energy approach yields better agreement with experimental observations (e.g. regression rate and temperature sensitivity), than the high activation energy approach.
Simulation and Analysis on Multiple Steady States of an Industrial Acetic Acid Dehydration System
Institute of Scientific and Technical Information of China (English)
李绍军; 黄定伟
2011-01-01
In this work, an industrial acetic acid dehydration system via heterogeneous azeotropic distillation is simulated by Aspen Plus software. Residue curves are used to analyze the distillating behavior, and appropriate operating region of the system is determined. Based on steady states simulation, a sensitivity analysis is carried out to detect the output multiple steady states in the system. Different solution branches are observered when the flow rates of the feed stream and the organic reflux stream are selected as manipulated variables. The performance of the column under different steady states is different. A method is oroposed to achieve the desired steady state.
Steady State Dynamic Operating Behavior of Universal Motor
Directory of Open Access Journals (Sweden)
Muhammad Khan Burdi
2015-01-01
Full Text Available A detailed investigation of the universal motor is developed and used for various dynamic steady state and transient operating conditions of loads. In the investigation, output torque, motor speed, input current, input/output power and efficiency are computed, compared and analyzed for different loads. While this paper discusses the steady-state behavior of the universal motor, another companion paper, ?Transient dynamic behavior of universal motor?, will discuss its transient behavior in detail. A non-linear generalized electric machine model of the motor is considered for the analysis. This study was essential to investigate effect of output load on input current, power, speed and efficiency of the motor during operations. Previously such investigation is not known
A steady state theory for processive cellulases
DEFF Research Database (Denmark)
Cruys-Bagger, Nicolaj; Olsen, Jens Elmerdahl; Præstgaard, Eigil;
2013-01-01
. This has significant kinetic implications, for example the maximal specific rate (Vmax/E0) for processive cellulases is much lower than the catalytic rate constant (kcat). We discuss how relationships based on this theory may be used in both comparative and mechanistic analyses of cellulases....... remains to be fully developed. In this paper, we suggest a deterministic kinetic model that relies on a processive set of enzyme reactions and a quasi steady-state assumption. It is shown that this approach is practicable in the sense that it leads to mathematically simple expressions for the steady......-state rate, and only requires data from standard assay techniques as experimental input. Specifically, it is shown that the processive reaction rate at steady state may be expressed by a hyperbolic function related to the conventional Michaelis–Menten equation. The main difference is a ‘kinetic processivity...
Li, Wan-Tong; Wang, Jia-Bing; Zhang, Li
2016-08-01
This paper is concerned with the new types of entire solutions other than traveling wave solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats. We first establish the existence and properties of spatially periodic solutions connecting two steady states. Then new types of entire solutions are constructed by combining the rightward and leftward pulsating traveling fronts with different speeds and a spatially periodic solution. Finally, for a class of special heterogeneous reaction, we further establish the uniqueness of entire solutions and the continuous dependence of such an entire solution on parameters, such as wave speeds and the shifted variables. In other words, we build a five-dimensional manifold of solutions and the traveling wave solutions are on the boundary of the manifold.
Steady state magnetic field configurations for the earth's magnetotail
Hau, L.-N.; Wolf, R. A.; Voigt, G.-H.; Wu, C. C.
1989-01-01
A two-dimensional, force-balance magnetic field model is presented. The theoretical existence of a steady state magnetic field configuration that is force-balanced and consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD is demonstrated. A numerical solution is obtained for a two-dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The results are consistent with the convection time sequences reported by Erickson (1985).
Optimal operation of Petlyuk distillation: Steady-state behavior
Ivar J. Halvorsen; Sigurd Skogestad
2001-01-01
The "Petlyuk" or "dividing-wall" or "fully thermally coupled" distillation column is an interesting alternative to the conventional cascaded binary columns for separation of multi-component mixtures. However, the industrial use has been limited, and difficulties in operation have been reported as one reason. With three product compositions controlled, the system has two degrees of freedom left for on-line optimization. We show that the steady-state optimal solution surface is quite narrow, an...
Steady states in a structured epidemic model with Wentzell boundary condition
Calsina, Angel
2011-01-01
We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the p...
Basin stability measure of different steady states in coupled oscillators.
Rakshit, Sarbendu; Bera, Bidesh K; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-05
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-01-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis. PMID:28378760
Steady-State Creep of Asphalt Concrete
Directory of Open Access Journals (Sweden)
Alibai Iskakbayev
2017-02-01
Full Text Available This paper reports the experimental investigation of the steady-state creep process for fine-grained asphalt concrete at a temperature of 20 ± 2 °С and under stress from 0.055 to 0.311 MPa under direct tension and was found to occur at a constant rate. The experimental results also determined the start, the end point, and the duration of the steady-state creep process. The dependence of these factors, in addition to the steady-state creep rate and viscosity of the asphalt concrete on stress is satisfactorily described by a power function. Furthermore, it showed that stress has a great impact on the specific characteristics of asphalt concrete: stress variation by one order causes their variation by 3–4.5 orders. The described relations are formulated for the steady-state of asphalt concrete in a complex stressed condition. The dependence is determined between stress intensity and strain rate intensity.
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...
Oscillations and multiple steady states in active membrane transport models.
Vieira, F M; Bisch, P M
1994-01-01
The dynamic behavior of some non-linear extensions of the six-state alternating access model for active membrane transport is investigated. We use stoichio-metric network analysis to study the stability of steady states. The bifurcation analysis has been done through standard numerical methods. For the usual six-state model we have proved that there is only one steady state, which is globally asymptotically stable. When we added an autocatalytic step we found self-oscillations. For the competition between a monomer cycle and a dimer cycle, with steps of dimer formation, we have also found self-oscillations. We have also studied models involving the formation of a complex with other molecules. The addition of two steps for formation of a complex of the monomer with another molecule does not alter either the number or the stability of steady states of the basic six-state model. The model which combines the formation of a complex with an autocatalytic step shows both self-oscillations and multiple steady states. The results lead us to conclude that oscillations could be produced by active membrane transport systems if the transport cycle contains a sufficiently large number of steps (six in the present case) and is coupled to at least one autocatalytic reaction,. Oscillations are also predicted when the monomer cycle is coupled to a dimer cycle. In fact, the autocatalytic reaction can be seen as a simplification of the model involving competition between monomer and dimer cycles, which seems to be a more realistic description of biological systems. A self-regulation mechanism of the pumps, related to the multiple stationary states, is expected only for a combined effect of autocatalysis and formation of complexes with other molecules. Within the six-state model this model also leads to oscillation.
Kim, Jin Il; Song, Hyun-Seob; Sunkara, Sunil R; Lali, Arvind; Ramkrishna, Doraiswami
2012-01-01
We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments.
Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Energy Technology Data Exchange (ETDEWEB)
Thingna, Juzar [Institute of Physics, University of Augsburg, Universitätsstrasse 1 D-86135 Augsburg (Germany); Nanosystems Initiative Munich, Schellingrstrasse 4, D-80799 München (Germany); Zhou, Hangbo [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore); NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117456 (Singapore); Wang, Jian-Sheng, E-mail: phywjs@nus.edu.sg [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore)
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Evaluation of a steady-state test of foam stability
Hutzler, Stefan; Lösch, Dörte; Carey, Enda; Weaire, Denis; Hloucha, Matthias; Stubenrauch, Cosima
2011-02-01
We have evaluated a steady-state test of foam stability, based on the steady-state height of a foam produced by a constant velocity of gas flow. This test is mentioned in the book by Bikerman [Foams, Springer, Berlin, 1973] and an elementary theory was developed for it by Verbist et al. [J. Phys. Condens. Matter 8 (1996) p. 3715]. For the study, we used an aqueous solution of the cationic surfactant dodecyl trimethylammonium bromide, C12TAB, at a concentration of two times the critical micelle concentration (2 cmc). During foam generation, bubbles collapse at the top of the column which, in turn, eventually counterbalances the rate of bubble production at the bottom. The resulting balance can be described mathematically by an appropriate solution of the foam drainage equation under specified boundary conditions. Our experimental findings are in agreement with the theoretical predictions of a diverging foam height at a critical gas velocity and a finite foam height in the limit of zero velocity. We identify a critical liquid fraction below which a foam is unstable as an important parameter for characterizing foam stability. Furthermore, we deduce an effective viscosity of the liquid which flows through the foam. Currently unexplained are two experimental observations, namely sudden changes of the steady-state foam height in experiments that run over several hours and a reduction in foam height once an overflow of the foam from the containing vessel has occurred.
On the use of steady-state signal equations for 2D TrueFISP imaging.
Coolen, Bram F; Heijman, Edwin; Nicolay, Klaas; Strijkers, Gustav J
2009-07-01
To explain the signal behavior in 2D-TrueFISP imaging, a slice excitation profile should be considered that describes a variation of effective flip angles and magnetization phases after excitation. These parameters can be incorporated into steady-state equations to predict the final signal within a pixel. The use of steady-state equations assumes that excitation occurs instantaneously, although in reality this is a nonlinear process. In addition, often the flip angle variation within the slice excitation profile is solely considered when using steady-state equations, while TrueFISP is especially known for its sensitivity to phase variations. The purpose of this study was therefore to evaluate the precision of steady-state equations in calculating signal intensities in 2D TrueFISP imaging. To that end, steady-state slice profiles and corresponding signal intensities were calculated as function of flip angle, RF phase advance and pulse shape. More complex Bloch simulations were considered as a gold standard, which described every excitation within the sequence until steady state was reached. They were used to analyze two different methods based on steady-state equations. In addition, measurements on phantoms were done with corresponding imaging parameters. Although the Bloch simulations described the steady-state slice profile formation better than methods based on steady-state equations, the latter performed well in predicting the steady-state signal resulting from it. In certain cases the phase variation within the slice excitation profile did not even have to be taken into account.
环形单圈管冻结稳态温度场解析解%Analytical solution to steady-state temperature field of single-circle-pipe freezing
Institute of Scientific and Technical Information of China (English)
胡向东; 陈锦; 汪洋; 李伟平
2013-01-01
Artificial ground freezing is widely used in the construction of underground engineering. The calculation of freezing temperature field is not only the basement of theory research on artificial ground freezing, but also an important basis of the freezing construction design. Single-circle-pipe freezing method is often applied to artificial ground freezing projects, while the analytical solution of this situation has never been published. Thus it's necessary to get the solution to benefit our engineering practice. Based on the theory of analogy between thermal and hydraulic problems, using conformal mapping, mirror reflection of sources and sinks, and the superposition of potential function, this paper gives an analytical solution to the steady-state temperature field of single-circle-pipe freezing and demonstrates its correctness by numerical thermal analysis. Comparison of the analytical solution with the numerical thermal analysis shows that the analytical solution is precise enough and will afford reasonable guidance in single-circle-pipe freezing projects. A simplified formula is also given and is proven to be precise enough. Based on the simplified formula, the thickness formula of the outer part of frozen wall is derived. The analytical solution, simplified formula and thickness formula can provide guidance and theoretical basement for construction and design of single-circle-pipe freezing projects.%人工地层冻结技术被广泛应用于地下工程施工中.冻结温度场的计算是人工冻结法理论研究的基础,也是冻结施工设计的重要依据.人工地层冻结施工常使用环形单圈冻结管冻结,而至今尚无关于其温度场的解析解.基于水-热异类相似原理,根据传热过程与地下水流动相似的特点,利用保角映射、汇源反映和势函数叠加原理,类比推导了环形单圈冻结管稳态温度场解析解,并用热学数值模拟方法加以验证,同时提出了简化的解析公式.结果表
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
On Steady-State Tropical Cyclones
2014-01-01
circulation (Ooyama, 1969; Shapiro and Willoughby , 1982). Above the frictional boundary layer, this steady-state circulation must be along absolute angular...u′ sin λ〉 on the right-hand side of this equation. ‖According to axisymmetric balance dynamics (Ooyama, 1969; Shapiro and Willoughby , 1982), the...such as the diabatic heating rate and frictional and eddy processes (Shapiro and Willoughby , 1982; Shapiro and Montgomery, 1993; Vigh and Schubert, 2009
STEADY-STATE MODEL OF SOLAR WIND ELECTRONS REVISITED
Energy Technology Data Exchange (ETDEWEB)
Yoon, Peter H.; Kim, Sunjung; Choe, G. S., E-mail: yoonp@umd.edu [School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of)
2015-10-20
In a recent paper, Kim et al. put forth a steady-state model for the solar wind electrons. The model assumed local equilibrium between the halo electrons, characterized by an intermediate energy range, and the whistler-range fluctuations. The basic wave–particle interaction is assumed to be the cyclotron resonance. Similarly, it was assumed that a dynamical steady state is established between the highly energetic superhalo electrons and high-frequency Langmuir fluctuations. Comparisons with the measured solar wind electron velocity distribution function (VDF) during quiet times were also made, and reasonable agreements were obtained. In such a model, however, only the steady-state solution for the Fokker–Planck type of electron particle kinetic equation was considered. The present paper complements the previous analysis by considering both the steady-state particle and wave kinetic equations. It is shown that the model halo and superhalo electron VDFs, as well as the assumed wave intensity spectra for the whistler and Langmuir fluctuations, approximately satisfy the quasi-linear wave kinetic equations in an approximate sense, thus further validating the local equilibrium model constructed in the paper by Kim et al.
On Typicality in Nonequilibrium Steady States
Evans, Denis J.; Williams, Stephen R.; Searles, Debra J.; Rondoni, Lamberto
2016-08-01
From the statistical mechanical viewpoint, relaxation of macroscopic systems and response theory rest on a notion of typicality, according to which the behavior of single macroscopic objects is given by appropriate ensembles: ensemble averages of observable quantities represent the measurements performed on single objects, because " almost all" objects share the same fate. In the case of non-dissipative dynamics and relaxation toward equilibrium states, " almost all" is referred to invariant probability distributions that are absolutely continuous with respect to the Lebesgue measure. In other words, the collection of initial micro-states (single systems) that do not follow the ensemble is supposed to constitute a set of vanishing, phase space volume. This approach is problematic in the case of dissipative dynamics and relaxation to nonequilibrium steady states, because the relevant invariant distributions attribute probability 1 to sets of zero volume, while evolution commonly begins in equilibrium states, i.e., in sets of full phase space volume. We consider the relaxation of classical, thermostatted particle systems to nonequilibrium steady states. We show that the dynamical condition known as Ω T-mixing is necessary and sufficient for relaxation of ensemble averages to steady state values. Moreover, we find that the condition known as weak T-mixing applied to smooth observables is sufficient for ensemble relaxation to be independent of the initial ensemble. Lastly, we show that weak T-mixing provides a notion of typicality for dissipative dynamics that is based on the (non-invariant) Lebesgue measure, and that we call physical ergodicity.
Solution and Positive Solution to Nonlinear Cantilever Beam Equations
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the "height" of nonlinear term is appropriate on a bounded set.
Enzyme Kinetics: A critique of the quasi-steady-state approximation
Bhattacharyya, Kamal
2013-01-01
The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and hence emergence of the Michaelis-Menten kinetics, with various substrate-enzyme ratios. But, conclusions vary. We solve here the desired set of coupled nonlinear differential equations by invoking a new set of dimensionless variables. Approximate solutions are obtained via the power-series method aided by Pade approximants. The scheme works very successfully in furnishing the initial dynamics at least up to the region where existence of any steady state can be checked. A few conditions for its validity are put forward and tested against the findings. Temporal profiles of the substrate and the product are analyzed in addition to that of the complex to gain further insights into legitimacy of the above approximation. Some recent observations like the reactant stationary approxim...
On circulating power of steady state tokamaks
Energy Technology Data Exchange (ETDEWEB)
Itoh, Kimitaka [National Inst. for Fusion Science, Nagoya (Japan); Itoh, Sanae; Fukuyama, Atsushi; Yagi, Masatoshi
1996-03-01
Circulating power for the sustenance and profile control of the steady state tokamak plasmas is discussed. The simultaneous fulfillment of the MHD stability at high beta value, the improved confinement and the stationary equilibrium requires the rotation drive as well as the current drive. In addition to the current drive efficiency, the efficiency for the rotation drive is investigated. The direct rotation drive by the external torque, such as the case of beam injection, is not efficient enough. The mechanism and the magnitude of the spontaneous plasma rotation are studied. (author)
Aziz, Taha; Mahomed, F M
2014-01-01
In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.
Snijkers, F.
2016-03-31
We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.
Symmetrized solutions for nonlinear stochastic differential equations
Directory of Open Access Journals (Sweden)
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
On the multiplicity of solutions of the nonlinear reactive transport model
Directory of Open Access Journals (Sweden)
Elyas Shivanian
2014-06-01
Full Text Available The generalization of the nonlinear reaction–diffusion model in porous catalysts the so called one dimensional steady state reactive transport model is revisited. This model, which originates also in fluid and solute transport in soft tissues and microvessels, has been recently given analytical solution in terms of Taylor’s series for different families of reaction terms. This article considers the mentioned model without advective transport in the case of including Michaelis–Menten reaction term and shows that it is exactly solvable and furthermore, gives analytical exact solution in the implicit form for further physical interpretation. It is also revealed that the problem may admit unique or dual or even more triple solutions in some domains for the parameters of the model.
The closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for nonlinear systems
Chen, Lincong; Sun, Jian-Qiao
2016-12-01
In this paper, we propose a new method to obtain the closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for single degree of freedom nonlinear systems under external and parametric Gaussian white noise excitations. The assumed stationary probability density function consists of an exponential polynomial with a logarithmic term to account for parametric excitations. The undetermined coefficients in the assumed solution are computed with the help of an iterative method of weighted residue. We have found that the iterative process generates a sequence of solutions that converge to the exact solutions if they exist. Three examples with known exact steady-state probability density functions are used to demonstrate the convergence of the proposed method.
ANALYTICAL SOLUTION OF NONLINEAR BAROTROPIC VORTICITY EQUATION
Institute of Scientific and Technical Information of China (English)
WANG Yue-peng; SHI Wei-hui
2008-01-01
The stability of nonlinear barotropic vorticity equation was proved. The necessary and sufficient conditions for the initial value problem to be well-posed were presented. Under the conditions of well-posedness, the corresponding analytical solution was also gained.
GLOBAL SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Ye Yaojun
2005-01-01
In this paper we study the existence of global solutions to the Cauchy problem of nonlinear Schrodinger equation by establishing time weight function spaces and using the contraction mapping principle.
Interpolation of steady-state concentration data by inverse modeling.
Schwede, Ronnie L; Cirpka, Olaf A
2010-01-01
In most groundwater applications, measurements of concentration are limited in number and sparsely distributed within the domain of interest. Therefore, interpolation techniques are needed to obtain most likely values of concentration at locations where no measurements are available. For further processing, for example, in environmental risk analysis, interpolated values should be given with uncertainty bounds, so that a geostatistical framework is preferable. Linear interpolation of steady-state concentration measurements is problematic because the dependence of concentration on the primary uncertain material property, the hydraulic conductivity field, is highly nonlinear, suggesting that the statistical interrelationship between concentration values at different points is also nonlinear. We suggest interpolating steady-state concentration measurements by conditioning an ensemble of the underlying log-conductivity field on the available hydrological data in a conditional Monte Carlo approach. Flow and transport simulations for each conditional conductivity field must meet the measurements within their given uncertainty. The ensemble of transport simulations based on the conditional log-conductivity fields yields conditional statistical distributions of concentration at points between observation points. This method implicitly meets physical bounds of concentration values and non-Gaussianity of their statistical distributions and obeys the nonlinearity of the underlying processes. We validate our method by artificial test cases and compare the results to kriging estimates assuming different conditional statistical distributions of concentration. Assuming a beta distribution in kriging leads to estimates of concentration with zero probability of concentrations below zero or above the maximal possible value; however, the concentrations are not forced to meet the advection-dispersion equation.
Steady state effects in a two-pulse diffusion-weighted sequence
Energy Technology Data Exchange (ETDEWEB)
Zubkov, Mikhail; Stait-Gardner, Timothy; Price, William S. [Nanoscale Organisation and Dynamics Group, School of Science and Health, University of Western Sydney, Sydney (Australia); Stilbs, Peter [Division of Applied Physical Chemistry, Department of Chemistry, KTH Royal Institute of Technology, SE-10044 Stockholm (Sweden)
2015-04-21
In conventional nuclear magnetic resonance (NMR) diffusion measurements a significant amount of experimental time is used up by magnetization recovery, serving to prevent the formation of the steady state, as in the latter case the manifestation of diffusion is modulated by multiple applications of the pulse sequence and conventional diffusion coefficient inference procedures are generally not applicable. Here, an analytical expression for diffusion-related effects in a two-pulse NMR experiment (e.g., pulsed-gradient spin echo) in the steady state mode (with repetition times less than the longitudinal relaxation time of the sample) is derived by employing a Fourier series expansion within the solution of the Bloch-Torrey equations. Considerations are given for the transition conditions between the full relaxation and the steady state experiment description. The diffusion coefficient of a polymer solution (polyethylene glycol) is measured by a two-pulse sequence in the full relaxation mode and for a range of repetition times, approaching the rapid steady state experiment. The precision of the fitting employing the presented steady state solution by far exceeds that of the conventional fitting. Additionally, numerical simulations are performed yielding results strongly supporting the proposed description of the NMR diffusion measurements in the steady state.
Transient and steady-state velocity of domain walls for a complete range of drive fields
Bourne, H. C., Jr.; Bartran, D. S.
1974-01-01
Approximate analytic solutions for transient and steady-state 180 deg domain wall motion in bulk magnetic material are obtained from the dynamic torque equations with a Gilbert damping term. The results for the Walker region in which the transient solution approaches the familiar Walker steady-state solution are presented in a slightly new form for completeness. An analytic solution corresponding to larger drive fields predicts an oscillatory motion with an average value which decreases with drive field for reasonable values of the damping parameter. These results agree with those obtained by a computer solution of the torque equation and those obtained with the assumption of a very large anisotropy field.
Energy Technology Data Exchange (ETDEWEB)
Wang, Qian [Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350, Shuangliu, Chengdu 610209 (China); University of the Chinese Academy of Sciences, Beijing 100039 (China); Li, Bincheng, E-mail: bcli@ioe.ac.cn [Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350, Shuangliu, Chengdu 610209 (China); School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054 (China)
2015-09-28
Spatially resolved steady-state photocarrier radiometric (PCR) imaging technique is developed to characterize the electronic transport properties of silicon wafers. Based on a nonlinear PCR theory, simulations are performed to investigate the effects of electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) on the steady-state PCR intensity profiles. The electronic transport parameters of an n-type silicon wafer are simultaneously determined by fitting the measured steady-state PCR intensity profiles to the three-dimensional nonlinear PCR model. The determined transport parameters are in good agreement with the results obtained by the conventional modulated PCR technique with multiple pump beam radii.
Magnetic sensor for steady state tokamak
Energy Technology Data Exchange (ETDEWEB)
Neyatani, Yuzuru; Mori, Katsuharu; Oguri, Shigeru; Kikuchi, Mitsuru [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
1996-06-01
A new type of magnetic sensor has been developed for the measurement of steady state magnetic fields without DC-drift such as integration circuit. The electromagnetic force induced to the current which leads to the sensor was used for the measurement. For the high frequency component which exceeds higher than the vibration frequency of sensor, pick-up coil was used through the high pass filter. From the results using tokamak discharges, this sensor can measure the magnetic field in the tokamak discharge. During {approx}2 hours measurement, no DC drift was observed. The sensor can respond {approx}10ms of fast change of magnetic field during disruptions. We confirm the extension of measured range to control the current which leads to the sensor. (author).
Frozen steady states in active systems
Schaller, Volker; Hammerich, Benjamin; Frey, Erwin; Bausch, Andreas R
2011-01-01
Even simple active systems can show a plethora of intriguing phenomena and often we find complexity were we would have expected simplicity. One striking example is the occurrence of a quiescent or absorbing state with frozen fluctuations that at first sight seems to be impossible for active matter driven by the incessant input of energy. While such states were reported for externally driven systems through macroscopic shear or agitation, the investigation of frozen active states in inherently active systems like cytoskeletal suspensions or active gels is still at large. Using high density motility assay experiments, we demonstrate that frozen steady states can arise in active systems if active transport is coupled to growth processes. The experiments are complemented by agent-based simulations which identify the coupling between self-organization, growth and mechanical properties to be responsible for the pattern formation process.
Steady state modeling of desiccant wheels
DEFF Research Database (Denmark)
Bellemo, Lorenzo; Elmegaard, Brian; Kærn, Martin Ryhl
2014-01-01
Desiccant wheels are rotary desiccant dehumidifiers used in air conditioning and drying applications. The modeling of simultaneous heat and mass transfer in these components is crucial for estimating their performances, as well as for simulating and optimizing their implementation in complete sys...... be taken into account in a future version of the model. More experimental data have to be gathered to implement eventual missing phenomena and validate the model for all input parameters....... systems. A steady state two-dimensional model is formulated and implemented aiming to obtain good accuracy and short computational times. Comparison with experimental data from the literature shows that the model reproduces the physical behavior of desiccant wheels. Mass diffusion in the desiccant should......Desiccant wheels are rotary desiccant dehumidifiers used in air conditioning and drying applications. The modeling of simultaneous heat and mass transfer in these components is crucial for estimating their performances, as well as for simulating and optimizing their implementation in complete...
Fluctuations When Driving Between Nonequilibrium Steady States
Riechers, P M
2016-01-01
Maintained by environmental fluxes, biological systems are thermodynamic processes that operate far from equilibrium without detailed-balance dynamics. Yet, they often exhibit well defined nonequilibrium steady states (NESSs). More importantly, critical thermodynamic functionality arises directly from transitions among their NESSs, driven by environmental switching. Here, we identify constraints on excess thermodynamic quantities that ride above the NESS housekeeping background. We do this by extending the Crooks fluctuation theorem to transitions among NESSs, without invoking an unphysical dual dynamics. This and corresponding integral fluctuation theorems determine how much work must be expended when controlling systems maintained far from equilibrium. This generalizes feedback control theory, showing that Maxwellian Demons can leverage mesoscopic-state information to take advantage of the excess energetics in NESS transitions. Altogether, these point to universal thermodynamic laws that are immediately app...
Progress Toward Steady-State Operation on Tore Supra
Institute of Scientific and Technical Information of China (English)
J. Jacquinot; G. T. Hoang; the Tore Supra Team
2004-01-01
Important technological and physics issues related to steady-state operation required for next step are being examined on Tore Supra, after a major upgrade of internal components in order to increase the heat extraction capability to 25 MW for 1000 s. Here, we show first experimental results, where all the plasma facing components were actively cooled during pulses exceeding four minutes, with reactor-relevant heat load. New physics was observed in non-inductively driven plasmas, including a stationary peaked radial profile of the plasma density generated by an anomalous inward pinch; and a regime characterized by sinusoidal oscillations of central electron temperature, governed by non-linear coupling between heat transport and plasma current analogous to a predator-prey mechanism.
Gedeon, M.; Mallants, D.
2012-04-01
Radionuclide concentration predictions in aquifers play an important role in estimating impact of planned surface disposal of radioactive waste in Belgium, developed by the Belgian Agency for Radioactive Waste and Enriched Fissile Materials (ONDRAF), who also coordinates and leads the corresponding research. Long-term concentration predictions are based on a steady-state flow solution obtained by a cascade of multi-scale models from the catchment to the detailed (site) scale performed in MODFLOW. To test the concept and accuracy of the groundwater flow solution and conservativeness of the concentration predictions obtained therewith, a transient model, considered more realistic, was set up in a sub-domain of the intermediate scale steady-state model. Besides the modelling domain reduction, the transient model was and exact copy of the steady-state model, having the infiltration as the only time-varying parameter. The transient model was run for a twenty-year period, whereas the results were compared to the steady-state results based on infiltration value and observations averaged over the same period. The comparison of the steady-state and transient flow solutions includes the analyses of the goodness of fit, the parameter sensitivities, relative importance of the individual observations and one-percent sensitivity maps. The steady-state and transient flow solutions were subsequently translated into a site-scale transport model, used to predict the radionuclide concentrations in a hypothetical well in the aquifers. The translation of the flow solutions between the models of distinct scales was performed using the Local grid refinement method available in MODFLOW. In the site-scale models, MT3DMS transport simulations were performed to obtain respective concentration predictions in a hypothetical well, situated at 70 meters from the disposal tumuli. The equilibrium concentrations based on a constant source flux achieved using a steady-state solution were then
Analytic solutions of nonlinear Cournot duopoly game
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2005-01-01
Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.
Boufadel, Michel C.
2000-09-01
Two laboratory experiments were conducted to investigate the effects of tides and buoyancy on beach hydraulics in the presence of a seaward groundwater flow due to an elevated "regional" water table. In the first experiment, case 1, the difference in concentration between the salt water at sea and the water of the regional aquifer was small, 2.4 g L-1, such that it did not engender density gradients; the salt acts as a tracer in this case. In the second experiment, case 2, the difference was ˜32.0 g L-1, which creates a significant density gradient. This case corresponds to the presence of fresh groundwater in the subsurface of the coasts of the continental United States. The experiments were numerically simulated by the marine unsaturated (MARUN) model, a numerical model for density-and-viscosity-dependent flows in two-dimensional variably saturated media. The long-term experimental and numerical results showed that the seawater plume entered the beach from the sea and occupied most of the intertidal zone. The maximum depth of the seawater plume was near the midsection of the intertidal zone, and it decreased near the low and high tide lines. When viewed in the context of case 2, these results indicate an inverted salinity distribution in beaches subjected to tides with salt water from sea overtopping the freshwater lens. For both cases, water from the regional aquifer moved seaward beneath the seawater in the intertidal zone and pinched out near the low tide mark. We also noted that beach hydraulics are highly two dimensional with water entering the beach at a near-vertical angle and leaving it at a near-horizontal angle, which casts doubts on analyses of beach hydraulics based on the Dupuit assumption. Findings from this work have direct implications within the practice of bioremediation of oil spills on beaches. We found that applying dissolved nutrients on the beach surface at low tide is superior to applying them in a trench landward of the beach. This is because the residence time of the nutrient plume in the bioremediation zone of the beach in the prior situation is longer than that in the latter.
Steady-state and non-steady state operation of counter-current chromatography devices.
Kostanyan, Artak E; Ignatova, Svetlana N; Sutherland, Ian A; Hewitson, Peter; Zakhodjaeva, Yulya A; Erastov, Andrey A
2013-11-01
Different variants of separation processes based on steady-state (continuous sample loading) and non-steady state (batch) operating modes of CCC columns have been analyzed and compared. The analysis is carried out on the basis of the modified equilibrium cell model, which takes into account both mechanisms of band broadening - interphase mass transfer and axial mixing. A full theoretical treatment of the intermittent counter-current chromatography with short sample loading time is performed. Analytical expressions are presented allowing the simulation of the intermittent counter-current chromatography separations for various experimental conditions. Chromatographic and extraction separations have been compared and advantages and disadvantages of the two methods have been evaluated. Further technical development of the CCC machines to implement counter-current extraction separations is considered.
Steady-state creep in the mantle
Directory of Open Access Journals (Sweden)
G. RANALLI
1977-06-01
Full Text Available SUMMARY - The creep equations for steady-state flow of olivine at high
pressure and temperature are compared in an attempt to elucidate the rheological
behaviour of the mantle. Results are presented in terms of applied deformation
maps and curves of effective viscosity v depth.
In the upper mantle, the transition stress between dislocation and diffusion
creep is between 10 to 102 bar (as orders of magnitude for grain sizes from
0.01 to 1 cm. The asthenosphere under continents is deeper, and has higher
viscosity, than under oceans. Predominance of one creep mechanism above the
others depends on grain size, strain rate, and volume fraction of melt; the
rheological response can be different for different geodynamic processes.
In the lower mantle, on the other hand, dislocation creep is predominant
at all realistic grain sizes and strain rates. If the effective viscosity has to be only
slightly higher than in the upper mantle, as some interpretations of glacioisostatic
rebound suggest, then the activation volume cannot be larger than
11 cm3 mole^1.
Steady State Vapor Bubble in Pool Boiling
Zou, An; Chanana, Ashish; Agrawal, Amit; Wayner, Peter C.; Maroo, Shalabh C.
2016-02-01
Boiling, a dynamic and multiscale process, has been studied for several decades; however, a comprehensive understanding of the process is still lacking. The bubble ebullition cycle, which occurs over millisecond time-span, makes it extremely challenging to study near-surface interfacial characteristics of a single bubble. Here, we create a steady-state vapor bubble that can remain stable for hours in a pool of sub-cooled water using a femtosecond laser source. The stability of the bubble allows us to measure the contact-angle and perform in-situ imaging of the contact-line region and the microlayer, on hydrophilic and hydrophobic surfaces and in both degassed and regular (with dissolved air) water. The early growth stage of vapor bubble in degassed water shows a completely wetted bubble base with the microlayer, and the bubble does not depart from the surface due to reduced liquid pressure in the microlayer. Using experimental data and numerical simulations, we obtain permissible range of maximum heat transfer coefficient possible in nucleate boiling and the width of the evaporating layer in the contact-line region. This technique of creating and measuring fundamental characteristics of a stable vapor bubble will facilitate rational design of nanostructures for boiling enhancement and advance thermal management in electronics.
Steady State Vapor Bubble in Pool Boiling.
Zou, An; Chanana, Ashish; Agrawal, Amit; Wayner, Peter C; Maroo, Shalabh C
2016-02-03
Boiling, a dynamic and multiscale process, has been studied for several decades; however, a comprehensive understanding of the process is still lacking. The bubble ebullition cycle, which occurs over millisecond time-span, makes it extremely challenging to study near-surface interfacial characteristics of a single bubble. Here, we create a steady-state vapor bubble that can remain stable for hours in a pool of sub-cooled water using a femtosecond laser source. The stability of the bubble allows us to measure the contact-angle and perform in-situ imaging of the contact-line region and the microlayer, on hydrophilic and hydrophobic surfaces and in both degassed and regular (with dissolved air) water. The early growth stage of vapor bubble in degassed water shows a completely wetted bubble base with the microlayer, and the bubble does not depart from the surface due to reduced liquid pressure in the microlayer. Using experimental data and numerical simulations, we obtain permissible range of maximum heat transfer coefficient possible in nucleate boiling and the width of the evaporating layer in the contact-line region. This technique of creating and measuring fundamental characteristics of a stable vapor bubble will facilitate rational design of nanostructures for boiling enhancement and advance thermal management in electronics.
Fluctuations When Driving Between Nonequilibrium Steady States
Riechers, Paul M.; Crutchfield, James P.
2017-08-01
Maintained by environmental fluxes, biological systems are thermodynamic processes that operate far from equilibrium without detailed-balanced dynamics. Yet, they often exhibit well defined nonequilibrium steady states (NESSs). More importantly, critical thermodynamic functionality arises directly from transitions among their NESSs, driven by environmental switching. Here, we identify the constraints on excess heat and dissipated work necessary to control a system that is kept far from equilibrium by background, uncontrolled "housekeeping" forces. We do this by extending the Crooks fluctuation theorem to transitions among NESSs, without invoking an unphysical dual dynamics. This and corresponding integral fluctuation theorems determine how much work must be expended when controlling systems maintained far from equilibrium. This generalizes thermodynamic feedback control theory, showing that Maxwellian Demons can leverage mesoscopic-state information to take advantage of the excess energetics in NESS transitions. We also generalize an approach recently used to determine the work dissipated when driving between functionally relevant configurations of an active energy-consuming complex system. Altogether, these results highlight universal thermodynamic laws that apply to the accessible degrees of freedom within the effective dynamic at any emergent level of hierarchical organization. By way of illustration, we analyze a voltage-gated sodium ion channel whose molecular conformational dynamics play a critical functional role in propagating action potentials in mammalian neuronal membranes.
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Breakdown of the resistor-network model for steady-state hopping conduction
Energy Technology Data Exchange (ETDEWEB)
Emin, D. [Sandia National Labs., Albuquerque, NM (United States); Kuper, C.G. [Technion-Israel Inst. of Tech., Haifa (Israel). Dept. of Physics
1996-05-01
General master equations are used to study steady-state hopping transport in a disordered solid. We express a site`s occupancy in terms of its quasi-electrochemical potential (QECP); currents flow between sites whose QECP`s differ. Coupled nonlinear circuit equations for the QECP`s result from the steady-state condition and the boundary condition that the total QECP drop is the applied emf. When the site-to-site QECP differences are much smaller than the thermal energy, K{sub B}t, the effect of current flow on site occupancies is ignorable. These equations then reduce to those of a resistance network. However, the resistor-network model fails: (a) at low temperatures, (b) with increasing disorder, and (c) with increasing emf. We therefore study hopping conduction beyond this approximation. Exact examples show the importance of current-induced charge redistribution in non-ohmic steady-state flow.
Diehl, S; Zambrano, J; Carlsson, B
2016-01-01
A reduced model of a completely stirred-tank bioreactor coupled to a settling tank with recycle is analyzed in its steady states. In the reactor, the concentrations of one dominant particulate biomass and one soluble substrate component are modelled. While the biomass decay rate is assumed to be constant, growth kinetics can depend on both substrate and biomass concentrations, and optionally model substrate inhibition. Compressive and hindered settling phenomena are included using the Bürger-Diehl settler model, which consists of a partial differential equation. Steady-state solutions of this partial differential equation are obtained from an ordinary differential equation, making steady-state analysis of the entire plant difficult. A key result showing that the ordinary differential equation can be replaced with an approximate algebraic equation simplifies model analysis. This algebraic equation takes the location of the sludge-blanket during normal operation into account, allowing for the limiting flux capacity caused by compressive settling to easily be included in the steady-state mass balance equations for the entire plant system. This novel approach grants the possibility of more realistic solutions than other previously published reduced models, comprised of yet simpler settler assumptions. The steady-state concentrations, solids residence time, and the wastage flow ratio are functions of the recycle ratio. Solutions are shown for various growth kinetics; with different values of biomass decay rate, influent volumetric flow, and substrate concentration.
Steady-state properties of driven magnetic reconnection in 2D electron magnetohydrodynamics.
Chacón, L; Simakov, Andrei N; Zocco, A
2007-12-07
We formulate a rigorous nonlinear analytical model that describes the dynamics of the diffusion (reconnection) region in driven systems in the context of electron magnetohydrodynamics (EMHD). A steady-state analysis yields allowed geometric configurations and associated reconnection rates. In addition to the well-known open X-point geometry, elongated configurations are found possible. The model predictions have been validated numerically with two-dimensional EMHD nonlinear simulations, and are in excellent agreement with previously published work.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2016-09-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G) -expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2017-02-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Quantally fed steady-state domain distributions in Stochastic Inflation
Bellini, M; Deza, R R; Bellini, Mauricio; Sisterna, Pablo D.; Deza, Roberto R.
2000-01-01
Within the framework of stochastic inflationary cosmology we derive esteady-state distributions P_c(V) of domains in comoving coordinates, under the assumption of slow-rolling and for two specific choices of the coarse-grained inflaton potential $V(\\Phi)$. We model the process as a Starobinsky-like equation in V-space plus a time-independent source term P_w(V) which carries (phenomenologically) quantum-mechanical information drawn from either of two known solutions of the Wheeler-De Witt equation: Hartle-Hawking's and Vilenkin's wave functions. The presence of the source term leads to the existence of nontrivial steady-state distributions P^w_c(V). The relative efficiencies of both mechanisms at different scales are compared for the proposed potentials.
Locating CVBEM collocation points for steady state heat transfer problems
Hromadka, T.V.
1985-01-01
The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.
Optimal operation of Petlyuk distillation: Steady-state behavior
Directory of Open Access Journals (Sweden)
Ivar J. Halvorsen
2001-07-01
Full Text Available The "Petlyuk" or "dividing-wall" or "fully thermally coupled" distillation column is an interesting alternative to the conventional cascaded binary columns for separation of multi-component mixtures. However, the industrial use has been limited, and difficulties in operation have been reported as one reason. With three product compositions controlled, the system has two degrees of freedom left for on-line optimization. We show that the steady-state optimal solution surface is quite narrow, and depends strongly on disturbances and design parameters. Thus it seems difficult to achieve the potential energy savings compared to conventional approaches without a good control strategy. We discuss candidate variables which may be used as feedback variables in order to keep the column operation close to optimal in a "self-optimizing" control scheme.
Periodic solutions of nonlinear vibrating beams
Directory of Open Access Journals (Sweden)
J. Berkovits
2003-01-01
Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
The approximate solutions of nonlinear Boussinesq equation
Lu, Dianhen; Shen, Jie; Cheng, Yueling
2016-04-01
The homotopy analysis method (HAM) is introduced to solve the generalized Boussinesq equation. In this work, we establish the new analytical solution of the exponential function form. Applying the homotopy perturbation method to solve the variable coefficient Boussinesq equation. The results indicate that this method is efficient for the nonlinear models with variable coefficients.
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...
Directory of Open Access Journals (Sweden)
M. D. Mhlongo
2014-01-01
Full Text Available One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.
Steady state, erosional continuity, and the topography of landscapes developed in layered rocks
Perne, Matija; Covington, Matthew D.; Thaler, Evan A.; Myre, Joseph M.
2017-01-01
The concept of topographic steady state has substantially informed our understanding of the relationships between landscapes, tectonics, climate, and lithology. In topographic steady state, erosion rates are equal everywhere, and steepness adjusts to enable equal erosion rates in rocks of different strengths. This conceptual model makes an implicit assumption of vertical contacts between different rock types. Here we hypothesize that landscapes in layered rocks will be driven toward a state of erosional continuity, where retreat rates on either side of a contact are equal in a direction parallel to the contact rather than in the vertical direction. For vertical contacts, erosional continuity is the same as topographic steady state, whereas for horizontal contacts it is equivalent to equal rates of horizontal retreat on either side of a rock contact. Using analytical solutions and numerical simulations, we show that erosional continuity predicts the form of flux steady-state landscapes that develop in simulations with horizontally layered rocks. For stream power erosion, the nature of continuity steady state depends on the exponent, n, in the erosion model. For n = 1, the landscape cannot maintain continuity. For cases where n ≠ 1, continuity is maintained, and steepness is a function of erodibility that is predicted by the theory. The landscape in continuity steady state can be quite different from that predicted by topographic steady state. For n < 1 continuity predicts that channels incising subhorizontal layers will be steeper in the weaker rock layers. For subhorizontal layered rocks with different erodibilities, continuity also predicts larger slope contrasts than in topographic steady state. Therefore, the relationship between steepness and erodibility within a sequence of layered rocks is a function of contact dip. For the subhorizontal limit, the history of layers exposed at base level also influences the steepness-erodibility relationship. If uplift rate
Quasi-steady state conditions in heterogeneous aquifers during pumping tests
Zha, Yuanyuan; Yeh, Tian-Chyi J.; Shi, Liangsheng; Huang, Shao-Yang; Wang, Wenke; Wen, Jet-Chau
2017-08-01
Classical Thiem's well hydraulic theory, other aquifer test analyses, and flow modeling efforts often assume the existence of ;quasi-steady; state conditions. That is, while drawdowns due to pumping continue to grow, the hydraulic gradient in the vicinity of the pumping well does not change significantly. These conditions have built upon two-dimensional and equivalent homogeneous conceptual models, but few field data have been available to affirm the existence of these conditions. Moreover, effects of heterogeneity and three-dimensional flow on this quasi-steady state concept have not been thoroughly investigated and discussed before. In this study, we first present a quantitative definition of quasi-steady state (or steady-shape conditions) and steady state conditions based on the analytical solution of two- or three-dimensional flow induced by pumping in unbounded, homogeneous aquifers. Afterward, we use a stochastic analysis to investigate the influence of heterogeneity on the quasi-steady state concept in heterogeneous aquifers. The results of the analysis indicate that the time to reach an approximate quasi-steady state in a heterogeneous aquifer could be quite different from that estimated based on a homogeneous model. We find that heterogeneity of aquifer properties, especially hydraulic conductivity, impedes the development of the quasi-steady state condition before the flow reaching steady state. Finally, 280 drawdown-time data from the hydraulic tomographic survey conducted at a field site corroborate our finding that the quasi-steady state condition likely would not take place in heterogeneous aquifers unless pumping tests last a long period. Research significance (1) Approximate quasi-steady and steady state conditions are defined for two- or three-dimensional flow induced by pumping in unbounded, equivalent homogeneous aquifers. (2) Analysis demonstrates effects of boundary condition, well screen interval, and heterogeneity of parameters on the
Steady-state time-periodic finite element analysis of a brushless DC motor drive considering motion
Directory of Open Access Journals (Sweden)
Jagieła Mariusz
2015-09-01
Full Text Available This paper aims at providing a framework for comprehensive steady-state time-domain analysis of rotating machines considering motion. The steady-state waveforms of electromagnetic and circuit quantities are computed via iterative solution of the nonlinear field-circuit-and-motion problem with constraints of time periodicity. The cases with forced speed and forced load torque are considered. A comparison of execution times with a conventional time-stepping transient model is carried out for two different machines. The numerical stability of a time-periodic model with forced speed is shown to be worse than that of traditional transient time-stepping one, although the model converges within a reasonable number of iterations. This is not the case if forced load via equation of mechanical balance is accounted for. To ensure convergence of the iterative process the physical equation of motion is replaced by the fixed-point equation. In this way the model delivers time-periodic solutions regarding not only the electromagnetic quantities but also the rotational speed.
Analytical solution of strongly nonlinear Duffing oscillators
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A.M. El-Naggar
2016-06-01
Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.
2014-01-01
Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate
Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard
2014-06-26
A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for
Solutions manual to accompany Nonlinear programming
Bazaraa, Mokhtar S; Shetty, C M
2014-01-01
As the Solutions Manual, this book is meant to accompany the main title, Nonlinear Programming: Theory and Algorithms, Third Edition. This book presents recent developments of key topics in nonlinear programming (NLP) using a logical and self-contained format. The volume is divided into three sections: convex analysis, optimality conditions, and dual computational techniques. Precise statements of algortihms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations, and numerous exercises to aid readers in understanding the concepts a
Particle Velocity Fluctuations in Steady State Sedimentation: Stratification Controlled Correlations
Segrè, P N
2007-01-01
The structure and dynamics of steady state sedimentation of semi-concentrated ($\\phi=0.10$) monodisperse spheres are studied in liquid fluidized beds. Laser turbidity and particle imaging methods are used to measure the particle velocity fluctuations and the steady state concentration profiles. Using a wide range of particle and system sizes, we find that the measured gradients $\
Steady-state spectroscopy of new biological probes
Abou-Zied, Osama K.
2007-02-01
The steady state absorption and fluorescence spectroscopy of 2-(2'-hydroxyphenyl)benzoxazole (HBO) and (2,2'-bipyridine)-3,3'-diol (BP(OH) II) were studied here free in solution and in human serum albumin (HSA) in order to test their applicability as new biological probes. HBO and BP(OH) II are known to undergo intramolecular proton transfers in the excited state. Their absorption and fluorescence spectra are sensitive to environmental change from hydrophilic to hydrophobic, thus allowing the opportunity to use them as environment-sensitive probes. The effect of water on the steady state spectra of the two molecules also shows unique features which may position them as water sensors in biological systems. For HBO in buffer, fluorescence is only due to the syn-keto tautomer, whereas in HSA the fluorescence is due to four species in equilibrium in the excited state (the syn-keto tautomer, the anti-enol tautomer, the solvated syn-enol tautomer, and the anion species of HBO). Analysis of the fluorescence spectra of HBO in HSA indicates that HBO is exposed to less water in the HBO:HSA complex. For the BP(OH) II molecule, unique absorption due to water was observed in the spectral region of 400-450 nm. This absorption decreases in the presence of HSA due to less accessibility to water as a result of binding to HSA. Fluorescence of BP(OH) II is due solely to the di-keto tautomer after double proton transfer in the excited state. The fluorescence peak of BP(OH) II shows a red-shift upon HSA recognition which is attributed to the hydrophobic environment inside the binding site of HSA. We discuss also the effect of probe-inclusion inside well-defined hydrophobic cavities of cyclodextrins.
Steady-State Performance of Kalman Filter for DPLL
Institute of Scientific and Technical Information of China (English)
QIAN Yi; CUI Xiaowei; LU Mingquan; FENG Zhenming
2009-01-01
For certain system models, the structure of the Kalman filter is equivalent to a second-order vari-able gain digital phase-locked loop (DPLL). To apply the knowledge of DPLLs to the design of Kalman filters, this paper studies the steady-state performance of Kalman filters for these system models. The results show that the steady-state Kalman gain has the same form as the DPLL gain. An approximate simple form for the steady-state Kalman gain is used to derive an expression for the equivalent loop bandwidth of the Kalman filter as a function of the process and observation noise variances. These results can be used to analyze the steady-state performance of a Kalman filter with DPLL theory or to design a Kalman filter model with the same steady-state performance as a given DPLL.
Steady State of Pedestrian Flow in Bottleneck Experiments
Liao, Weichen; Seyfried, Armin; Chraibi, Mohcine; Drzycimski, Kevin; Zheng, Xiaoping; Zhao, Ying
2015-01-01
Experiments with pedestrians could depend strongly on initial conditions. Comparisons of the results of such experiments require to distinguish carefully between transient state and steady state. In this work, a feasible algorithm - Cumulative Sum Control Chart - is proposed and improved to automatically detect steady states from density and speed time series of bottleneck experiments. The threshold of the detection parameter in the algorithm is calibrated using an autoregressive model. Comparing the detected steady states with previous manually selected ones, the modified algorithm gives more reproducible results. For the applications, three groups of bottleneck experiments are analysed and the steady states are detected. The study about pedestrian flow shows that the difference between the flows in all states and in steady state mainly depends on the ratio of pedestrian number to bottleneck width. When the ratio is higher than a critical value (approximately 115 persons/m), the flow in all states is almost ...
Steady states and stability in metabolic networks without regulation.
Ivanov, Oleksandr; van der Schaft, Arjan; Weissing, Franz J
2016-07-21
Metabolic networks are often extremely complex. Despite intensive efforts many details of these networks, e.g., exact kinetic rates and parameters of metabolic reactions, are not known, making it difficult to derive their properties. Considerable effort has been made to develop theory about properties of steady states in metabolic networks that are valid for any values of parameters. General results on uniqueness of steady states and their stability have been derived with specific assumptions on reaction kinetics, stoichiometry and network topology. For example, deep results have been obtained under the assumptions of mass-action reaction kinetics, continuous flow stirred tank reactors (CFSTR), concordant reaction networks and others. Nevertheless, a general theory about properties of steady states in metabolic networks is still missing. Here we make a step further in the quest for such a theory. Specifically, we study properties of steady states in metabolic networks with monotonic kinetics in relation to their stoichiometry (simple and general) and the number of metabolites participating in every reaction (single or many). Our approach is based on the investigation of properties of the Jacobian matrix. We show that stoichiometry, network topology, and the number of metabolites that participate in every reaction have a large influence on the number of steady states and their stability in metabolic networks. Specifically, metabolic networks with single-substrate-single-product reactions have disconnected steady states, whereas in metabolic networks with multiple-substrates-multiple-product reactions manifolds of steady states arise. Metabolic networks with simple stoichiometry have either a unique globally asymptotically stable steady state or asymptotically stable manifolds of steady states. In metabolic networks with general stoichiometry the steady states are not always stable and we provide conditions for their stability. In order to demonstrate the biological
Existence and stabilizability of steady-state for semilinear pulse-width sampler controlled system
Directory of Open Access Journals (Sweden)
JinRong Wang
2011-01-01
Full Text Available In this paper, we study the steady-state of a semilinear pulse-width sampler controlled system on infinite dimensional spaces. Firstly, by virtue of Schauder's fixed point theorem, the existence of periodic solutions is given. Secondly, utilizing a generalized Gronwall inequality given by us and the Banach fixed point theorem, the existence and stabilizability of a steady-state for the semilinear control system with pulse-width sampler is also obtained. At last, an example is given for demonstration.
Steady-state creep of complexly reinforced shallow metal-composite shells
Yankovskii, A. P.
2010-05-01
The problem of deformation of shallow shells of variable thickness reinforced with fibers of constant cross section, whose all phases operate under the conditions of steady-state creep, is formulated. The system of resolving equations and the corresponding boundary conditions are analyzed, and the procedure for solving this problem is developed. A way of approximate solution of such problems in the case of transient creep is indicated. The particular calculations performed show that the compliance of thin-walled structures, under the conditions of steady-state creep, greatly depends on the structure of reinforcement.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Steady-State Crack Growth in Rate-Sensitive Single Crystals
DEFF Research Database (Denmark)
Juul, Kristian Jørgensen; Nielsen, Kim Lau; Niordson, Christian Frithiof
2016-01-01
The characteristics of the active plastic zone surrounding a crack growingin a single crystal (FCC, BCC, and HCP) at constant velocity is investigated for ModeI loading under plane strain assumptions. The framework builds upon a steady-state relation bringing the desired solution out in a frame...
Computing Bifurcation Diagrams of Steady State KuramotoSivashinsky Equation by Difference Method
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
Utilizing difference formulae, we obtained the discrete systems of steady state Kuramoto-Sivashinsky (K-S) equation. Applied Newton's method and continuation technology to the systems, the bifurcated solutions are derived, and the bifurcation diagrams are constructed. All the results are successful and satisfactory.
Analysis of Plasticity, Fracture and Friction in Steady State Plate Cutting
DEFF Research Database (Denmark)
Simonsen, Bo Cerup; Wierzbicki, Tomasz
1996-01-01
A closed form solution to the problem of steady state wedge cutting through a ductile metal plate is presented. The considered problem is an idealization of a ship bottom raking process, i.e. a continuous cutting damage of a ship bottom by a hard knife-like rock in a grounding event. A new...
Steady-state decoupling and design of linear multivariable systems
Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of a linear time-invariant multivariable system is presented. This criterion consists of a set of inequalities which, when satisfied, will cause the steady states of a system to be decoupled. Stability analysis and a new design technique for such systems are given. A new and simple connection between single-loop and multivariable cases is found. These results are then applied to the compensation design for NASA STOL C-8A aircraft. Both steady-state decoupling and stability are justified through computer simulations.
Comparison of Numerical Approaches to a Steady-State Landscape Equation
Bachman, S.; Peckham, S.
2008-12-01
A mathematical model of an idealized fluvial landscape has been developed, in which a land surface will evolve to preserve dendritic channel networks as the surface is lowered. The physical basis for this model stems from the equations for conservation of mass for water and sediment. These equations relate the divergence of the 2D vector fields showing the unit-width discharge of water and sediment to the excess rainrate and tectonic uplift on the land surface. The 2D flow direction is taken to be opposite to the water- surface gradient vector. These notions are combined with a generalized Manning-type flow resistance formula and a generalized sediment transport law to give a closed mathematical system that can, in principle, be solved for all variables of interest: discharge of water and sediment, land surface height, vertically- averaged flow velocity, water depth, and shear stress. The hydraulic geometry equations (Leopold et. al, 1964, 1995) are used to incorporate width, depth, velocity, and slope of river channels as powers of the mean-annual river discharge. Combined, they give the unit- width discharge of the stream as a power, γ, of the water surface slope. The simplified steady-state model takes into account three components among those listed above: conservation of mass for water, flow opposite the gradient, and a slope-discharge exponent γ = -1 to reflect mature drainage networks. The mathematical representation of this model appears as a second-order hyperbolic partial differential equation (PDE) where the diffusivity is inversely proportional to the square of the local surface slope. The highly nonlinear nature of this PDE has made it very difficult to solve both analytically and numerically. We present simplistic analytic solutions to this equation which are used to test the validity of the numerical algorithms. We also present three such numerical approaches which have been used in solving the differential equation. The first is based on a
Directory of Open Access Journals (Sweden)
Zaidon M. Shakoor
2013-05-01
Full Text Available In this research, two models are developed to simulate the steady state fixed bed reactor used for styrene production by ethylbenzene dehydrogenation. The first is one-dimensional model, considered axial gradient only while the second is two-dimensional model considered axial and radial gradients for same variables.The developed mathematical models consisted of nonlinear simultaneous equations in multiple dependent variables. A complete description of the reactor bed involves partial, ordinary differential and algebraic equations (PDEs, ODEs and AEs describing the temperatures, concentrations and pressure drop across the reactor was given. The model equations are solved by finite differences method. The reactor models were coded with Mat lab 6.5 program and various numerical techniques were used to obtain the desired solution.The simulation data for both models were validated with industrial reactor results with a very good concordance.
Current Pressure Transducer Application of Model-based Prognostics Using Steady State Conditions
Teubert, Christopher; Daigle, Matthew J.
2014-01-01
Prognostics is the process of predicting a system's future states, health degradation/wear, and remaining useful life (RUL). This information plays an important role in preventing failure, reducing downtime, scheduling maintenance, and improving system utility. Prognostics relies heavily on wear estimation. In some components, the sensors used to estimate wear may not be fast enough to capture brief transient states that are indicative of wear. For this reason it is beneficial to be capable of detecting and estimating the extent of component wear using steady-state measurements. This paper details a method for estimating component wear using steady-state measurements, describes how this is used to predict future states, and presents a case study of a current/pressure (I/P) Transducer. I/P Transducer nominal and off-nominal behaviors are characterized using a physics-based model, and validated against expected and observed component behavior. This model is used to map observed steady-state responses to corresponding fault parameter values in the form of a lookup table. This method was chosen because of its fast, efficient nature, and its ability to be applied to both linear and non-linear systems. Using measurements of the steady state output, and the lookup table, wear is estimated. A regression is used to estimate the wear propagation parameter and characterize the damage progression function, which are used to predict future states and the remaining useful life of the system.
Reliable and Efficient Procedure for Steady-State Analysis of Nonautonomous and Autonomous Systems
Directory of Open Access Journals (Sweden)
J. Dobes
2012-04-01
Full Text Available The majority of contemporary design tools do not still contain steady-state algorithms, especially for the autonomous systems. This is mainly caused by insufficient accuracy of the algorithm for numerical integration, but also by unreliable steady-state algorithms themselves. Therefore, in the paper, a very stable and efficient procedure for the numerical integration of nonlinear differential-algebraic systems is defined first. Afterwards, two improved methods are defined for finding the steady state, which use this integration algorithm in their iteration loops. The first is based on the idea of extrapolation, and the second utilizes nonstandard time-domain sensitivity analysis. The two steady-state algorithms are compared by analyses of a rectifier and a C-class amplifier, and the extrapolation algorithm is primarily selected as a more reliable alternative. Finally, the method based on the extrapolation naturally cooperating with the algorithm for solving the differential-algebraic systems is thoroughly tested on various electronic circuits: Van der Pol and Colpitts oscillators, fragment of a large bipolar logical circuit, feedback and distributed microwave oscillators, and power amplifier. The results confirm that the extrapolation method is faster than a classical plain numerical integration, especially for larger circuits with complicated transients.
Robinson-Trautman solution with nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Tahamtan, T.; Svitek, O. [Charles University in Prague, Faculty of Mathematics and Physics, Institute of Theoretical Physics, Prague 8 (Czech Republic)
2016-06-15
Explicit Robinson-Trautman solutions with an electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all studied cases the electromagnetic field singularity is removed while the gravitational one persists. The models resolving the curvature singularity in spherically symmetric spacetimes could not be generalized to the Robinson-Trautman geometry using the generating method developed in this paper, which indicates that the removal of a singularity in the associated spherically symmetric case might be just a consequence of high symmetry. We show that the obtained solutions are generally of algebraic type II and reduce to type D in spherical symmetry. Asymptotically they tend to the spherically symmetric case as well. (orig.)
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Steady states in Leith's model of turbulence
Grebenev, V. N.; Griffin, A.; Medvedev, S. B.; Nazarenko, S. V.
2016-09-01
We present a comprehensive study and full classification of the stationary solutions in Leith’s model of turbulence with a generalised viscosity. Three typical types of boundary value problems are considered: Problems 1 and 2 with a finite positive value of the spectrum at the left (right) and zero at the right (left) boundaries of a wave number range, and Problem 3 with finite positive values of the spectrum at both boundaries. Settings of these problems and analysis of existence of their solutions are based on a phase-space analysis of orbits of the underlying dynamical system. One of the two fixed points of the underlying dynamical system is found to correspond to a ‘sharp front’ where the energy flux and the spectrum vanish at the same wave number. The other fixed point corresponds to the only exact power-law solution—the so-called dissipative scaling solution. The roles of the Kolmogorov, dissipative and thermodynamic scaling, as well as of sharp front solutions, are discussed.
Enhancement of the steady-state magnetization in TROSY experiments
Energy Technology Data Exchange (ETDEWEB)
Riek, Roland [Institut fuer Molekularbiologie und Biophysik Eidgenoessische Technische Hochschule Hoenggerberg (Switzerland)], E-mail: rr@mol.biol.ethz.ch
2001-10-15
Under the condition that the longitudinal relaxation time of spin I is shorter than the longitudinal relaxation time of spin S the steady-state magnetization in [S,I]-TROSY-type experiments can be enhanced by intermediate storage of a part of the steady-state magnetization of spin I on spin S with a pulse sequence element during the relaxation delay. It is demonstrated with samples ranging in size from the 1 kDa cyclosporin to the 110 kDa {sup 15}N,{sup 2}H-labeled dihydroneopterin Aldolase that intermediate storage of steady-state magnetization in a [{sup 15}N,{sup 1}H]-TROSY experiment yields a signal gain of 10-25%. The method proposed here for intermediate storage of steady-state magnetization can be implemented in any [{sup 15}N,{sup 1}H]-TROSY-type experiments.
Steady state and time resolved spectroscopy of photoswitchable systems
Hou, Lili
2013-01-01
Steady state en time resolved spectroscopie zijn twee fundamentele methodes voor het bestuderen van fotochemische processen. In dit proefschrift zijn drie zelf-opgezette spectroscopische systemen beschreven, waarmee samen met andere spectroscopische methoden verscheidende met licht schakelbare syste
Analytic description of adaptive network topologies in a steady state.
Wieland, Stefan; Nunes, Ana
2015-06-01
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in such active steady states. These distributions are shown to agree quantitatively with simulations except when rewiring is much faster than state update and used to predict and to explain general properties of steady-state topologies. The method generalizes easily to other coevolutionary dynamics.
Steady-state leaching of tritiated water from silica gel
DEFF Research Database (Denmark)
Das, H.A.; Hou, Xiaolin
2009-01-01
Aqueous leaching of tritium from silica gel, loaded by absorption of water vapor, makes part of reactor de-commissioning. It is found to follow the formulation of steady-state diffusion.......Aqueous leaching of tritium from silica gel, loaded by absorption of water vapor, makes part of reactor de-commissioning. It is found to follow the formulation of steady-state diffusion....
Steady-state leaching of tritiated water from silica gel
DEFF Research Database (Denmark)
Das, H.A.; Hou, Xiaolin
2009-01-01
Aqueous leaching of tritium from silica gel, loaded by absorption of water vapor, makes part of reactor de-commissioning. It is found to follow the formulation of steady-state diffusion.......Aqueous leaching of tritium from silica gel, loaded by absorption of water vapor, makes part of reactor de-commissioning. It is found to follow the formulation of steady-state diffusion....
The Budyko functions under non-steady-state conditions
Moussa, Roger; Lhomme, Jean-Paul
2016-12-01
The Budyko functions relate the evaporation ratio E / P (E is evaporation and P precipitation) to the aridity index Φ = Ep / P (Ep is potential evaporation) and are valid on long timescales under steady-state conditions. A new physically based formulation (noted as Moussa-Lhomme, ML) is proposed to extend the Budyko framework under non-steady-state conditions taking into account the change in terrestrial water storage ΔS. The variation in storage amount ΔS is taken as negative when withdrawn from the area at stake and used for evaporation and positive otherwise, when removed from the precipitation and stored in the area. The ML formulation introduces a dimensionless parameter HE = -ΔS / Ep and can be applied with any Budyko function. It represents a generic framework, easy to use at various time steps (year, season or month), with the only data required being Ep, P and ΔS. For the particular case where the Fu-Zhang equation is used, the ML formulation with ΔS ≤ 0 is similar to the analytical solution of Greve et al. (2016) in the standard Budyko space (Ep / P, E / P), a simple relationship existing between their respective parameters. The ML formulation is extended to the space [Ep / (P - ΔS), E / (P - ΔS)] and compared to the formulations of Chen et al. (2013) and Du et al. (2016). The ML (or Greve et al., 2016) feasible domain has a similar upper limit to that of Chen et al. (2013) and Du et al. (2016), but its lower boundary is different. Moreover, the domain of variation of Ep / (P - ΔS) differs: for ΔS ≤ 0, it is bounded by an upper limit 1 / HE in the ML formulation, while it is only bounded by a lower limit in Chen et al.'s (2013) and Du et al.'s (2016) formulations. The ML formulation can also be conducted using the dimensionless parameter HP = -ΔS / P instead of HE, which yields another form of the equations.
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Extension of Variable Separable Solutions for Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
JIA Hua-Bing; ZHANG Shun-Li; XU Wei; ZHU Xiao-Ning; WANG Yong-Mao; LOU Sen-Yue
2008-01-01
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separablecation, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
ADI type preconditioners for the steady state inhomogeneous Vlasov equation
Gasteiger, Markus; Ostermann, Alexander; Tskhakaya, David
2016-01-01
The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov based methods like GMRES or relexation schemes) is computationally expensive. In the former case the slowest timescale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an ADI type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speedup of close to two orders of magnitude (even for intermediate grid sizes) with respect to the not preconditio...
Dynamic steady-state of periodically-driven quantum systems
Yudin, V I; Basalaev, M Yu; Kovalenko, D
2015-01-01
Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an asymptotic solution ($t$$\\to$$+\\infty$) due to relaxation processes. The presented derivation simultaneously contains a simple computational algorithm non-using both Floquet and Fourier theories, i.e. our method automatically guarantees a full account of all frequency components. The description is accompanied by the examples demonstrating a simplicity and high efficiency of our method. In particular, for three-level $\\Lambda$-system we calculate the lineshape and field-induced shift of the dark resonance formed by the field with periodically modulated phase. For two-level atom we obtain the analytical expressions for signal of the direct frequency comb spectroscopy with rectangular light pulses. In this case it was shown the radical dependence of the spectroscopy lineshape on pul...
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Institute of Scientific and Technical Information of China (English)
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
Multiple steady states in coupled flow tank reactors
Hunt, Katharine L. C.; Kottalam, J.; Hatlee, Michael D.; Ross, John
1992-05-01
Coupling between continuous-flow, stirred tank reactors (CSTR's), each having multiple steady states, can produce new steady states with different concentrations of the chemical species in each of the coupled tanks. In this work, we identify a kinetic potential ψ that governs the deterministic time evolution of coupled tank reactors, when the reaction mechanism permits a single-variable description of the states of the individual tanks; examples include the iodate-arsenous acid reaction, a cubic model suggested by Noyes, and two quintic models. Stable steady states correspond to minima of ψ, and unstable steady states to maxima or saddle points; marginally stable states typically correspond to saddle-node points. We illustrate the variation in ψ due to changes in the rate constant for external material intake (k0) and for exchange between tanks (kx). For fixed k0 values, we analyze the changes in numbers and types of steady states as kx increases from zero. We show that steady states disappear by pairwise coalescence; we also show that new steady states may appear with increasing kx, when the reaction mechanism is sufficiently complex. For fixed initial conditions, the steady state ultimately reached in a mixing experiment may depend on the exchange rate constant as a function of time, kx(t) : Adiabatic mixing is obtained in the limit of slow changes in kx(t) and instantaneous mixing in the limit as kx(t)→∞ while t remains small. Analyses based on the potential ψ predict the outcome of mixing experiments for arbitrary kx(t). We show by explicit counterexamples that a prior theory developed by Noyes does not correctly predict the instability points or the transitions between steady states of coupled tanks, to be expected in mixing experiments. We further show that the outcome of such experiments is not connected to the relative stability of steady states in individual tank reactors. We find that coupling may effectively stabilize the tanks. We provide
An axisymmetric steady state vortex ring model
Wang, Ruo-Qian
2016-01-01
Based on the solution of Atanasiu et al. (2004), a theoretical model for axisymmetric vortex flows is derived in the present study by solving the vorticity transport equation for an inviscid, incompressible fluid in cylindrical coordinates. The model can describe a variety of axisymmetric flows with particular boundary conditions at a moderately high Reynolds number. This paper shows one example: a high Reynolds number laminar vortex ring. The model can represent a family of vortex rings by specifying the modulus function using a Rayleigh distribution function. The characteristics of this vortex ring family are illustrated by numerical methods. For verification, the model results compare well with the recent direct numerical simulations (DNS) in terms of the vorticity distribution and streamline patterns, cross-sectional areas of the vortex core and bubble, and radial vorticity distribution through the vortex center. Most importantly, the asymmetry and elliptical outline of the vorticity profile are well capt...
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
Coexistence of steady state for a diffusive prey-predator model with harvesting
Directory of Open Access Journals (Sweden)
Yan Li
2016-07-01
Full Text Available In this article, we study a diffusive prey-predator model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting, subject to homogeneous Dirichlet boundary conditions. Treating the prey harvesting parameter as a bifurcation parameter, we obtain the existence, bifurcation and stability of coexistence steady state solutions. We use the method of upper and lower solutions, degree theory in cones, and bifurcation theory. The conclusions show the importance of prey harvesting in the model.
Energy Technology Data Exchange (ETDEWEB)
Kaprielian, S.; Clements, K. (Dept. of Electrical Engineering, Worcester Polytechnic Inst., Worcester, MA (US)); Turi, J. (Texas Univ., Richardson, TX (United States))
1992-05-01
A nonlinear control strategy to improve the steady-state stability of a weak AC/DC power system is presented. The approach described in this paper is based on the extension of feedback linearization techniques to nonlinear descriptor system models. This method produces a nonlinear control strategy which is capable of enhancing system performance for various system operating conditions. This claim is supported with simulation results.
Human auditory steady state responses to binaural and monaural beats.
Schwarz, D W F; Taylor, P
2005-03-01
Binaural beat sensations depend upon a central combination of two different temporally encoded tones, separately presented to the two ears. We tested the feasibility to record an auditory steady state evoked response (ASSR) at the binaural beat frequency in order to find a measure for temporal coding of sound in the human EEG. We stimulated each ear with a distinct tone, both differing in frequency by 40Hz, to record a binaural beat ASSR. As control, we evoked a beat ASSR in response to both tones in the same ear. We band-pass filtered the EEG at 40Hz, averaged with respect to stimulus onset and compared ASSR amplitudes and phases, extracted from a sinusoidal non-linear regression fit to a 40Hz period average. A 40Hz binaural beat ASSR was evoked at a low mean stimulus frequency (400Hz) but became undetectable beyond 3kHz. Its amplitude was smaller than that of the acoustic beat ASSR, which was evoked at low and high frequencies. Both ASSR types had maxima at fronto-central leads and displayed a fronto-occipital phase delay of several ms. The dependence of the 40Hz binaural beat ASSR on stimuli at low, temporally coded tone frequencies suggests that it may objectively assess temporal sound coding ability. The phase shift across the electrode array is evidence for more than one origin of the 40Hz oscillations. The binaural beat ASSR is an evoked response, with novel diagnostic potential, to a signal that is not present in the stimulus, but generated within the brain.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
Geomorphic and Thermal Steady State Regimes: Reality or Wishful Thinking?
Lock, J.; Furlong, K.
2003-04-01
In many tectonic geomorphic studies, it is assumed that rates of uplift within an orogen are matched by rates of exhumation producing a steady-state orogen. However, the tools used to determine exhumation are thermally driven (e.g. Fission Track, U-Th/He) and exhumation can substantially perturb the crustal thermal regime. Since knowing the thermal regime is key to determining exhumation from thermochronology, problems arise. In order to interpret a rate of exhumation we make the assumption that an area is in thermal 'steady state', which in young active orogens unlikely exists. Taiwan, the Southern Alps, Fiordland, and Nanga Parbat are relatively young mountain belts that have begun to uplift or have experienced increased rates of uplift during the past 5-10 Ma. As there is a time lag between the onset of uplift and achieving geomorphic steady state and again between reaching geomorphic steady state and thermal steady state, these orogens may be too young to have achieved this final stage. Additionally, young orogens may not have experienced a constant rate of uplift and denudation in the time over which the thermochronometers average. Certainly, in the case of the Southern Alps, present uplift rates can not have existed since uplift begun. Therefore, an apparent age is recording a transient thermal state. Even in a case where geomorphic steady state exists i.e. exhumation balances uplift, it is unlikely that a thermal steady state has been reached. This precludes the simple interpretation of exhumation rates often made. When multiple thermochronometers are used, inconsistencies can arise. For example, an increase in the rate of uplift is often observed when comparing the rates of exhumation using different thermochronometers. Our modeling shows that in some cases this phenomena is actually eliminated by considering the transient nature of the thermal regime following the onset of uplift and exhumation of an active orogen. To accurately determine exhumation rate
Soil residence time: A window into landscape morphologic steady state
Almond, P. C.; Roering, J. J.
2005-12-01
For a landscape in true morphologic steady state the erosion rate and the average residence time of the debris mantle regolith (including the soils) are everywhere equal. Where other factors influencing soil properties such as climate, organisms and parent material are relatively invariant the degree of weathering and extent of pedological development in the debris mantle regolith should be spatially invariant. The corollary to this argument, commonly exploited in soil-geomorphic analysis, is that variation in debris mantle regolith development in a landscape reflects inheritance of older geomorphic surfaces and hence departure from steady state, at least over some time and space scale. The Oregon Coast Range (OCR) experiences a constant rate of rock uplift and has escaped the effects of Pleistocene glacial and periglacial processes. Furthermore, rock uplift and denudation rates have been shown to be approximately in balance, and consequently the OCR is promoted as being a good candidate for a (flux) steady state landscape. This is, however, not a sufficient condition for morphologic steady state, which is often assumed in numerical landscape simulations. The rock underlying the OCR is relatively homogeneous turbidites of the Tyee formation, and climatic and vegetation factors are relatively uniform over large areas. The degree of weathering and pedological development of the regolith on hillslopes should therefore dominantly reflect variation in regolith residence time, such that significant variation implies non-morphologic-steady state conditions. Indeed, spatial variation in soil/regolith age indicates the extent of departure from morphologic steady state. We have observed ubiquitous but localised deep, highly weathered regoliths and soils on ridge tops in the OCR. The extent, depth, geometry and elevational distribution of these deep regolith patches combined with relative measures of their age derived from total element and meteoric 10Be inventory will enable
Generalized Analytical Solutions for Nonlinear Positive-Negative Index Couplers
Directory of Open Access Journals (Sweden)
Zh. Kudyshev
2012-01-01
Full Text Available We find and analyze a generalized analytical solution for nonlinear wave propagation in waveguide couplers with opposite signs of the linear refractive index, nonzero phase mismatch between the channels, and arbitrary nonlinear coefficients.
The exact solutions for a nonisospectral nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Ning Tongke [Finance College, Shanghai Normal University, Shanghai 200234 (China)], E-mail: tkning@shnu.edu.cn; Zhang Weiguo; Jia Gao [Science College, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2009-10-30
In this paper, lax pair for the nonisospectral nonlinear Schroedinger hierarchy is given, the time dependence of nonisospectral scattering data is derived and exact solutions for the nonisospectral nonlinear Schroedinger hierarchy are obtained through the inverse scattering transform.
Wang, Jai-Ching
1994-01-01
The lateral solute segregation that results from a curved solid-liquid interface shape during steady state unidirectional solidification of a binary alloy system has been studied both analytically and numerically by Coriell, Bosivert, Rehm, and Sekerka. The system under their study is a two dimensional rectangular system. However, most real growth systems are cylindrical systems. Thus, in a previous study, we have followed Coriell etc. formalism and obtained analytical results for lateral solute segregation for an azimuthal symmetric cylindrical binary melt system during steady state solidification process. The solid-liquid interface shape is expressed as a series combination of Bessel functions. In this study a computer program has been developed to simulate the lateral solute segregation.
SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions.
Solutions of some class of nonlinear PDEs in mathematical physics
Directory of Open Access Journals (Sweden)
Shoukry El-Ganaini
2016-04-01
As a result, exact traveling wave solutions involving parameters have been obtained for the considered nonlinear equations in a concise manner. When these parameters are chosen as special values, the solitary wave solutions are derived. It is shown that the proposed technique provides a more powerful mathematical tool for constructing exact solutions for a broad variety of nonlinear PDEs in mathematical physics.
Exact solutions for some nonlinear systems of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com
2009-04-30
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.
Structural simplification of chemical reaction networks in partial steady states.
Madelaine, Guillaume; Lhoussaine, Cédric; Niehren, Joachim; Tonello, Elisa
2016-11-01
We study the structural simplification of chemical reaction networks with partial steady state semantics assuming that the concentrations of some but not all species are constant. We present a simplification rule that can eliminate intermediate species that are in partial steady state, while preserving the dynamics of all other species. Our simplification rule can be applied to general reaction networks with some but few restrictions on the possible kinetic laws. We can also simplify reaction networks subject to conservation laws. We prove that our simplification rule is correct when applied to a module of a reaction network, as long as the partial steady state is assumed with respect to the complete network. Michaelis-Menten's simplification rule for enzymatic reactions falls out as a special case. We have implemented an algorithm that applies our simplification rules repeatedly and applied it to reaction networks from systems biology.
Some new solutions of nonlinear evolution equations with variable coefficients
Virdi, Jasvinder Singh
2016-05-01
We construct the traveling wave solutions of nonlinear evolution equations (NLEEs) with variable coefficients arising in physics. Some interesting nonlinear evolution equations are investigated by traveling wave solutions which are expressed by the hyperbolic functions, the trigonometric functions and rational functions. The applied method will be used in further works to establish more entirely new solutions for other kinds of such nonlinear evolution equations with variable coefficients arising in physics.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Steady state decoupling and design of linear multivariable systems
Huang, J. Y.; Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of linear multivariable systems is developed. The criterion consists of n(n-1) inequalities with the type numbers of the compensator transfer functions as the unknowns. These unknowns can be chosen to satisfy the inequalities and hence achieve a steady state decoupling scheme. It turns out that pure integrators in the loops play an important role. An extended root locus design method is then developed to take care of the stability and transient response. The overall procedure is applied to the compensation design for STOL C-8A aircraft in the approach mode.
Electric machines steady state, transients, and design with Matlab
Boldea, Ion
2009-01-01
Part I: Steady StateIntroductionElectric Energy and Electric MachinesBasic Types of Transformers and Electric MachinesLosses and EfficiencyPhysical Limitations and RatingsNameplate RatingsMethods of AnalysisState of the Art and Perspective Electric TransformersAC Coil with Magnetic Core and Transformer Principles Magnetic Materials in EMs and Their LossesElectric Conductors and Their Skin EffectsComponents of Single- and 3-Phase TransformersFlux Linkages and Inductances of Single-Phase TransformersCircuit Equations of Single-Phase Transformers With Core LossesSteady State and Equivalent Circui
Mapping current fluctuations of stochastic pumps to nonequilibrium steady states
Rotskoff, Grant M.
2017-03-01
We show that current fluctuations in a stochastic pump can be robustly mapped to fluctuations in a corresponding time-independent nonequilibrium steady state. We thus refine a recently proposed mapping so that it ensures equivalence of not only the averages, but also optimal representation of fluctuations in currents and density. Our mapping leads to a natural decomposition of the entropy production in stochastic pumps similar to the "housekeeping" heat. As a consequence of the decomposition of entropy production, the current fluctuations in weakly perturbed stochastic pumps are shown to satisfy a universal bound determined by the steady state entropy production.
Emergence of advance waves in a steady-state universe
Energy Technology Data Exchange (ETDEWEB)
Hobart, R.H.
1979-10-01
In standard Wheeler-Feynman electrodynamics advanced waves from any source are absolutely canceled by the advanced waves from the absorber responding to that source. The present work shows this cancellation fails over cosmic distances in a steady-state universe. A test of the view proposed earlier, in a paper which assumed failure of cancellation ad hoc, that zero-point fluctuations of the electromagnetic field are such emergent advanced waves, is posed. The view entails anomalous slowing of spontaneous transition rates at longer emission wavelengths; available data go against this, furnishing additional argument against the suspect assumption that the universe is steady-state.
Exact solitary wave solutions of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
Non-steady-state transport of superthermal electrons in the plasmasphere
Khazanov, George V.; Liemohn, Michael W.; Gombosi, Tamas I.; Nagy, Andrew F.
1993-01-01
Numerical solutions to the time-dependent kinetic equation, which describes the transport of superthermal electrons in the splasmasphere between the two conjugate ionospheres, are presented. The model calculates the distribution function as a function of time, field-aligned distance, energy, and pitch-angle. The processes of refilling, depleting, and establishing steady-state conditions of superthermal electrons in the plasmasphere are discussed.
A Generalized Approach for the Steady-State Analysis of Dual-Bridge Resonant Converters
Gao-Yuan Hu; Xiaodong Li; Bo-Yue Luan
2014-01-01
In this paper, a dual-bridge DC/DC resonant converter with a generalized series and parallel resonant tank is analyzed. A general approach based on Fundamental Harmonic Approximation is used to find the universal steady-state solutions. The analysis results for particular resonant tank configurations are exemplified with several typical resonant tank configurations respectively. The corresponded soft-switching conditions are discussed too. To illustrate the usefulness of the generalized appro...
Nonlinear system guidance in the presence of transmission zero dynamics
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
A Family of Exact Solutions for the Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, the nonlinear Schrodinger (NLS) equation was analytically solved. Firstly, the stationary solutions of NLSequation were explicitly given by the elliptic functions. Then a family of exact solutions of NLS equation were obtained from these sta-tionary solutions by a method for finding new exact solutions from the stationary solutions of integrable evolution equations.
Exact periodic wave solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/43/37/375209
2010-01-01
We show that the two-dimensional, nonlinear Schr\\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: juan.belmonte@uclm.es; Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: gabriel.fernandez@uclm.es
2009-01-19
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.
The Enlisted Steady State-Simulation (ESS-SIM) Tool
2014-07-01
1 Model design ...current inven- tories. A simulation of the transition from a current inventory toward the steady state is required for such an understanding. Model design ...described by paygrade (e.g., the Navy needs 100 E-5 OS personnel). • Longevity (length of service): Many personnel policies address longevity (e.g., Zone A
The concave river long profile: a morphodynamic steady state?
Blom, A.
2011-12-01
By definition, a morphodynamic steady state is governed by a spatially constant sediment transport rate. As the sediment transport rate is a function of shear stress associated with skin friction, the morphodynamic steady state has been considered to be governed by a spatially constant bed slope. For this reason, the typical concave river long profile has been considered to be a quasi-steady state. The river's steady state has been considered to be one with a spatially constant bed slope, with tributaries inducing a stepwise decrease in bed slope in streamwise direction. Yet, for the sediment transport rate to be spatially constant, it rather is the product of water surface slope and water depth associated with skin friction that needs to be constant. This implies that physical mechanisms that induce streamwise variation in the sediment transport rate can be compensated by a streamwise variation in bed slope so as to guarantee a spatially constant sediment transport rate. Following the river course, such physical mechanisms can be bedrock exposure, partial transport, and a spatially lagging bedform growth. At locations where tributaries increase the water discharge, the above mechanisms cause the river bed profile to be upward concave over a significant reach. At bifucations or at locations where river widening prevails, the river bed profile is upward convex.
ONLINE MONITORING STEADY STATE STABILITY LIMIT PADA SISTEM INTERKONEKSI SULSELRABAR
2015-01-01
Pada beberapa dekade terakhir, fenomena black-out (pemadaman total)akibat voltage collapse mengalami peningkatan.Hal ini disebabkan oleh peningkatan konsumen pemakai listrik yang tidak sebanding dengan peningkatan pembangkit dan pengembangan jaringan transmisi. Berdasarkan kenyataan dilapangan, ketidakstabilan steady state sangat berhubungan dengan rendahnya ketersediaan daya aktif/reaktif, level tegangan yang rendah, dan besarnya perubahan tegangan untuk perubahan beban atau daya pembangkit....
Principle of Entropy Maximization for Nonequilibrium Steady States
DEFF Research Database (Denmark)
Shapiro, Alexander; Stenby, Erling Halfdan
2002-01-01
The goal of this contribution is to find out to what extent the principle of entropy maximization, which serves as a basis for the equilibrium thermodynamics, may be generalized onto non-equilibrium steady states. We prove a theorem that, in the system of thermodynamic coordinates, where entropy...
Combined Steady-State and Dynamic Heat Exchanger Experiment
Luyben, William L.; Tuzla, Kemal; Bader, Paul N.
2009-01-01
This paper describes a heat-transfer experiment that combines steady-state analysis and dynamic control. A process-water stream is circulated through two tube-in-shell heat exchangers in series. In the first, the process water is heated by steam. In the second, it is cooled by cooling water. The equipment is pilot-plant size: heat-transfer areas…
Steady state nutrition by transpiration controlled nutrient supply
Braakhekke, W.G.; Labe, D.A.
1990-01-01
Programmed nutrient addition with a constant relative addition rate has been advocated as a suitable research technique for inducing steady state nutrition in exponentially growing plants. Transpiration controlled nutrient supply is proposed as an alternative technique for plants with a short or no
ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.
Restitution slope is principally determined by steady-state action potential duration.
Shattock, Michael J; Park, Kyung Chan; Yang, Hsiang-Yu; Lee, Angela W C; Niederer, Steven; MacLeod, Kenneth T; Winter, James
2017-06-01
The steepness of the action potential duration (APD) restitution curve and local tissue refractoriness are both thought to play important roles in arrhythmogenesis. Despite this, there has been little recognition of the apparent association between steady-state APD and the slope of the restitution curve. The objective of this study was to test the hypothesis that restitution slope is determined by APD and to examine the relationship between restitution slope, refractoriness and susceptibility to VF. Experiments were conducted in isolated hearts and ventricular myocytes from adult guinea pigs and rabbits. Restitution curves were measured under control conditions and following intervention to prolong (clofilium, veratridine, bretylium, low [Ca]e, chronic transverse aortic constriction) or shorten (catecholamines, rapid pacing) ventricular APD. Despite markedly differing mechanisms of action, all interventions that prolonged the action potential led to a steepening of the restitution curve (and vice versa). Normalizing the restitution curve as a % of steady-state APD abolished the difference in restitution curves with all interventions. Effects on restitution were preserved when APD was modulated by current injection in myocytes pre-treated with the calcium chelator BAPTA-AM - to abolish the intracellular calcium transient. The non-linear relation between APD and the rate of repolarization of the action potential is shown to underpin the common influence of APD on the slope of the restitution curve. Susceptibility to VF was found to parallel changes in APD/refractoriness, rather than restitution slope. Steady-state APD is the principal determinant of the slope of the ventricular electrical restitution curve. In the absence of post-repolarization refractoriness, factors that prolong the action potential would be expected to steepen the restitution curve. However, concomitant changes in tissue refractoriness act to reduce susceptibility to sustained VF. Dependence on
Numerical Studies of Two-Fluid Axisymmetric Steady-States with Flow in Ohmic NSTX-like Plasmas
Ferraro, Nathaniel; Jardin, Stephen
2008-11-01
Axisymmetric steady-states of the resistive two-fluid equations, including flow and gyroviscosity, are obtained by evolving these nonlinear equations from an initial ideal MHD equilibrium using the code M3D-C^1 [1], which has now been extended to toroidal geometry. Steady-states for high-β, inductively driven discharges in diverted NSTX geometries are studied. Excellent agreement with theoretical predictions of cross-surface Pfirsch-Schlüter flows in the axisymmetric steady-states is found. The dependence of flow velocities with resistivity is explored. It is found that in the two-fluid model, the statistical steady-state may be a fixed point, a limit cycle, or chaotic, depending on the parameters. Two-fluid terms lead to a preferred direction of toroidal rotation. The inclusion of gyroviscosity is observed to alter the character of the steady-state. The three-dimensional linear stability of simple equilibria in this two-fluid model are also explored using M3D-C^1 [2]. [1] N. Ferraro, S. Jardin. Phys. Plasmas 13:092101 (2006). [2] S. Jardin, N. Ferraro, J. Breslau, J. Chen, and M. Chance. Initial results for linear 3D Toroidal Two-Fluid stability using M3D-C1. APS DPP Conference, Dallas, TX (2008).
Exact solutions for nonlinear partial fractional differential equations
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Saleh Omran
2012-01-01
In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved (G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.
Three positive doubly periodic solutions of a nonlinear telegraph system
Institute of Scientific and Technical Information of China (English)
Fang-lei WANG; Yu-kun AN
2009-01-01
This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.
Solution of continuous nonlinear PDEs through order completion
Oberguggenberger, MB
1994-01-01
This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e......We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...
Approximate solution of a nonlinear partial differential equation
Vajta, M.
2007-01-01
Nonlinear partial differential equations (PDE) are notorious to solve. In only a limited number of cases can we find an analytic solution. In most cases, we can only apply some numerical scheme to simulate the process described by a nonlinear PDE. Therefore, approximate solutions are important for t
Positive periodic solutions for third-order nonlinear differential equations
Directory of Open Access Journals (Sweden)
Jingli Ren
2011-05-01
Full Text Available For several classes of third-order constant coefficient linear differential equations we obtain existence and uniqueness of periodic solutions utilizing explicit Green's functions. We discuss an iteration method for constant coefficient nonlinear differential equations and provide new conditions for the existence of periodic positive solutions for third-order time-varying nonlinear and neutral differential equations.
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
DEFF Research Database (Denmark)
Deng, Yujia
the reactive sites for the ORR, thus leading toa decrease in activity as compared to that in HClO4 electrolyte solution. At steady state theORR activity is inhibited in all the three acid electrolyte solutions as compared to transientconditions. The ORR can reach its diffusion limited current in both HClO4...
Logarithmic singularities of solutions to nonlinear partial differential equations
Tahara, Hidetoshi
2007-01-01
We construct a family of singular solutions to some nonlinear partial differential equations which have resonances in the sense of a paper due to T. Kobayashi. The leading term of a solution in our family contains a logarithm, possibly multiplied by a monomial. As an application, we study nonlinear wave equations with quadratic nonlinearities. The proof is by the reduction to a Fuchsian equation with singular coefficients.
Steady-state responses of a belt-drive dynamical system under dual excitations
Ding, Hu
2016-02-01
The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete-continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the firing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Furthermore, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numerical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pulley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foundation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.
Oxygen consumption dynamics in steady-state tumour models.
Grimes, David Robert; Fletcher, Alexander G; Partridge, Mike
2014-09-01
Oxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the underlying physics limits the resolution to the millimetre domain, whereas oxygen tension varies over a micrometre scale. If the distribution of oxygen in the tumour micro-environment can be accurately estimated, then the effect of potential dose escalation to these hypoxic regions could be better modelled, allowing more realistic simulation of biologically adaptive treatments. Reaction-diffusion models are commonly used for modelling oxygen dynamics, with a variety of functional forms assumed for the dependence of oxygen consumption rate (OCR) on cellular status and local oxygen availability. In this work, we examine reaction-diffusion models of oxygen consumption in spherically and cylindrically symmetric geometries. We consider two different descriptions of oxygen consumption: one in which the rate of consumption is constant and one in which it varies with oxygen tension in a hyperbolic manner. In each case, we derive analytic approximations to the steady-state oxygen distribution, which are shown to closely match the numerical solutions of the equations and accurately predict the extent to which oxygen can diffuse. The derived expressions relate the limit to which oxygen can diffuse into a tissue to the OCR of that tissue. We also demonstrate that differences between these functional forms are likely to be negligible within the range of literature estimates of the hyperbolic oxygen constant, suggesting that the constant consumption rate approximation suffices for modelling oxygen dynamics for most values of OCR. These approximations also allow the rapid identification of situations where hyperbolic consumption forms can result in significant differences from constant
Action-at-a-distance electrodynamics in quasi-steady-state cosmology
Indian Academy of Sciences (India)
Kaustubh Sudhir Deshpande
2014-09-01
Action-at-a-distance electrodynamics – alternative approach to field theory – can be extended to cosmological models using conformal symmetry. An advantage of this is that, the origin of arrow of time in electromagnetism can be attributed to the cosmological structure. Different cosmological models can be investigated, based on Wheeler–Feynman absorber theory, and only those models can be considered viable for our Universe which have net full retarded electromagnetic interactions, i.e., forward direction of time. This work evaluates the quasi-steady-state model and demonstrates that it admits full retarded and not advanced solution. Thus, quasi-steady-state cosmology (QSSC) satisfies this necessary condition for a correct cosmological model, based on action-at-a-distance formulation.
Mass transfer mathematical model for one-side plate steady-state ultrafiltration
Institute of Scientific and Technical Information of China (English)
QIU Yun-ren; ZHANG Qi-xiu
2005-01-01
A mass transfer mathematical model was developed based on one-side plate steady-state ultrafiltration (UF), and the numerical solution was obtained by Crank-Nicolson finite difference method. The effects of the feed concentration, channel length, axial velocity, and diffusion coefficient on the concentration at membrane surface and the concentration profiles were investigated. Furthermore, the operation parameters and the parameters of membrane module were all transformed into dimensionless ones, and the parameter rejection was included in the mass transfer model, therefore, it can be used to calculate the steady-state ultrafiltration with different rejections. The model was used for the calculation of the ultrafiltration of metal-cutting oil emulsion. The results show that the concentration polarization can be reduced by increasing the axial velocity to some extent, but the reduction of concentration polarization is very small when the resistance of ultrafiltration is very great.
Nonlinear stability of cosmological solutions in massive gravity
De Felice, Antonio; Lin, Chunshan; Mukohyama, Shinji
2013-01-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Ion-selective supported liquid membranes placed under steady-state diffusion control.
Tompa, Károly; Birbaum, Karin; Malon, Adam; Vigassy, Tamás; Bakker, Eric; Pretsch, Ernö
2005-12-01
Supported liquid membranes are used here to establish steady-state concentration profiles across ion-selective membranes rapidly and reproducibly. This opens up new avenues in the area of nonequilibrium potentiometry, where reproducible accumulation and depletion processes at ion-selective membranes may be used to gain valuable analytical information about the sample. Until today, drifting signals originating from a slowly developing concentration profile across the ion-selective membrane made such approaches impractical in zero current potentiometry. Here, calcium- and silver-selective membranes were placed between two identical aqueous electrolyte solutions, and the open circuit potential was monitored upon changing the composition of one solution. Steady state was reached in approximately 1 min with 25-microm porous polypropylene membranes filled with bis(2-ethylhexyl) sebacate doped with ionophore and lipophilic ion exchanger. Ion transport across the membrane resulted on the basis of nonsymmetric ion-exchange processes at both membrane sides. The steady-state potential was calculated as the sum of the two membrane phase boundary potentials, and good correspondence to experiment was observed. Concentration polarizations in the contacting aqueous phases were confirmed with stirring experiments. It was found that interferences (barium in the case of calcium electrodes and potassium with silver electrodes) induce a larger potential change than expected with the Nicolsky equation because they influence the level of polarization of the primary ion (calcium or silver) that remains potential determining.
Numerical Investigation of the Steady State of a Driven Thin Film Equation
Directory of Open Access Journals (Sweden)
A. J. Hutchinson
2013-01-01
Full Text Available A third-order ordinary differential equation with application in the flow of a thin liquid film is considered. The boundary conditions come from Tanner's problem for the surface tension driven flow of a thin film. Symmetric and nonsymmetric finite difference schemes are implemented in order to obtain steady state solutions. We show that a central difference approximation to the third derivative in the model equation produces a solution curve with oscillations. A difference scheme based on a combination of forward and backward differences produces a smooth accurate solution curve. The stability of these schemes is analysed through the use of a von Neumann stability analysis.
Tabiś, Bolesław; Skoneczny, Szymon
2013-07-20
Nonlinear properties of a bioreactor with a developed microbiological predator-prey food chain are discussed. The presence of the predator microorganism completely changes the position and stability of the stationary states. A wide range of unstable steady states appears, associated with high amplitude oscillations of the state variables. Without automatic control such a system can only operate in transient states, with the yield undergoing periodic changes following the dynamics of the stable limit cycle. Technologically, this is undesirable. It has been shown that the oscillations can be removed by employing continuous P or PI controllers. Moreover, with a PI-controller, the predator can be eliminated from the system.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, Àngel
2013-12-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
High magnetic field test of bismuth Hall sensors for ITER steady state magnetic diagnostic
Duran, I.; Entler, S.; Kohout, M.; Kočan, M.; Vayakis, G.
2016-11-01
Performance of bismuth Hall sensors developed for the ITER steady state magnetic diagnostic was investigated for high magnetic fields in the range ±7 T. Response of the sensors to the magnetic field was found to be nonlinear particularly within the range ±1 T. Significant contribution of the planar Hall effect to the sensors output voltage causing undesirable cross field sensitivity was identified. It was demonstrated that this effect can be minimized by the optimization of the sensor geometry and alignment with the magnetic field and by the application of "current-spinning technique."
Optomechanical self-oscillations in an anharmonic potential: engineering a nonclassical steady state
Grimm, Manuel; Bruder, Christoph; Lörch, Niels
2016-09-01
We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical model is developed to characterize the limit cycle for large mechanical amplitudes corresponding to a weak nonlinearity. As a result, we predict conditions to achieve subpoissonian phonon statistics in the steady state, indicating classically forbidden behavior. We compare with numerical simulations and find very good agreement. Our model is quite general and can be applied to other physical systems such as trapped ions or superconducting circuits.
Energy Technology Data Exchange (ETDEWEB)
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Exact solutions for the cubic-quintic nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Zhu Jiamin [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)]. E-mail: zjm64@163.com; Ma Zhengyi [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China); Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 (China)
2007-08-15
In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
Caffarelli, Luis; Nirenberg, Louis
2011-01-01
The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.
New traveling wave solutions for nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Analysis of slow transitions between nonequilibrium steady states
Mandal, Dibyendu; Jarzynski, Christopher
2016-06-01
Transitions between nonequilibrium steady states obey a generalized Clausius inequality, which becomes an equality in the quasistatic limit. For slow but finite transitions, we show that the behavior of the system is described by a response matrix whose elements are given by a far-from-equilibrium Green-Kubo formula, involving the decay of correlations evaluated in the nonequilibrium steady state. This result leads to a fluctuation-dissipation relation between the mean and variance of the nonadiabatic entropy production, Δ {{s}\\text{na}} . Furthermore, our results extend—to nonequilibrium steady states—the thermodynamic metric structure introduced by Sivak and Crooks for analyzing minimal-dissipation protocols for transitions between equilibrium states.
Hydrodynamics of stratified epithelium: steady state and linearized dynamics
Yeh, Wei-Ting
2015-01-01
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic description for tissue dynamics at long-wavelength, long-time limit is developed, and the analysis reveals important insight for the dynamics of an epithelium close to its steady state. When the proliferative cells occupy a thin region close to the basal membrane, the relaxation rate towards the steady state is enhanced by cell division and cell apoptosis. On the other hand, when the region where proliferative cells reside becomes sufficiently thick, a flow induced by cell apoptosis close to the apical surface could enhance small perturbations. This destabilizing mechanism is general for continuous self-renewal multi-layered tissues, it could be related to the origin of certain tissue morphology and developing pattern.
Hydrodynamics of stratified epithelium: Steady state and linearized dynamics
Yeh, Wei-Ting; Chen, Hsuan-Yi
2016-05-01
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue are assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic description of tissue dynamics at the long-wavelength, long-time limit is developed, and the analysis reveals important insights into the dynamics of an epithelium close to its steady state. When the proliferative cells occupy a thin region close to the basal membrane, the relaxation rate towards the steady state is enhanced by cell division and cell apoptosis. On the other hand, when the region where proliferative cells reside becomes sufficiently thick, a flow induced by cell apoptosis close to the apical surface enhances small perturbations. This destabilizing mechanism is general for continuous self-renewal multilayered tissues; it could be related to the origin of certain tissue morphology, tumor growth, and the development pattern.
Nonequilibrium Steady States of a Stochastic Model System.
Zhang, Qiwei
We study the nonequilibrium steady state of a stochastic lattice gas model, originally proposed by Katz, Lebowitz and Spohn (Phys. Rev. B 28: 1655 (1983)). Firstly, we solve the model on some small lattices exactly in order to see the general dependence of the steady state upon different parameters of the model. Nextly, we derive some analytical results for infinite lattice systems by taking some suitable limits. We then present some renormalization group results for the continuum version of the model via field theoretical techniques, the supersymmetry of the critical dynamics in zero field is also explored. Finally, we report some very recent 3-D Monte Carlo simulation results, which have been obtained by applying Multi-Spin-Coding techniques on a CDC vector supercomputer - Cyber 205 at John von Neumann Center.
Task-specific stability of multifinger steady-state action.
Reschechtko, Sasha; Zatsiorsky, Vladimir M; Latash, Mark L
2015-01-01
The authors explored task-specific stability during accurate multifinger force production tasks with different numbers of instructed fingers. Subjects performed steady-state isometric force production tasks and were instructed not to interfere voluntarily with transient lifting-and-lowering perturbations applied to the index finger. The main results were (a) intertrial variance in the space of finger modes at steady states was larger within the subspace that had no effect on the total force (the uncontrolled manifold [UCM]); (b) perturbations caused large deviations of finger modes within the UCM (motor equivalence); and (c) deviations caused by the perturbation showed larger variance within the UCM. No significant effects of the number of task fingers were noted in any of the 3 indicators. The results are discussed within the frameworks of the UCM and referent configuration hypotheses. The authors conclude, in particular, that all the tasks were effectively 4-finger tasks with different involvement of task and nontask fingers.
Non-equilibrium steady states in supramolecular polymerization
Sorrenti, Alessandro; Leira-Iglesias, Jorge; Sato, Akihiro; Hermans, Thomas M.
2017-06-01
Living systems use fuel-driven supramolecular polymers such as actin to control important cell functions. Fuel molecules like ATP are used to control when and where such polymers should assemble and disassemble. The cell supplies fresh ATP to the cytosol and removes waste products to sustain steady states. Artificial fuel-driven polymers have been developed recently, but keeping them in sustained non-equilibrium steady states (NESS) has proven challenging. Here we show a supramolecular polymer that can be kept in NESS, inside a membrane reactor where ATP is added and waste removed continuously. Assembly and disassembly of our polymer is regulated by phosphorylation and dephosphorylation, respectively. Waste products lead to inhibition, causing the reaction cycle to stop. Inside the membrane reactor, however, waste can be removed leading to long-lived NESS conditions. We anticipate that our approach to obtain NESS can be applied to other stimuli-responsive materials to achieve more life-like behaviour.
Approach to steady-state transport in nanoscale conductors.
Bushong, Neil; Sai, Na; Di Ventra, Massimiliano
2005-12-01
We show, using a tight-binding model and time-dependent density-functional theory, that a quasi-steady-state current can be established dynamically in a finite nanoscale junction without any inelastic effects. This is simply due to the geometrical constriction experienced by the electron wave packets as they propagate through the junction. We also show that in this closed nonequilibrium system two local electron occupation functions can be defined on each side of the nanojunction which approach Fermi distributions with increasing number of atoms in the electrodes. The resultant conductance and current-voltage characteristics at quasi-steady state are in agreement with those calculated within the static scattering approach.
Steady-state Physics, Effective Temperature Dynamics in Holography
Kundu, Arnab
2013-01-01
Using the gauge-gravity duality, we argue that for a certain class of out-of-equilibrium steady-state systems in contact with a heat bath at a given temperature, the macroscopic physics can be captured by an effective thermodynamic description. The steady-state is obtained by applying a constant electric field that results in a stationary current flow. Within holography, we consider generic probe systems where an open string equivalence principle and an open string metric govern the effective thermodynamics. This description comes equipped with an effective temperature, which is larger than the bath temperature, and a corresponding effective entropy. For conformal or scale-invariant theories, certain scaling behaviours follow immediately. In general, in the large electric field limit, this effective temperature is also observed to obey certain generic relations with various physical parameters in the system.
Multiplying steady-state culture in multi-reactor system.
Erm, Sten; Adamberg, Kaarel; Vilu, Raivo
2014-11-01
Cultivation of microorganisms in batch experiments is fast and economical but the conditions therein change constantly, rendering quantitative data interpretation difficult. By using chemostat with controlled environmental conditions the physiological state of microorganisms is fixed; however, the unavoidable stabilization phase makes continuous methods resource consuming. Material can be spared by using micro scale devices, which however have limited analysis and process control capabilities. Described herein are a method and a system combining the high throughput of batch with the controlled environment of continuous cultivations. Microorganisms were prepared in one bioreactor followed by culture distribution into a network of bioreactors and continuation of independent steady state experiments therein. Accelerostat cultivation with statistical analysis of growth parameters demonstrated non-compromised physiological state following distribution, thus the method effectively multiplied steady state culture of microorganisms. The theoretical efficiency of the system was evaluated in inhibitory compound analysis using repeated chemostat to chemostat transfers.
Extending Molecular Theory to Steady-State Diffusing Systems
Energy Technology Data Exchange (ETDEWEB)
FRINK,LAURA J. D.; SALINGER,ANDREW G.; THOMPSON,AIDAN P.
1999-10-22
Predicting the properties of nonequilibrium systems from molecular simulations is a growing area of interest. One important class of problems involves steady state diffusion. To study these cases, a grand canonical molecular dynamics approach has been developed by Heffelfinger and van Swol [J. Chem. Phys., 101, 5274 (1994)]. With this method, the flux of particles, the chemical potential gradients, and density gradients can all be measured in the simulation. In this paper, we present a complementary approach that couples a nonlocal density functional theory (DFT) with a transport equation describing steady-state flux of the particles. We compare transport-DFT predictions to GCMD results for a variety of ideal (color diffusion), and nonideal (uphill diffusion and convective transport) systems. In all cases excellent agreement between transport-DFT and GCMD calculations is obtained with diffusion coefficients that are invariant with respect to density and external fields.
Visual steady state in relation to age and cognitive function
DEFF Research Database (Denmark)
Horwitz, Anna; Dyhr Thomsen, Mia; Wiegand, Iris
2017-01-01
examine the steady-state VEP power response (SSVEP-PR) in the alpha (8Hz) and gamma (36Hz) bands in 54 males (avg. age: 62.0 years) and compare these with 10 young healthy participants (avg. age 27.6 years). Furthermore, we correlate the individual alpha-to-gamma difference in relative visual-area power......, global cognition, executive function, memory, and education (p
Anthropic-principle arguments against steady-state cosmological theories
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J. (Tulane Univ., New Orleans, LA (USA))
1982-04-01
Steady-state theories are very difficult to rule out on observational grounds, particularly if they are adjusted to contain a three-degree isotropic thermal-background radiation. However, anthropic-principle arguments can be used to rule out virtually any cosmological theory which has the universe stationary in the large. For example, anthropic considerations show that the perfect cosmological principle is self-contradictory.
Approach to steady state transport in nanoscale conductors
2005-01-01
We show, using a tight-binding model and time-dependent density-functional theory, that a quasi-steady state current can be established dynamically in a finite nanoscale junction without any inelastic effects. This is simply due to the geometrical constriction experienced by the electron wavepackets as they propagate through the junction. We also show that in this closed non-equilibrium system two local electron occupation functions can be defined on each side of the nanojunction which approa...
The Approach to Steady State Using Homogeneous and Cartesian Coordinates
Directory of Open Access Journals (Sweden)
D. F. Gochberg
2013-01-01
Full Text Available Repeating an arbitrary sequence of RF pulses and magnetic field gradients will eventually lead to a steady-state condition in any magnetic resonance system. While numerical methods can quantify this trajectory, analytic analysis provides significantly more insight and a means for faster calculation. Recently, an analytic analysis using homogeneous coordinates was published. The current work further develops this line of thought and compares the relative merits of using a homogeneous or a Cartesian coordinate system.
Steady state equivalence among autocatalytic peroxidase-oxidase reactions
Méndez-González, José; Femat, Ricardo
2016-12-01
Peroxidase-oxidase is an enzymatic reaction that can exhibit dynamical scenarios such as bistability, sustained oscillations, and Shilnikov chaos. In this work, we apply the chemical reaction network theory approach to find kinetic constants such that the associated mass action kinetics ordinary differential equations induced by three four dimensional structurally different enzymatic reaction systems can support the same steady states for several chemical species despite differences in their chemical nature.
Multiple Color Stimulus Induced Steady State Visual Evoked Potentials
2007-11-02
evoked potentials, multiple color, FFT, bispectrum I. INTRODUCTION Visual evoked potential ( VEP ) is the electrical response of...brain under visual stimulation, which can be recorded from the scalp over the visual cortex of the brain. A distinction is made between transient VEP ...and steady-state VEP (SSVEP) based on the stimulation frequencies. The former arises when the stimulation frequencies are less than 2 Hz. However
Steady state nutrition by transpiration controlled nutrient supply
Braakhekke, W.G.; Labe, D. A.
1990-01-01
Programmed nutrient addition with a constant relative addition rate has been advocated as a suitable research technique for inducing steady state nutrition in exponentially growing plants. Transpiration controlled nutrient supply is proposed as an alternative technique for plants with a short or no exponential growth phase. A two-weeks experiment with transpiration controlled nitrogen supply to Pennisetum americanum was carried out to evaluate this method. After an adaptation phase a constant...
Steady-state and dynamic models for particle engulfment during solidification
Tao, Yutao; Yeckel, Andrew; Derby, Jeffrey J.
2016-06-01
Steady-state and dynamic models are developed to study the physical mechanisms that determine the pushing or engulfment of a solid particle at a moving solid-liquid interface. The mathematical model formulation rigorously accounts for energy and momentum conservation, while faithfully representing the interfacial phenomena affecting solidification phase change and particle motion. A numerical solution approach is developed using the Galerkin finite element method and elliptic mesh generation in an arbitrary Lagrangian-Eulerian implementation, thus allowing for a rigorous representation of forces and dynamics previously inaccessible by approaches using analytical approximations. We demonstrate that this model accurately computes the solidification interface shape while simultaneously resolving thin fluid layers around the particle that arise from premelting during particle engulfment. We reinterpret the significance of premelting via the definition an unambiguous critical velocity for engulfment from steady-state analysis and bifurcation theory. We also explore the complicated transient behaviors that underlie the steady states of this system and posit the significance of dynamical behavior on engulfment events for many systems. We critically examine the onset of engulfment by comparing our computational predictions to those obtained using the analytical model of Rempel and Worster [29]. We assert that, while the accurate calculation of van der Waals repulsive forces remains an open issue, the computational model developed here provides a clear benefit over prior models for computing particle drag forces and other phenomena needed for the faithful simulation of particle engulfment.
Phase-field study of three-dimensional steady-state growth shapes in directional solidification.
Gurevich, Sebastian; Karma, Alain; Plapp, Mathis; Trivedi, Rohit
2010-01-01
We use a quantitative phase-field approach to study directional solidification in various three-dimensional geometries for realistic parameters of a transparent binary alloy. The geometries are designed to study the steady-state growth of spatially extended hexagonal arrays, linear arrays in thin samples, and axisymmetric shapes constrained in a tube. As a basis to address issues of dynamical pattern selection, the phase-field simulations are specifically geared to identify ranges of primary spacings for the formation of the classically observed "fingers" (deep cells) with blunt tips and "needles" with parabolic tips. Three distinct growth regimes are identified that include a low-velocity regime with only fingers forming, a second intermediate-velocity regime characterized by coexistence of fingers and needles that exist on separate branches of steady-state growth solutions for small and large spacings, respectively, and a third high-velocity regime where those two branches merge into a single one. Along the latter, the growth shape changes continuously from fingerlike to needlelike with increasing spacing. These regimes are strongly influenced by crystalline anisotropy with the third regime extending to lower velocity for larger anisotropy. Remarkably, however, steady-state shapes and tip undercoolings are only weakly dependent on the growth geometry. Those results are used to test existing theories of directional finger growth as well as to interpret the hysteretic nature of the cell-to-dendrite transition.
Steady state statistical correlations predict bistability in reaction motifs.
Chakravarty, Suchana; Barik, Debashis
2017-03-01
Various cellular decision making processes are regulated by bistable switches that take graded input signals and convert them to binary all-or-none responses. Traditionally, a bistable switch generated by a positive feedback loop is characterized either by a hysteretic signal response curve with two distinct signaling thresholds or by characterizing the bimodality of the response distribution in the bistable region. To identify the intrinsic bistability of a feedback regulated network, here we propose that bistability can be determined by correlating higher order moments and cumulants (≥2) of the joint steady state distributions of two components connected in a positive feedback loop. We performed stochastic simulations of four feedback regulated models with intrinsic bistability and we show that for a bistable switch with variation of the signal dose, the steady state variance vs. covariance adopts a signatory cusp-shaped curve. Further, we find that the (n + 1)th order cross-cumulant vs. nth order cross-cumulant adopts a closed loop structure for at least n = 3. We also propose that our method is capable of identifying systems without intrinsic bistability even though the system may show bimodality in the marginal response distribution. The proposed method can be used to analyze single cell protein data measured at steady state from experiments such as flow cytometry.
Nonequilibrium Steady State Thermodynamics and Fluctuations for Stochastic Systems
Taniguchi, Tooru; Cohen, E. G. D.
2008-02-01
We use the work done on and the heat removed from a system to maintain it in a nonequilibrium steady state for a thermodynamic-like description of such a system as well as of its fluctuations. Based on an extended Onsager-Machlup theory for nonequilibrium steady states we indicate two ambiguities, not present in an equilibrium state, in defining such work and heat: one due to a non-uniqueness of time-reversal procedures and another due to multiple possibilities to separate heat into work and an energy difference in nonequilibrium steady states. As a consequence, for such systems, the work and heat satisfy multiple versions of the first and second laws of thermodynamics as well as of their fluctuation theorems. Unique laws and relations appear only to be obtainable for concretely defined systems, using physical arguments to choose the relevant physical quantities. This is illustrated on a number of systems, including a Brownian particle in an electric field, a driven torsion pendulum, electric circuits and an energy transfer driven by a temperature difference.
Ideal MHD Stability of ITER Steady State Scenarios with ITBs
Energy Technology Data Exchange (ETDEWEB)
F.M. Poli, C.E. Kessel, S. Jardin, J. Manickam, M. Chance, J. Chen
2011-07-27
One of ITER goals is to demonstrate feasibility of continuous operations using non-inductive current drive. Two main candidates have been identified for advanced operations: the long duration, high neutron fluency hybrid scenario and the steady state scenario, both operating at a plasma current lower than the reference ELMy scenario [1][2] to minimize the required current drive. The steady state scenario targets plasmas with current 7-10 MA in the flat-top, 50% of which will be provided by the self-generated, pressure-driven bootstrap current. It has been estimated that, in order to obtain a fusion gain Q > 5 at a current of 9 MA, it should be ΒN > 2.5 and H > 1.5 [3]. This implies the presence of an Internal Transport Barrier (ITB). This work discusses how the stability of steady state scenarios with ITBs is affected by the external heating sources and by perturbations of the equilibrium profiles.
Transient and steady-state currents in epoxy resin
Energy Technology Data Exchange (ETDEWEB)
Guillermin, Christophe [Schneider Electric Industries S.A.S., 37 quai Paul-Louis Merlin, 38050 Grenoble Cedex 9 (France); Rain, Pascal [Laboratoire d' Electrostatique et de Materiaux Dielectriques (LEMD), CNRS, 25 avenue des Martyrs, 38042 Grenoble Cedex 9 (France); Rowe, Stephen W [Schneider Electric Industries S.A.S., 37 quai Paul-Louis Merlin, 38050 Grenoble Cedex 9 (France)
2006-02-07
Charging and discharging currents have been measured in a diglycidyl ether of bisphenol-A epoxy resin with and without silica fillers, below and above its glass transition temperature T{sub g} = 65 deg. C. Both transient and steady-state current densities have been analysed. The average applied fields ranged from 3 to 35 kV mm{sup -1} with a sample thickness of 0.5 mm. Above T{sub g}, transient currents suggested a phenomenon of charge injection forming trapped space charges even at low fields. Steady-state currents confirmed that the behaviour was not Ohmic and suggested Schottky-type injection. Below T{sub g}, the current is not controlled by the metal-dielectric interface but by the conduction in the volume: the current is Ohmic at low fields and both transient and steady-state currents suggest a phenomenon of space-charge limited currents at high fields. The field threshold is similar in the filler-free and the filled resin. Values in the range 12-17 kV mm{sup -1} have been measured.
Steady states of continuous-time open quantum walks
Liu, Chaobin; Balu, Radhakrishnan
2017-07-01
Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always converges to a steady state regardless of the initial state when a graph is connected. When the graph is both connected and regular, it is shown that the steady state is the maximally mixed state. As shown by the examples in this article, the steady states of CTOQW can be very unusual and complicated even though the underlying graphs are simple. The examples demonstrate that the structure of a graph can affect quantum coherence in CTOQW through a long-time run. Precisely, the quantum coherence persists throughout the evolution of the CTOQW when the underlying topology is certain irregular graphs (such as a path or a star as shown in the examples). In contrast, the quantum coherence will eventually vanish from the open quantum system when the underlying topology is a regular graph (such as a cycle).
Cavitation modeling for steady-state CFD simulations
Hanimann, L.; Mangani, L.; Casartelli, E.; Widmer, M.
2016-11-01
Cavitation in hydraulic turbomachines is an important phenomenon to be considered for performance predictions. Correct analysis of the cavitation onset and its effect on the flow field while diminishing the pressure level need therefore to be investigated. Even if cavitation often appears as an unsteady phenomenon, the capability to compute it in a steady state formulation for the design and assessment phase in the product development process is very useful for the engineer. In the present paper the development and corresponding application of a steady state CFD solver is presented, based on the open source toolbox OpenFOAM®. In the first part a review of different cavitation models is presented. Adopting the mixture-type cavitation approach, various models are investigated and developed in a steady state CFD RANS solver. Particular attention is given to the coupling between cavitation and turbulence models as well as on the underlying numerical procedure, especially the integration in the pressure- correction step of pressure-based solvers, which plays an important role in the stability of the procedure. The performance of the proposed model is initially assessed on simple cases available in the open literature. In a second step results for different applications are presented, ranging from airfoils to pumps.
SBWR Model for Steady-State and Transient Analysis
Directory of Open Access Journals (Sweden)
Gilberto Espinosa-Paredes
2008-01-01
Full Text Available This paper presents a model of a simplified boiling water reactor (SBWR to analyze the steady-state and transient behavior. The SBWR model is based on approximations of lumped and distributed parameters to consider neutronics and natural circulation processes. The main components of the model are vessel dome, downcomer, lower plenum, core (channel and fuel, upper plenum, pressure, and level controls. Further consideration of the model is the natural circulation path in the internal circuit of the reactor, which governs the safety performance of the SBWR. To demonstrate the applicability of the model, the predictions were compared with plant data, manufacturer_s predictions, and RELAP5 under steady-state and transient conditions of a typical BWR. In steady-state conditions, the profiles of the main variables of the SBWR core such as superficial velocity, void fraction, temperatures, and convective heat transfer coefficient are presented and analyzed. The transient behavior of SBWR was analyzed during the closure of all main steam line isolation valves (MSIVs. Our results in this transient show that the cooling system due to natural circulation in the SBWR is around 70% of the rated core flow. According to the results shown here, one of the main conclusions of this work is that the simplified model could be very helpful in the licensing process.
Majeed, Muhammad Usman
2017-07-19
Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
Overview of EAST experiments on the development of high-performance steady-state scenario
Wan, B. N.; Liang, Y. F.; Gong, X. Z.; Li, J. G.; Xiang, N.; Xu, G. S.; Sun, Y. W.; Wang, L.; Qian, J. P.; Liu, H. Q.; Zhang, X. D.; Hu, L. Q.; Hu, J. S.; Liu, F. K.; Hu, C. D.; Zhao, Y. P.; Zeng, L.; Wang, M.; Xu, H. D.; Luo, G. N.; Garofalo, A. M.; Ekedahl, A.; Zhang, L.; Zhang, X. J.; Huang, J.; Ding, B. J.; Zang, Q.; Li, M. H.; Ding, F.; Ding, S. Y.; Lyu, B.; Yu, Y. W.; Zhang, T.; Zhang, Y.; Li, G. Q.; Xia, T. Y.; the EAST Team; Collaborators
2017-10-01
The EAST research program aims to demonstrate steady-state long-pulse advanced high-performance H-mode operations with ITER-like poloidal configuration and RF-dominated heating schemes. Since the 2014 IAEA FEC, EAST has been upgraded with all ITER-relevant auxiliary heating and current drive systems, enabling the investigation of plasma profile control by the coupling/integration of various auxiliary heating combinations. Fully non-inductive steady-state H-mode plasma (H 98,y2 > 1.1) was extended over 60 s for the first time with sole RF heating plus good power coupling and impurity and particle control. By means of the 4.6 GHz and 2.45 GHz LHCD systems, H-mode can be obtained and maintained at relatively high density, even up to n e ~ 4.5 × 1019 m-3, where a current drive effect is still observed. Significant progress has been achieved on EAST, including: (i) demonstration of a steady-state scenario (fully non-inductive with V loop ~ 0.0 V at high β P ~ 1.8 and high-performance in upper single-null (ɛ ~ 1.6) configuration with the tungsten divertor; (ii) discovery of a stationary H-mode regime with no/small ELM using 4.6 GHz LHCD, and; (iii) achievement of ELM suppression in slowly rotating H-mode plasma with n = 1 and 2 RMP compatible with long-pulse operations. The new advances in scenario development provide an integrated solution in achieving long-pulse steady-state operations on EAST.
Indian Academy of Sciences (India)
Hasan Çallioğlu
2011-02-01
An analytical thermoelasticity solution for a disc made of functionally graded materials (FGMs) is presented. Infinitesimal deformation theory of elasticity and power law distribution for functional gradation are used in the solution procedure. Some relative results for the stress and displacement components along the radius are presented due to internal pressure, external pressure, centrifugal force and steady state temperature. From the results, it is found that the grading indexes play an important role in determining the thermomechanical responses of FG disc and in optimal design of these structures.
Energy Technology Data Exchange (ETDEWEB)
Joshi, Neeraj Kumar; Tewari, Neeraj; Arora, Priyanka; Rautela, Ranjana; Pant, Sanjay [Photophysics Laboratory, Department of Physics, DSB Campus, Kumaun University, Nainital 263002, Uttarakhand (India); Joshi, Hem Chandra, E-mail: hem_sup@yahoo.co.uk [Institute for Plasma Research, Laser Diagnostics Division, Bhat, Near Indira Bridge, Gandhinagar 382428, Gujarat (India)
2015-02-15
The fluorescence quenching of quinidine in acidified aqueous solution by various halides (Cl{sup −}, Br{sup −} and I{sup −}) was studied using steady state and time resolved fluorescence techniques. The quenching process was characterized by Stern–Volmer (S–V) plots. Possibility of conformers (one is not quenched by halide and the other is quenched) is invoked to explain the observed results. - Highlights: • Fluorescence quenching of quinidine in acidified aqueous solution by halides. • Various quenching parameters have been estimated. • Possibility of conformers is invoked to explain the observed results.
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
2013-01-01
arXiv:1210.8106v2 [gr-qc] 11 Feb 2013 Late Time Acceleration of the 3-Space in a Higher Dimensional Steady State Universe in Dilaton Gravity Özgür Akarsua , b, Tekin Derelia a Department of Physics, Koç University, 34450 Sarıyer, İstanbul, Turkey b Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy Abstract We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an ar...
New travelling wave solutions for nonlinear stochastic evolution equations
Indian Academy of Sciences (India)
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Fan, Fan; Luxenburger, Andreas; Painter, Gavin F; Blanchard, John S
2007-10-09
Mycobacterium tuberculosis and many other members of the Actinomycetes family produce mycothiol, i.e., 1-d-myo-inosityl-2-(N-acetyl-l-cysteinyl)amido-2-deoxy-alpha-d-glucopyranoside (MSH or AcCys-GlcN-Ins), to act against oxidative and antibiotic stress. The biosynthesis of MSH is essential for cell growth and has been proposed to proceed via a biosynthetic pathway involving four key enzymes, MshA-MshD. The MSH biosynthetic enzymes present potential targets for inhibitor design. With this as a long-term goal, we have carried out a kinetic and mechanistic characterization, using steady-state and pre-steady-state approaches, of the recombinant Mycobacterium smegmatis MshC. MshC catalyzes the ATP-dependent condensation of GlcN-Ins and cysteine to form Cys-GlcN-Ins. Initial velocity and inhibition studies show that the steady-state kinetic mechanism of MshC is a Bi Uni Uni Bi Ping Pong mechanism, with ATP binding followed by cysteine binding, release of PPi, binding of GlcN-Ins, followed by the release of Cys-GlcN-Ins and AMP. The steady-state kinetic parameters were determined to be kcat equal to 3.15 s-1, and Km values of 1.8, 0.1, and 0.16 mM for ATP, cysteine, and GlcN-Ins, respectively. A stable bisubstrate analogue, 5'-O-[N-(l-cysteinyl)sulfamonyl]adenosine, exhibits competitive inhibition versus ATP and noncompetitive inhibition versus cysteine, with an inhibition constant of approximately 306 nM versus ATP. Single-turnover reactions of the first and second half reactions were determined using rapid-quench techniques, giving rates of approximately 9.4 and approximately 5.2 s-1, respectively, consistent with the cysteinyl adenylate being a kinetically competent intermediate in the reaction by MshC.
Jacobi elliptic function solutions of some nonlinear PDEs
Energy Technology Data Exchange (ETDEWEB)
Liu Jianbin; Yang Lei; Yang Kongqing
2004-05-17
Based on a subtle balance method, a given function expansion is applied to several nonlinear PDEs, which contain generalized KdV equations, coupled equations and complex equations and so on. A series of periodic solutions, solitary wave solutions and singular solutions are obtained by the aid of symbolic computation.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
A Comprehensive Analytical Solution of the Nonlinear Pendulum
Ochs, Karlheinz
2011-01-01
In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…
Existence of solutions for a nonlinear degenerate elliptic system
Directory of Open Access Journals (Sweden)
Nguyen Minh
2004-07-01
Full Text Available In this paper, we study the existence of solutions for degenerate elliptic systems. We use the sub-super solution method, and the existence of classical and weak solutions. Some sub-supersolutions are constructed explicitly, when the nonlinearities have critical or supercritical growth.
Analytic solutions of a class of nonlinearly dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, M-C [System Engineering Institute of Tianjin University, Tianjin, 300072 (China); Zhao, X-S; Liu, X [Tianjin University of Technology and Education, Tianjin, 300222 (China)], E-mail: mchwang123@163.com.cn, E-mail: xszhao@mail.nwpu.edu.cn, E-mail: liuxinhubei@163.com.cn
2008-02-15
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently.
A Comprehensive Analytical Solution of the Nonlinear Pendulum
Ochs, Karlheinz
2011-01-01
In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Almost Periodic Viscosity Solutions of Nonlinear Parabolic Equations
Directory of Open Access Journals (Sweden)
Zhang Shilin
2009-01-01
Full Text Available We generalize the comparison result 2007 on Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron's method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations under usual hypotheses.
Bounds for solutions to retarded nonlinear double integral inequalities
Directory of Open Access Journals (Sweden)
Sabir Hussain
2014-12-01
Full Text Available We present bounds for the solution to three types retarded nonlinear integral inequalities in two variables. By doing this, we generalizing the results presented in [3,12]. To illustrate our results, we present some applications.
Stochasticity in numerical solutions of the nonlinear Schroedinger equation
Shen, Mei-Mei; Nicholson, D. R.
1987-01-01
The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.
The theorem on existence of singular solutions to nonlinear equations
Directory of Open Access Journals (Sweden)
Prusinska А.
2005-01-01
Full Text Available The aim of this paper is to present some applications of pregularity theory to investigations of nonlinear multivalued mappings. The main result addresses to the problem of existence of solutions to nonlinear equations in the degenerate case when the linear part is singular at the considered initial point. We formulate conditions for existence of solutions of equation F(x = 0 when first p - 1 derivatives of F are singular.
Mimicking Nonequilibrium Steady States with Time-Periodic Driving
Raz, O.; Subaşı, Y.; Jarzynski, C.
2016-04-01
Under static conditions, a system satisfying detailed balance generically relaxes to an equilibrium state in which there are no currents. To generate persistent currents, either detailed balance must be broken or the system must be driven in a time-dependent manner. A stationary system that violates detailed balance evolves to a nonequilibrium steady state (NESS) characterized by fixed currents. Conversely, a system that satisfies instantaneous detailed balance but is driven by the time-periodic variation of external parameters—also known as a stochastic pump (SP)—reaches a periodic state with nonvanishing currents. In both cases, these currents are maintained at the cost of entropy production. Are these two paradigmatic scenarios effectively equivalent? For discrete-state systems, we establish a mapping between nonequilibrium stationary states and stochastic pumps. Given a NESS characterized by a particular set of stationary probabilities, currents, and entropy production rates, we show how to construct a SP with exactly the same (time-averaged) values. The mapping works in the opposite direction as well. These results establish a proof of principle: They show that stochastic pumps are able to mimic the behavior of nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics. Nonequilibrium steady states and stochastic pumps are often used to model, respectively, biomolecular motors driven by chemical reactions and artificial molecular machines steered by the variation of external, macroscopic parameters. Our results loosely suggest that anything a biomolecular machine can do, an artificial molecular machine can do equally well. We illustrate this principle by showing that kinetic proofreading, a NESS mechanism that explains the low error rates in biochemical reactions, can be effectively mimicked by a constrained periodic driving.
Relaxation versus adiabatic quantum steady-state preparation
Venuti, Lorenzo Campos; Albash, Tameem; Marvian, Milad; Lidar, Daniel; Zanardi, Paolo
2017-04-01
Adiabatic preparation of the ground states of many-body Hamiltonians in the closed-system limit is at the heart of adiabatic quantum computation, but in reality systems are always open. This motivates a natural comparison between, on the one hand, adiabatic preparation of steady states of Lindbladian generators and, on the other hand, relaxation towards the same steady states subject to the final Lindbladian of the adiabatic process. In this work we thus adopt the perspective that the goal is the most efficient possible preparation of such steady states, rather than ground states. Using known rigorous bounds for the open-system adiabatic theorem and for mixing times, we are then led to a disturbing conclusion that at first appears to doom efforts to build physical quantum annealers: relaxation seems to always converge faster than adiabatic preparation. However, by carefully estimating the adiabatic preparation time for Lindbladians describing thermalization in the low-temperature limit, we show that there is, after all, room for an adiabatic speedup over relaxation. To test the analytically derived bounds for the adiabatic preparation time and the relaxation time, we numerically study three models: a dissipative quasifree fermionic chain, a single qubit coupled to a thermal bath, and the "spike" problem of n qubits coupled to a thermal bath. Via these models we find that the answer to the "which wins" question depends for each model on the temperature and the system-bath coupling strength. In the case of the "spike" problem we find that relaxation during the adiabatic evolution plays an important role in ensuring a speedup over the final-time relaxation procedure. Thus, relaxation-assisted adiabatic preparation can be more efficient than both pure adiabatic evolution and pure relaxation.
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Steady state estimation of soil organic carbon using satellite-derived canopy leaf area index
Fang, Yilin; Liu, Chongxuan; Huang, Maoyi; Li, Hongyi; Leung, L. Ruby
2014-12-01
Estimation of soil organic carbon (SOC) stock using models typically requires long term spin-up of the carbon-nitrogen (CN) models, which has become a bottleneck for global modeling. We report a new numerical approach to estimate global SOC stock that can alleviate long spin-up. The approach uses satellite-based canopy leaf area index (LAI) and takes advantage of a reaction-based biogeochemical module—Next Generation BioGeoChemical Module (NGBGC) that was recently developed and incorporated in version 4 of the Community Land Model (CLM4). Although NGBGC uses the same CN mechanisms as in CLM4CN, it can be easily configured to run prognostic or steady state simulations. The new approach was applied at point and global scales and compared with SOC derived from spin-up by running NGBGC in the prognostic mode, and SOC from the Harmonized World Soil Database (HWSD). The steady state solution is comparable to the spin-up value when the satellite LAI is close to that from the spin-up solution, and largely captured the global variability of the HWSD SOC across the different dominant plant functional types (PFTs). The correlation between the simulated and HWSD SOC was, however, weak at both point and global scales, suggesting the needs for improving the biogeochemical processes described in CLM4 and updating HWSD. Besides SOC, the steady state solution also includes all other state variables simulated by a spin-up run, which makes the tested approach a promising tool to efficiently estimate global SOC distribution and evaluate and compare multiple aspects simulated by different CN mechanisms in the model.
Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media
Bazeia, D; Raposo, and E.P.
1998-01-01
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1+1 dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.
Steady-State Plasmas in KT5D Magnetized Torus
Institute of Scientific and Technical Information of China (English)
ZHU Zhenhua; LIU Wandong; WAN Baonian; ZHAO Yanping; LI Jiangang; YAN Longwen; YANG Qingwei; DING Xuantong; XU Min; YU Yi; WANG Zhijiang; LU Ronghua; WEN Yizhi; YU Changxuan; MA Jinxiu; WAN Shude
2007-01-01
Steady-state plasma generated by electron cyclotron resonance (ECR) wave in the KT5D magnetized torus was studied using a fast high-resolution camera and Langmuir probes. It was found that both the discharge patterns taken by the camera and the plasma parameters measured by the probes were very sensitive to the working gas pressure and the magnetic configuration of the torus both without and with vertical fields. There existed fast vertical motion of the plasma. Tentative discussion is presented about the observed phenomena such as the bright resonance layer at a high gas pressure and the wave absorption mechanism at a low pressure. Further explanations should be found.
Steady State Stokes Flow Interpolation for Fluid Control
DEFF Research Database (Denmark)
Bhatacharya, Haimasree; Nielsen, Michael Bang; Bridson, Robert
2012-01-01
Fluid control methods often require surface velocities interpolated throughout the interior of a shape to use the velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics — velocity extrapolation in the normal direction and potential flow...... — suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures...... the rotational components and is suitable for controlling liquid animations where tangential motion is pronounced, such as in a breaking wave...
Quantum-classical correspondence in steady states of nonadiabatic systems
Energy Technology Data Exchange (ETDEWEB)
Fujii, Mikiya; Yamashita, Koichi [Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656 (Japan); CREST, JST, Tokyo 113-8656 (Japan)
2015-12-31
We first present nonadiabatic path integral which is exact formulation of quantum dynamics in nonadiabatic systems. Then, by applying the stationary phase approximations to the nonadiabatic path integral, a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow degree of freedom, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels.
Full steady-state operation in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Kazarian-Vibert, F.; Litaudon, X.; Moreau, D.; Arslanbekov, R.; Hoang, G.T.; Peysson, Y.
1996-06-01
In order to produce fully non-inductive, Lower Hybrid (LH) driven discharges in a systematic and reproducible manner, new operation modes have been studied on the superconducting TORE SUPRA tokamak. It is shown that this operation mode allows to reach full steady-state within a characteristic time of a few seconds. The underlying physics is described and a detailed analysis of the experiments is made. It is shown, in particular, that this operation scenario generates stable stationary plasmas with improved confinement, so that the so-called `LHEP` regime can be extrapolated to continuous operation. (K.A.). 19 refs.
Full steady state LH scenarios in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Kazarian-Vibert, F.; Litaudon, X.; Arslanbekov, R.; Hoang, G.T.; Moreau, D.; Peysson, Y. [Association Euratom-CEA, Centre d`Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
1995-12-31
Lower Hybrid discharge have been realised in Tore Supra using feed-back control of the primary circuit voltage such that the loop voltage was maintained exactly to zero near the plasma surface. This new scenario allows the plasma current to float and quickly reach an equilibrium value determined by the current drive efficiency and Lower Hybrid power. Recent experimental results show that, with the new constant flux scenario the coupled plasma and primary currents reach a steady state in less than 10 s which is a good agreement with theoretical expectations. A complete analysis of this scenario is presented. (authors). 8 refs., 3 figs.
Steady-state models of glucose-perturbed Dictyostelium discoideum
Energy Technology Data Exchange (ETDEWEB)
Wright, B.E.; Reimers, J.M.
1988-10-15
Young sorocarps of Dictyostelium discoideum were incubated in the presence of 50 mM (/sup 14/C)glucose, and nine metabolites were isolated over a period of 60 min to determine their specific radioactivity. The program TFLUX was used to construct models consisting of 17 metabolite pools and 40 reactions (excluding external pools). Net glucose uptake was 10% or less in the two experiments chosen for extensive analysis, and a single steady-state model was adequate to describe the data in both cases. Despite differences in metabolite levels, flux, and labeling kinetics, the models of glucose-perturbed metabolism confirm earlier conclusions regarding metabolic compartments.
Steady State Vacuum Ultraviolet Exposure Facility With Automated Calibration Capability
Stueber, Thomas J.; Sechkar, Edward A.; Dever, Joyce A.; Banks, Bruce A.
2000-01-01
NASA Glenn Research Center at Lewis Field designed and developed a steady state vacuum ultraviolet automated (SSVUVa) facility with in situ VUV intensity calibration capability. The automated feature enables a constant accelerated VUV radiation exposure over long periods of testing without breaking vacuum. This test facility is designed to simultaneously accommodate four isolated radiation exposure tests within the SSVUVa vacuum chamber. Computer-control of the facility for long, term continuous operation also provides control and recording of thermocouple temperatures, periodic recording of VUV lamp intensity, and monitoring of vacuum facility status. This paper discusses the design and capabilities of the SSVUVa facility.
Steady-state grain growth in UO{sub 2}
Energy Technology Data Exchange (ETDEWEB)
Galinari, C.M.; Lameiras, F.S. [CDTN/CNEN, Belo Horizonte (Brazil)
1998-06-05
The authors have observed steady-state grain growth in sintered UO{sub 2} pellets of nuclear purity at 2,003 K under H{sub 2}. The behavior of the grain size distribution at different instants is consistent with the grain growth model proposed by one of the authors. The total number of grains was estimated using the Saltykov`s method, and the evolution is in accordance with the model proposed by Rhines and Craig. The parabolic growth law was observed for the mean intercept length with n = 0.4.
Typical pure nonequilibrium steady states and irreversibility for quantum transport.
Monnai, Takaaki; Yuasa, Kazuya
2016-07-01
It is known that each single typical pure state in an energy shell of a large isolated quantum system well represents a thermal equilibrium state of the system. We show that such typicality holds also for nonequilibrium steady states (NESS's). We consider a small quantum system coupled to multiple infinite reservoirs. In the long run, the total system reaches a unique NESS. We identify a large Hilbert space from which pure states of the system are to be sampled randomly and show that the typical pure states well describe the NESS. We also point out that the irreversible relaxation to the unique NESS is important to the typicality of the pure NESS's.
Optimising performance in steady state for a supermarket refrigeration system
DEFF Research Database (Denmark)
Green, Torben; Kinnaert, Michel; Razavi-Far, Roozbeh
2012-01-01
Using a supermarket refrigeration system as an illustrative example, the paper postulates that by appropriately utilising knowledge of plant operation, the plant wide performance can be optimised based on a small set of variables. Focusing on steady state operations, the total system performance...... is shown to predominantly be influenced by the suction pressure. Employing appropriate performance function leads to conclusions on the choice of set-point for the suction pressure that are contrary to the existing practice. Analysis of the resulting data leads to a simple method for finding optimal...
Dendritic cell-development in steady-state and inflammation
Schmid, Michael Alexander
2010-01-01
Dendritic cells (DC), the major antigen-presenting cells, continuously need to be regenerated from bone marrow (BM) hematopoietic stem and progenitor cells (HSPC). What intermediate progenitors exist on the way to DC generation and what external factors act on these in steady-state and during inflammation, has not been addressed in detail. Flt3L is a non-redundant cytokine in DC development and the generation of DCs was shown to proceed along both Flt3+ common lymphoid and common myeloid prog...
Multiple nonequilibrium steady states for one-dimensional heat flow.
Zhang, F; Isbister, D J; Evans, D J
2001-08-01
A nonequilibrium molecular dynamics model of heat flow in one-dimensional lattices is shown to have multiple steady states for any fixed heat field strength f(e) ranging from zero to a certain positive value. We demonstrate that, depending on the initial conditions, there are at least two possibilities for the system's evolution: (i) formation of a stable traveling wave (soliton), and (ii) chaotic motion throughout the entire simulation. The percentage of the soliton-generating trajectories is zero for small field strength f(e), but increases sharply to unity over a critical region of the parameter f(e).
Typical pure nonequilibrium steady states and irreversibility for quantum transport
Monnai, Takaaki; Yuasa, Kazuya
2016-07-01
It is known that each single typical pure state in an energy shell of a large isolated quantum system well represents a thermal equilibrium state of the system. We show that such typicality holds also for nonequilibrium steady states (NESS's). We consider a small quantum system coupled to multiple infinite reservoirs. In the long run, the total system reaches a unique NESS. We identify a large Hilbert space from which pure states of the system are to be sampled randomly and show that the typical pure states well describe the NESS. We also point out that the irreversible relaxation to the unique NESS is important to the typicality of the pure NESS's.
A Novel Wireless TCP and its Steady State Throughput Model
Institute of Scientific and Technical Information of China (English)
YAO Ling; JI Hong; YUE Guang-xin
2004-01-01
Unlike wired networks, random packet loss due to bit errors may cause significant performance degradation of Transmission Control Protocol (TCP). We propose and study a novel end-to-end congestion control mechanism called TCP-LD (Loss Detection) that is simple and effective for dealing with random packet loss. We also give its steady state throughput model. Both the ns2 and numerical simulation results show that our scheme can achieve significant throughput improvements without adversely affecting other concurrent TCP connections, including other concurrent Reno connections both in wired and wireless environment.
Non-steady-state aerosol filtration in nanostructured fibrous media.
Przekop, Rafal; Gradoń, Leon
2011-06-28
The filtration of aerosol particles using composites of nano- and microsized fibrous structures is a promising method for the effective separation of nanoparticles from gases. A multi-scale physical system describing the flow pattern and particle deposition at a non-steady-state condition requires an advanced method of modelling. The combination of lattice Boltzmann and Brownian dynamics was used for analysis of the particle deposition pattern in a fibrous system. The dendritic structures of deposits for neutral and charged fibres and particles are present. The efficiency of deposition, deposit morphology, porosity and fractal dimension were calculated for a selected operational condition of the process.
Nonequilibrium steady-state circulation and heat dissipation functional.
Qian, H
2001-08-01
A nonequilibrium steady-state (NESS), different from an equilibrium, is sustained by circular balance rather than detailed balance. The circular fluxes are driven by energy input and heat dissipation, accompanied by a positive entropy production. Based on a Master equation formalism for NESS, we show the circulation is intimately related to the recently studied Gallavotti-Cohen symmetry of heat dissipation functional, which in turn suggests a Boltzmann's formulalike relation between rate constants and energy in NESS. Expanding this unifying view on NESS to diffusion is discussed.
Stabilizing unstable steady states using multiple delay feedback control.
Ahlborn, Alexander; Parlitz, Ulrich
2004-12-31
Feedback control with different and independent delay times is introduced and shown to be an efficient method for stabilizing fixed points (equilibria) of dynamical systems. In comparison to other delay based chaos control methods multiple delay feedback control is superior for controlling steady states and works also for relatively large delay times (sometimes unavoidable in experiments due to system dead times). To demonstrate this approach for stabilizing unstable fixed points we present numerical simulations of Chua's circuit and a successful experimental application for stabilizing a chaotic frequency doubled Nd-doped yttrium aluminum garnet laser.
Bartolo, Nicola; Casteels, Wim; Ciuti, Cristiano
2016-01-01
We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P-representation formalism, we are able to explore any regime, including photon blockade, multi-photon resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multi-modality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.
New Methods for Processing and Quantifying VO2 Kinetics to Steady State: VO2 Onset Kinetics
Directory of Open Access Journals (Sweden)
Craig R. McNulty
2017-09-01
Full Text Available Current methods of oxygen uptake (VO2 kinetics data handling may be too simplistic for the complex physiology involved in the underlying physiological processes. Therefore, the aim of this study was to quantify the VO2 kinetics to steady state across the full range of sub-ventilatory threshold work rates, with a particular focus on the VO2 onset kinetics. Ten healthy, moderately trained males participated in five bouts of cycling. Each bout involved 10 min at a percentage of the subject's ventilation threshold (30, 45, 60, 75, 90% from unloaded cycling. The VO2 kinetics was quantified using the conventional mono-exponential time constant (tau, τ, as well as the new methods for VO2 onset kinetics. Compared to linear modeling, non-linear modeling caused a deterioration of goodness of fit (main effect, p < 0.001 across all exercise intensities. Remainder kinetics were also improved using a modified application of the mono-exponential model (main effect, p < 0.001. Interestingly, the slope from the linear regression of the onset kinetics data is similar across all subjects and absolute exercise intensities, and thereby independent of subject fitness and τ. This could indicate that there are no functional limitations between subjects during this onset phase, with limitations occurring for the latter transition to steady state. Finally, the continuing use of mono-exponential modeling could mask important underlying physiology of more instantaneous VO2 responses to steady state. Consequently, further research should be conducted on this new approach to VO2 onset kinetics.
Magnetic brane solutions of Lovelock gravity with nonlinear electrodynamics
Hendi, Seyed Hossein; Panahiyan, Shahram
2015-01-01
In this paper, we consider logarithmic and exponential forms of nonlinear electrodynamics as a source and obtain magnetic brane solutions of the Lovelock gravity. Although these solutions have no curvature singularity and no horizon, they have a conic singularity with a deficit angle. We investigate the effects of nonlinear electrodynamics and the Lovelock gravity on the value of deficit angle and find that various terms of Lovelock gravity do not affect deficit angle. Next, we generalize our solutions to spinning cases with maximum rotating parameters in arbitrary dimensions and calculate the conserved quantities of the solutions. Finally, we consider nonlinear electrodynamics as a correction of the Maxwell theory and investigate the properties of the solutions.
Solutions to a nonlinear drift-diffusion model for semiconductors
Directory of Open Access Journals (Sweden)
Weifu Fang
1999-05-01
Full Text Available A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
Generalized Nonlinear Proca Equation and its Free-Particle Solutions
Nobre, F D
2016-01-01
We introduce a non-linear extension of Proca's field theory for massive vector (spin $1$) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter $q$ (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit $q \\rightarrow 1$. We derive the nonlinear Proca equation from a Lagrangian that, besides the usual vectorial field $\\Psi^{\\mu}(\\vec{x},t)$, involves an additional field $\\Phi^{\\mu}(\\vec{x},t)$. We obtain exact time dependent soliton-like solutions for these fields having the...
Steady-state thermal Herschel-Bulkley flow with Tresca's friction law
Directory of Open Access Journals (Sweden)
Farid Messelmi
2010-04-01
Full Text Available We consider a mathematical model which describes the steady-state flow of a Herschel-Bulkley fluid whose the consistency and the yield limit depend on the temperature and with mixed boundary conditions, including a frictional boundary condition. We derive a weak formulation of the coupled system of motion and energy equations which consists of a variational inequality for the velocity field. We prove the existence of weak solutions. In the asymptotic limit case of a high thermal conductivity, the temperature becomes a constant solving an implicit total energy equation involving the consistency function and the yield limit.
Bourne, H. C., Jr.; Bartran, D. S.
1974-01-01
Approximate analytic solutions for transient and steady-state 180 deg domain-wall motion in bulk magnetic material are obtained from the dynamic torque equations with a Gilbert damping term. The results for the Walker region in which the transient solution approaches the familiar Walker steady-state solution are presented in a slightly new form for completeness. An analytic solution corresponding to larger drive fields predicts an oscillatory motion with an average value of the velocity which decreases with drive field for reasonable values of the damping parameter. These results agree with those obtained by others from a computer solution of the torque equation and those obtained by others with the assumption of a very large anisotropy field.
Indian Academy of Sciences (India)
R S Kaushal; Ranjit Kumar; Awadhesh Prasad
2006-08-01
Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.
Directory of Open Access Journals (Sweden)
Jinmyoung Seok
2015-07-01
Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.
Steady-state flow properties of amorphous materials
Jadhao, Vikram; O'Connor, Thomas; Robbins, Mark
2015-03-01
Molecular dynamics (MD) simulations are used to investigate the steady-state shear flow curves of a standard glass model: the bidisperse Lennard-Jones system. For a wide range of temperatures in the neighborhood of the glass transition temperature Tg predicted by the mode coupling theory, we compute the steady-state shear stress and viscosity as a function of the shear rate γ ˙. At temperatures near and above Tg, the stress crosses over from linear Newtonian behavior at low rates to power law shear-thinning at high rates. As T decreases below Tg, the stress shows a plateau, becoming nearly rate-independent at low γ ˙. There is a weak increase in stress that is consistent with Eyring theory for activated flow of a solid. We find that when the strain rate is reduced to extremely low values, Newtonian behavior appears once more. Insights gained from these simulations are applied to the computation of flow curves of a well-established boundary lubricant: squalane. In the elastohydrodynamic regime, squalane responds like a glassy solid with an Eyring-like response, but at low rates it has a relatively small Newtonian viscosity. Supported by the Army Research Laboratory under Grant W911NF-12-2-0022.
Transient and steady-state selection in the striatal microcircuit.
Tomkins, Adam; Vasilaki, Eleni; Beste, Christian; Gurney, Kevin; Humphries, Mark D
2013-01-01
Although the basal ganglia have been widely studied and implicated in signal processing and action selection, little information is known about the active role the striatal microcircuit plays in action selection in the basal ganglia-thalamo-cortical loops. To address this knowledge gap we use a large scale three dimensional spiking model of the striatum, combined with a rate coded model of the basal ganglia-thalamo-cortical loop, to asses the computational role the striatum plays in action selection. We identify a robust transient phenomena generated by the striatal microcircuit, which temporarily enhances the difference between two competing cortical inputs. We show that this transient is sufficient to modulate decision making in the basal ganglia-thalamo-cortical circuit. We also find that the transient selection originates from a novel adaptation effect in single striatal projection neurons, which is amenable to experimental testing. Finally, we compared transient selection with models implementing classical steady-state selection. We challenged both forms of model to account for recent reports of paradoxically enhanced response selection in Huntington's disease patients. We found that steady-state selection was uniformly impaired under all simulated Huntington's conditions, but transient selection was enhanced given a sufficient Huntington's-like increase in NMDA receptor sensitivity. Thus our models provide an intriguing hypothesis for the mechanisms underlying the paradoxical cognitive improvements in manifest Huntington's patients.
Transient and steady-state selection in the striatal microcircuit
Directory of Open Access Journals (Sweden)
Adam eTomkins
2014-01-01
Full Text Available Although the basal ganglia have been widely studied and implicated in signal processing and action selection, little information is known about the active role the striatal microcircuit plays in action selection in the basal ganglia-thalamo-cortical loops. To address this knowledge gap we use a large scale three dimensional spiking model of the striatum, combined with a rate coded model of the basal ganglia-thalamo-cortical loop, to asses the computational role the striatum plays in action selection. We identify a robust transient phenomena generated by the striatal microcircuit, which temporarily enhances the difference between two competing cortical inputs. We show that this transient is sufficient to modulate decision making in the basal ganglia-thalamo-cortical circuit. We also find that the transient selection originates from a novel adaptation effect in single striatal projection neurons, which is amenable to experimental testing. Finally, we compared transient selection with models implementing classical steady-state selection. We challenged both forms of model to account for recent reports of paradoxically enhanced response selection in Huntington's Disease patients. We found that steady-state selection was uniformly impaired under all simulated Huntington's conditions, but transient selection was enhanced given a sufficient Huntington's-like increase in NMDA receptor sensitivity. Thus our models provide an intriguing hypothesis for the mechanisms underlying the paradoxical cognitive improvements in manifest Huntington's patients.
Classical Orbital Paramagnetism in Non-equilibrium Steady State
Indian Academy of Sciences (India)
Avinash A. Deshpande; N. Kumar
2017-09-01
We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-Markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be paramagnetic for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo–Anderson type non-Markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-Markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr–van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.
Steady States and Universal Conductance in a Quenched Luttinger Model
Langmann, Edwin; Lebowitz, Joel L.; Mastropietro, Vieri; Moosavi, Per
2016-05-01
We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian {H_{λ}} with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian {H_{λ'}} which differs from {H_{λ}} by the strength of the interaction. Asymptotically in time, as {t to &infty}; , after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference {μ+ - μ-} between right- (+) and left- (-) moving fermions obtained from the two-point correlation function. Both I and {μ+ - μ-} depend on {λ} and {λ'} . Only for the case {λ = λ' = 0} does {μ+ - μ-} equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, {G = I/(μ+ - μ-)} , has a universal value equal to the conductance quantum {e^2/h} for the spinless case.
Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism.
Fleming, R M T; Thiele, I; Provan, G; Nasheuer, H P
2010-06-07
The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.
Steady-State ALPS for Real-Valued Problems
Hornby, Gregory S.
2009-01-01
The two objectives of this paper are to describe a steady-state version of the Age-Layered Population Structure (ALPS) Evolutionary Algorithm (EA) and to compare it against other GAs on real-valued problems. Motivation for this work comes from our previous success in demonstrating that a generational version of ALPS greatly improves search performance on a Genetic Programming problem. In making steady-state ALPS some modifications were made to the method for calculating age and the method for moving individuals up layers. To demonstrate that ALPS works well on real-valued problems we compare it against CMA-ES and Differential Evolution (DE) on five challenging, real-valued functions and on one real-world problem. While CMA-ES and DE outperform ALPS on the two unimodal test functions, ALPS is much better on the three multimodal test problems and on the real-world problem. Further examination shows that, unlike the other GAs, ALPS maintains a genotypically diverse population throughout the entire search process. These findings strongly suggest that the ALPS paradigm is better able to avoid premature convergence then the other GAs.
Classical Orbital Paramagnetism in Non-equilibrium Steady State
Deshpande, Avinash A.; Kumar, N.
2017-09-01
We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-Markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be paramagnetic for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo-Anderson type non-Markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-Markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr-van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.
Steady States and Universal Conductance in a Quenched Luttinger Model
Langmann, Edwin; Lebowitz, Joel L.; Mastropietro, Vieri; Moosavi, Per
2017-01-01
We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian {H_{λ}} with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian {H_{λ'}} which differs from {H_{λ}} by the strength of the interaction. Asymptotically in time, as {t to ∞}, after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference {μ+ - μ-} between right- (+) and left- (-) moving fermions obtained from the two-point correlation function. Both I and {μ+ - μ-} depend on {λ} and {λ'}. Only for the case {λ = λ' = 0} does {μ+ - μ-} equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, {G = I/(μ+ - μ-)}, has a universal value equal to the conductance quantum {e^2/h} for the spinless case.
Nonequilibrium many-body steady states via Keldysh formalism
Maghrebi, Mohammad F.; Gorshkov, Alexey V.
2016-01-01
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
Indian Academy of Sciences (India)
Nilanjan Coomar; Ravikiran Kadoli
2010-02-01
Internal cooling passages and thermal barrier coatings (TBCs) are presently used to control metal temperatures in gas turbine blades. Functionally graded materials (FGMs), which are typically mixtures of ceramic and metal, have been proposed for use in turbine blades because they possess smooth property gradients thereby rendering them more durable under thermal loads. In the present work, a functionally graded model of an air-cooled turbine blade with airfoil geometry conforming to the NACA0012 is developed which is then used in a ﬁnite element algorithm to obtain a non-linear steady state solution to the heat equation for the blade under convection and radiation boundary conditions. The effects of external gas temperature, coolant temperature, surface emissivity changes and different average ceramic/metal content of the blade on the temperature distributions are examined. Simulations are also carried out to compare cooling effectiveness of functionally graded blades with that of blades having TBC. The results highlight the effect of including radiation in the simulation and also indicate that external gas temperature inﬂuences the blade heat transfer more strongly. It is also seen that graded blades with about 70% ceramic content can deliver better cooling effectiveness than conventional blades with TBC.
Koroglu, Batikan; Armstrong, Mike; Cappelli, Mark; Chernov, Alex; Crowhurst, Jonathan; Mehl, Marco; Radousky, Harry; Rose, Timothy; Zaug, Joe
2016-10-01
The high temperature chemistry of rapidly condensing matter is under investigation using a steady state inductively coupled plasma (ICP) flow reactor. The objective is to study chemical processes on cooling time scales similar to that of a low yield nuclear fireball. The reactor has a nested set of gas flow rings that provide flexibility in the control of hydrodynamic conditions and mixing of chemical components. Initial tests were run using two different aqueous solutions (ferric nitrate and uranyl nitrate). Chemical reactants passing through the plasma torch undergo non-linear cooling from 10,000K to 1,000K on time scales of <0.1 to 0.5s depending on flow conditions. Optical spectroscopy measurements were taken at different positions along the flow axis to observe the in situ spatial and temporal evolution of chemical species at different temperatures. The current data offer insights into the changes in oxide chemistry as a function of oxygen fugacity. The time resolved measurements will also serve as a validation target for the development of kinetic models that will be used to describe chemical fractionation during nuclear fireball condensation. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force
Energy Technology Data Exchange (ETDEWEB)
Vega Reyes, Francisco, E-mail: fvega@unex.es; Santos, Andrés, E-mail: andres@unex.es [Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz (Spain)
2015-11-15
We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to the particle translational velocities. We work out an analytical solution of the corresponding velocity distribution function from a Sonine polynomial expansion that displays energy non-equipartition between the translational and rotational modes, translational and rotational kurtoses, and translational-rotational velocity correlations. By comparison with a numerical solution of the Boltzmann kinetic equation (by means of the direct simulation Monte Carlo method), we show that our analytical solution provides a good description that is quantitatively very accurate in certain ranges of inelasticity and roughness. We also find three important features that make the forced granular gas steady state very different from the homogeneous cooling state (attained by an unforced granular gas). First, the marginal velocity distributions are always close to a Maxwellian. Second, there is a continuous transition to the purely smooth limit (where the effects of particle rotations are ignored). And third, the angular translational-rotational velocity correlations show a preference for a quasiperpendicular mutual orientation (which is called “lifted-tennis-ball” behavior)
2005-12-01
choice of a steady state control is completely independent from the choice of a stabilizing control law. This separation is key for the methods we will...develop for steady state optimization in later sections. Combining the steady state with the stabilizing control , we can express the control law as u...for stabilizing control and optimization methods for steady state control, both unconstrained and constrained, we were able to produce promising results
REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS
Institute of Scientific and Technical Information of China (English)
YeCaier; PanZuliang
2003-01-01
Nonlinear partial differetial equation(NLPDE)is converted into ordinary differential equation(ODE)via a new ansatz.Using undetermined function method,the ODE obtained above is replaced by a set of algebraic equations which are solved out with the aid of Mathematica.The exact solutions and solitary solutions of NLPDE are obtained.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
Viscosity solutions of fully nonlinear functional parabolic PDE
Directory of Open Access Journals (Sweden)
Liu Wei-an
2005-01-01
Full Text Available By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.
Stable Solution of Nonlinear Age-structuredForest Evolution System
Institute of Scientific and Technical Information of China (English)
WANGDing-jiang; ZHAOTing-fang
2004-01-01
This paper studies the dynamical behavior of a class of total area dependent nonlinear age-structured forest evolution model. We give the problem of equal value for the forest system, and discuss the stable solution of system. We obtained the necessary and sufficient conditions for there exists the stable solution.
Singular solutions of fully nonlinear elliptic equations and applications
Armstrong, Scott N; Smart, Charles K
2011-01-01
We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\\'en-Lindel\\"of result as well as a principle of positive singularities in certain Lipschitz domains.
A procedure to construct exact solutions of nonlinear evolution equations
Indian Academy of Sciences (India)
Adem Cengiz Çevikel; Ahmet Bekir; Mutlu Akar; Sait San
2012-09-01
In this paper, we implemented the functional variable method for the exact solutions of the Zakharov-Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin-Bona-Mohany (mBBM) and the modified kdV-Kadomtsev-Petviashvili (kdV-KP) equation. By using this scheme, we found some exact solutions of the above-mentioned equation. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider-applicability for handling nonlinear wave equations.
Steady-state ab initio laser theory for complex gain media
Cerjan, Alexander; Stone, A Douglas
2014-01-01
We derive and test a generalization of Steady-State Ab Initio Laser Theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient Finite Difference Time Domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over betw...
Steady-state ab initio laser theory for complex gain media.
Cerjan, Alexander; Chong, Y D; Stone, A Douglas
2015-03-09
We derive and test a generalization of the steady-state ab initio laser theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient finite difference time domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes.
Steady-State Flows in Two-Fluid Models of NSTX and DIII-D Plasmas
Ferraro, N. M.; Jardin, S. C.; Chen, J.
2009-05-01
Accurate axisymmetric steady-states of a comprehensive two-fluid model are calculated for plasmas in diverted NSTX and DIII-D geometries using the M3D-C^1 code [1]. It is found that gyroviscosity may have a significant effect on the flows in steady-state when a localized density source is present. The model implemented in M3D-C^1 self-consistently includes the effects of flows, anisotropic viscosity, anisotropic thermal conductivity, and resistivity. Results for ohmically driven plasmas are presented. New capabilities of M3D-C^1 allow the three-dimensional linear stability of axisymmetric equilibria to be calculated; these capabilities and preliminary stability results are discussed. Also discussed are recent and future extensions to M3D-C^1, including heuristic bootstrap current models, coupling to a physics-based transport model, and nonlinear non-axisymmetric capability. 3pt[1] S. C. Jardin, J. Breslau, N. Ferraro, J. Comput. Phys, 226 (2007) 2146
Lower bounds for ballistic current and noise in non-equilibrium quantum steady states
Directory of Open Access Journals (Sweden)
Benjamin Doyon
2015-03-01
Full Text Available Let an infinite, homogeneous, many-body quantum system be unitarily evolved for a long time from a state where two halves are independently thermalized. One says that a non-equilibrium steady state emerges if there are nonzero steady currents in the central region. In particular, their presence is a signature of ballistic transport. We analyze the consequences of the current observable being a conserved density; near equilibrium this is known to give rise to linear wave propagation and a nonzero Drude peak. Using the Lieb–Robinson bound, we derive, under a certain regularity condition, a lower bound for the non-equilibrium steady-state current determined by equilibrium averages. This shows and quantifies the presence of ballistic transport far from equilibrium. The inequality suggests the definition of “nonlinear sound velocities”, which specialize to the sound velocity near equilibrium in non-integrable models, and “generalized sound velocities”, which encode generalized Gibbs thermalization in integrable models. These are bounded by the Lieb–Robinson velocity. The inequality also gives rise to a bound on the energy current noise in the case of pure energy transport. We show that the inequality is satisfied in many models where exact results are available, and that it is saturated at one-dimensional criticality.
Traveling wave solutions for some factorized nonlinear PDEs
Cornejo-Pérez, Octavio
2009-01-01
In this work, some new special traveling wave solutions of the convective Fisher equation, the time-delayed Burgers-Fisher equation, the Burgers-Fisher equation and a nonlinear dispersive-dissipative equation (Kakutani and Kawahara 1970 J. Phys. Soc. Japan 29 1068) are obtained through the factorization technique. All of them share the same type of factorization scheme, which reduces the original equation to a Riccati equation of the same kind, whose general solution is given in terms of Bessel and Neumann functions. In addition, some novel particular solutions of the nonlinear dispersive-dissipative equation are provided.
Wormhole Solutions in the Presence of Nonlinear Maxwell Field
Directory of Open Access Journals (Sweden)
S. H. Hendi
2014-01-01
Full Text Available In generalizing the Maxwell field to nonlinear electrodynamics, we look for the magnetic solutions. We consider a suitable real metric with a lower bound on the radial coordinate and investigate the properties of the solutions. We find that in order to have a finite electromagnetic field near the lower bound, we should replace the Born-Infeld theory with another nonlinear electrodynamics theory. Also, we use the cut-and-paste method to construct wormhole structure. We generalize the static solutions to rotating spacetime and obtain conserved quantities.
Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables
Directory of Open Access Journals (Sweden)
Yaobing Zhao
2014-01-01
Full Text Available This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Indian Academy of Sciences (India)
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
Power Series Solution for Solving Nonlinear Burgers-Type Equations
Directory of Open Access Journals (Sweden)
E. López-Sandoval
2015-01-01
Full Text Available Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.
Bifurcation of solutions of nonlinear Sturm–Liouville problems
Directory of Open Access Journals (Sweden)
Gulgowski Jacek
2001-01-01
Full Text Available A global bifurcation theorem for the following nonlinear Sturm–Liouville problem is given Moreover we give various versions of existence theorems for boundary value problems The main idea of these proofs is studying properties of an unbounded connected subset of the set of all nontrivial solutions of the nonlinear spectral problem , associated with the boundary value problem , in such a way that .
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Power Series Solution for Solving Nonlinear Burgers-Type Equations
López-Sandoval, E.; Mello, A.; Godina-Nava, J. J.; Samana, A. R.
2015-01-01
Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.
National Research Council Canada - National Science Library
M A Hye; M M Rahman; L Nowsher Ali; S Afrin
2013-01-01
... steady solutions with two- and four-vortex solutions are obtained by the Newton-Raphson iteration method. Then, in order to investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the solutions are obtained, and it is found that the steady-state flow turns into periodic flow through ...
Microchemostat array with small-volume fraction replenishment for steady-state microbial culture.
Park, Jaewon; Wu, Jianzhang; Polymenis, Michael; Han, Arum
2013-11-07
A chemostat is a bioreactor in which microorganisms can be cultured at steady-state by controlling the rate of culture medium inflow and waste outflow, thus maintaining media composition over time. Even though many microbial studies could greatly benefit from studying microbes in steady-state conditions, high instrument cost, complexity, and large reagent consumption hamper the routine use of chemostats. Microfluidic-based chemostats (i.e. microchemostats) can operate with significantly smaller reagent consumption while providing accurate chemostatic conditions at orders of magnitude lower cost compared to conventional chemostats. Also, microchemostats have the potential to significantly increase the throughput by integrating arrays of microchemostats. We present a microchemostat array with a unique two-depth culture chamber design that enables small-volume fraction replenishment of culture medium as low as 1% per replenishment cycle in a 250 nl volume. A system having an array of 8 microchemostats on a 40 × 60 mm(2) footprint could be automatically operated in parallel by a single controller unit as a demonstration for potential high throughput microbial studies. The model organism, Saccharomyces cerevisiae, successfully reached a stable steady-state of different cell densities as a demonstration of the chemostatic functionality by programming the dilution rates. Chemostatic functionality of the system was further confirmed by quantifying the budding index as a function of dilution rate, a strong indicator of growth-dependent cell division. In addition, the small-volume fraction replenishment feature minimized the cell density fluctuation during the culture. The developed system provides a robust, low-cost, and higher throughput solution to furthering studies in microbial physiology.
Steady-State Diffusion of Water through Soft-Contact LensMaterials
Energy Technology Data Exchange (ETDEWEB)
Fornasiero, Francesco; Krull, Florian; Radke, Clayton J.; Prausnitz, JohnM.
2005-01-31
Water transport through soft contact lenses (SCL) is important for acceptable performance on the human eye. Chemical-potential gradient-driven diffusion rates of water through soft-contact-lens materials are measured with an evaporation-cell technique. Water is evaporated from the bottom surface of a lens membrane by impinging air at controlled flow rate and humidity. The resulting weight loss of a water reservoir covering the top surface of the contact-lens material is recorded as a function of time. New results are reported for a conventional hydrogel material (SofLens{trademark} One Day, hilafilcon A, water content at saturation W{sub 10} = 70 weight %) and a silicone hydrogel material (PureVision{trademark}, balafilcon A, W{sub 10} = 36 %), with and without surface oxygen plasma treatment. Also, previously reported data for a conventional HEMA-SCL (W{sub 10} = 38 %) hydrogel are reexamined and compared with those for SofLens{trademark} One Day and PureVision{trademark} hydrogels. Measured steady-state water fluxes are largest for SofLens{trademark} One Day, followed by PureVision{trademark} and HEMA. In some cases, the measured steady-state water fluxes increase with rising relative air humidity. This increase, due to an apparent mass-transfer resistance at the surface (trapping skinning), is associated with formation of a glassy skin at the air/membrane interface when the relative humidity is below 55-75%. Steady-state water-fluxes are interpreted through an extended Maxwell-Stefan diffusion model for a mixture of species starkly different in size. Thermodynamic nonideality is considered through Flory-Rehner polymer-solution theory. Shrinking/swelling is self-consistently modeled by conservation of the total polymer mass. Fitted Maxwell-Stefan diffusivities increase significantly with water concentration in the contact lens.
Steady States in SIRS Epidemical Model of Mobile Individuals
Zhang, Duan-Ming; He, Min-Hua; Yu, Xiao-Ling; Pan, Gui-Jun; Sun, Hong-Zhang; Su, Xiang-Ying; Sun, Fan; Yin, Yan-Ping; Li, Rui; Liu, Dan
2006-01-01
We consider an epidemical model within socially interacting mobile individuals to study the behaviors of steady states of epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds δc and pc below which infectious disease dies out. For the population density δ far above δc, it is found that there is linear relationship between contact rate λ and the population density δ in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.
Steady-State Density Functional Theory for Finite Bias Conductances.
Stefanucci, G; Kurth, S
2015-12-09
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.
NASA Lewis Steady-State Heat Pipe Code Architecture
Mi, Ye; Tower, Leonard K.
2013-01-01
NASA Glenn Research Center (GRC) has developed the LERCHP code. The PC-based LERCHP code can be used to predict the steady-state performance of heat pipes, including the determination of operating temperature and operating limits which might be encountered under specified conditions. The code contains a vapor flow algorithm which incorporates vapor compressibility and axially varying heat input. For the liquid flow in the wick, Darcy s formula is employed. Thermal boundary conditions and geometric structures can be defined through an interactive input interface. A variety of fluid and material options as well as user defined options can be chosen for the working fluid, wick, and pipe materials. This report documents the current effort at GRC to update the LERCHP code for operating in a Microsoft Windows (Microsoft Corporation) environment. A detailed analysis of the model is presented. The programming architecture for the numerical calculations is explained and flowcharts of the key subroutines are given
Steady State Rheological Characteristic of Semisolid Magnesium Alloy
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Isothermal compressive experiments at different temperatures, strain rates and holding time for semisolid AZ91D, Zr modified AZ91D and MB15 alloy with higher solid volume fraction were carried out by using Gleeble-15000 simulator and the true stress-strain curves were given directly. The relationship of apparent viscosity vs temperature, shear rate and holding time of the three kinds of semi-solid magnesium alloys, as well as isothermal steady state rheological characteristic and mechanical behavior were studied. The results show that the three magnesium alloys had the characteristic of shear-thinning. The rheological characteristic of the semi-solid MB15 is different from that of semi-solid AZ91D. The semi-solid MB15 has higher apparent viscosity and deformation resistance.
Factorised steady states and condensation transitions in nonequilibrium systems
Indian Academy of Sciences (India)
M R Evans
2005-06-01
Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium – for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the `zero-range process' and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several `condensation' transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.
Manifest and Subtle Cyclic Behavior in Nonequilibrium Steady States
Zia, R K P; Mandal, Dibyendu; Fox-Kemper, Baylor
2016-01-01
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the system settles in a stationary state, it will be a nonequilibrium steady state (NESS), with time independent probability distribution as well as persistent probability current loops. The observable consequences of the latter are explored. In particular, cyclic behavior of some form must be present: some are prominent and manifest, while others are more obscure and subtle. We present a theoretical framework to analyze such properties, introducing the notion of "probability angular momentum" and its distribution. Using several examples, we illustrate the manifest and subtle categories and how best to distinguish between them. These techniques can be applied to reveal the NESS nature of a wide range of systems in a large variety of areas. We illustrate with one application: var...
Dust remobilization in fusion plasmas under steady state conditions
Tolias, P.; Ratynskaia, S.; De Angeli, M.; De Temmerman, G.; Ripamonti, D.; Riva, G.; Bykov, I.; Shalpegin, A.; Vignitchouk, L.; Brochard, F.; Bystrov, K.; Bardin, S.; Litnovsky, A.
2016-02-01
The first combined experimental and theoretical studies of dust remobilization by plasma forces are reported. The main theoretical aspects of remobilization in fusion devices under steady state conditions are analyzed. In particular, the dominant role of adhesive forces is highlighted and generic remobilization conditions—direct lift-up, sliding, rolling—are formulated. A novel experimental technique is proposed, based on controlled adhesion of dust grains on tungsten samples combined with detailed mapping of the dust deposition profile prior and post plasma exposure. Proof-of-principle experiments in the TEXTOR tokamak and the EXTRAP-T2R reversed-field pinch are presented. The versatile environment of the linear device Pilot-PSI allowed for experiments with different magnetic field topologies and varying plasma conditions that were complemented with camera observations.
Entanglement structure of non-equilibrium steady states
Mahajan, Raghu; Mumford, Sam; Tubman, Norm; Swingle, Brian
2016-01-01
We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach is based on the structure of entanglement in the NESS. With reasonable physical assumptions, we show that a NESS close to local equilibrium is lightly entangled and can be represented via a computationally efficient tensor network. We further argue that the NESS may be found by dynamically evolving the system within a manifold of appropriate low entanglement states. A physically realistic law of dynamical evolution is Markovian open system dynamics, or the Lindblad equation. We explore this approach in a well-studied free fermion model where comparisons with the literature are possible. We study both electrical and thermal currents with and without disorder, and compute entropic quantities such as mutual information and conditional mutual information. We conclude with a di...
Stationary Distribution and Thermodynamic Relation in Nonequilibrium Steady States
Komatsu, Teruhisa S.
2010-01-01
We describe our recent attempts toward statistical mechanics and thermodynamics for nonequilibrium steady states (NESS) realized, e.g., in a heat conducting system. Our first result is a simple expression of the probability distribution (of microscopic states) of a NESS. Our second result is a natural extension of the thermodynamic Clausius relation and a definition of an accompanying entropy in NESS. This entropy coincides with the normalization constant appearing in the above mentioned microscopic expression of NESS, and has an expression similar to the Shannon entropy (with a further symmetrization). The NESS entropy proposed here is a clearly defined measurable quantity even in a system with a large degrees of freedom. We numerically measure the NESS entropy in hardsphere fluid systems with a heat current, by observing energy exchange between the system and the heat baths when the temperatures of the baths are changed according to specified protocols.
Steady-State Chemotactic Response in E. coli
Kafri, Yariv
2007-01-01
The bacterium E. coli maneuvers itself to regions with high chemoattractant concentrations by performing two stereotypical moves: `runs', in which it moves in near straight lines, and `tumbles', in which it does not advance but changes direction randomly. The duration of each move is stochastic and depends upon the chemoattractant concentration experienced in the recent past. We relate this stochastic behavior to the steady-state density of a bacterium population, and we derive the latter as a function of chemoattractant concentration. In contrast to earlier treatments, here we account for the effects of temporal correlations and variable tumbling durations. A range of behaviors obtains, that depends subtly upon several aspects of the system - memory, correlation, and tumbling stochasticity in particular.
Fast Prediction Method for Steady-State Heat Convection
Wáng, Yì
2012-03-14
A reduced model by proper orthogonal decomposition (POD) and Galerkin projection methods for steady-state heat convection is established on a nonuniform grid. It was verified by thousands of examples that the results are in good agreement with the results obtained from the finite volume method. This model can also predict the cases where model parameters far exceed the sample scope. Moreover, the calculation time needed by the model is much shorter than that needed for the finite volume method. Thus, the nonuniform POD-Galerkin projection method exhibits high accuracy, good suitability, and fast computation. It has universal significance for accurate and fast prediction. Also, the methodology can be applied to more complex modeling in chemical engineering and technology, such as reaction and turbulence. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Full steady state LH scenarios in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Kazarian-Vilbert, F.; Litaudon, X.; Arslanbekov, R.; Hoang, G.T.; Moreau, D.; Peysson, Y. [Association EURATOM-CEA sur la fusion, Departement de Recherches sur la Fusion Controlee, Centre d`detudes de Cadarache, F-13108 Saint-Paul-Lez-Durance (France)
1996-02-01
Lower hybrid discharges have been realised in Tore Supra using feed-back control of the primary circuit voltage (V{sub oh}) such that the loop voltage was maintained exactly zero near the plasma surface. This new scenario allows the plasma current to float and quickly reach an equilibrium value determined by the current drive efficiency and Lower Hybrid power. Recent experimental results show that, with the new {open_quote}{open_quote}constant flux{close_quote}{close_quote} scenario the coupled plasma and primary currents reach a steady state in less than 10 s which is in good agreement with theoretical expectations. A complete analysis of this scenario is presented. {copyright} {ital 1996 American Institute of Physics.}
An Adsorption Equilibria Model for Steady State Analysis
Ismail, Azhar Bin
2016-02-29
The investigation of adsorption isotherms is a prime factor in the ongoing development of adsorption cycles for a spectrum of advanced, thermally-driven engineering applications, including refrigeration, natural gas storage, and desalination processes. In this work, a novel semi-empirical mathematical model has been derived that significantly enhances the prediction of the steady state uptake in adsorbent surfaces. This model, a combination of classical Langmuir and a novel modern adsorption isotherm equation, allows for a higher degree of regression of both energetically homogenous and heterogeneous adsorbent surfaces compared to several isolated classical and modern isotherm models, and has the ability to regress isotherms for all six types under the IUPAC classification. Using a unified thermodynamic framework, a single asymmetrical energy distribution function (EDF) has also been proposed that directly relates the mathematical model to the adsorption isotherm types. This fits well with the statistical rate theory approach and offers mechanistic insights into adsorption isotherms.
Analysis of steady-state ductile crack growth
DEFF Research Database (Denmark)
Niordson, Christian
1999-01-01
the finite element mesh remains fixed relative to the tip of the growing crack. Fracture is modelled using two different local crack growth criteria. One is a crack opening displacement criterion, while the other is a model in which a cohesive zone is imposed in front of the crack tip along the fracture zone......The fracture strength under quasi-static steady-state crack growth in an elastic-plastic material joined by a laser weld is analyzed. Laser welding gives high mismatch between the yield stress within the weld and the yield stress in the base material. This is due to the fast termic cycle, which....... Both models predict that in general a thinner laser weld gives higher interface strength. Furthermore, both fracture criteria show, that the preferred path of the crack is close outside the weld material; a phenomenon also observed in experiments....
Modelling of pulsed and steady-state DEMO scenarios
Giruzzi, G.; Artaud, J. F.; Baruzzo, M.; Bolzonella, T.; Fable, E.; Garzotti, L.; Ivanova-Stanik, I.; Kemp, R.; King, D. B.; Schneider, M.; Stankiewicz, R.; Stępniewski, W.; Vincenzi, P.; Ward, D.; Zagórski, R.
2015-07-01
Scenario modelling for the demonstration fusion reactor (DEMO) has been carried out using a variety of simulation codes. Two DEMO concepts have been analysed: a pulsed tokamak, characterized by rather conventional physics and technology assumptions (DEMO1) and a steady-state tokamak, with moderately advanced physics and technology assumptions (DEMO2). Sensitivity to impurity concentrations, radiation, and heat transport models has been investigated. For DEMO2, the impact of current driven non-inductively by neutral beams has been studied by full Monte Carlo simulations of the fast ion distribution. The results obtained are a part of a more extensive research and development (R&D) effort carried out in the EU in order to develop a viable option for a DEMO reactor, to be adopted after ITER for fusion energy research.
Thermodynamics and phase coexistence in nonequilibrium steady states
Dickman, Ronald
2016-09-01
I review recent work focussing on whether thermodynamics can be extended to nonequilibrium steady states (NESS), in particular, the possibility of consistent definitions of temperature T and chemical potential μ for NESS. The testing-grounds are simple lattice models with stochastic dynamics. Each model includes a drive that maintains the system far from equilibrium, provoking particle and/or energy flows; for zero drive the system relaxes to equilibrium. Analysis and numerical simulation show that for spatially uniform NESS, consistent definitions of T and μ are possible via coexistence with an appropriate reservoir, if (and in general only if) a particular kind of rate (that proposed by Sasa and Tasaki) is used for exchanges of particles and energy between systems. The program fails, however, for nonuniform systems. The functions T and μ describing isolated phases cannot be used to predict the properties of coexisting phases in a single, phase-separated system.
Computational complexity of nonequilibrium steady states of quantum spin chains
Marzolino, Ugo; Prosen, Tomaž
2016-03-01
We study nonequilibrium steady states (NESS) of spin chains with boundary Markovian dissipation from the computational complexity point of view. We focus on X X chains whose NESS are matrix product operators, i.e., with coefficients of a tensor operator basis described by transition amplitudes in an auxiliary space. Encoding quantum algorithms in the auxiliary space, we show that estimating expectations of operators, being local in the sense that each acts on disjoint sets of few spins covering all the system, provides the answers of problems at least as hard as, and believed by many computer scientists to be much harder than, those solved by quantum computers. We draw conclusions on the hardness of the above estimations.
Petri nets for steady state analysis of metabolic systems.
Voss, Klaus; Heiner, Monika; Koch, Ina
2011-01-01
Computer assisted analysis and simulation of biochemical pathways can improve the understanding of the structure and the dynamics of cell processes considerably. The construction and quantitative analysis of kinetic models is often impeded by the lack of reliable data. However, as the topological structure of biochemical systems can be regarded to remain constant in time, a qualitative analysis of a pathway model was shown to be quite promising as it can render a lot of useful knowledge, e. g., about its structural invariants. The topic of this paper are pathways whose substances have reached a dynamic concentration equilibrium (steady state). It is argued that appreciated tools from biochemistry and also low-level Petri nets can yield only part of the desired results, whereas executable high-level net models lead to a number of valuable additional insights by combining symbolic analysis and simulation.
Steady state analysis of metabolic pathways using Petri nets.
Voss, Klaus; Heiner, Monika; Koch, Ina
2003-01-01
Computer assisted analysis and simulation of biochemical pathways can improve the understanding of the structure and the dynamics of cell processes considerably. The construction and quantitative analysis of kinetic models is often impeded by the lack of reliable data. However, as the topological structure of biochemical systems can be regarded to remain constant in time, a qualitative analysis of a pathway model was shown to be quite promising as it can render a lot of useful knowledge, e. g., about its structural invariants. The topic of this paper are pathways whose substances have reached a dynamic concentration equilibrium (steady state). It is argued that appreciated tools from biochemistry and also low-level Petri nets can yield only part of the desired results, whereas executable high-level net models lead to a number of valuable additional insights by combining symbolic analysis and simulation.
Steady State Thermal Analyses of SCEPTOR X-57 Wingtip Propulsion
Schnulo, Sydney L.; Chin, Jeffrey C.; Smith, Andrew D.; Dubois, Arthur
2017-01-01
Electric aircraft concepts enable advanced propulsion airframe integration approaches that promise increased efficiency as well as reduced emissions and noise. NASA's fully electric Maxwell X-57, developed under the SCEPTOR program, features distributed propulsion across a high aspect ratio wing. There are 14 propulsors in all: 12 high lift motor that are only active during take off and climb, and 2 larger motors positioned on the wingtips that operate over the entire mission. The power electronics involved in the wingtip propulsion are temperature sensitive and therefore require thermal management. This work focuses on the high and low fidelity heat transfer analysis methods performed to ensure that the wingtip motor inverters do not reach their temperature limits. It also explores different geometry configurations involved in the X-57 development and any thermal concerns. All analyses presented are performed at steady state under stressful operating conditions, therefore predicting temperatures which are considered the worst-case scenario to remain conservative.
Dissipative production of a maximally entangled steady state
Lin, Y; Reiter, F; Tan, T R; Bowler, R; S\\orensen, A S; Leibfried, D; Wineland, D J
2013-01-01
Entangled states are a key resource in fundamental quantum physics, quantum cryp-tography, and quantum computation [1].To date, controlled unitary interactions applied to a quantum system, so-called "quantum gates", have been the most widely used method to deterministically create entanglement [2]. These processes require high-fidelity state preparation as well as minimizing the decoherence that inevitably arises from coupling between the system and the environment and imperfect control of the system parameters. Here, on the contrary, we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion qubits independent of their initial state. While previous works along this line involved the application of sequences of multiple time-dependent gates [3] or generated entanglement of atomic ensembles dissipatively but relied on a measurement record for steady-state entanglement [4], we implement the process in a continuous time-indepen...
Steady-state, cavity-less, multimode superradiance
Greenberg, Joel A
2012-01-01
The study of collective light-matter interactions, where the dynamics of an individual scatterer depend on the state of the entire multi-scatterer system, has recently received much attention in the areas of fundamental research and photonic technologies. Cold atomic vapors represent an exciting system for studying such effects because light-based manipulation of internal and center-of-mass atomic states lead to reduced instability thresholds and new phonomena. Previous investigations required single-mode cavities to realize strong light mediated atom-atom interactions, though, which limits the observable phenomena. Here we demonstrate steady-state, mirrorless superradiance in a cold vapor pumped by weak optical fields. Beyond a critical pumping strength, the vapor spontaneously transforms into a spatially self-organized state: a density grating forms. Scattering of the pump beams off this grating generates new optical fields that act back on the vapor to enhance the atomic organization. This system has appli...
Extending the definition of entropy to nonequilibrium steady states.
Ruelle, David P
2003-03-18
We study the nonequilibrium statistical mechanics of a finite classical system subjected to nongradient forces xi and maintained at fixed kinetic energy (Hoover-Evans isokinetic thermostat). We assume that the microscopic dynamics is sufficiently chaotic (Gallavotti-Cohen chaotic hypothesis) and that there is a natural nonequilibrium steady-state rho(xi). When xi is replaced by xi + deltaxi, one can compute the change deltarho of rho(xi) (linear response) and define an entropy change deltaS based on energy considerations. When xi is varied around a loop, the total change of S need not vanish: Outside of equilibrium the entropy has curvature. However, at equilibrium (i.e., if xi is a gradient) we show that the curvature is zero, and that the entropy S(xi + deltaxi) near equilibrium is well defined to second order in deltaxi.
Avoiding Rebound through a Steady-State Economy
DEFF Research Database (Denmark)
Nørgaard, Jørgen
2008-01-01
is considered to be limited primarily by productive capacity with little concern for ecological costs and limits. In such a development aiming at unlimited growth it would from a long term environmental perspective be close to irrelevant to reach for more efficient use of energy at the end-users, since it would...... only buy some time. From this perspective, the environmental problem with the rebound effect is not the higher energy efficiency, which pushes towards lower flows of resources through the economy, but rather the conventional economy which rebounds the savings, because of its quest for higher flows....... In this chapter, I shall take the rebound debate further by discussing the possible role of energy efficiency in a sustainable economy that is based on the notion of ‘sufficiency’. The assumption is that globally we need to achieve a ‘steady-state economy’. Considering the urgent need for better material...
ANALYTICAL SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
胡建兰; 张汉林
2003-01-01
The following partial differential equations are studied: generaliz ed fifth-orderKdV equation, water wave equation, Kupershmidt equation, couples KdV equation. Theanalytical solutions to these problems via using various ansaiz es by introducing a second-order ordinary differential equation are found out.
Laguna Verde BWRs operational experience: steady-state fuel performance
Energy Technology Data Exchange (ETDEWEB)
Cuevas V, G. F.; Bravo S, J. M. [Global Nuclear Fuel - Americas, 3901 Castle Hayne Road, Wilmington, 28401 North Carolina (United States); Casillas, J. L., E-mail: gabriel.cuevas-vivas@gnf.co [General Electric Hitachi Nuclear Energy, 1989 Little Orchard St. Romm 239, San Jose, 95125 California (United States)
2010-10-15
The two BWR at Laguna Verde nuclear power station are finishing 21 and 15 years of continuous successful operation as of 2010. During Unit 1 and 2 commercial operations only Ge/GNF fuel designs have been employed; fuel lattice designs 8 x 8 and 10 x 10 were used at the reactor, with an original licensed thermal power (OLTP: 1931 MWt) and the reactor's first power up-rates of 5%. GNF fuel will be also used for the second EPU to reach 120% of OLTP in the near future. Thermal and gamma traversing in-core probes (Tip) are used for power monitoring purposes along with the Ge (now GNF-A) core monitoring system, 3-dimensional Monicore{sup TM}. GNF-A has also participated by preparing the core management plan that is regularly fine-tuned in collaboration with Comision Federal de Electricidad (CFE owner of the Laguna Verde reactors). For determination of thermal margins and eigenvalue prediction, GNF-A employs the NRC-licensed steady-state core simulator PANAC11. Tip comparisons are routinely used to adapt power distributions for a better thermal margin calculation. Over the years, several challenges have appeared in the near and long term fuel management planning such as increasing cycle length, optimization of the thermal margins, rated power increase, etc. Each challenge has been successfully overcome via operational strategy, code improvements and better fuel designs. This paper summarizes Laguna Verde Unit 1 and 2 steady-state performance from initial commercial operation, with a discussion of the nuclear and thermal-hydraulic design features, as well as of the operational strategies that set and interesting benchmark for future fuel applications, code development and operation of the BWRs. (Author)
A mathematical model of pan evaporation under steady state conditions
Lim, Wee Ho; Roderick, Michael L.; Farquhar, Graham D.
2016-09-01
In the context of changing climate, global pan evaporation records have shown a spatially-averaged trend of ∼ -2 to ∼ -3 mm a-2 over the past 30-50 years. This global phenomenon has motivated the development of the "PenPan" model (Rotstayn et al., 2006). However, the original PenPan model has yet to receive an independent experimental evaluation. Hence, we constructed an instrumented US Class A pan at Canberra Airport (Australia) and monitored it over a three-year period (2007-2010) to uncover the physics of pan evaporation under non-steady state conditions. The experimental investigations of pan evaporation enabled theoretical formulation and parameterisation of the aerodynamic function considering the wind, properties of air and (with or without) the bird guard effect. The energy balance investigation allowed for detailed formulation of the short- and long-wave radiation associated with the albedos and the emissivities of the pan water surface and the pan wall. Here, we synthesise and generalise those earlier works to develop a new model called the "PenPan-V2" model for application under steady state conditions (i.e., uses a monthly time step). Two versions (PenPan-V2C and PenPan-V2S) are tested using pan evaporation data available across the Australian continent. Both versions outperformed the original PenPan model with better representation of both the evaporation rate and the underlying physics of a US Class A pan. The results show the improved solar geometry related calculations (e.g., albedo, area) for the pan system led to a clear improvement in representing the seasonal cycle of pan evaporation. For general applications, the PenPan-V2S is simpler and suited for applications including an evaluation of long-term trends in pan evaporation.
A two-dimensional MHD global coronal model - Steady-state streamers
Wang, A.-H.; Wu, S. T.; Suess, S. T.; Poletto, G.
1992-01-01
A 2D, time-dependent, numerical, MHD model for the simulation of coronal streamers from the solar surface to 15 solar is presented. Three examples are given; for dipole, quadrupole and hexapole (Legendre polynomials P1, P2, and P3) initial field topologies. The computed properties are density, temperature, velocity, and magnetic field. The calculation is set up as an initial-boundary value problem wherein a relaxation in time produces the steady state solution. In addition to the properties of the solutions, their accuracy is discussed. Besides solutions for dipole, quadrupole, and hexapole geometries, the model use of realistic values for the density and Alfven speed while still meeting the requirement that the flow speed be super-Alfvenic at the outer boundary by extending the outer boundary to 15 solar radii.
Stochastic modeling of the steady-state variability in isometric force.
Stitt, Joseph P; Newell, Karl M
2009-07-01
This paper presents the stochastic modeling of isometric force variability in the steady-state time series recorded from the index finger of young adults in the act of attempting to hold different levels of constant force. The isometric force time series were examined by assuming that the stochastic (random) models were linear. System identification techniques were employed to estimate the parameters of each linear model. Once the models were parameterized, the values of the estimated parameters were compared to determine if a single linear time-invariant model was applicable across the entire isometric force range. Although the overall random models were found to be nonlinear functions of the target force level, within a fixed target level, linear modeling provided adequate estimates of the underlying processes thus enabling the use of well-known linear system identification algorithms.
From arteries to boreholes: Steady-state response of a poroelastic cylinder to fluid injection
Auton, Lucy C
2016-01-01
The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurisation of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large deformations and, hence, to strong deviations from a classical, linear-poroelastic response. Here, we study this problem by analysing the steady-state response of a poroelastic cylinder to fluid injection. We consider the qualitative and quantitative impacts of kinematic and constitutive nonlinearity, highlighting the strong impact of deformation-dependent permeability. We show that the wall thickness (thick vs. thin) and the outer boundary condition (free vs. constrained) play a central role in controlling th...
Tan, Yikun; Rivera, Jimmy G Lafontaine; Contador, Carolina A; Asenjo, Juan A; Liao, James C
2011-01-01
Dynamic models of metabolism are instrumental for gaining insight and predicting possible outcomes of perturbations. Current approaches start from the selection of lumped enzyme kinetics and determine the parameters within a large parametric space. However, kinetic parameters are often unknown and obtaining these parameters requires detailed characterization of enzyme kinetics. In many cases, only steady-state fluxes are measured or estimated, but these data have not been utilized to construct dynamic models. Here, we extend the previously developed Ensemble Modeling methodology by allowing various kinetic rate expressions and employing a more efficient solution method for steady states. We show that anchoring the dynamic models to the same flux reduces the allowable parameter space significantly such that sampling of high dimensional kinetic parameters becomes meaningful. The methodology enables examination of the properties of the model's structure, including multiple steady states. Screening of models based on limited steady-state fluxes or metabolite profiles reduces the parameter space further and the remaining models become increasingly predictive. We use both succinate overproduction and central carbon metabolism in Escherichia coli as examples to demonstrate these results. Published by Elsevier Inc.
Chemostat-cultivated Escherichia coli at high dilution rate: multiple steady states and drift.
Majewski, R A; Domach, M M
1990-06-20
The representation of metabolic network reaction kinetics in a scaled, polynomial form can allow for the prediction of multiple steady states. The polynomial formalism is used to study chemostat-cultured Escherichia coli which has been observed to exhibit two multiple steady states under ammonium ion-limited growth conditions: a high cell density-low ammonium ion concentration steady state and a low cell density-high ammonium ion concentration steady state. Additionally, the low-cell-density steady state has been observed to drift to the high-cell-density steady state. Inspection of the steady-state rate expressions for the ammonium ion transport/assimilation network (in polynomial form) suggests that at low ammonium ion concentrations, two steady states are possible. One corresponds to heavy use of the glutamine synthetase-glutamate synthase (GLNS-GS) branch and the second to heavy use of the glutamate dehydrogenase (GDH) branch. Realization of the predicted intracellular steady states is also found to be dependent on the parameters of the transport process. Moreover, the two steady states differ in where their energy intensity lies. To explain the drift, GLNS, which is inducible under low ammonium ion concentrations, is suggested to be a "memory element." A chemostat-based model is developed to illustrate that perturbations in dilution rate can lead to drift between the two steady states provided that the disturbance in dilution rate is sufficiently large and/or long in duration.
Jordan, Paul; Brunschwig, Hadassa; Luedin, Eric
2008-01-01
The approach of Bayesian mixed effects modeling is an appropriate method for estimating both population-specific as well as subject-specific times to steady state. In addition to pure estimation, the approach allows to determine the time until a certain fraction of individuals of a population has reached steady state with a pre-specified certainty. In this paper a mixed effects model for the parameters of a nonlinear pharmacokinetic model is used within a Bayesian framework. Model fitting by means of Markov Chain Monte Carlo methods as implemented in the Gibbs sampler as well as the extraction of estimates and probability statements of interest are described. Finally, the proposed approach is illustrated by application to trough data from a multiple dose clinical trial.
Chen, Zeyuan; Chu, Liang; Galbavy, Edward S.; Ram, Keren; Anastasio, Cort
2016-08-01
While the hydroxyl radical (•OH) in the snowpack is likely a dominant oxidant for organic species and bromide, little is known about the kinetics or steady-state concentrations of •OH on/in snow and ice. Here we measure the formation rate, lifetime, and concentration of •OH for illuminated polar snow samples studied in the laboratory and in the field. Laboratory studies show that •OH kinetics and steady-state concentrations are essentially the same for a given sample studied as ice and liquid; this is in contrast to other photooxidants, which show a concentration enhancement in ice relative to solution as a result of kinetic differences in the two phases. The average production rate of •OH in samples studied at Summit, Greenland, is 5 times lower than the average measured in the laboratory, while the average •OH lifetime determined in the field is 5 times higher than in the laboratory. These differences indicate that the polar snows we studied in the laboratory are affected by contamination, despite significant efforts to prevent this; our results suggest similar contamination may be a widespread problem in laboratory studies of ice chemistry. Steady-state concentrations of •OH in clean snow studied in the field at Summit, Greenland, range from (0.8 to 3) × 10-15 M, comparable to values reported for midlatitude cloud and fog drops, rain, and deliquesced marine particles, even though impurity concentrations in the snow samples are much lower. Partitioning of firn air •OH to the snow grains will approximately double the steady-state concentration of snow-grain hydroxyl radical, leading to an average [•OH] in near-surface, summer Summit snow of approximately 4 × 10-15 M. At this concentration, the •OH-mediated lifetimes of organics and bromide in Summit snow grains are approximately 3 days and 7 h, respectively, suggesting that hydroxyl radical is a major oxidant for both species.
Steady state, continuity, and the curious behavior of steep channels in layered rocks
Covington, M. D.; Perne, M.; Thaler, E.; Myre, J. M.
2016-12-01
Considerations of landscape steady state have substantially informed our understanding of the relationships between landscapes, tectonics, climate, and lithology. Topographic steady state, where topography is fixed in time, is a particularly important tool in the interpretation of landscape features, such as bedrock channel profiles, within a context of uplift patterns and rock strength. However, topographic steady state cannot strictly be attained in a landscape with layered rocks with non-vertical contacts. We show that an assumption of channel continuity, where channel retreat rates in the direction parallel to a contact are equal above and below the contact, provides a more general description of steady state landscapes in layered rocks, and that topographic steady state is a special case of the steady state derived from continuity. We demonstrate that modeled landscapes approach continuity steady state using 1D simulations and full landscape evolution models. Contrary to common conceptions, continuity predicts that channels will be steeper in weaker rocks in the case of subhorizontal rock layers when the stream power erosion exponent n<1. For subhorizontal layered rocks with different erodibilities, continuity also predicts larger slope contrasts than would be predicted by topographic steady state. Continuity steady state is a type of flux steady state, where uplift is balanced on average by erosion. The differences between topographic steady state and continuity steady state are most pronuced for steep channels in subhorizontal layered rocks. Consequently, cratonic and plateau settings are most likely to produce the effects predicted by continuity steady state. These settings remain relatively underexplored within the bedrock channel literature. Though examples illustrated here utilze the stream power erosion law, continuity steady state provides a general mathematical tool that can be used to explore the development of landscapes in layered rocks using any
Jacobs, Christian T; Kramer, Stephan C; Funke, Simon W
2016-01-01
Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the co...
Li, Ke; Deb, Kalyanmoy; Zhang, Qingfu; Zhang, Qiang
2016-11-08
Nondominated sorting (NDS), which divides a population into several nondomination levels (NDLs), is a basic step in many evolutionary multiobjective optimization (EMO) algorithms. It has been widely studied in a generational evolution model, where the environmental selection is performed after generating a whole population of offspring. However, in a steady-state evolution model, where a population is updated right after the generation of a new candidate, the NDS can be extremely time consuming. This is especially severe when the number of objectives and population size become large. In this paper, we propose an efficient NDL update method to reduce the cost for maintaining the NDL structure in steady-state EMO. Instead of performing the NDS from scratch, our method only updates the NDLs of a limited number of solutions by extracting the knowledge from the current NDL structure. Notice that our NDL update method is performed twice at each iteration. One is after the reproduction, the other is after the environmental selection. Extensive experiments fully demonstrate that, comparing to the other five state-of-the-art NDS methods, our proposed method avoids a significant amount of unnecessary comparisons, not only in the synthetic data sets, but also in some real optimization scenarios. Last but not least, we find that our proposed method is also useful for the generational evolution model.
Computation of steady-state probability distributions in stochastic models of cellular networks.
Directory of Open Access Journals (Sweden)
Mark Hallen
2011-10-01
Full Text Available Cellular processes are "noisy". In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry.
Global solution for coupled nonlinear Klein-Gordon system
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2007-01-01
The global solution for a coupled nonlinear Klein-Gordon system in twodimensional space was studied.First,a sharp threshold of blowup and global existenoe for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.
Exact solutions to a nonlinear dispersive model with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Yin Jun [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China); Lai Shaoyong [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)], E-mail: laishaoy@swufe.edu.cn; Qing Yin [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)
2009-05-15
A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.
SINGULAR AND RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Adomian solution of a nonlinear quadratic integral equation
Directory of Open Access Journals (Sweden)
E.A.A. Ziada
2013-04-01
Full Text Available We are concerned here with a nonlinear quadratic integral equation (QIE. The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of Adomian’s series solution. Two methods are used to solve these type of equations; ADM and repeated trapezoidal method. The obtained results are compared.
Iterative Solution for Systems of Nonlinear Two Binary Operator Equations
Institute of Scientific and Technical Information of China (English)
ZHANGZhi-hong; LIWen-feng
2004-01-01
Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are imnroved and generalized.
Adaptive relaxation for the steady-state analysis of Markov chains
Horton, Graham
1994-01-01
We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.
Wave Number Method for Three-Dimensional Steady-State Acoustic Problems
Institute of Scientific and Technical Information of China (English)
HUANG Fei; HE Zeng; WEI Jun-hong; PENG Wei-cai
2007-01-01
Based on the indirect Trefftz approach, a wave number method (WNM) is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method (BEM), the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.
Mantle Sulfur Cycle: A Case for Non-Steady State ?
Cartigny, Pierre; Labidi, Jabrane
2016-04-01
Data published over the last 5 years show that the early inference that mantle is isotopically homogeneous is no more valid. Instead, new generation data on lavas range over a significant 34S/32S variability of up to 5‰ with δ 34S values often correlated to Sr- and Nd-isotope compositions. This new set of data also reveals the Earth's mantle to have a sub-chondritic 34S/32S ratio, by about ˜ 1‰. We will present at the conference our published and unpublished data on samples characterizing the different mantle components (i.e. EM1, EM2, HIMU and LOMU). All illustrate 34S-enrichments compared to MORB with Δ 33S and Δ 36S values indistinguishable from CDT or chondrites at the 0.03‰ level. These data are consistent with the recycling of subducted components carrying sulfur with Δ 33S and Δ 36S-values close to zero. Archean rocks commonly display Δ 33S and Δ 36S values deviating from zero by 1 to 10 ‰. The lack of variations for Δ 33S and Δ 36S values in present day lava argue against the sampling of any subducted protolith of Archean age in their mantle source. Instead, our data are consistent with the occurrence of Proterozoic subducted sulfur in the source of the EM1, EM2, LOMU and HIMU endmember at the St-Helena island. This is in agreement with the age of those components early derived through the use of the Pb isotope systematic. Currently, the negative δ 34S-values of the depleted mantle seem to be associated with mostly positive values of enriched components. This would be inconsistent with the concept a steady state of sulfur. Assuming that the overall observations of recycled sulfur are not biased, the origin of such a non-steady state remains unclear. It could be related to the relatively compatible behavior of sulfur during partial melting, as the residue of present-day melting can be shown to always contain significant amounts of sulfide (50{%} of what is observed in a fertile source). This typical behavior likely prevents an efficient
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Linear iterative technique for solution of nonlinear thermal network problems
Energy Technology Data Exchange (ETDEWEB)
Seabourn, C.M.
1976-11-01
A method for rapid and accurate solution of linear and/or nonlinear thermal network problems is described. It is a matrix iterative process that converges for nodal temperatures and variations of thermal conductivity with temperature. The method is computer oriented and can be changed easily for design studies.
Multiple solutions to some singular nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Monica Lazzo
2001-01-01
Full Text Available We consider the equation $$ - h^2 Delta u + V_varepsilon(x u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.
The Local Stability of Solutions for a Nonlinear Equation
Directory of Open Access Journals (Sweden)
Haibo Yan
2014-01-01
Full Text Available The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R by assuming that the initial value only lies in the space L1(R∩L∞(R.
Exact periodic solution in coupled nonlinear Schrodinger equations
Institute of Scientific and Technical Information of China (English)
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
Exact solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Peng, Yan-Ze
2003-08-11
Exact solutions to some nonlinear partial differential equations, including (2+1)-dimensional breaking soliton equation, sine-Gordon equation and double sine-Gordon equation, are studied by means of the mapping method proposed by the author recently. Many new results are presented. A simple review of the method is finally given.
EXISTENCE OF SOLUTIONS OF NONLINEAR FRACTIONAL PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
K. BALACHANDRAN; S. KIRUTHIKA; J.J. TRUJILLO
2013-01-01
This article deals with the existence of solutions of nonlinear fractional pantograph equations.Such model can be considered suitable to be applied when the corresponding process occurs through strongly anomalous media.The results are obtained using fractional calculus and fixed point theorems.An example is provided to illustrate the main result obtained in this article.
Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs
Directory of Open Access Journals (Sweden)
Marco Calahorrano
2004-04-01
Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$
Riccati-parameter solutions of nonlinear second-order ODEs
Energy Technology Data Exchange (ETDEWEB)
Reyes, M A [Instituto de Fisica, Universidad de Guanajuato, Leon, Guanajuato (Mexico); Rosu, H C [PotosIInstitute of Science and Technology, Apdo Postal 3-74 Tangamanga, 78231 San Luis PotosI (Mexico)], E-mail: hcr@ipicyt.edu.mx
2008-07-18
It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure.
Bailey, Harry E.; Beam, Richard M.
1991-01-01
Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.
Yongky, Andrew; Lee, Jongchan; Le, Tung; Mulukutla, Bhanu Chandra; Daoutidis, Prodromos; Hu, Wei-Shou
2015-07-01
Continuous culture for the production of biopharmaceutical proteins offers the possibility of steady state operations and thus more consistent product quality and increased productivity. Under some conditions, multiplicity of steady states has been observed in continuous cultures of mammalian cells, wherein with the same dilution rate and feed nutrient composition, steady states with very different cell and product concentrations may be reached. At those different steady states, cells may exhibit a high glycolysis flux with high lactate production and low cell concentration, or a low glycolysis flux with low lactate and high cell concentration. These different steady states, with different cell concentration, also have different productivity. Developing a mechanistic understanding of the occurrence of steady state multiplicity and devising a strategy to steer the culture toward the desired steady state is critical. We establish a multi-scale kinetic model that integrates a mechanistic intracellular metabolic model and cell growth model in a continuous bioreactor. We show that steady state multiplicity exists in a range of dilution rate in continuous culture as a result of the bistable behavior in glycolysis. The insights from the model were used to devise strategies to guide the culture to the desired steady state in the multiple steady state region. The model provides a guideline principle in the design of continuous culture processes of mammalian cells.
Institute of Scientific and Technical Information of China (English)
Zilun Chen; Jing Hou; Zongfu Jiang
2007-01-01
A theoretical analysis of the pump-induced temperature change and associated thermal phase shift occurring in a fiber laser is presented. The temperature rise and thermal phase shift from the moment when pump is turned on to steady-state in fiber lasers, such as Yb-doped fiber laser, are numerical calculated.With the same parameters, the numerical solution is in good agreement with the finite-element (ANSYS software) simulation.
Institute of Scientific and Technical Information of China (English)
Deng Yinbin; Yang Fen
2008-01-01
This article is contributed to the Cauchy problem u/t = △u + K(ㄧxㄧ)up in Rn x (0,T), u(x,0) =(ψ)(x) in Rn; with initial function(ψ)≠0. The stability of positive radial steady state, which are positive solutions of △u + K(ㄧxㄧ)up =0, is obtained when p is critical for general K(ㄧxㄧ).
Quasi-steady state aerodynamics of the cheetah tail
Directory of Open Access Journals (Sweden)
Amir Patel
2016-08-01
Full Text Available During high-speed pursuit of prey, the cheetah (Acinonyx jubatus has been observed to swing its tail while manoeuvring (e.g. turning or braking but the effect of these complex motions is not well understood. This study demonstrates the potential of the cheetah's long, furry tail to impart torques and forces on the body as a result of aerodynamic effects, in addition to the well-known inertial effects. The first-order aerodynamic forces on the tail are quantified through wind tunnel testing and it is observed that the fur nearly doubles the effective frontal area of the tail without much mass penalty. Simple dynamic models provide insight into manoeuvrability via simulation of pitch, roll and yaw tail motion primitives. The inertial and quasi-steady state aerodynamic effects of tail actuation are quantified and compared by calculating the angular impulse imparted onto the cheetah's body and its shown aerodynamic effects contribute to the tail's angular impulse, especially at the highest forward velocities.
Quasi-steady state aerodynamics of the cheetah tail
Boje, Edward; Fisher, Callen; Louis, Leeann; Lane, Emily
2016-01-01
ABSTRACT During high-speed pursuit of prey, the cheetah (Acinonyx jubatus) has been observed to swing its tail while manoeuvring (e.g. turning or braking) but the effect of these complex motions is not well understood. This study demonstrates the potential of the cheetah's long, furry tail to impart torques and forces on the body as a result of aerodynamic effects, in addition to the well-known inertial effects. The first-order aerodynamic forces on the tail are quantified through wind tunnel testing and it is observed that the fur nearly doubles the effective frontal area of the tail without much mass penalty. Simple dynamic models provide insight into manoeuvrability via simulation of pitch, roll and yaw tail motion primitives. The inertial and quasi-steady state aerodynamic effects of tail actuation are quantified and compared by calculating the angular impulse imparted onto the cheetah's body and its shown aerodynamic effects contribute to the tail's angular impulse, especially at the highest forward velocities. PMID:27412267
The Path of Carbon in Photosynthesis XX. The Steady State
Calvin, M.; Massini, Peter
1952-09-01
The separation of the phenomenon of photosynthesis in green plants into a photochemical reaction and into the light-dependent reduction of carbon dioxide is discussed, The reduction of carbon dioxide and the fate of the assimilated carbon were investigated with the help of the tracer technique (exposure of the planks to the radioactive C{sup 14}O{sub 2}) and of paper chromatography. A reaction cycle is proposed in which phosphoglyceric acid is the first isolable assimilations product. Analyses of the algal extracts which had assimilated radioactive carbon dioxide in a stationary condition ('steady-state' photosynthesis) for a long time provided further information concerning the proposed cycle and permitted the approximate estimation, for a number of compounds of what fraction of each compound was taking part in the cycle. The earlier supposition that light influences the respiration cycle was confirmed. The possibility of the assistance of {alpha}-lipoic acid, or of a related substance, in this influence and in the photosynthesis cycle, is discussed.
Quasi-steady state aerodynamics of the cheetah tail.
Patel, Amir; Boje, Edward; Fisher, Callen; Louis, Leeann; Lane, Emily
2016-08-15
During high-speed pursuit of prey, the cheetah (Acinonyx jubatus) has been observed to swing its tail while manoeuvring (e.g. turning or braking) but the effect of these complex motions is not well understood. This study demonstrates the potential of the cheetah's long, furry tail to impart torques and forces on the body as a result of aerodynamic effects, in addition to the well-known inertial effects. The first-order aerodynamic forces on the tail are quantified through wind tunnel testing and it is observed that the fur nearly doubles the effective frontal area of the tail without much mass penalty. Simple dynamic models provide insight into manoeuvrability via simulation of pitch, roll and yaw tail motion primitives. The inertial and quasi-steady state aerodynamic effects of tail actuation are quantified and compared by calculating the angular impulse imparted onto the cheetah's body and its shown aerodynamic effects contribute to the tail's angular impulse, especially at the highest forward velocities.
Stable Gene Regulatory Network Modeling From Steady-State Data
Directory of Open Access Journals (Sweden)
Joy Edward Larvie
2016-04-01
Full Text Available Gene regulatory networks represent an abstract mapping of gene regulations in living cells. They aim to capture dependencies among molecular entities such as transcription factors, proteins and metabolites. In most applications, the regulatory network structure is unknown, and has to be reverse engineered from experimental data consisting of expression levels of the genes usually measured as messenger RNA concentrations in microarray experiments. Steady-state gene expression data are obtained from measurements of the variations in expression activity following the application of small perturbations to equilibrium states in genetic perturbation experiments. In this paper, the least absolute shrinkage and selection operator-vector autoregressive (LASSO-VAR originally proposed for the analysis of economic time series data is adapted to include a stability constraint for the recovery of a sparse and stable regulatory network that describes data obtained from noisy perturbation experiments. The approach is applied to real experimental data obtained for the SOS pathway in Escherichia coli and the cell cycle pathway for yeast Saccharomyces cerevisiae. Significant features of this method are the ability to recover networks without inputting prior knowledge of the network topology, and the ability to be efficiently applied to large scale networks due to the convex nature of the method.
Regulation of steady-state neutrophil homeostasis by macrophages
Gordy, Claire; Pua, Heather; Sempowski, Gregory D.
2011-01-01
The timely clearance of apoptotic neutrophils from inflammation sites is an important function of macrophages; however, the role of macrophages in maintaining neutrophil homeostasis under steady-state conditions is less well understood. By conditionally deleting the antiapoptotic gene cellular FLICE-like inhibitory protein (C-FLIP) in myeloid cells, we have generated a novel mouse model deficient in marginal zone and bone marrow stromal macrophages. These mice develop severe neutrophilia, splenomegaly, extramedullary hematopoiesis, decreased body weight, and increased production of granulocyte colony-stimulating factor (G-CSF) and IL-1β, but not IL-17. c-FLIPf/f LysM-Cre mice exhibit delayed clearance of circulating neutrophils, suggesting that failure of macrophages to efficiently clear apoptotic neutrophils causes production of cytokines that drive excess granulopoiesis. Further, blocking G-CSF but not IL-1R signaling in vivo rescues this neutrophilia, suggesting that a G-CSF–dependent, IL-1β–independent pathway plays a role in promoting neutrophil production in mice with defective clearance of apoptotic cells. PMID:20980680
Attentional modulation of auditory steady-state responses.
Directory of Open Access Journals (Sweden)
Yatin Mahajan
Full Text Available Auditory selective attention enables task-relevant auditory events to be enhanced and irrelevant ones suppressed. In the present study we used a frequency tagging paradigm to investigate the effects of attention on auditory steady state responses (ASSR. The ASSR was elicited by simultaneously presenting two different streams of white noise, amplitude modulated at either 16 and 23.5 Hz or 32.5 and 40 Hz. The two different frequencies were presented to each ear and participants were instructed to selectively attend to one ear or the other (confirmed by behavioral evidence. The results revealed that modulation of ASSR by selective attention depended on the modulation frequencies used and whether the activation was contralateral or ipsilateral. Attention enhanced the ASSR for contralateral activation from either ear for 16 Hz and suppressed the ASSR for ipsilateral activation for 16 Hz and 23.5 Hz. For modulation frequencies of 32.5 or 40 Hz attention did not affect the ASSR. We propose that the pattern of enhancement and inhibition may be due to binaural suppressive effects on ipsilateral stimulation and the dominance of contralateral hemisphere during dichotic listening. In addition to the influence of cortical processing asymmetries, these results may also reflect a bias towards inhibitory ipsilateral and excitatory contralateral activation present at the level of inferior colliculus. That the effect of attention was clearest for the lower modulation frequencies suggests that such effects are likely mediated by cortical brain structures or by those in close proximity to cortex.
Nonequilibrium steady states of ideal bosonic and fermionic quantum gases
Vorberg, Daniel; Wustmann, Waltraut; Schomerus, Henning; Ketzmerick, Roland; Eckardt, André
2015-12-01
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013), 10.1103/PhysRevLett.111.240405]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
Steady-state and dynamic network modes for perceptual expectation.
Choi, Uk-Su; Sung, Yul-Wan; Ogawa, Seiji
2017-01-12
Perceptual expectation can attenuate repetition suppression, the stimulus-induced neuronal response generated by repeated stimulation, suggesting that repetition suppression is a top-down modulatory phenomenon. However, it is still unclear which high-level brain areas are involved and how they interact with low-level brain areas. Further, the temporal range over which perceptual expectation can effectively attenuate repetition suppression effects remains unclear. To elucidate the details of this top-down modulatory process, we used two short and long inter-stimulus intervals for a perceptual expectation paradigm of paired stimulation. We found that top-down modulation enhanced the response to the unexpected stimulus when repetition suppression was weak and that the effect disappeared at 1,000 ms prior to stimulus exposure. The high-level areas involved in this process included the left inferior frontal gyrus (IFG_L) and left parietal lobule (IPL_L). We also found two systems providing modulatory input to the right fusiform face area (FFA_R): one from IFG_L and the other from IPL_L. Most importantly, we identified two states of networks through which perceptual expectation modulates sensory responses: one is a dynamic state and the other is a steady state. Our results provide the first functional magnetic resonance imaging (fMRI) evidence of temporally nested networks in brain processing.
Glaucoma affects steady state VEP contrast thresholds before psychophysics.
Vaegan; Rahman, Anmar M A; Sanderson, Gordon F
2008-07-01
Frequency doubling technology (FDT) is a recent psychophysical test for glaucoma. It measures the contrast threshold to low spatial frequency, high temporal frequency sinusoidal luminance profile bars. We wanted to confirm, with stricter controls, Vaegan and Hollow's report that contrast thresholds of steady state visual evoked potentials (ssVEPs) to a stimulus resembling the central field of the FDT test was more sensitive to glaucoma than the subjective threshold to the same stimulus and to start to optimize the technique. A double masked trial using 57 eyes of 42 subjects. Both thresholds were estimated by modified binary search. In psychophysical testing, subjects were given a two alternative forced choice task. In ssVEP testing a significant signal in any one of eight channels was deemed to be a detection. In some subjects electrode positions were compared, both eyes were tested, tests were repeated to estimate reliability, stimulus frequencies were varied or full contrast functions were obtained. Thresholds and percent abnormal increased as a function of glaucoma severity for ssVEPs but not for psychophysics. Both threshold measures were reliable. Interocular correlations were low. SsVEP amplitude against contrast functions had similar thresholds to those found by modified binary search. The data was too irregular for individual thresholds to be estimated from a fitted exponential. Amplitudes were greatest at 7 to 10 Hz, psychophysical thresholds at 18.29 Hz, when formal controls were used, as they had in a less controlled previous study at 7.14 Hz.
Interaction-induced mode switching in steady-state microlasers.
Ge, Li; Liu, David; Cerjan, Alexander; Rotter, Stefan; Cao, Hui; Johnson, Steven G; Türeci, Hakan E; Stone, A Douglas
2016-01-11
We demonstrate that due to strong modal interactions through cross-gain saturation, the onset of a new lasing mode can switch off an existing mode via a negative power slope. In this process of interaction-induced mode switching (IMS) the two involved modes maintain their identities, i.e. they do not change their spatial field patterns or lasing frequencies. For a fixed pump profile, a simple analytic criterion for the occurrence of IMS is given in terms of their self- and cross-interaction coefficients and non-interacting thresholds, which is verified for the example of a two-dimensional microdisk laser. When the spatial pump profile is varied as the pump power is increased, IMS can be induced even when it would not occur with a fixed pump profile, as we show for two coupled laser cavities. Our findings apply to steady-state lasing and are hence different from dynamical mode switching or hopping. IMS may have potential applications in robust and flexible all-optical switching.
Full steady-state operation in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Kazarian-Vibert, F.; Litaudon, X.; Moreau, D.; Arslanbekov, R.; Hoang, G.T.; Peysson, Y. [Association Euratom-CEA, Centre d`Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
1996-12-01
In order to produce fully non-inductive, lower hybrid (LH) driven discharges in a systematic and reproducible manner, new operation modes have been studied on the superconducting Tore Supra tokamak. To cope with some uncertainties in the LH current drive efficiency (e.g. profile dependences), the plasma current is not imposed a priori, but evolves freely until the equilibrium (which depends on the LH power level) is reached. The voltage applied on the primary circuit no longer controls the plasma current. In an `open loop` scenario in which this voltage is present and constant, the timescale required to attain the equilibrium is the longest characteristic time of the coupled plasma-poloidal field coils system ({approx} 60 s). In order to obtain a stationary state faster, a new feedback scheme has been implemented in which the primary circuit voltage is controlled in such a way that the flux consumption vanishes. It is shown that this operation mode allows full steady-state to be reached within a characteristic time of a few seconds. The underlying physics is described and a detailed analysis of the experiments is made. It is shown, in particular, that this operation scenario generates stable stationary plasmas with improved confinement, so that the so-called `LHEP` regime can be extrapolated to continuous operation. (Author).
Grand canonical steady-state simulation of nucleation
Horsch, Martin
2009-01-01
Grand canonical molecular dynamics (GCMD) is applied to the nucleation process in a metastable phase near the spinodal, where nucleation occurs almost instantaneously and is limited to a very short time interval. With a variant of Maxwell's demon, proposed by McDonald [Am. J. Phys. 31: 31 (1963)], all nuclei exceeding a specified size are removed. In such a steady-state simulation, the nucleation process is sampled over an arbitrary timespan and all properties of the metastable state, including the nucleation rate, can be obtained with an increased precision. As an example, a series of GCMD simulations with McDonald's demon is carried out for homogeneous vapor to liquid nucleation of the truncated-shifted Lennard-Jones (tsLJ) fluid, covering the entire relevant temperature range. The results are in agreement with direct non-equilibrium MD simulation in the canonical ensemble. It is confirmed for supersaturated vapors of the tsLJ fluid that the classical nucleation theory underpredicts the nucleation rate by t...
Nonequilibrium steady states of ideal bosonic and fermionic quantum gases.
Vorberg, Daniel; Wustmann, Waltraut; Schomerus, Henning; Ketzmerick, Roland; Eckardt, André
2015-12-01
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
Steady State Response Analysis of a Tubular Piezoelectric Print Head.
Chang, Jiaqing; Liu, Yaxin; Huang, Bo
2016-01-12
In recent years, inkjet technology has played an important role in industrial materials printing and various sensors fabrication, but the mechanisms of the inkjet print head should be researched more elaborately. The steady state deformation analysis of a tubular piezoelectric print head, which can be classified as a plane strain problem because the radii of the tubes are considerably smaller than the lengths, is discussed in this paper. The geometric structure and the boundary conditions are all axisymmetric, so a one-dimensional mathematical model is constructed. By solving the model, the deformation field and stress field, as well as the electric potential distribution of the piezoelectric tube and glass tube, are obtained. The results show that the deformations are on the nanometer scale, the hoop stress is larger than the radial stress on the whole, and the potential is not linearly distributed along the radial direction. An experiment is designed to validate these computations. A discussion of the effect of the tubes' thicknesses on the system deformation status is provided.
Development of the ITER Advanced Steady State and Hybrid Scenarios
Energy Technology Data Exchange (ETDEWEB)
C.E. Kessel, D. Campbell, T. Casper, Y. Gribov, and J. Snipes
2010-09-24
Full discharge simulations are performed to examine the plasma current rampup, flattop and rampdown phases self-consistently with the poloidal field (PF) coils and their limitations, plasma transport evolution, and heating/current drive (H/CD) sources. Steady state scenarios are found that obtain 100% non-inductive current with Ip = 7.3-10.0 MA, βN ~ 2.5 for H98 = 1.6, Q’s range from 3 to 6, n/nGr = 0.75-1.0, and NB, IC, EC, and LH source have been examined. The scenarios remain within CS/PF coil limits by advancing the pre-magnetization by 40 Wb. Hybrid scenarios have been identified with 35-40% non-inductive current for Ip = 12.5 MA, H98 ~ 1.25, with q(0) reaching 1 at or after the end of rampup. The equilibrium operating space for the hybrid shows a large range of scenarios can be accommodated, and access 925-1300 s flattop burn durations.
A theory of nonequilibrium steady states in quantum chaotic systems
Wang, Pei
2017-09-01
Nonequilibrium steady state (NESS) is a quasistationary state, in which exist currents that continuously produce entropy, but the local observables are stationary everywhere. We propose a theory of NESS under the framework of quantum chaos. In an isolated quantum system whose density matrix follows a unitary evolution, there exist initial states for which the thermodynamic limit and the long-time limit are noncommutative. The density matrix \\hat ρ of these states displays a universal structure. Suppose that \\renewcommand{\\ket}[1]{{\\vert #1 >}} \\ketα and \\renewcommand{\\ket}[1]{{\\vert #1 >}} \\ketβ are different eigenstates of the Hamiltonian with energies E_α and E_β , respectively. \\renewcommand{\\bra}[1]{} \\braα\\hat ρ \\ketβ behaves as a random number which has zero mean. In thermodynamic limit, the variance of \\renewcommand{\\bra}[1]{} \\braα\\hat ρ \\ketβ is a smooth function of ≤ft\\vert E_α-E_β\\right\\vert , scaling as 1/≤ft\\vert E_α-E_β\\right\\vert 2 in the limit ≤ft\\vert E_α-E_β\\right\\vert \\to 0 . If and only if this scaling law is obeyed, the initial state evolves into NESS in the long time limit. We present numerical evidence of our hypothesis in a few chaotic models. Furthermore, we find that our hypothesis indicates the eigenstate thermalization hypothesis (ETH) for current operators in a bipartite system.
Steady-state evolution of debris disks around A stars
Wyatt, M C; Su, K Y L; Rieke, G H; Greaves, J S; Beichman, C A; Bryden, G
2007-01-01
In this paper a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of main sequence A stars. All stars are assumed to have planetesimal belts with a distribution of initial masses and radii. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium whereupon the mass falls off oc 1/t. We find that the detection statistics and trends seen at both 24 and 70um can be fitted well by the model. While there is no need to invoke stochastic evolution or delayed stirring to explain the statistics, a moderate rate of stochastic events is not ruled out. Potentially anomalous systems are identified by a high dust luminosity compared with the maximum permissible in the model (HD3003, HD38678, HD115892, HD172555). Their planetesimals may have unusual properties (high strength or low eccentricity) or this dust could be transient. While transient phenomena are also favored for a few systems in the literature, ...
Classical quasi-steady state reduction-A mathematical characterization
Goeke, Alexandra; Walcher, Sebastian; Zerz, Eva
2017-04-01
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar (heuristically motivated) mathematical procedure: Set the rate of change for certain (a priori chosen) variables equal to zero and use the resulting algebraic equations to obtain a system of smaller dimension for the remaining variables. This procedure will generally be valid only for certain parameter ranges. We start by showing that the reduction is accurate if and only if the corresponding parameter is what we call a QSS parameter value, and that the reduction is approximately accurate if and only if the corresponding parameter is close to a QSS parameter value. The QSS parameter values can be characterized by polynomial equations and inequations, hence parameter ranges for which QSS reduction is valid are accessible in an algorithmic manner. A defining characteristic of a QSS parameter value is that the algebraic variety defined by the QSS relations is invariant for the differential equation. A closer investigation of the associated systems shows the existence of further invariant sets; here singular perturbations enter the picture in a natural manner. We compare QSS reduction and singular perturbation reduction, and show that, while they do not agree in general, they do, up to lowest order in a small parameter, for a quite large and relevant class of examples. This observation, in turn, allows the computation of QSS reductions even in cases where an explicit resolution of the polynomial equations is not possible.
Visual steady state in relation to age and cognitive function
Dyhr Thomsen, Mia; Wiegand, Iris; Horwitz, Henrik; Klemp, Marc; Nikolic, Miki; Rask, Lene; Lauritzen, Martin; Benedek, Krisztina
2017-01-01
Neocortical gamma activity is crucial for sensory perception and cognition. This study examines the value of using non-task stimulation-induced EEG oscillations to predict cognitive status in a birth cohort of healthy Danish males (Metropolit) with varying cognitive ability. In particular, we examine the steady-state VEP power response (SSVEP-PR) in the alpha (8Hz) and gamma (36Hz) bands in 54 males (avg. age: 62.0 years) and compare these with 10 young healthy participants (avg. age 27.6 years). Furthermore, we correlate the individual alpha-to-gamma difference in relative visual-area power (ΔRV) with cognitive scores for the older adults. We find that ΔRV decrease with age by just over one standard deviation when comparing young with old participants (p<0.01). Furthermore, intelligence is significantly negatively correlated with ΔRV in the older adult cohort, even when processing speed, global cognition, executive function, memory, and education (p<0.05). In our preferred specification, an increase in ΔRV of one standard deviation is associated with a reduction in intelligence of 48% of a standard deviation (p<0.01). Finally, we conclude that the difference in cerebral rhythmic activity between the alpha and gamma bands is associated with age and cognitive status, and that ΔRV therefore provide a non-subjective clinical tool with which to examine cognitive status in old age. PMID:28245274
Non-steady state population kinetics of intravenous phenytoin.
Frame, B; Beal, S L
1998-08-01
This observational study explored the effects of demographics, sickness, and polypharmacy on the non-steady state population pharmacokinetics of intravenous phenytoin. One hundred fifteen patients were studied. Models were developed using the NONMEM program with hybrid first-order conditional estimation. A Michaelis-Menten model with delayed induction was preferred over a Michaelis-Menten model without induction, a Michaelis-Menten model with immediate induction, or a linear model with delayed induction. When the data were fit to a Michaelis-Menten model with delayed induction, the volume of distribution (Vd) was found to depend on weight and serum albumin. The Vd was estimated to be 0.95 l/kg, assuming an albumin level of 3 g/dl. The Michaelis-Menten constant (km) was estimated to be 7.9 mg/l. The baseline maximum metabolic rate was 580 mg/day for a 70-kg patient. The average time to onset of induction was 59.5 hours. If a fever developed after induction began, it increased the extent of induction. This model was evaluated retrospectively in 26 additional patients, yielding a mean prediction error of -0.4 mg/l (-3.0-2.2 mg/l) and a mean absolute prediction error of 4.7 mg/l (3.2-6.2 mg/l) based on two-level feedback. Given the large interindividual variances in maximum metabolic rate, phenytoin levels should be measured frequently.
Models of steady state cooling flows in elliptical galaxies
Vedder, Peter W.; Trester, Jeffrey J.; Canizares, Claude R.
1988-01-01
A comprehensive set of steady state models for spherically symmetric cooling flows in early-type galaxies is presented. It is found that a reduction of the supernova (SN) rate in ellipticals produces a decrease in the X-ray luminosity of galactic cooling flows and a steepening of the surface brightness profile. The mean X-ray temperature of the cooling flow is not affected noticeably by a change in the SN rate. The external pressure around a galaxy does not markedly change the luminosity of the gas within the galaxy but does change the mean temperature of the gas. The presence of a dark matter halo in a galaxy only changes the mean X-ray temperature slightly. The addition of a distribution of mass sinks which remove material from the general accretion flow reduces L(X) very slightly, flattens the surface brightness profile, and reduces the central surface brightness level to values close to those actually observed. A reduction in the stellar mass-loss rate only slightly reduces the X-ray luminosity of the cooling flow and flattens the surface brightness by a small amount.
Multiple repetition time balanced steady-state free precession imaging.
Cukur, Tolga; Nishimura, Dwight G
2009-07-01
Although balanced steady-state free precession (bSSFP) imaging yields high signal-to-noise ratio (SNR) efficiency, the bright lipid signal is often undesirable. The bSSFP spectrum can be shaped to suppress the fat signal with scan-efficient alternating repetition time (ATR) bSSFP. However, the level of suppression is limited, and the pass-band is narrow due to its nonuniform shape. A multiple repetition time (TR) bSSFP scheme is proposed that creates a broad stop-band with a scan efficiency comparable with ATR-SSFP. Furthermore, the pass-band signal uniformity is improved, resulting in fewer shading/banding artifacts. When data acquisition occurs in more than a single TR within the multiple-TR period, the echoes can be combined to significantly improve the level of suppression. The signal characteristics of the proposed technique were compared with bSSFP and ATR-SSFP. The multiple-TR method generates identical contrast to bSSFP, and achieves up to an order of magnitude higher stop-band suppression than ATR-SSFP. In vivo studies at 1.5 T and 3 T demonstrate the superior fat-suppression performance of multiple-TR bSSFP.
Kinematical Analysis along Maximal Lactate Steady State Swimming Intensity
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Pedro Figueiredo, Rafael Nazario, Marisa Sousa, Jailton Gregório Pelarigo, João Paulo Vilas-Boas, Ricardo Fernandes
2014-09-01
Full Text Available The purpose of this study was to conduct a kinematical analysis during swimming at the intensity corresponding to maximal lactate steady state (MLSS. Thirteen long distance swimmers performed, in different days, an intermittent incremental protocol of n x 200 m until exhaustion and two to four 30-min submaximal constant speed bouts to determine the MLSS. The video analysis, using APAS System (Ariel Dynamics Inc., USA, allowed determining the following relevant swimming determinants (in five moments of the 30-min test: 0, 25, 50, 75, and 100%: stroke rate, stroke length, trunk incline, intracyclic velocity variation, propelling efficiency, index of coordination and the time allotted to propulsion per distance unit. An ANOVA for repeated measures was used to compare the parameters mean values along each moment of analysis. Stoke rate tended to increase and stroke length to decrease along the test; a tendency to decrease was also found for intracyclic velocity variation and propelling efficiency whereas the index of coordination and the propulsive impulse remained stable during the MLSS test. It can be concluded that the MLSS is not only an intensity to maintain without a significant increase of blood lactate concentration, but a concomitant stability for some biomechanical parameters exists (after an initial adaptation. However, efficiency indicators seem to be more sensitive to changes occurring during swimming at this threshold intensity.
The inductive, steady-state sustainment of stable spheromaks
Hossack, A. C.; Jarboe, T. R.; Morgan, K. D.; Sutherland, D. A.; Hansen, C. J.; Everson, C. J.; Penna, J. M.; Nelson, B. A.
2016-10-01
Inductive helicity injection current drive with imposed perturbations has led to the breakthrough of spheromak sustainment while maintaining stability. Sustained spheromaks show coherent, imposed plasma motion and low plasma-generated mode activity, indicating stability. Additionally, record current gain of 3.9 has been achieved with evidence of pressure confinement. The Helicity Injected Torus - Steady Inductive (HIT-SI) experiment studies efficient, steady-state current drive for magnetic confinement plasmas using a novel experimental method which is ideal for low aspect ratio, toroidal geometries and is compatible with closed flux surfaces. Analysis of surface magnetic probes indicates large n = 0 and 1 toroidal Fourier mode amplitudes and little energy in higher modes. Biorthogonal decomposition shows that almost all of the n = 1 energy is imposed by the injectors, rather than plasma-generated. Ion Doppler spectroscopy (IDS) measurements show coherent, imposed plasma motion of +/-2.5 cm in the region inside r 10 cm (a = 23 cm) and the size of the separate spheromak is consistent with that predicted by Imposed-dynamo Current Drive (IDCD). Coherent motion indicates that the spheromak is stable and a lack of plasma-generated n = 1 energy indicates that the maximum q is maintained below 1 for stability during sustainment.
Steady state relativistic stellar dynamics around a massive black hole
Bar-Or, Ben
2015-01-01
A massive black hole (MBH) consumes stars whose orbits evolve into the small phase-space volume of unstable orbits, the "loss-cone", which take them directly into the MBH, or close enough to interact strongly with it. The resulting phenomena: tidal heating and tidal disruption, binary capture and hyper-velocity star ejection, gravitational wave (GW) emission by inspiraling compact remnants, or hydrodynamical interactions with an accretion disk, are of interest as they can produce observable signatures and thereby reveal the existence of the MBH, affect its mass and spin evolution, probe strong gravity, and provide information on stars and gas near the MBH. The continuous loss of stars and the processes that resupply them shape the central stellar distribution. We investigate relativistic stellar dynamics near the loss-cone of a non-spinning MBH in steady-state analytically and by Monte Carlo simulations of the diffusion of the orbital parameters. These take into account Newtonian mass precession due to enclos...
Ising game: Nonequilibrium steady states of resource-allocation systems
Xin, C.; Yang, G.; Huang, J. P.
2017-04-01
Resource-allocation systems are ubiquitous in the human society. But how external fields affect the state of such systems remains poorly explored due to the lack of a suitable model. Because the behavior of spins pursuing energy minimization required by physical laws is similar to that of humans chasing payoff maximization studied in game theory, here we combine the Ising model with the market-directed resource-allocation game, yielding an Ising game. Based on the Ising game, we show theoretical, simulative and experimental evidences for a formula, which offers a clear expression of nonequilibrium steady states (NESSs). Interestingly, the formula also reveals a convertible relationship between the external field (exogenous factor) and resource ratio (endogenous factor), and a class of saturation as the external field exceeds certain limits. This work suggests that the Ising game could be a suitable model for studying external-field effects on resource-allocation systems, and it could provide guidance both for seeking more relations between NESSs and equilibrium states and for regulating human systems by choosing NESSs appropriately.
The Path of Carbon in Photosynthesis. XX. The Steady State
Energy Technology Data Exchange (ETDEWEB)
Calvin, M.; Massini, Peter
1952-09-01
The separation of the phenomenon of photosynthesis in green plants into a photochemical reaction and into the light-dependent reduction of carbon dioxide is discussed, The reduction of carbon dioxide and the fate of the assimilated carbon were investigated with the help of the tracer technique (exposure of the planks to the radioactive C{sup 14}O{sub 2}) and of paper chromatography. A reaction cycle is proposed in which phosphoglyceric acid is the first isolable assimilations product. Analyses of the algal extracts which had assimilated radioactive carbon dioxide in a stationary condition ('steady-state' photosynthesis) for a long time provided further information concerning the proposed cycle and permitted the approximate estimation, for a number of compounds of what fraction of each compound was taking part in the cycle. The earlier supposition that light influences the respiration cycle was confirmed. The possibility of the assistance of {alpha}-lipoic acid, or of a related substance, in this influence and in the photosynthesis cycle, is discussed.
Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers
de S. Teixeira, Renan; S. de B. Alves, Leonardo
2017-03-01
Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steady-states usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steady-states of unstable flows. Steady governing equations could be solved instead, by employing Newton-type methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steady-state to be reached. This approach does not require a good initial condition and works well for self-excited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multi-step schemes. A few chosen test cases
Generalized nonlinear Proca equation and its free-particle solutions
Energy Technology Data Exchange (ETDEWEB)
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
Interpolation inequalities for weak solutions of nonlinear parabolic systems
Directory of Open Access Journals (Sweden)
Floridia Giuseppe
2011-01-01
Full Text Available Abstract The authors investigate differentiability of the solutions of nonlinear parabolic systems of order 2 m in divergence form of the following type ∑ | α | ≤ m ( - 1 | α | D α a α X , D u + ∂ u ∂ t = 0 . The achieved results are inspired by the paper of Marino and Maugeri 2008, and the methods there applied. This note can be viewed as a continuation of the study of regularity properties for solutions of systems started in Ragusa 2002, continued in Ragusa 2003 and Floridia and Ragusa 2012 and also as a generalization of the paper by Capanato and Cannarsa 1981, where regularity properties of the solutions of nonlinear elliptic systems with quadratic growth are reached. Mathematics Subject Classification (2000 Primary 35K41, 35K55. Secondary 35B65, 35B45, 35D10
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Exact travelling wave solutions of nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt)]. E-mail: asoliman_99@yahoo.com; Abdou, M.A. [Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-04-15
An extended Fan-sub equation method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. The key idea of this method is to take full advantage of the general elliptic equation, involving five parameters, which has more new solutions and whose degeneracies can lead to special sub equation involving three parameters. As an illustration of the extended Fan method, more new solutions are obtained for three models namely, generalized KdV, Drinfeld-Sokolov system and RLW equation.
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
Properties of positive solutions to a nonlinear parabolic problem
Institute of Scientific and Technical Information of China (English)
2007-01-01
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.
Directory of Open Access Journals (Sweden)
Sima Ziaee
2016-09-01
Full Text Available This article attempts to investigate the effects of small scale parameter on steady state response of functionally graded nano-beams resting on a viscous foundation to super-harmonic excitation. A simple power-law distribution is used to model the variation of material property graded in the thickness direction. The dimensionless partial differential equation of motion is derived by using Euler-Bernoulli beam theory, von-Karman geometric nonlinearity and Eringen’s nonlocal elasticity theory. Using multiple scale method, one can find the governing equations of steady state response of functionally graded nano-beams excited by distributed harmonic force. The small scale parameter (e0a is changed between 0 and 2 to investigate the effects of small scale on steady state response of excited functionally graded nano-beams due to lack of information. The study of the effects of small scale parameter on backbone curves shows that an increase in the small scale parameter often decreases the dimensionless peak response although the type of loading can change the relationship between small scale parameter and the dimensionless peak response.
Exact solutions of certain nonlinear chemotaxis diffusion reaction equations
Indian Academy of Sciences (India)
MISHRA AJAY; KAUSHAL R S; PRASAD AWADHESH
2016-05-01
Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in theconstructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.
Institute of Scientific and Technical Information of China (English)
刘柱彬; 邱彤; 赵劲松
2014-01-01
聚合过程是强放热的非线性过程，这类过程一般存在多稳态现象，且不同的稳态具有不同的局部稳定性。采用气相卧式搅拌釜聚丙烯反应器的Innovene工艺是目前生产聚丙烯最先进的工艺之一。本文开展了该反应器的稳态模拟与多稳态分析研究，对平稳生产、新牌号开发都有着重要的意义。利用Polymer Plus建立了更符合实际且适用于稳定性研究的气相卧式搅拌釜聚丙烯反应器非等温模型，以GPC数据进行聚丙烯反应网络的参数反演。通过灵敏度分析求解系统的多稳态解，通过推理分析的方式判断各个反应区域的稳定性，解决了该问题多稳态研究中的稳定性判断问题，并通过稳定性分析，从本质安全角度出发识别出适于操作的稳态点范围。%The strongly exothermic polymerization process is a nonlinear process which generally have multi-stable phenomenon. Different steady state has different local stability. The Innovene process which uses gas-phase horizontal stirred bed reactor, is one of the most advanced technology for propylene polymerization. A reactor model using Polymer Plus was built. This model is more consistent with actual cases and suitable for steady-state multiplicity analysis. The reaction parameters were obtained by fitting the GPC data of products. The steady-state multiplicity characteristics by the sensitivity analysis of steady-state model were also analyzed. An inferential analysis method for judging the stability of steady-state solutions was proposed, and the intrinsically safe operating range for each reactor area was identified finally. This is an important work for the stable operation and the development of new grades of polypropylene.
Directory of Open Access Journals (Sweden)
Franklin D. Rincón
2015-04-01
Full Text Available This paper introduces a novel steady-state identification (SSI method based on the auto-regressive model with exogenous inputs (ARX. This method allows the SSI with reduced tuning by analyzing the identifiability properties of the system. In particular, the singularity of the model matrices is used as an index for steady-state determination. In this contribution, the novel SSI method is compared to other available techniques, namely the F-like test, wavelet transform and a polynomial-based approach. These methods are implemented for SSI of three different case studies. In the first case, a simulated dataset is used for calibrating the output-based SSI methods. The second case corresponds to a literature nonlinear continuous stirred-tank reactor (CSTR example running at different steady states in which the ARX-based approach is tuned with the available input-output data. Finally, an industrial case with real data of a depropanizer column from PETROBRAS S.A. considering different pieces of equipment is analyzed. The results for a reflux drum case indicate that the wavelet and the F-like test can satisfactorily detect the steady-state periods after careful tuning and when respecting their hypothesis, i.e., smooth data for the wavelet method and the presence of variance in the data for the F-like test. Through a heat exchanger case with different measurement frequencies, we demonstrate the advantages of using the ARX-based method over the other techniques, which include the aspect of online implementation.
Energy Technology Data Exchange (ETDEWEB)
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Hopf and steady state bifurcation analysis in a ratio-dependent predator-prey model
Zhang, Lai; Liu, Jia; Banerjee, Malay
2017-03-01
In this paper, we perform spatiotemporal bifurcation analysis in a ratio-dependent predator-prey model and derive explicit conditions for the existence of non-constant steady states that emerge through steady state bifurcation from related constant steady states. These explicit conditions are numerically verified in details and further compared to those conditions ensuring Turing instability. We find that (1) Turing domain is identical to the parametric domain where there exists only steady state bifurcation, which implies that Turing patterns are stable non-constant steady states, but the opposite is not necessarily true; (2) In non-Turing domain, steady state bifurcation and Hopf bifurcation act in concert to determine the emergent spatial patterns, that is, non-constant steady state emerges through steady state bifurcation but it may be unstable if the destabilising effect of Hopf bifurcation counteracts the stabilising effect of diffusion, leading to non-stationary spatial patterns; (3) Coupling diffusion into an ODE model can significantly enrich population dynamics by inducing alternative non-constant steady states (four different states are observed, two stable and two unstable), in particular when diffusion interacts with different types of bifurcation; (4) Diffusion can promote species coexistence by saving species which otherwise goes to extinction in the absence of diffusion.