Stochastic Evolution Equations Driven by Fractional Noises
2016-11-28
paper is to establish the weak convergence, in the topology of the Skorohod space, of the ν-symmetric Riemann sums for functionals of the fractional...stochastic heat equation with fractional-colored noise: existence of the solution. ALEA Lat. Am. J. Probab. Math . Stat. 4 (2008), 57–87. [8] P. Carmona, Y...Hu: Strong disorder implies strong localization for directed polymers in a random environment. ALEA Lat. Am. J. Probab. Math . Stat. 2 (2006), 217
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Electroweak evolution equations
International Nuclear Information System (INIS)
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
Evolution equations for Killing fields
International Nuclear Information System (INIS)
Coll, B.
1977-01-01
The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein--Maxwell space--times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set
Nonlocal higher order evolution equations
Rossi, Julio D.; Schö nlieb, Carola-Bibiane
2010-01-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Lie symmetries for systems of evolution equations
Paliathanasis, Andronikos; Tsamparlis, Michael
2018-01-01
The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.
PC analysis of stochastic differential equations driven by Wiener noise
Le Maitre, Olivier
2015-03-01
A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.
Optimal Control for Stochastic Delay Evolution Equations
Energy Technology Data Exchange (ETDEWEB)
Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)
2016-08-15
In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.
Subordination principle for fractional evolution equations
Bazhlekova, E.G.
2000-01-01
The abstract Cauchy problem for the fractional evolution equation Daa = Au, a > 0, (1) where A is a closed densely de??ned operator in a Banach space, is investigated. The subordination principle, presented earlier in [J. P r ??u s s, Evolutionary In- tegral Equations and Applications. Birkh??auser,
Advanced functional evolution equations and inclusions
Benchohra, Mouffak
2015-01-01
This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.
Bessaih, Hakima; Efendiev, Yalchin; Maris, Florin
2015-01-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior
Moving interfaces and quasilinear parabolic evolution equations
Prüss, Jan
2016-01-01
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...
Reduced equations of motion for quantum systems driven by diffusive Markov processes.
Sarovar, Mohan; Grace, Matthew D
2012-09-28
The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.
Nonlinear evolution equations having a physical meaning
International Nuclear Information System (INIS)
Nakach, R.
1976-06-01
The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr
Emmy Noether and Linear Evolution Equations
Directory of Open Access Journals (Sweden)
P. G. L. Leach
2013-01-01
Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.
Effective evolution equations from quantum mechanics
Leopold, Nikolai
2018-01-01
The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{−1/2}. At time zero it is assumed that almost all charges a...
PC analysis of stochastic differential equations driven by Wiener noise
Le Maitre, Olivier; Knio, Omar
2015-01-01
A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads
Spatial evolution equation of wind wave growth
Institute of Scientific and Technical Information of China (English)
WANG; Wei; (王; 伟); SUN; Fu; (孙; 孚); DAI; Dejun; (戴德君)
2003-01-01
Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.
Semigroup methods for evolution equations on networks
Mugnolo, Delio
2014-01-01
This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...
Differential equations driven by rough paths with jumps
Friz, Peter K.; Zhang, Huilin
2018-05-01
We develop the rough path counterpart of Itô stochastic integration and differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.
Evolution equations for extended dihadron fragmentation functions
International Nuclear Information System (INIS)
Ceccopieri, F.A.; Bacchetta, A.
2007-03-01
We consider dihadron fragmentation functions, describing the fragmentation of a parton in two unpolarized hadrons, and in particular extended dihadron fragmentation functions, explicitly dependent on the invariant mass, M h , of the hadron pair. We first rederive the known results on M h -integrated functions using Jet Calculus techniques, and then we present the evolution equations for extended dihadron fragmentation functions. Our results are relevant for the analysis of experimental measurements of two-particle-inclusive processes at different energies. (orig.)
Complete integrability of the difference evolution equations
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Ivanov, M.I.; Kulish, P.P.
1980-01-01
The class of exactly solvable nonlinear difference evolution equations (DEE) related to the discrete analog of the one-dimensional Dirac problem L is studied. For this starting from L we construct a special linear non-local operator Λ and obtain the expansions of w and σ 3 deltaw over its eigenfunctions, w being the potential in L. This allows us to obtain compact expressions for the integrals of motion and to prove that these DEE are completely integrable Hamiltonian systems. Moreover, it is shown that there exists a hierarchy of Hamiltonian structures, generated by Λ, and the action-angle variables are explicity calculated. As particular cases the difference analog of the non-linear Schroedinger equation and the modified Korteweg-de-Vries equation are considered. The quantization of these Hamiltonian system through the use of the quantum inverse scattering method is briefly discussed [ru
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.; Baer, M.
2000-01-01
We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast
Existence families, functional calculi and evolution equations
deLaubenfels, Ralph
1994-01-01
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, ...
Critical spaces for quasilinear parabolic evolution equations and applications
Prüss, Jan; Simonett, Gieri; Wilke, Mathias
2018-02-01
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.
Existence of solutions of abstract fractional impulsive semilinear evolution equations
Directory of Open Access Journals (Sweden)
K. Balachandran
2010-01-01
Full Text Available In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.
Decomposition of a hierarchy of nonlinear evolution equations
International Nuclear Information System (INIS)
Geng Xianguo
2003-01-01
The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations
Completely integrable operator evolution equations. II
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)
Transformation properties of the integrable evolution equations
International Nuclear Information System (INIS)
Konopelchenko, B.G.
1981-01-01
Group-theoretical properties of partial differential equations integrable by the inverse scattering transform method are discussed. It is shown that nonlinear transformations typical to integrable equations (symmetry groups, Baecklund-transformations) and these equations themselves are contained in a certain universal nonlinear transformation group. (orig.)
The fundamental solutions for fractional evolution equations of parabolic type
Directory of Open Access Journals (Sweden)
Mahmoud M. El-Borai
2004-01-01
Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.
Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations
International Nuclear Information System (INIS)
Yu Jianping; Sun Yongli
2008-01-01
This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations
Momentum equation for arc-driven rail guns
International Nuclear Information System (INIS)
Batteh, J.H.
1984-01-01
In several models of arc-driven rail guns, the rails are assumed to be infinitely high to simplify the calculation of the electromagnetic fields which appear in the momentum equation for the arc. This assumption leads to overestimates of the arc pressures and accelerations by approximately a factor of 2 for typical rail-gun geometries. In this paper, we develop a simple method for modifying the momentum equation to account for the effect of finite-height rails on the performance of the rail gun and the properties of the arc. The modification is based on an integration of the Lorentz force across the arc cross section at each axial location in the arc. Application of this technique suggests that, for typical rail-gun geometries and moderately long arcs, the momentum equation appropriate for infinite-height rails can be retained provided that the magnetic pressure term in the equation is scaled by a factor which depends on the effective inductance of the gun. The analysis also indicates that the magnetic pressure gradient actually changes sign near the arc/projectile boundary because of the magnetic fields associated with the arc current
Systems of evolution equations and the singular perturbation method
International Nuclear Information System (INIS)
Mika, J.
Several fundamental theorems are presented important for the solution of linear evolution equations in the Banach space. The algorithm is deduced extending the solution of the system of singularly perturbed evolution equations into an asymptotic series with respect to a small positive parameter. The asymptotic convergence is shown of an approximate solution to the accurate solution. Singularly perturbed evolution equations of the resonance type were analysed. The special role is considered of the asymptotic equivalence of P1 equations obtained as the first order approximation if the spherical harmonics method is applied to the linear Boltzmann equation, and the diffusion equations of the linear transport theory where the small parameter approaches zero. (J.B.)
QCD evolution equations for high energy partons in nuclear matter
Kinder-Geiger, Klaus; Geiger, Klaus; Mueller, Berndt
1994-01-01
We derive a generalized form of Altarelli-Parisi equations to decribe the time evolution of parton distributions in a nuclear medium. In the framework of the leading logarithmic approximation, we obtain a set of coupled integro- differential equations for the parton distribution functions and equations for the virtuality (``age'') distribution of partons. In addition to parton branching processes, we take into account fusion and scattering processes that are specific to QCD in medium. Detailed balance between gain and loss terms in the resulting evolution equations correctly accounts for both real and virtual contributions which yields a natural cancellation of infrared divergences.
Lectures on nonlinear evolution equations initial value problems
Racke, Reinhard
2015-01-01
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...
Physical entropy, information entropy and their evolution equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.
Evolution equation for classical and quantum light in turbulence
CSIR Research Space (South Africa)
Roux, FS
2015-06-01
Full Text Available Recently, an infinitesimal propagation equation was derived for the evolution of orbital angular momentum entangled photonic quantum states through turbulence. The authors will discuss its derivation and application within both classical and quantum...
Effective average action for gauge theories and exact evolution equations
International Nuclear Information System (INIS)
Reuter, M.; Wetterich, C.
1993-11-01
We propose a new nonperturbative evolution equation for Yang-Mills theories. It describes the scale dependence of an effective action. The running of the nonabelian gauge coupling in arbitrary dimension is computed. (orig.)
An application of transverse momentum dependent evolution equations in QCD
International Nuclear Information System (INIS)
Ceccopieri, Federico A.; Trentadue, Luca
2008-01-01
The properties and behaviour of the solutions of the recently obtained k t -dependent QCD evolution equations are investigated. When used to reproduce transverse momentum spectra of hadrons in Semi-Inclusive DIS, an encouraging agreement with data is found. The present analysis also supports at the phenomenological level the factorization properties of the Semi-Inclusive DIS cross-sections in terms of k t -dependent distributions. Further improvements and possible developments of the proposed evolution equations are envisaged
On a new series of integrable nonlinear evolution equations
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.
1980-10-01
Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)
Prolongation Structure of Semi-discrete Nonlinear Evolution Equations
International Nuclear Information System (INIS)
Bai Yongqiang; Wu Ke; Zhao Weizhong; Guo Hanying
2007-01-01
Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schroedinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
Comment on connections between nonlinear evolution equations
International Nuclear Information System (INIS)
Fuchssteiner, B.; Hefter, E.F.
1981-01-01
An open problem raised in a recent paper by Chodos is treated. We explain the reason for the interrelation between the conservation laws of the Korteweg-de Vries (KdV) and sine-Gordon equations. We point out that it is due to a corresponding connection between the infinite-dimensional Abelian symmetry groups of these equations. While it has been known for a long time that a Baecklund transformation (in this case the Miura transformation) connects corresponding members of the KdV and the sine-Gordon families, it is quite obvious that no Baecklund transformation can exist between different members of these families. And since the KdV and sine-Gordon equations do not correspond to each other, one cannot expect a Baecklund transformation between them; nevertheless we can give explicit relations between their two-soliton solutions. No inverse scattering techniques are used in this paper
Fermionic covariant prolongation structure theory for supernonlinear evolution equation
International Nuclear Information System (INIS)
Cheng Jipeng; Wang Shikun; Wu Ke; Zhao Weizhong
2010-01-01
We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schroedinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Baecklund transformation.
Hamiltonian structures of some non-linear evolution equations
International Nuclear Information System (INIS)
Tu, G.Z.
1983-06-01
The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)
Diffusion equations and the time evolution of foreign exchange rates
Energy Technology Data Exchange (ETDEWEB)
Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, Universidade de Brasília, Brasília DF 70910-900 (Brazil); Fonseca, Regina C.B. da [Department of Mathematics, Instituto Federal de Goiás, Goiânia GO 74055-110 (Brazil); Gleria, Iram, E-mail: iram@fis.ufal.br [Institute of Physics, Federal University of Alagoas, Brazil, Maceió AL 57072-900 (Brazil)
2013-10-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Diffusion equations and the time evolution of foreign exchange rates
Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram
2013-10-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Diffusion equations and the time evolution of foreign exchange rates
International Nuclear Information System (INIS)
Figueiredo, Annibal; Castro, Marcio T. de; Fonseca, Regina C.B. da; Gleria, Iram
2013-01-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
On the solution of fractional evolution equations
International Nuclear Information System (INIS)
Kilbas, Anatoly A; Pierantozzi, Teresa; Trujillo, Juan J; Vazquez, Luis
2004-01-01
This paper is devoted to the solution of the bi-fractional differential equation ( C D α t u)(t, x) = λ( L D β x u)(t, x) (t>0, -∞ 0 and λ ≠ 0, with the initial conditions lim x→±∞ u(t,x) = 0 u(0+,x)=g(x). Here ( C D α t u)(t, x) is the partial derivative coinciding with the Caputo fractional derivative for 0 L D β x u)(t, x)) is the Liouville partial fractional derivative ( L D β t u)(t, x)) of order β > 0. The Laplace and Fourier transforms are applied to solve the above problem in closed form. The fundamental solution of these problems is established and its moments are calculated. The special case α = 1/2 and β = 1 is presented, and its application is given to obtain the Dirac-type decomposition for the ordinary diffusion equation
International Nuclear Information System (INIS)
Pierantozzi, T.; Vazquez, L.
2005-01-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case
Fitness-driven deactivation in network evolution
International Nuclear Information System (INIS)
Xu, Xin-Jian; Peng, Xiao-Long; Fu, Xin-Chu; Small, Michael
2010-01-01
Individual nodes in evolving real-world networks typically experience growth and decay—that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive ageing mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with a possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, C(k) ∼ k −1 and C ∼ n −1 , where k and n refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and ageing of networks where intrinsic features of individual nodes drive their popularity, and hence degree
Evolution of cooperation driven by incremental learning
Li, Pei; Duan, Haibin
2015-02-01
It has been shown that the details of microscopic rules in structured populations can have a crucial impact on the ultimate outcome in evolutionary games. So alternative formulations of strategies and their revision processes exploring how strategies are actually adopted and spread within the interaction network need to be studied. In the present work, we formulate the strategy update rule as an incremental learning process, wherein knowledge is refreshed according to one's own experience learned from the past (self-learning) and that gained from social interaction (social-learning). More precisely, we propose a continuous version of strategy update rules, by introducing the willingness to cooperate W, to better capture the flexibility of decision making behavior. Importantly, the newly gained knowledge including self-learning and social learning is weighted by the parameter ω, establishing a strategy update rule involving innovative element. Moreover, we quantify the macroscopic features of the emerging patterns to inspect the underlying mechanisms of the evolutionary process using six cluster characteristics. In order to further support our results, we examine the time evolution course for these characteristics. Our results might provide insights for understanding cooperative behaviors and have several important implications for understanding how individuals adjust their strategies under real-life conditions.
On the solution of fractional evolution equations
Energy Technology Data Exchange (ETDEWEB)
Kilbas, Anatoly A [Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk (Belarus); Pierantozzi, Teresa [Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense, E-28040 Madrid (Spain); Trujillo, Juan J [Departamento de Analisis Matematico, Universidad de la Laguna, 38271 La Laguna-Tenerife (Spain); Vazquez, Luis [Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense, E-28040 Madrid (Spain)
2004-03-05
This paper is devoted to the solution of the bi-fractional differential equation ({sup C}D{sup {alpha}}{sub t}u)(t, x) = {lambda}({sup L}D{sup {beta}}{sub x}u)(t, x) (t>0, -{infinity}
Finite difference evolution equations and quantum dynamical semigroups
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1983-12-01
We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)
Periodic feedback stabilization for linear periodic evolution equations
Wang, Gengsheng
2016-01-01
This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.
Almost Periodic Solutions for Impulsive Fractional Stochastic Evolution Equations
Directory of Open Access Journals (Sweden)
Toufik Guendouzi
2014-08-01
Full Text Available In this paper, we consider the existence of square-mean piecewise almost periodic solutions for impulsive fractional stochastic evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, fractional calculus, fixed point technique and stochastic analysis theory and methods adopted directly from deterministic fractional equations. Some known results are improved and generalized.
From BBGKY hierarchy to non-Markovian evolution equations
International Nuclear Information System (INIS)
Gerasimenko, V.I.; Shtyk, V.O.; Zagorodny, A.G.
2009-01-01
The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy for these microscopic distributions and their average values is formulated. The microscopic derivation of the generalized evolution equation for the average value of the microscopic phase density is given, and the non-Markovian generalization of the Fokker-Planck collision integral is proposed
On the evolution equations, solvable through the inverse scattering method
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Khristov, E.Kh.
1979-01-01
The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation
Topological soliton solutions for some nonlinear evolution equations
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Ahmet Bekir
2014-03-01
Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.
Effective evolution equations from many-body quantum mechanics
International Nuclear Information System (INIS)
Benedikter, Niels Patriz
2014-01-01
Systems of interest in physics often consist of a very large number of interacting particles. In certain physical regimes, effective non-linear evolution equations are commonly used as an approximation for making predictions about the time-evolution of such systems. Important examples are Bose-Einstein condensates of dilute Bose gases and degenerate Fermi gases. While the effective equations are well-known in physics, a rigorous justification is very difficult. However, a rigorous derivation is essential to precisely understand the range and the limits of validity and the quality of the approximation. In this thesis, we prove that the time evolution of Bose-Einstein condensates in the Gross-Pitaevskii regime can be approximated by the time-dependent Gross-Pitaevskii equation, a cubic non-linear Schroedinger equation. We then turn to fermionic systems and prove that the evolution of a degenerate Fermi gas can be approximated by the time-dependent Hartree-Fock equation (TDHF) under certain assumptions on the semiclassical structure of the initial data. Finally, we extend the latter result to fermions with relativistic kinetic energy. All our results provide explicit bounds on the error as the number of particles becomes large. A crucial methodical insight on bosonic systems is that correlations can be modeled by Bogolyubov transformations. We construct initial data appropriate for the Gross-Pitaevskii regime using a Bogolyubov transformation acting on a coherent state, which amounts to studying squeezed coherent states. As a crucial insight for fermionic systems, we point out a semiclassical structure in states close to the ground state of fermions in a trap. As a convenient language for studying the dynamics of fermionic systems, we use particle-hole transformations.
Spectral transform and solvability of nonlinear evolution equations
International Nuclear Information System (INIS)
Degasperis, A.
1979-01-01
These lectures deal with an exciting development of the last decade, namely the resolving method based on the spectral transform which can be considered as an extension of the Fourier analysis to nonlinear evolution equations. Since many important physical phenomena are modeled by nonlinear partial wave equations this method is certainly a major breakthrough in mathematical physics. We follow the approach, introduced by Calogero, which generalizes the usual Wronskian relations for solutions of a Sturm-Liouville problem. Its application to the multichannel Schroedinger problem will be the subject of these lectures. We will focus upon dynamical systems described at time t by a multicomponent field depending on one space coordinate only. After recalling the Fourier technique for linear evolution equations we introduce the spectral transform method taking the integral equations of potential scattering as an example. The second part contains all the basic functional relationships between the fields and their spectral transforms as derived from the Wronskian approach. In the third part we discuss a particular class of solutions of nonlinear evolution equations, solitons, which are considered by many physicists as a first step towards an elementary particle theory, because of their particle-like behaviour. The effect of the polarization time-dependence on the motion of the soliton is studied by means of the corresponding spectral transform, leading to new concepts such as the 'boomeron' and the 'trappon'. The rich dynamic structure is illustrated by a brief report on the main results of boomeron-boomeron and boomeron-trappon collisions. In the final section we discuss further results concerning important properties of the solutions of basic nonlinear equations. We introduce the Baecklund transform for the special case of scalar fields and demonstrate how it can be used to generate multisoliton solutions and how the conservation laws are obtained. (HJ)
Data-driven discovery of partial differential equations.
Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan
2017-04-01
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
Allen, Rebecca; Reis, Tim; Sun, Shuyu
2013-01-01
-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE
Existence results for impulsive evolution differential equations with state-dependent delay
Eduardo Hernandez M.; Rathinasamy Sakthivel; Sueli Tanaka Aki
2008-01-01
We study the existence of mild solution for impulsive evolution abstract differential equations with state-dependent delay. A concrete application to partial delayed differential equations is considered.
Evolution equations for connected and disconnected sea parton distributions
Liu, Keh-Fei
2017-08-01
It has been revealed from the path-integral formulation of the hadronic tensor that there are connected sea and disconnected sea partons. The former is responsible for the Gottfried sum rule violation primarily and evolves the same way as the valence. Therefore, the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations can be extended to accommodate them separately. We discuss its consequences and implications vis-á-vis lattice calculations.
BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows
Shaing, K. C.
2010-07-01
A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.
Garno, Joshua; Ouellet, Frederick; Koneru, Rahul; Balachandar, Sivaramakrishnan; Rollin, Bertrand
2017-11-01
An analytic model to describe the hydrodynamic forces on an explosively driven particle is not currently available. The Maxey-Riley-Gatignol (MRG) particle force equation generalized for compressible flows is well-studied in shock-tube applications, and captures the evolution of particle force extracted from controlled shock-tube experiments. In these experiments only the shock-particle interaction was examined, and the effects of the contact line were not investigated. In the present work, the predictive capability of this model is considered for the case where a particle is explosively ejected from a rigid barrel into ambient air. Particle trajectory information extracted from simulations is compared with experimental data. This configuration ensures that both the shock and contact produced by the detonation will influence the motion of the particle. The simulations are carried out using a finite volume, Euler-Lagrange code using the JWL equation of state to handle the explosive products. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program,under Contract No. DE-NA0002378.
Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas
International Nuclear Information System (INIS)
Drallos, P.J.; Riley, M.E.
1995-01-01
We present a method for the numerical solution of the Boltzmann equation (BE) describing plasma electrons. We apply the method to a capacitively-coupled, radio-frequency-driven He discharge in parallel-plate (quasi-1D) geometry which contains time scales for physical processes spanning six orders of magnitude. Our BE solution procedure uses the method of characteristics for the Vlasov operator with interpolation in phase space at early time, allowing storage of the distribution function on a fixed phase-space grid. By alternating this BE method with a fluid description of the electrons, or with a novel time-cycle-average equation method, we compute the periodic steady state of a He plasma by time evolution from startup conditions. We find that the results compare favorably with measured current-voltage, plasma density, and ''cited state densities in the ''GEC'' Reference Cell. Our atomic He model includes five levels (some are summed composites), 15 electronic transitions, radiation trapping, and metastable-metastable collisions
Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas
Energy Technology Data Exchange (ETDEWEB)
Drallos, P.J.; Riley, M.E.
1995-01-01
We present a method for the numerical solution of the Boltzmann equation (BE) describing plasma electrons. We apply the method to a capacitively-coupled, radio-frequency-driven He discharge in parallel-plate (quasi-1D) geometry which contains time scales for physical processes spanning six orders of magnitude. Our BE solution procedure uses the method of characteristics for the Vlasov operator with interpolation in phase space at early time, allowing storage of the distribution function on a fixed phase-space grid. By alternating this BE method with a fluid description of the electrons, or with a novel time-cycle-average equation method, we compute the periodic steady state of a He plasma by time evolution from startup conditions. We find that the results compare favorably with measured current-voltage, plasma density, and ``cited state densities in the ``GEC`` Reference Cell. Our atomic He model includes five levels (some are summed composites), 15 electronic transitions, radiation trapping, and metastable-metastable collisions.
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
Directory of Open Access Journals (Sweden)
Malinowski Marek T.
2015-01-01
Full Text Available We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors. The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect to data of the equation is also presented. We consider equations driven by semimartingale Z and equations driven by processes A;M from decomposition of Z, where A is a process of finite variation and M is a local martingale. These equations are not equivalent. Finally, we show that the analysis of the set-valued stochastic integral equations can be extended to a case of fuzzy stochastic integral equations driven by semimartingales under Osgood type condition. To obtain our results we use the set-valued and fuzzy Maruyama type approximations and Bihari’s inequality.
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-06-18
We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.
Operations involving momentum variables in non-Hamiltonian evolution equations
International Nuclear Information System (INIS)
Benatti, F.; Ghirardi, G.C.; Rimini, A.; Weber, T.
1988-02-01
Non-Hamiltonian evolution equations have been recently considered for the description of various physical processes. Among this type of equations the class which has been more extensively studied is the one usually referred to as Quantum Dynamical Semigroup equations (QDS). In particular an equation of the QDS type has been considered as the basis for a model, called Quantum Mechanics with Spontaneous Localization (QMSL), which has been shown to exhibit some very interesting features allowing to overcome most of the conceptual difficulties of standard quantum theory, QMSL assumes a modification of the pure Schroedinger evolution by assuming the occurrence, at random times, of stochastic processes for the wave function corresponding formally to approximate position measurements. In this paper, we investigate the consequences of modifying and/or enlarging the class of the considered stochastic processes, by considering the spontaeous occurrence of approximate momentum and of simultaneous position and momentum measurements. It is shown that the considered changes in the elementary processes have unacceptable consequences. In particular they either lead to drastic modifications in the dynamics of microsystems or are completely useless from the point of view of the conceptual advantages that one was trying to get from QMSL. The present work supports therefore the idea that QMSL, as originally formulated, can be taken as the basic scheme for the generalizations which are still necessary in order to make it appropriate for the description of systems of identical particles and to meet relativistic requirements. (author). 14 refs
Operations involving momentum variables in non-Hamiltonian evolution equation
International Nuclear Information System (INIS)
Benatti, F.; Ghirardi, G.C.; Weber, T.; Rimini, A.
1988-01-01
Non-Hamiltonian evolution equations have been recently considered for the description of various physical processes. Among these types of equations the class which has been more extensively studied is the one usually referred to as quantum-dynamical semi-group equations (QDS). In particular an equation of the QDS type has been considered as the basis for a model, called quantum mechanics with spontaneous localization (QMSL), which has been shown to exhibit some very interesting features allowing us to overcome most of the conceptual difficulties of standard quantum theory. QMSL assumes a modification of the pure Schroedinger evolution by assuming the occurrence, at random times, of stochastic processes for the wave function corresponding formally to approximate position measurements. In this paper the consequences of modifying and/or enlarging the class of the considered stochastic processes, by considering the spontaneous occurrence of approximate momentum and of simultaneous position and momentum measurements, are investigated. It is shown that the considered changes in the elementary processes have unacceptable consequences. In particular they either lead to drastic modification in the dynamics of microsystems or are completely useless from the point of view of the conceptual advantages that one was trying to get from QMSL. The present work supports therefore the idea that QMSL, as originally formulated, can be taken as the basic scheme for the generalizations which are still necessary in order to make it appropriate for the description of systems of identical particles and to meet relativistic requirements
DYNAMICALLY DRIVEN EVOLUTION OF THE INTERSTELLAR MEDIUM IN M51
International Nuclear Information System (INIS)
Koda, Jin; Scoville, Nick; Potts, Ashley E.; Carpenter, John M.; Corder, Stuartt A.; Patience, Jenny; Sargent, Anneila I.; Sawada, Tsuyoshi; La Vigne, Misty A.; Vogel, Stuart N.; White, Stephen M.; Zauderer, B. Ashley; Pound, Marc W.; Wright, Melvyn C. H.; Plambeck, Richard L.; Bock, Douglas C. J.; Hawkins, David; Hodges, Mark; Lamb, James W.; Kemball, Athol
2009-01-01
Massive star formation occurs in giant molecular clouds (GMCs); an understanding of the evolution of GMCs is a prerequisite to develop theories of star formation and galaxy evolution. We report the highest-fidelity observations of the grand-design spiral galaxy M51 in carbon monoxide (CO) emission, revealing the evolution of GMCs vis-a-vis the large-scale galactic structure and dynamics. The most massive GMCs (giant molecular associations (GMAs)) are first assembled and then broken up as the gas flow through the spiral arms. The GMAs and their H 2 molecules are not fully dissociated into atomic gas as predicted in stellar feedback scenarios, but are fragmented into smaller GMCs upon leaving the spiral arms. The remnants of GMAs are detected as the chains of GMCs that emerge from the spiral arms into interarm regions. The kinematic shear within the spiral arms is sufficient to unbind the GMAs against self-gravity. We conclude that the evolution of GMCs is driven by large-scale galactic dynamics-their coagulation into GMAs is due to spiral arm streaming motions upon entering the arms, followed by fragmentation due to shear as they leave the arms on the downstream side. In M51, the majority of the gas remains molecular from arm entry through the interarm region and into the next spiral arm passage.
How Evolution May Work Through Curiosity-Driven Developmental Process.
Oudeyer, Pierre-Yves; Smith, Linda B
2016-04-01
Infants' own activities create and actively select their learning experiences. Here we review recent models of embodied information seeking and curiosity-driven learning and show that these mechanisms have deep implications for development and evolution. We discuss how these mechanisms yield self-organized epigenesis with emergent ordered behavioral and cognitive developmental stages. We describe a robotic experiment that explored the hypothesis that progress in learning, in and for itself, generates intrinsic rewards: The robot learners probabilistically selected experiences according to their potential for reducing uncertainty. In these experiments, curiosity-driven learning led the robot learner to successively discover object affordances and vocal interaction with its peers. We explain how a learning curriculum adapted to the current constraints of the learning system automatically formed, constraining learning and shaping the developmental trajectory. The observed trajectories in the robot experiment share many properties with those in infant development, including a mixture of regularities and diversities in the developmental patterns. Finally, we argue that such emergent developmental structures can guide and constrain evolution, in particular with regard to the origins of language. Copyright © 2016 Cognitive Science Society, Inc.
Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2004-01-01
-called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...
Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation
Barashenkov, I V
2003-01-01
The well-known effect of the linear damping on the moving nonlinear Schrodinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable.
Travelling solitons in the damped driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.
2003-01-01
The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable
Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces
Ruess, W. M.; Phong, V. Q.
Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.; Stoffa, Paul L.
2010-01-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.
2010-07-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Higher order Lie-Baecklund symmetries of evolution equations
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Roy Chowdhury, K.; Paul, S.
1983-10-01
We have considered in detail the analysis of higher order Lie-Baecklund symmetries for some representative nonlinear evolution equations. Until now all such symmetry analyses have been restricted only to the first order of the infinitesimal parameter. But the existence of Baecklund transformation (which can be shown to be an overall sum of higher order Lie-Baecklund symmetries) makes it necessary to search for such higher order Lie-Baecklund symmetries directly without taking recourse to the Baecklund transformation or inverse scattering technique. (author)
Nonlinear evolution equations for waves in random media
International Nuclear Information System (INIS)
Pelinovsky, E.; Talipova, T.
1994-01-01
The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs
Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation
Directory of Open Access Journals (Sweden)
V. O. Vakhnenko
2016-01-01
Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.
Network evolution driven by dynamics applied to graph coloring
International Nuclear Information System (INIS)
Wu Jian-She; Li Li-Guang; Yu Xin; Jiao Li-Cheng; Wang Xiao-Hua
2013-01-01
An evolutionary network driven by dynamics is studied and applied to the graph coloring problem. From an initial structure, both the topology and the coupling weights evolve according to the dynamics. On the other hand, the dynamics of the network are determined by the topology and the coupling weights, so an interesting structure-dynamics co-evolutionary scheme appears. By providing two evolutionary strategies, a network described by the complement of a graph will evolve into several clusters of nodes according to their dynamics. The nodes in each cluster can be assigned the same color and nodes in different clusters assigned different colors. In this way, a co-evolution phenomenon is applied to the graph coloring problem. The proposed scheme is tested on several benchmark graphs for graph coloring
Neutron star evolutions using tabulated equations of state with a new execution model
Anderson, Matthew; Kaiser, Hartmut; Neilsen, David; Sterling, Thomas
2012-03-01
The addition of nuclear and neutrino physics to general relativistic fluid codes allows for a more realistic description of hot nuclear matter in neutron star and black hole systems. This additional microphysics requires that each processor have access to large tables of data, such as equations of state, and in large simulations the memory required to store these tables locally can become excessive unless an alternative execution model is used. In this talk we present neutron star evolution results obtained using a message driven multi-threaded execution model known as ParalleX as an alternative to using a hybrid MPI-OpenMP approach. ParalleX provides the user a new way of computation based on message-driven flow control coordinated by lightweight synchronization elements which improves scalability and simplifies code development. We present the spectrum of radial pulsation frequencies for a neutron star with the Shen equation of state using the ParalleX execution model. We present performance results for an open source, distributed, nonblocking ParalleX-based tabulated equation of state component capable of handling tables that may even be too large to read into the memory of a single node.
Solving Partial Differential Equations Using a New Differential Evolution Algorithm
Directory of Open Access Journals (Sweden)
Natee Panagant
2014-01-01
Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.
Bessaih, Hakima
2015-04-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.
Symbolic computation of exact solutions for a nonlinear evolution equation
International Nuclear Information System (INIS)
Liu Yinping; Li Zhibin; Wang Kuncheng
2007-01-01
In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here
Loss of Energy Concentration in Nonlinear Evolution Beam Equations
Garrione, Maurizio; Gazzola, Filippo
2017-12-01
Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation u_{tt} + u_{xxxx} + f(u)= g(x, t) in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities f and for some forcing terms g, highlighting some of their structural properties and performing some numerical simulations.
An x-space analysis of evolution equations: Soffer's inequality and the non-forward evolution
International Nuclear Information System (INIS)
Cafarella, Alessandro; Coriano, Claudio; Guzzi, Marco
2003-01-01
We analyze the use of algorithms based in x-space for the solution of renormalization group equations of DGLAP-type and test their consistency by studying bounds among partons distributions - in our specific case Soffer's inequality and the perturbative behaviour of the nucleon tensor charge - to next-to-leading order in QCD. A discussion of the perturbative resummation implicit in these expansions using Mellin moments is included. We also comment on the (kinetic) proof of positivity of the evolution of h1, using a kinetic analogy and illustrate the extension of the algorithm to the evolution of generalized parton distributions. We prove positivity of the non-forward evolution in a special case and illustrate a Fokker-Planck approximation to it. (author)
International Nuclear Information System (INIS)
Alvarez-Estrada, R.F.
1979-01-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly
The presentation of explicit analytical solutions of a class of nonlinear evolution equations
International Nuclear Information System (INIS)
Feng Jinshun; Guo Mingpu; Yuan Deyou
2009-01-01
In this paper, we introduce a function set Ω m . There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ω m . A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.
Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
International Nuclear Information System (INIS)
Ebaid, A.
2007-01-01
Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method
A data-driven alternative to the fractional Fokker–Planck equation
International Nuclear Information System (INIS)
Pressé, Steve
2015-01-01
Anomalous diffusion processes are ubiquitous in biology and arise in the transport of proteins, vesicles and other particles. Such anomalously diffusive behavior is attributed to a number of factors within the cell including heterogeneous environments, active transport processes and local trapping/binding. There are a number of microscopic principles—such as power law jump size and/or waiting time distributions—from which the fractional Fokker–Planck equation (FFPE) can be derived and used to provide mechanistic insight into the origins of anomalous diffusion. On the other hand, it is fair to ask if other microscopic principles could also have given rise to the evolution of an observed density profile that appears to be well fit by an FFPE. Here we discuss another possible mechanistic alternative that can give rise to densities like those generated by FFPEs. Rather than to fit a density (or concentration profile) using a solution to the spatial FFPE, we reconstruct the profile generated by an FFPE using a regular FPE with a spatial and time-dependent force. We focus on the special case of the spatial FFPE for superdiffusive processes. This special case is relevant to, for example, active transport in a biological context. We devise a prescription for extracting such forces on synthetically generated data and provide an interpretation to the forces extracted. In particular, the time-dependence of forces could tell us about ATP depletion or changes in the cell's metabolic activity. Modeling anomalous behavior with normal diffusion driven by these effective forces yields an alternative mechanistic picture that, ultimately, could help motivate future experiments. (paper)
Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation
Energy Technology Data Exchange (ETDEWEB)
Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel
2009-06-15
A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)
Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation
International Nuclear Information System (INIS)
Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel
2009-01-01
A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)
Wave functions, evolution equations and evolution kernels form light-ray operators of QCD
International Nuclear Information System (INIS)
Mueller, D.; Robaschik, D.; Geyer, B.; Dittes, F.M.; Horejsi, J.
1994-01-01
The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light-ray operators. These operators appear as large momentum limit of non-local hardron operators or as summed up local operators in light-cone expansions. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli-Parisi and the Brodsky-Lepage kernels) are derived and explicitly checked for the existing two-loop calculations of QCD. Technical basis of these resluts are support and analytically properties of the anomalous dimensions of light-ray operators obtained with the help of the α-representation of Green's functions. (orig.)
Laser driven shock wave experiments for equation of state studies at megabar pressures
Pant, H C; Senecha, V K; Bandyopadhyay, S; Rai, V N; Khare, P; Bhat, R K; Gupta, N K; Godwal, B K
2002-01-01
We present the results from laser driven shock wave experiments for equation of state (EOS) studies of gold metal. An Nd:YAG laser chain (2 J, 1.06 mu m wavelength, 200 ps pulse FWHM) is used to generate shocks in planar Al foils and Al + Au layered targets. The EOS of gold in the pressure range of 9-13 Mbar is obtained using the impedance matching technique. The numerical simulations performed using the one-dimensional radiation hydrodynamic code support the experimental results. The present experimental data show remarkable agreement with the existing standard EOS models and with other experimental data obtained independently using laser driven shock wave experiments.
International Nuclear Information System (INIS)
Eichmann, U.A.; Draayer, J.P.; Ludu, A.
2002-01-01
A potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves reduction of a third-order partial differential equation to a first-order ordinary differential equation. The potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation. In particular, the paper deals with the so-called K(n, m) equations. Starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation. As a result, e.g., all equations with linear dispersion join the same equivalence class with the Korteweg-deVries equation being its representative, and all soliton solutions of higher order nonlinear equations are thus equivalent to the KdV soliton. Certain equations with both linear and quadratic dispersions can also be treated within this equivalence class. (author)
Symplectic and Hamiltonian structures of nonlinear evolution equations
International Nuclear Information System (INIS)
Dorfman, I.Y.
1993-01-01
A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium
International Nuclear Information System (INIS)
Beretta, G.P.
1986-01-01
This paper addresses a mathematical problem relevant to the question of nonequilibrium and irreversibility, namely, that of ''designing'' a general evolution equation capable of describing irreversible but conservative relaxtion towards equilibrium. The objective is to present an interesting mathematical solution to this design problem, namely, a new nonlinear evolution equation that satisfies a set of very stringent relevant requirements. Three different frameworks are defined from which the new equation could be adopted, with entirely different interpretations. Some useful well-known mathematics involving Gram determinants are presented and a nonlinear evolution equation is given which meets the stringent design specifications
Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations
International Nuclear Information System (INIS)
Li Jina; Zhang Shunli
2008-01-01
We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauchy problems for systems of ordinary differential equations (ODEs). We classify a class of fourth-order evolution equations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to show the main reduction procedure. These reductions cannot be derived within the framework of the standard Lie approach, which hints that the technique presented here is something essential for the dimensional reduction of evolution equations
Equations of State: Gateway to Planetary Origin and Evolution (Invited)
Melosh, J.
2013-12-01
Research over the past decades has shown that collisions between solid bodies govern many crucial phases of planetary origin and evolution. The accretion of the terrestrial planets was punctuated by planetary-scale impacts that generated deep magma oceans, ejected primary atmospheres and probably created the moons of Earth and Pluto. Several extrasolar planetary systems are filled with silicate vapor and condensed 'tektites', probably attesting to recent giant collisions. Even now, long after the solar system settled down from its violent birth, a large asteroid impact wiped out the dinosaurs, while other impacts may have played a role in the origin of life on Earth and perhaps Mars, while maintaining a steady exchange of small meteorites between the terrestrial planets and our moon. Most of these events are beyond the scale at which experiments are possible, so that our main research tool is computer simulation, constrained by the laws of physics and the behavior of materials during high-speed impact. Typical solar system impact velocities range from a few km/s in the outer solar system to 10s of km/s in the inner system. Extrasolar planetary systems expand that range to 100s of km/sec typical of the tightly clustered planetary systems now observed. Although computer codes themselves are currently reaching a high degree of sophistication, we still rely on experimental studies to determine the Equations of State (EoS) of materials critical for the correct simulation of impact processes. The recent expansion of the range of pressures available for study, from a few 100 GPa accessible with light gas guns up to a few TPa from current high energy accelerators now opens experimental access to the full velocity range of interest in our solar system. The results are a surprise: several groups in both the USA and Japan have found that silicates and even iron melt and vaporize much more easily in an impact than previously anticipated. The importance of these findings is
Traveling solitary wave solutions to evolution equations with nonlinear terms of any order
International Nuclear Information System (INIS)
Feng Zhaosheng
2003-01-01
Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...
International Nuclear Information System (INIS)
Barth, Andrea; Lang, Annika
2012-01-01
In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, càdlàg, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L 2 and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler–Maruyama approximation. Finally, simulations complete the paper.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Directory of Open Access Journals (Sweden)
Xiao-Li Ding
2018-01-01
Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Application of Exp-function method for (2 + 1)-dimensional nonlinear evolution equations
International Nuclear Information System (INIS)
Bekir, Ahmet; Boz, Ahmet
2009-01-01
In this paper, the Exp-function method is used to construct solitary and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. (2 + 1)-dimensional breaking soliton (Calogero) equation, modified Zakharov-Kuznetsov and Konopelchenko-Dubrovsky equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.
Energy Technology Data Exchange (ETDEWEB)
Balanov, A.G.; Janson, N.B. E-mail: n.janson@lancaster.ac.uk; McClintock, P.V.E.; Tucker, R.W.; Wang, C.H.T
2003-01-01
Using techniques from dynamical systems analysis we explore numerically the solution space, under parametric variation, of a neutral differential delay equation that arises naturally in the Cosserat description of torsional waves on a driven drill-string.
International Nuclear Information System (INIS)
Balanov, A.G.; Janson, N.B.; McClintock, P.V.E.; Tucker, R.W.; Wang, C.H.T.
2003-01-01
Using techniques from dynamical systems analysis we explore numerically the solution space, under parametric variation, of a neutral differential delay equation that arises naturally in the Cosserat description of torsional waves on a driven drill-string
Nonlinear evolution equations and Painlevé test
Steeb, Willi-Hans
1988-01-01
This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlevé test, Painlevé property and integrability. Both ordinary differential equations and partial differential equations are considered.
On an improved method for solving evolution equations of higher ...
African Journals Online (AJOL)
In this paper we introduce a new algebraic procedure to compute new classes of solutions of (1+1)-nonlinear partial differential equations (nPDEs) both of physical and technical relevance. The basic assumption is that the unknown solution(s) of the nPDE under consideration satisfy an ordinary differential equation (ODE) of ...
Laser driven shock wave experiments for equation of state studies at megabar pressures
International Nuclear Information System (INIS)
Pant, H C; Shukla, M; Senecha, V K; Bandyopadhyay, S; Rai, V N; Khare, P; Bhat, R K; Gupta, N K; Godwal, B K
2002-01-01
We present the results from laser driven shock wave experiments for equation of state (EOS) studies of gold metal. An Nd:YAG laser chain (2 J, 1.06 μm wavelength, 200 ps pulse FWHM) is used to generate shocks in planar Al foils and Al + Au layered targets. The EOS of gold in the pressure range of 9-13 Mbar is obtained using the impedance matching technique. The numerical simulations performed using the one-dimensional radiation hydrodynamic code support the experimental results. The present experimental data show remarkable agreement with the existing standard EOS models and with other experimental data obtained independently using laser driven shock wave experiments
Xiao-Li Ding; Juan J. Nieto
2018-01-01
In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...
An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
International Nuclear Information System (INIS)
Rinne, Oliver
2010-01-01
We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational cost. The formulation is based on an earlier axisymmetric evolution scheme, adapted to time slices of constant mean curvature. Ideas from a previous study by Moncrief and the author are applied in order to regularize the formally singular evolution equations at future null infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime are obtained, including a gravitational perturbation. The Bondi news function is evaluated at future null infinity.
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
Allen, Rebecca
2013-01-01
The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently
The Liouville equation for flavour evolution of neutrinos and neutrino wave packets
Energy Technology Data Exchange (ETDEWEB)
Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de [Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany)
2016-12-01
We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over a trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.
Gas-evolution oscillators. 10. A model based on a delay equation
Energy Technology Data Exchange (ETDEWEB)
Bar-Eli, K.; Noyes, R.M. [Univ. of Oregon, Eugene, OR (United States)
1992-09-17
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas.
Gas-evolution oscillators. 10. A model based on a delay equation
International Nuclear Information System (INIS)
Bar-Eli, K.; Noyes, R.M.
1992-01-01
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
1Computer Engineering Technique Department, Al-Rafidain University College, Baghdad, ... applied to extract solutions are tan–cot method and functional variable approaches. ... Consider the nonlinear partial differential equation in the form.
Evolution of human-driven fire regimes in Africa
CSIR Research Space (South Africa)
Archibald, S
2012-01-01
Full Text Available stream_source_info Archibald_2012.pdf.txt stream_content_type text/plain stream_size 6587 Content-Encoding ISO-8859-1 stream_name Archibald_2012.pdf.txt Content-Type text/plain; charset=ISO-8859-1 The evolution of human...-tropical countries. re j human evolution j Africa j savanna j human ignition F ire has been a part of the earth system for billions of years(?) but recently - within the last million years at most - humans have provided a new and di erent source of ignition...
Analytic treatment of nonlinear evolution equations using first ...
Indian Academy of Sciences (India)
1. — journal of. July 2012 physics pp. 3–17. Analytic treatment of nonlinear evolution ... Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics, ... (2.2) is integrated where integration constants are considered zeros.
Phase-space formalism: Operational calculus and solution of evolution equations in phase-space
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.
1995-05-01
Phase-space formulation of physical problems offers conceptual and practical advantages. A class of evolution type equations, describing the time behaviour of a physical system, using an operational formalism useful to handle time ordering problems has been described. The methods proposed generalize the algebraic ordering techniques developed to deal with the ordinary Schroedinger equation, and how they are taylored suited to treat evolution problems both in classical and quantum dynamics has been studied
Preservation of support and positivity for solutions of degenerate evolution equations
International Nuclear Information System (INIS)
Ambrose, David M; Wright, J Douglas
2010-01-01
We prove that sufficiently smooth solutions of equations of a certain class have two interesting properties. These evolution equations are in a sense degenerate, in that every term on the right-hand side of the evolution equation has either the unknown or its first spatial derivative as a factor. We first find a conserved quantity for the equation: the measure of the set on which the solution is non-zero. Second, we show that solutions which are initially non-negative remain non-negative for all times. These properties rely heavily upon the degeneracy of the leading order term. When the equation is more degenerate, we are able to prove that there are additional conserved quantities: the measure of the set on which the solution is positive and the measure of the set on which the solution is negative. To illustrate these results, we give examples of equations with nonlinear dispersion which have solutions in spaces with sufficient regularity to satisfy the hypotheses of the support and positivity theorems. An important family of equations with nonlinear dispersion are the Rosenau–Hyman compacton equations; there is no existence theory yet for these equations, but the known solutions of the compacton equations are of lower regularity than is needed for the preceding theorems. We prove an additional positivity theorem which applies to solutions of the same family of equations in a function space which includes some solutions of compacton equations
Zhang, W.; Wang, S.; Ma, Z. W.
2017-06-01
The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with f c d = 0.01 and δ c d < 0.04 , the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.
Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains
Adler, V. E.
2018-04-01
We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.
Solving nonlinear evolution equation system using two different methods
Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.
2015-12-01
This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.
Algebraic models for the hierarchy structure of evolution equations at small x
International Nuclear Information System (INIS)
Rembiesa, P.; Stasto, A.M.
2005-01-01
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit
Exact solutions for nonlinear evolution equations using Exp-function method
International Nuclear Information System (INIS)
Bekir, Ahmet; Boz, Ahmet
2008-01-01
In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations
Recombination-Driven Genome Evolution and Stability of Bacterial Species.
Dixit, Purushottam D; Pang, Tin Yau; Maslov, Sergei
2017-09-01
While bacteria divide clonally, horizontal gene transfer followed by homologous recombination is now recognized as an important contributor to their evolution. However, the details of how the competition between clonality and recombination shapes genome diversity remains poorly understood. Using a computational model, we find two principal regimes in bacterial evolution and identify two composite parameters that dictate the evolutionary fate of bacterial species. In the divergent regime, characterized by either a low recombination frequency or strict barriers to recombination, cohesion due to recombination is not sufficient to overcome the mutational drift. As a consequence, the divergence between pairs of genomes in the population steadily increases in the course of their evolution. The species lacks genetic coherence with sexually isolated clonal subpopulations continuously formed and dissolved. In contrast, in the metastable regime, characterized by a high recombination frequency combined with low barriers to recombination, genomes continuously recombine with the rest of the population. The population remains genetically cohesive and temporally stable. Notably, the transition between these two regimes can be affected by relatively small changes in evolutionary parameters. Using the Multi Locus Sequence Typing (MLST) data, we classify a number of bacterial species to be either the divergent or the metastable type. Generalizations of our framework to include selection, ecologically structured populations, and horizontal gene transfer of nonhomologous regions are discussed as well. Copyright © 2017 by the Genetics Society of America.
Evolution of cooperation driven by social-welfare-based migration
Li, Yan; Ye, Hang; Zhang, Hong
2016-03-01
Individuals' migration behavior may play a significant role in the evolution of cooperation. In reality, individuals' migration behavior may depend on their perceptions of social welfare. To study the relationship between social-welfare-based migration and the evolution of cooperation, we consider an evolutionary prisoner's dilemma game (PDG) in which an individual's migration depends on social welfare but not on the individual's own payoff. By introducing three important social welfare functions (SWFs) that are commonly studied in social science, we find that social-welfare-based migration can promote cooperation under a wide range of parameter values. In addition, these three SWFs have different effects on cooperation, especially through the different spatial patterns formed by migration. Because the relative efficiency of the three SWFs will change if the parameter values are changed, we cannot determine which SWF is optimal for supporting cooperation. We also show that memory capacity, which is needed to evaluate individual welfare, may affect cooperation levels in opposite directions under different SWFs. Our work should be helpful for understanding the evolution of human cooperation and bridging the chasm between studies of social preferences and studies of social cooperation.
PROTOPLANETARY DISK HEATING AND EVOLUTION DRIVEN BY SPIRAL DENSITY WAVES
Energy Technology Data Exchange (ETDEWEB)
Rafikov, Roman R., E-mail: rrr@ias.edu [Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States)
2016-11-10
Scattered light imaging of protoplanetary disks often reveals prominent spiral arms, likely excited by massive planets or stellar companions. Assuming that these arms are density waves, evolving into spiral shocks, we assess their effect on the thermodynamics, accretion, and global evolution of the disk. We derive analytical expressions for the direct (irreversible) heating, angular momentum transport, and mass accretion rate induced by disk shocks of arbitrary amplitude. These processes are very sensitive to the shock strength. We show that waves of moderate strength (density jump at the shock ΔΣ/Σ ∼ 1) result in negligible disk heating (contributing at the ∼1% level to the energy budget) in passive, irradiated protoplanetary disks on ∼100 au scales, but become important within several au. However, shock heating is a significant (or even dominant) energy source in disks of cataclysmic variables, stellar X-ray binaries, and supermassive black hole binaries, heated mainly by viscous dissipation. Mass accretion induced by the spiral shocks is comparable to (or exceeds) the mass inflow due to viscous stresses. Protoplanetary disks featuring prominent global spirals must be evolving rapidly, in ≲0.5 Myr at ∼100 au. A direct upper limit on the evolution timescale can be established by measuring the gravitational torque due to the spiral arms from the imaging data. We find that, regardless of their origin, global spiral waves must be important agents of the protoplanetary disk evolution. They may serve as an effective mechanism of disk dispersal and could be related to the phenomenon of transitional disks.
PROTOPLANETARY DISK HEATING AND EVOLUTION DRIVEN BY SPIRAL DENSITY WAVES
International Nuclear Information System (INIS)
Rafikov, Roman R.
2016-01-01
Scattered light imaging of protoplanetary disks often reveals prominent spiral arms, likely excited by massive planets or stellar companions. Assuming that these arms are density waves, evolving into spiral shocks, we assess their effect on the thermodynamics, accretion, and global evolution of the disk. We derive analytical expressions for the direct (irreversible) heating, angular momentum transport, and mass accretion rate induced by disk shocks of arbitrary amplitude. These processes are very sensitive to the shock strength. We show that waves of moderate strength (density jump at the shock ΔΣ/Σ ∼ 1) result in negligible disk heating (contributing at the ∼1% level to the energy budget) in passive, irradiated protoplanetary disks on ∼100 au scales, but become important within several au. However, shock heating is a significant (or even dominant) energy source in disks of cataclysmic variables, stellar X-ray binaries, and supermassive black hole binaries, heated mainly by viscous dissipation. Mass accretion induced by the spiral shocks is comparable to (or exceeds) the mass inflow due to viscous stresses. Protoplanetary disks featuring prominent global spirals must be evolving rapidly, in ≲0.5 Myr at ∼100 au. A direct upper limit on the evolution timescale can be established by measuring the gravitational torque due to the spiral arms from the imaging data. We find that, regardless of their origin, global spiral waves must be important agents of the protoplanetary disk evolution. They may serve as an effective mechanism of disk dispersal and could be related to the phenomenon of transitional disks.
Evolution equation for the shape function in the parton model approach to inclusive B decays
International Nuclear Information System (INIS)
Baek, Seungwon; Lee, Kangyoung
2005-01-01
We derive an evolution equation for the shape function of the b quark in an analogous way to the Altarelli-Parisi equation by incorporating the perturbative QCD correction to the inclusive semileptonic decays of the B meson. Since the parton picture works well for inclusive B decays due to the heavy mass of the b quark, the scaling feature manifests and the decay rate may be expressed by a single structure function describing the light-cone distribution of the b quark apart from the kinematic factor. The evolution equation introduces a q 2 dependence of the shape function and violates the scaling properties. We solve the evolution equation and discuss the phenomenological implication.
The Evolution of Open Magnetic Flux Driven by Photospheric Dynamics
Linker, Jon A.; Lionello, Roberto; Mikic, Zoran; Titov, Viacheslav S.; Antiochos, Spiro K.
2010-01-01
The coronal magnetic field is of paramount importance in solar and heliospheric physics. Two profoundly different views of the coronal magnetic field have emerged. In quasi-steady models, the predominant source of open magnetic field is in coronal holes. In contrast, in the interchange model, the open magnetic flux is conserved, and the coronal magnetic field can only respond to the photospheric evolution via interchange reconnection. In this view the open magnetic flux diffuses through the closed, streamer belt fields, and substantial open flux is present in the streamer belt during solar minimum. However, Antiochos and co-workers, in the form of a conjecture, argued that truly isolated open flux cannot exist in a configuration with one heliospheric current sheet (HCS) - it will connect via narrow corridors to the polar coronal hole of the same polarity. This contradicts the requirements of the interchange model. We have performed an MHD simulation of the solar corona up to 20R solar to test both the interchange model and the Antiochos conjecture. We use a synoptic map for Carrington Rotation 1913 as the boundary condition for the model, with two small bipoles introduced into the region where a positive polarity extended coronal hole forms. We introduce flows at the photospheric boundary surface to see if open flux associated with the bipoles can be moved into the closed-field region. Interchange reconnection does occur in response to these motions. However, we find that the open magnetic flux cannot be simply injected into closed-field regions - the flux eventually closes down and disconnected flux is created. Flux either opens or closes, as required, to maintain topologically distinct open and closed field regions, with no indiscriminate mixing of the two. The early evolution conforms to the Antiochos conjecture in that a narrow corridor of open flux connects the portion of the coronal hole that is nearly detached by one of the bipoles. In the later evolution, a
THE EVOLUTION OF OPEN MAGNETIC FLUX DRIVEN BY PHOTOSPHERIC DYNAMICS
International Nuclear Information System (INIS)
Linker, Jon A.; Lionello, Roberto; Mikic, Zoran; Titov, Viacheslav S.; Antiochos, Spiro K.
2011-01-01
The coronal magnetic field is of paramount importance in solar and heliospheric physics. Two profoundly different views of the coronal magnetic field have emerged. In quasi-steady models, the predominant source of open magnetic field is in coronal holes. In contrast, in the interchange model, the open magnetic flux is conserved, and the coronal magnetic field can only respond to the photospheric evolution via interchange reconnection. In this view, the open magnetic flux diffuses through the closed, streamer belt fields, and substantial open flux is present in the streamer belt during solar minimum. However, Antiochos and coworkers, in the form of a conjecture, argued that truly isolated open flux cannot exist in a configuration with one heliospheric current sheet-it will connect via narrow corridors to the polar coronal hole of the same polarity. This contradicts the requirements of the interchange model. We have performed an MHD simulation of the solar corona up to 20 R sun to test both the interchange model and the Antiochos conjecture. We use a synoptic map for Carrington rotation 1913 as the boundary condition for the model, with two small bipoles introduced into the region where a positive polarity extended coronal hole forms. We introduce flows at the photospheric boundary surface to see if open flux associated with the bipoles can be moved into the closed-field region. Interchange reconnection does occur in response to these motions. However, we find that the open magnetic flux cannot be simply injected into closed-field regions-the flux eventually closes down and disconnected flux is created. Flux either opens or closes, as required, to maintain topologically distinct open- and closed-field regions, with no indiscriminate mixing of the two. The early evolution conforms to the Antiochos conjecture in that a narrow corridor of open flux connects the portion of the coronal hole that is nearly detached by one of the bipoles. In the later evolution, a detached
Energy Technology Data Exchange (ETDEWEB)
Hautmann, F. [Rutherford Appleton Laboratory, Chilton (United Kingdom); Oxford Univ. (United Kingdom). Dept. of Theoretical Physics; Antwerpen Univ. (Belgium). Elementaire Deeltjes Fysica; Jung, H.; Lelek, A.; Zlebcik, R. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Radescu, V. [European Organization for Nuclear Research (CERN), Geneva (Switzerland)
2017-08-15
We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1 percent over a range of five orders of magnitude both in evolution scale and in longitudinal momentum fraction. We make predictions for the evolution of transverse momentum distributions. We perform fits to the high-precision deep inelastic scattering (DIS) structure function measurements, and we present a set of NLO TMD distributions based on the parton branching approach.
Coherence and chaos in the driven damped sine-Gordon equation: Measurement of the soliton spectrum
Energy Technology Data Exchange (ETDEWEB)
Overman, II, E A; McLaughlin, D W; Bishop, A R; Los Alamos National Lab., NM
1986-02-01
A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (PHI, PHIsub(t)) which is periodic in space. The procedure is applied to the field generated by a damped, driven sine-Gordon equation. This field can be either temporally periodic (locked to the driver) or chaotic. In either case the numerical measurement shows that the spatial structure can be described by only a few spatially localized (soliton wave-train) modes. The numerical procedure quantitatively identifies the presence, number and properties of these soliton wave-trains. For example, an increase of spatial symmetry is accompanied by the injection of additional solitons into the field. (orig.).
Xie, Bin
2018-01-01
In this paper, the main topic is to investigate the intermittent property of the one-dimensional stochastic heat equation driven by an inhomogeneous Brownian sheet, which is a noise deduced from the study of the catalytic super-Brownian motion. Under some proper conditions on the catalytic measure of the inhomogeneous Brownian sheet, we show that the solution is weakly full intermittent based on the estimates of moments of the solution. In particular, it is proved that the second moment of the solution grows at the exponential rate. The novelty is that the catalytic measure relative to the inhomogeneous noise is not required to be absolutely continuous with respect to the Lebesgue measure on R.
Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation
Directory of Open Access Journals (Sweden)
Wang Li
2017-06-01
Full Text Available In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations
International Nuclear Information System (INIS)
Liu Chunping; Liu Xiaoping
2004-01-01
First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions
Analysis of microstructural evolution driven by production bias
International Nuclear Information System (INIS)
Woo, C.H.; Semenov, A.A.; Singh, B.N.
1993-01-01
The concept of production bias was first considered in the preceding workshop in this series at Silkeborg in 1989. Since then, much work has been done to investigate the validity of the concept, and its usefulness in complementing the current theory of microstructure evolution based solely on the sink bias (e.g., dislocation bias) as a driving force. Comparison of the theory with experimental results clearly supports the concept. The present paper reviews and summarizes these investigations, and arrives at the following conclusions: a) the concept of production bias is consistent with the results of other works which indicates that, under cascade damage conditions, the effective rate of point-defect production is only a small fraction of the NRT displacement production rate; b) the defect accumulation under cascade damage conditions can be understood in terms of production bias; and c) although the existence of conventional dislocation bias due to point-defect dislocation interaction is not questioned, it does not seem to play any major role in the accumulation of defects under cascade damage conditions at elevated temperatures. (orig.)
The spectral transform as a tool for solving nonlinear discrete evolution equations
International Nuclear Information System (INIS)
Levi, D.
1979-01-01
In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)
Spin and energy evolution equations for a wide class of extended bodies
International Nuclear Information System (INIS)
Racine, Etienne
2006-01-01
We give a surface integral derivation of the leading-order evolution equations for the spin and energy of a relativistic body interacting with other bodies in the post-Newtonian expansion scheme. The bodies can be arbitrarily shaped and can be strongly self-gravitating. The effects of all mass and current multipoles are taken into account. As part of the computation one of the 2PN potentials parametrizing the metric is obtained. The formulae obtained here for spin and energy evolution coincide with those obtained by Damour, Soffel and Xu for the case of weakly self-gravitating bodies. By combining an Einstein-Infeld-Hoffman-type surface integral approach with multipolar expansions we extend the domain of validity of these evolution equations to a wide class of strongly self-gravitating bodies. This paper completes in a self-contained way a previous work by Racine and Flanagan on translational equations of motion for compact objects
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...
New prospects in direct, inverse and control problems for evolution equations
Fragnelli, Genni; Mininni, Rosa
2014-01-01
This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
International Nuclear Information System (INIS)
Zhaqilao,
2013-01-01
A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
Energy Technology Data Exchange (ETDEWEB)
Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn
2013-12-06
A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.
Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra
International Nuclear Information System (INIS)
Gerdt, V.P.; Kostov, N.A.
1989-01-01
In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs
Existence and uniqueness of mild and classical solutions of impulsive evolution equations
Directory of Open Access Journals (Sweden)
Annamalai Anguraj
2005-10-01
Full Text Available We consider the non-linear impulsive evolution equation $$displaylines{ u'(t=Au(t+f(t,u(t,Tu(t,Su(t, quad 0
Soliton evolution and radiation loss for the Korteweg--de Vries equation
International Nuclear Information System (INIS)
Kath, W.L.; Smyth, N.F.
1995-01-01
The time-dependent behavior of solutions of the Korteweg--de Vries (KdV) equation for nonsoliton initial conditions is considered. While the exact solution of the KdV equation can in principle be obtained using the inverse scattering transform, in practice it can be extremely difficult to obtain information about a solution's transient evolution by this method. As an alternative, we present here an approximate method for investigating this transient evolution which is based upon the conservation laws associated with the KdV equation. Initial conditions which form one or two solitons are considered, and the resulting approximate evolution is found to be in good agreement with the numerical solution of the KdV equation. Justification for the approximations employed is also given by way of the linearized inverse scattering solution of the KdV equation. In addition, the final soliton state determined from the approximate equations agrees very well with the final state determined from the exact inverse scattering transform solution
Eu, Byung Chan
2008-09-07
In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.
Existence of solutions for quasilinear random impulsive neutral differential evolution equation
Directory of Open Access Journals (Sweden)
B. Radhakrishnan
2018-07-01
Full Text Available This paper deals with the existence of solutions for quasilinear random impulsive neutral functional differential evolution equation in Banach spaces and the results are derived by using the analytic semigroup theory, fractional powers of operators and the Schauder fixed point approach. An application is provided to illustrate the theory. Keywords: Quasilinear differential equation, Analytic semigroup, Random impulsive neutral differential equation, Fixed point theorem, 2010 Mathematics Subject Classification: 34A37, 47H10, 47H20, 34K40, 34K45, 35R12
International Nuclear Information System (INIS)
Agarwal, Ravi P.; Baghli, Selma; Benchohra, Mouffak
2009-01-01
The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Frechet spaces, combined with the semigroup theory
Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation
International Nuclear Information System (INIS)
Aparicio, J.P.; Garcia Alvarez, E.T.
1995-01-01
The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism. ((orig.))
A generalized variational algebra and conserved densities for linear evolution equations
International Nuclear Information System (INIS)
Abellanas, L.; Galindo, A.
1978-01-01
The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach a rigorous characterization of the polynomial kernel of the variational derivative is given. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order. (Auth.)
Directory of Open Access Journals (Sweden)
V. Vijayakumar
2014-09-01
Full Text Available In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.
International Nuclear Information System (INIS)
Caraballo, T.; Kloeden, P.E.
2006-01-01
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions. A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations. Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions
Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions
Azadbakht, F. Teimoury; Boroun, G. R.
2018-02-01
We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.
Analytic solutions of QCD evolution equations for parton cascades inside nuclear matter at small x
International Nuclear Information System (INIS)
Geiger, K.
1994-01-01
An analytical method is presented to solve generalized QCD evolution equations for the time development of parton cascades in a nuclear environment. In addition to the usual parton branching processes in vacuum, these evolution equations provide a consistent description of interactions with the nuclear medium by accounting for stimulated branching processes, fusion, and scattering processes that are specific to QCD in a medium. Closed solutions for the spectra of produced partons with respect to the variables time, longitudinal momentum, and virtuality are obtained under some idealizing assumptions about the composition of the nuclear medium. Several characteristic features of the resulting parton distributions are discussed. One of the main conclusions is that the evolution of a parton shower in a medium is dilated as compared to free space and is accompanied by an enhancement of particle production. These effects become stronger with increasing nuclear density
Fast accelerator driven subcritical system for energy production: nuclear fuel evolution
International Nuclear Information System (INIS)
Barros, Graiciany de P.; Pereira, Claubia; Veloso, Maria A.F.; Costa, Antonella L.
2011-01-01
Accelerators Driven Systems (ADS) are an innovative type of nuclear system, which is useful for long-lived fission product transmutation and fuel regeneration. The ADS consist of a coupling of a sub-critical nuclear core reactor and a proton beam produced by a particle accelerator. These particles are injected into a target for the neutrons production by spallation reactions. The neutrons are then used to maintain the fission chain in the sub-critical core. The aim of this study is to investigate the nuclear fuel evolution of a lead cooled accelerator driven system used for energy production. The fuel studied is a mixture based upon "2"3"2Th and "2"3"3U. Since thorium is an abundant fertile material, there is hope for the thorium-cycle fuels for an accelerator driven sub-critical system. The target is a lead spallation target and the core is filled with a hexagonal lattice. High energy neutrons are used to reduce the negative reactivity caused by the presence of protoactinium, since this effect is most pronounced in the thermal range of the neutron spectrum. For that reason, such material is not added moderator to the system. In this work is used the Monte Carlo code MCNPX 2.6.0, that presents the the depletion/ burnup capability. The k_e_f_f evolution, the neutron energy spectrum in the core and the nuclear fuel evolution using ADS source (SDEF) and kcode-mode are evaluated during the burnup. (author)
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
International Nuclear Information System (INIS)
Maccari, A.
1997-01-01
Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio endash temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a open-quotes universalclose quotes character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. copyright 1997 American Institute of Physics
Solving QCD evolution equations in rapidity space with Markovian Monte Carlo
Golec-Biernat, K; Placzek, W; Skrzypek, M
2009-01-01
This work covers methodology of solving QCD evolution equation of the parton distribution using Markovian Monte Carlo (MMC) algorithms in a class of models ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test the other more sophisticated Monte Carlo programs, the so-called Constrained Monte Carlo (CMC) programs, which will be used as a building block in the parton shower MC. This is why the mapping of the evolution variables (eikonal variable and evolution time) into four-momenta is also defined and tested. The evolution time is identified with the rapidity variable of the emitted parton. The presented MMCs are tested independently, with ~0.1% precision, against the non-MC program APCheb especially devised for this purpose.
New Jacobian Matrix and Equations of Motion for a 6 d.o.f Cable-Driven Robot
Directory of Open Access Journals (Sweden)
Ali Afshari
2007-03-01
Full Text Available In this paper, we introduce a new method and new motion variables to study kinematics and dynamics of a 6 d.o.f cable-driven robot. Using these new variables and Lagrange equations, we achieve new equations of motion which are different in appearance and several aspects from conventional equations usually used to study 6 d.o.f cable robots. Then, we introduce a new Jacobian matrix which expresses kinematical relations of the robot via a new approach and is basically different from the conventional Jacobian matrix. One of the important characteristics of the new method is computational efficiency in comparison with the conventional method. It is demonstrated that using the new method instead of the conventional one, significantly reduces the computation time required to determine workspace of the robot as well as the time required to solve the equations of motion.
Nonlinear evolution-type equations and their exact solutions using inverse variational methods
International Nuclear Information System (INIS)
Kara, A H; Khalique, C M
2005-01-01
We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painleve properties are also suggested
International Nuclear Information System (INIS)
Baishya, R.; Jamil, U.; Sarma, J. K.
2009-01-01
In this paper the spin-dependent singlet and nonsinglet structure functions have been obtained by solving Dokshitzer, Gribov, Lipatov, Altarelli, Parisi evolution equations in leading order and next to leading order in the small x limit. Here we have used Taylor series expansion and then the method of characteristics to solve the evolution equations. We have also calculated t and x evolutions of deuteron structure functions, and the results are compared with the SLAC E-143 Collaboration data.
Neutron fluctuations in accelerator driven and power reactors via backward master equations
International Nuclear Information System (INIS)
Zhifeng Kuang
2000-05-01
The transport of neutrons in a reactor is a random process, and thus the number of neutrons in a reactor is a random variable. Fluctuations in the number of neutrons in a reactor can be divided into two categories, namely zero noise and power reactor noise. As the name indicates, they dominate (i.e. are observable) at different power levels. The reasons for their occurrences and utilization are also different. In addition, they are described via different mathematical tools, namely master equations and the Langevin equation, respectively. Zero noise carries information about some nuclear properties such as reactor reactivity. Hence methods such as Feynman- and Rossi-alpha methods have been established to determine the subcritical reactivity of a subcritical system. Such methods received a renewed interest recently with the advent of the so-called accelerator driven systems (ADS). Such systems, intended to be used either for energy production or transuranium transmutation, will use a subcritical core with a strong spallation source. A spallation source has statistical properties that are different from those of the traditionally used radioactive sources which were also assumed in the derivation of the Feynman- and Rossi-alpha formulae. Therefore it is necessary to re-derive the Feynman- and Rossi-alpha formulae. Such formulae for ADS have been derived recently but in simpler neutronic models. One subject of this thesis is the extension of such formulae to a more general case in which six groups of delayed neutron precursors are taken into account, and the full joint statistics of the prompt and all delayed groups is included. The involved complexity problems are solved with a combination of effective analytical techniques and symbolic algebra codes. Power reactor noise carries information about parametric perturbation of the system. Langevin technique has been used to extract such information. In such a treatment, zero noise has been neglected. This is a pragmatic
The Relationship between Nonconservative Schemes and Initial Values of Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
林万涛
2004-01-01
For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.
A class of periodic solutions of nonlinear wave and evolution equations
International Nuclear Information System (INIS)
Kashcheev, V.N.
1987-01-01
For the case of 1+1 dimensions a new heuristic method is proposed for deriving dels-similar solutions to nonlinear autonomous differential equations. If the differential function f is a polynomial, then: (i) in the case of even derivatives in f the solution is the ratio of two polynomials from the Weierstrass elliptic functions; (ii) in the case of any order derivatives in f the solution is the ratio of two polynomials from simple exponents. Numerous examples are given constructing such periodic solutions to the wave and evolution equations
International Nuclear Information System (INIS)
Turner, L.
1996-01-01
Adhering to the lore that vorticity is a critical ingredient of fluid turbulence, a triad of coupled helicity (vorticity) states of the incompressible Navier-Stokes fluid are followed. Effects of the remaining states of the fluid on the triad are then modeled as a simple driving term. Numerical solution of the equations yield attractors that seem strange and chaotic. This suggests that the unpredictability of nonlinear fluid dynamics (i.e., turbulence) may be traced back to the most primordial structure of the Navier-Stokes equation; namely, the driven triadic interaction. copyright 1996 The American Physical Society
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed
Directory of Open Access Journals (Sweden)
Loomis Eric
2013-11-01
Full Text Available Growth of hydrodynamic instabilities at the interfaces of inertial confinement fusion capsules (ICF due to ablator and fuel non-uniformities are a primary concern for the ICF program. Recently, observed jetting and parasitic mix into the fuel were attributed to isolated defects on the outer surface of the capsule. Strategies for mitigation of these defects exist, however, they require reduced uncertainties in Equation of State (EOS models prior to invoking them. In light of this, we have begun a campaign to measure the growth of isolated defects (bumps due to x-ray ablation Richtmyer-Meshkov in plastic ablators to validate these models. Experiments used hohlraums with radiation temperatures near 70 eV driven by 15 beams from the Omega laser (Laboratory for Laser Energetics, University of Rochester, NY, which sent a ∼1.25Mbar shock into a planar CH target placed over one laser entrance hole. Targets consisted of 2-D arrays of quasi-gaussian bumps (10 microns tall, 34 microns FWHM deposited on the surface facing into the hohlraum. On-axis radiography with a saran (Cl Heα − 2.76keV backlighter was used to measure bump evolution prior to shock breakout. Shock speed measurements were also performed to determine target conditions. Simulations using the LEOS 5310 and SESAME 7592 models required the simulated laser power be turned down to 80 and 88%, respectively to match observed shock speeds. Both LEOS 5310 and SESAME 7592 simulations agreed with measured bump areal densities out to 6 ns where ablative RM oscillations were observed in previous laser-driven experiments, but did not occur in the x-ray driven case. The QEOS model, conversely, over predicted shock speeds and under predicted areal density in the bump.
Strong Stellar-driven Outflows Shape the Evolution of Galaxies at Cosmic Dawn
Energy Technology Data Exchange (ETDEWEB)
Fontanot, Fabio; De Lucia, Gabriella [INAF—Astronomical Observatory of Trieste, via G.B. Tiepolo 11, I-34143 Trieste (Italy); Hirschmann, Michaela [Sorbonne Universités, UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014 Paris (France)
2017-06-20
We study galaxy mass assembly and cosmic star formation rate (SFR) at high redshift (z ≳ 4), by comparing data from multiwavelength surveys with predictions from the GAlaxy Evolution and Assembly (gaea) model. gaea implements a stellar feedback scheme partially based on cosmological hydrodynamical simulations, which features strong stellar-driven outflows and mass-dependent timescales for the re-accretion of ejected gas. In previous work, we have shown that this scheme is able to correctly reproduce the evolution of the galaxy stellar mass function (GSMF) up to z ∼ 3. We contrast model predictions with both rest-frame ultraviolet (UV) and optical luminosity functions (LFs), which are mostly sensitive to the SFR and stellar mass, respectively. We show that gaea is able to reproduce the shape and redshift evolution of both sets of LFs. We study the impact of dust on the predicted LFs, and we find that the required level of dust attenuation is in qualitative agreement with recent estimates based on the UV continuum slope. The consistency between data and model predictions holds for the redshift evolution of the physical quantities well beyond the redshift range considered for the calibration of the original model. In particular, we show that gaea is able to recover the evolution of the GSMF up to z ∼ 7 and the cosmic SFR density up to z ∼ 10.
Strong Stellar-driven Outflows Shape the Evolution of Galaxies at Cosmic Dawn
International Nuclear Information System (INIS)
Fontanot, Fabio; De Lucia, Gabriella; Hirschmann, Michaela
2017-01-01
We study galaxy mass assembly and cosmic star formation rate (SFR) at high redshift (z ≳ 4), by comparing data from multiwavelength surveys with predictions from the GAlaxy Evolution and Assembly (gaea) model. gaea implements a stellar feedback scheme partially based on cosmological hydrodynamical simulations, which features strong stellar-driven outflows and mass-dependent timescales for the re-accretion of ejected gas. In previous work, we have shown that this scheme is able to correctly reproduce the evolution of the galaxy stellar mass function (GSMF) up to z ∼ 3. We contrast model predictions with both rest-frame ultraviolet (UV) and optical luminosity functions (LFs), which are mostly sensitive to the SFR and stellar mass, respectively. We show that gaea is able to reproduce the shape and redshift evolution of both sets of LFs. We study the impact of dust on the predicted LFs, and we find that the required level of dust attenuation is in qualitative agreement with recent estimates based on the UV continuum slope. The consistency between data and model predictions holds for the redshift evolution of the physical quantities well beyond the redshift range considered for the calibration of the original model. In particular, we show that gaea is able to recover the evolution of the GSMF up to z ∼ 7 and the cosmic SFR density up to z ∼ 10.
Periodic Solutions and S-Asymptotically Periodic Solutions to Fractional Evolution Equations
Directory of Open Access Journals (Sweden)
Jia Mu
2017-01-01
Full Text Available This paper deals with the existence and uniqueness of periodic solutions, S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.
The population and decay evolution of a qubit under the time-convolutionless master equation
International Nuclear Information System (INIS)
Huang Jiang; Fang Mao-Fa; Liu Xiang
2012-01-01
We consider the population and decay of a qubit under the electromagnetic environment. Employing the time-convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Czech Academy of Sciences Publication Activity Database
Fiala, Zdeněk
2015-01-01
Roč. 226, č. 1 (2015), s. 17-35 ISSN 0001-5970 R&D Projects: GA ČR(CZ) GA103/09/2101 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * evolution equation of Lie-type * time-discrete integration Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.694, year: 2015 http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1
Dynamics of second order in time evolution equations with state-dependent delay
Czech Academy of Sciences Publication Activity Database
Chueshov, I.; Rezunenko, Oleksandr
123-124, č. 1 (2015), s. 126-149 ISSN 0362-546X R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor Subject RIV: BD - Theory of Information Impact factor: 1.125, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf
DEFF Research Database (Denmark)
Luján, Adela M.; Maciá, María D.; Yang, Liang
2011-01-01
, which are rarely eradicated despite intensive antibiotic therapy. Current knowledge indicates that three major adaptive strategies, biofilm development, phenotypic diversification, and mutator phenotypes [driven by a defective mismatch repair system (MRS)], play important roles in P. aeruginosa chronic...... infections, but the relationship between these strategies is still poorly understood. We have used the flow-cell biofilm model system to investigate the impact of the mutS associated mutator phenotype on development, dynamics, diversification and adaptation of P. aeruginosa biofilms. Through competition...... diversification, evidenced by biofilm architecture features and by a wider range and proportion of morphotypic colony variants, respectively. Additionally, morphotypic variants generated in mutator biofilms showed increased competitiveness, providing further evidence for mutator-driven adaptive evolution...
A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations
International Nuclear Information System (INIS)
Zhang Yufeng; Xu Xixiang
2004-01-01
A subalgebra of loop algebra A-bar 2 is first constructed, which has its own special feature. It follows that a new Liouville integrable hierarchy of evolution equations is obtained, possessing a tri-Hamiltonian structure, which is proved by us in this paper. Especially, three symplectic operators are constructed directly from recurrence relations. The conjugate operator of a recurrence operator is a hereditary symmetry. As reduction cases of the hierarchy presented in this paper, the celebrated MKdV equation and heat-conduction equation are engendered, respectively. Therefore, we call the hierarchy a generalized MKdV-H system. At last, a high-dimension loop algebra G-bar is constructed by making use of a proper scalar transformation. As a result, a type expanding integrable model of the MKdV-H system is given
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
International Nuclear Information System (INIS)
Caraballo, Tomas; Kloeden, Peter E.; Schmalfuss, Bjoern
2004-01-01
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities
Evolution of the cosmological horizons in a universe with countably infinitely many state equations
Energy Technology Data Exchange (ETDEWEB)
Margalef-Bentabol, Berta; Cepa, Jordi [Departamento de Astrofísica, Universidad de la Laguna, E-38205 La Laguna, Tenerife (Spain); Margalef-Bentabol, Juan, E-mail: bmb@cca.iac.es, E-mail: juanmargalef@estumail.ucm.es, E-mail: jcn@iac.es [Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, E-28040 Madrid (Spain)
2013-02-01
This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider a general accelerated universe with countably infinitely many constant state equations, and we obtain simple expressions in terms of their respective recession velocities that generalize the previous results for one and two state equations. We also provide a qualitative study of the values of the horizons and their velocities at the origin of the universe and at the far future, and we prove that these values only depend on one dominant state equation. Finally, we compare both horizons and determine when one is larger than the other.
arXiv GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations
Ghiglieri, J.
2017-05-23
Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T > 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1+n 2+n scatterings and for all 2 2 scatterings. The regime in which sphaleron processes gradually decouple so that baryon plus lepton number becomes a separate non-equilibrium variable is also considered.
A novel algebraic procedure for solving non-linear evolution equations of higher order
International Nuclear Information System (INIS)
Huber, Alfred
2007-01-01
We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest
Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method
International Nuclear Information System (INIS)
Fan Engui
2002-01-01
A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)
Population Thinking, Price’s Equation and the Analysis of Economic Evolution
DEFF Research Database (Denmark)
Andersen, Esben Sloth
2004-01-01
applicable to economic evolution due to the development of what may be called a general evometrics. Central to this evometrics is a method for partitioning evolutionary change developed by George Price into the selection effect and what may be called the innovation effect. This method serves surprisingly...... well as a means of accounting for evolution and as a starting point for the explanation of evolution. The applications of Price’s equation cover the partitioning and analysis of relatively short-term evolutionary change within individual industries as well as the study of more complexly structured...... populations of firms. By extrapolating these applications of Price’s evometrics, the paper suggests that his approach may play a central role in the emerging evolutionary econometrics....
Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum
2014-01-01
In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.
Zueva, Ksenia J; Lumme, Jaakko; Veselov, Alexey E; Kent, Matthew P; Lien, Sigbjørn; Primmer, Craig R
2014-01-01
Mechanisms of host-parasite co-adaptation have long been of interest in evolutionary biology; however, determining the genetic basis of parasite resistance has been challenging. Current advances in genome technologies provide new opportunities for obtaining a genome-scale view of the action of parasite-driven natural selection in wild populations and thus facilitate the search for specific genomic regions underlying inter-population differences in pathogen response. European populations of Atlantic salmon (Salmo salar L.) exhibit natural variance in susceptibility levels to the ectoparasite Gyrodactylus salaris Malmberg 1957, ranging from resistance to extreme susceptibility, and are therefore a good model for studying the evolution of virulence and resistance. However, distinguishing the molecular signatures of genetic drift and environment-associated selection in small populations such as land-locked Atlantic salmon populations presents a challenge, specifically in the search for pathogen-driven selection. We used a novel genome-scan analysis approach that enabled us to i) identify signals of selection in salmon populations affected by varying levels of genetic drift and ii) separate potentially selected loci into the categories of pathogen (G. salaris)-driven selection and selection acting upon other environmental characteristics. A total of 4631 single nucleotide polymorphisms (SNPs) were screened in Atlantic salmon from 12 different northern European populations. We identified three genomic regions potentially affected by parasite-driven selection, as well as three regions presumably affected by salinity-driven directional selection. Functional annotation of candidate SNPs is consistent with the role of the detected genomic regions in immune defence and, implicitly, in osmoregulation. These results provide new insights into the genetic basis of pathogen susceptibility in Atlantic salmon and will enable future searches for the specific genes involved.
Energy-driven surface evolution in beta-MnO2 structures
Energy Technology Data Exchange (ETDEWEB)
Yao, Wentao; Yuan, Yifei; Asayesh-Ardakani, Hasti; Huang, Zhennan; Long, Fei; Friedrich, Craig; Amine, Khalil; Lu, Jun; Shahbazian-Yassar, Reza
2018-01-01
Exposed crystal facets directly affect the electrochemical/catalytic performance of MnO2 materials during their applications in supercapacitors, rechargeable batteries, and fuel cells. Currently, the facet-controlled synthesis of MnO2 is facing serious challenges due to the lack of an in-depth understanding of their surface evolution mechanisms. Here, combining aberration-corrected scanning transmission electron microscopy (STEM) and high-resolution TEM, we revealed a mutual energy-driven mechanism between beta-MnO2 nanowires and microstructures that dominated the evolution of the lateral facets in both structures. The evolution of the lateral surfaces followed the elimination of the {100} facets and increased the occupancy of {110} facets with the increase in hydrothermal retention time. Both self-growth and oriented attachment along their {100} facets were observed as two different ways to reduce the surface energies of the beta-MnO2 structures. High-density screw dislocations with the 1/2 < 100 > Burgers vector were generated consequently. The observed surface evolution phenomenon offers guidance for the facet-controlled growth of beta-MnO2 materials with high performances for its application in metal-air batteries, fuel cells, supercapacitors, etc.
Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation
International Nuclear Information System (INIS)
Goryainov, V V
2015-01-01
The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution family of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles
Directory of Open Access Journals (Sweden)
Rice Sean H
2008-09-01
Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general
Assisted stellar suicide: the wind-driven evolution of the recurrent nova T Pyxidis
Knigge, Ch.; King, A. R.; Patterson, J.
2000-12-01
We show that the extremely high luminosity of the short-period recurrent nova T Pyx in quiescence can be understood if this system is a wind-driven supersoft x-ray source (SSS). In this scenario, a strong, radiation-induced wind is excited from the secondary star and accelerates the binary evolution. The accretion rate is therefore much higher than in an ordinary cataclysmic binary at the same orbital period, as is the luminosity of the white dwarf primary. In the steady state, the enhanced luminosity is just sufficient to maintain the wind from the secondary. The accretion rate and luminosity predicted by the wind-driven model for T Pyx are in good agreement with the observational evidence. X-ray observations with Chandra or XMM may be able to confirm T Pyx's status as a SSS. T Pyx's lifetime in the wind-driven state is on the order of a million years. Its ultimate fate is not certain, but the system may very well end up destroying itself, either via the complete evaporation of the secondary star, or in a Type Ia supernova if the white dwarf reaches the Chandrasekhar limit. Thus either the primary, the secondary, or both may currently be committing assisted stellar suicide.
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N. N. Romanova
1998-01-01
Full Text Available The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.
Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations
Jadach, S.; Płaczek, W.; Skrzypek, M.; Stokłosa, P.
2010-02-01
We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5×10. This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods. New version program summaryProgram title: EvolFMC v.2 Catalogue identifier: AEFN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including binary test data, etc.: 66 456 (7407 lines of C++ code) No. of bytes in distributed program, including test data, etc.: 412 752 Distribution format: tar.gz Programming language: C++ Computer: PC, Mac Operating system: Linux, Mac OS X RAM: Less than 256 MB Classification: 11.5 External routines: ROOT ( http://root.cern.ch/drupal/) Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations. Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons. Restrictions:Limited to the case of massless partons. Implemented in the LO and NLO approximations only. Weighted events only. Unusual features: Modified-DGLAP evolutions included up to the NLO level. Additional comments: Technical precision established at 5×10. Running time: For the 10 6 events at 100 GeV: DGLAP NLO: 27s; C-type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10
Chadha, Alka; Bora, Swaroop Nandan
2017-11-01
This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.
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Melon Fuksman J. D.
2018-01-01
Full Text Available The binary-driven hypernova (BdHN model has been introduced in the past years, to explain a subfamily of gamma-ray bursts (GRBs with energies Eiso ≥ 1052 erg associated with type Ic supernovae. Such BdHNe have as progenitor a tight binary system composed of a carbon-oxigen (CO core and a neutron star undergoing an induced gravitational collapse to a black hole, triggered by the CO core explosion as a supernova (SN. This collapse produces an optically-thick e+e- plasma, which expands and impacts onto the SN ejecta. This process is here considered as a candidate for the production of X-ray flares, which are frequently observed following the prompt emission of GRBs. In this work we follow the evolution of the e+e- plasma as it interacts with the SN ejecta, by solving the equations of relativistic hydrodynamics numerically. Our results are compatible with the Lorentz factors estimated for the sources that produce the flares, of typically Γ ≲ 4.
Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2010-01-01
Using repeated Laplace transforms, we turn coupled, integral-differential singlet DGLAP equations into NLO (next-to-leading) coupled algebraic equations, which we then decouple. After two Laplace inversions we find new tools for pQCD: decoupled NLO analytic solutions F s (x,Q 2 )=F s (F s0 (x),G 0 (x)), G(x,Q 2 )=G(F s0 (x), G 0 (x)). F s , G are known NLO functions and F s0 (x)≡F s (x,Q 0 2 ), G 0 (x)≡G(x,Q 0 2 ) are starting functions for evolution beginning at Q 2 =Q 0 2 . We successfully compare our u and d non-singlet valence quark distributions with MSTW results (Martin et al., Eur. Phys. J. C 63:189, 2009). (orig.)
Some Evolution Hierarchies Derived from Self-dual Yang-Mills Equations
International Nuclear Information System (INIS)
Zhang Yufeng; Hon, Y.C.
2011-01-01
We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra Ē of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson (GJ) hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simpler construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra g N . As an application, we apply the loop algebra E-tilde of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell (KN) hierarchy which, consisting of two arbitrary parameters α and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R 3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations. (general)
On an abstract evolution equation with a spectral operator of scalar type
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Marat V. Markin
2002-01-01
Full Text Available It is shown that the weak solutions of the evolution equation y′(t=Ay(t, t∈[0,T (0
Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics
Energy Technology Data Exchange (ETDEWEB)
Braun, V.M.; Strohmaier, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Manashov, A.N. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik; Moch, S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2017-03-15
Using the approach based on conformal symmetry we calculate the three-loop (NNLO) contribution to the evolution equation for flavor-nonsinglet leading twist operators in the MS scheme. The explicit expression for the three-loop kernel is derived for the corresponding light-ray operator in coordinate space. The expansion in local operators is performed and explicit results are given for the matrix of the anomalous dimensions for the operators up to seven covariant derivatives. The results are directly applicable to the renormalization of the pion light-cone distribution amplitude and flavor-nonsinglet generalized parton distributions.
Engen, Steinar; Saether, Bernt-Erik
2014-03-01
We analyze the stochastic components of the Robertson-Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity. © 2013 The Author(s). Evolution © 2013 The Society for the Study of Evolution.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Destrade, Michel; Goriely, Alain; Saccomandi, Giuseppe
2011-01-01
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation c...
Nonequilibrium steady state of a weakly-driven Kardar–Parisi–Zhang equation
Meerson, Baruch; Sasorov, Pavel V.; Vilenkin, Arkady
2018-05-01
We consider an infinite interface of d > 2 dimensions, governed by the Kardar–Parisi–Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability distribution of the interface height H at a point of the substrate, when the interface is initially flat. We show that, in stark contrast with the KPZ equation in d statistics of directed polymers in random potential.
Geometry of quantal adiabatic evolution driven by a non-Hermitian Hamiltonian
International Nuclear Information System (INIS)
Wu Zhaoyan; Yu Ting; Zhou Hongwei
1994-01-01
It is shown by using a counter example, which is exactly solvable, that the quantal adiabatic theorem does not generally hold for a non-Hermitian driving Hamiltonian, even if it varies extremely slowly. The condition for the quantal adiabatic theorem to hold for non-Hermitian driving Hamiltonians is given. The adiabatic evolutions driven by a non-Hermitian Hamiltonian provide examples of a new geometric structure, that is the vector bundle in which the inner product of two parallelly transported vectors generally changes. A new geometric concept, the attenuation tensor, is naturally introduced to describe the decay or flourish of the open quantum system. It is constructed in terms of the spectral projector of the Hamiltonian. (orig.)
Testing the Accuracy of Data-driven MHD Simulations of Active Region Evolution
Energy Technology Data Exchange (ETDEWEB)
Leake, James E.; Linton, Mark G. [U.S. Naval Research Laboratory, 4555 Overlook Avenue, SW, Washington, DC 20375 (United States); Schuck, Peter W., E-mail: james.e.leake@nasa.gov [NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 (United States)
2017-04-01
Models for the evolution of the solar coronal magnetic field are vital for understanding solar activity, yet the best measurements of the magnetic field lie at the photosphere, necessitating the development of coronal models which are “data-driven” at the photosphere. We present an investigation to determine the feasibility and accuracy of such methods. Our validation framework uses a simulation of active region (AR) formation, modeling the emergence of magnetic flux from the convection zone to the corona, as a ground-truth data set, to supply both the photospheric information and to perform the validation of the data-driven method. We focus our investigation on how the accuracy of the data-driven model depends on the temporal frequency of the driving data. The Helioseismic and Magnetic Imager on NASA’s Solar Dynamics Observatory produces full-disk vector magnetic field measurements at a 12-minute cadence. Using our framework we show that ARs that emerge over 25 hr can be modeled by the data-driving method with only ∼1% error in the free magnetic energy, assuming the photospheric information is specified every 12 minutes. However, for rapidly evolving features, under-sampling of the dynamics at this cadence leads to a strobe effect, generating large electric currents and incorrect coronal morphology and energies. We derive a sampling condition for the driving cadence based on the evolution of these small-scale features, and show that higher-cadence driving can lead to acceptable errors. Future work will investigate the source of errors associated with deriving plasma variables from the photospheric magnetograms as well as other sources of errors, such as reduced resolution, instrument bias, and noise.
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Jie Yang
Full Text Available BACKGROUND: Environmental stress can accelerate the directional selection and evolutionary rate of specific stress-response proteins to bring about new or altered functions, enhancing an organism's fitness to challenging environments. Plateau pika (Ochotona curzoniae, an endemic and keystone species on Qinghai-Tibetan Plateau, is a high hypoxia and low temperature tolerant mammal with high resting metabolic rate and non-shivering thermogenesis to cope in this harsh plateau environment. Leptin is a key hormone related to how these animals regulate energy homeostasis. Previous molecular evolutionary analysis helped to generate the hypothesis that adaptive evolution of plateau pika leptin may be driven by cold stress. METHODOLOGY/PRINCIPAL FINDINGS: To test the hypothesis, recombinant pika leptin was first purified. The thermogenic characteristics of C57BL/6J mice injected with pika leptin under warm (23±1°C and cold (5±1°C acclimation is investigated. Expression levels of genes regulating adaptive thermogenesis in brown adipose tissue and the hypothalamus are compared between pika leptin and human leptin treatment, suggesting that pika leptin has adaptively and functionally evolved. Our results show that pika leptin regulates energy homeostasis via reduced food intake and increased energy expenditure under both warm and cold conditions. Compared with human leptin, pika leptin demonstrates a superior induced capacity for adaptive thermogenesis, which is reflected in a more enhanced β-oxidation, mitochondrial biogenesis and heat production. Moreover, leptin treatment combined with cold stimulation has a significant synergistic effect on adaptive thermogenesis, more so than is observed with a single cold exposure or single leptin treatment. CONCLUSIONS/SIGNIFICANCE: These findings support the hypothesis that cold stress has driven the functional evolution of plateau pika leptin as an ecological adaptation to the Qinghai-Tibetan Plateau.
Evolution equation for the higher-twist B-meson distribution amplitude
International Nuclear Information System (INIS)
Braun, V.M.; Offen, N.; Manashov, A.N.; Regensburg Univ.; Sankt-Petersburg State Univ.
2015-07-01
We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large N c limit and can be solved exactly. The lowest anomalous dimension is separated from the remaining, continuous, spectrum by a finite gap. The corresponding eigenfunction coincides with the contribution of quark-gluon states to the two-particle DA φ - (ω) so that the evolution equation for the latter is the same as for the leading-twist DA φ + (ω) up to a constant shift in the anomalous dimension. Thus, ''genuine'' three-particle states that belong to the continuous spectrum effectively decouple from φ - (ω) to the leading-order accuracy. In turn, the scale dependence of the full three-particle DA turns out to be nontrivial so that the contribution with the lowest anomalous dimension does not become leading at any scale. The results are illustrated on a simple model that can be used in studies of 1/m b corrections to heavy-meson decays in the framework of QCD factorization or light-cone sum rules.
International Nuclear Information System (INIS)
Keanini, R.G.
2011-01-01
Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the
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Adela M Luján
Full Text Available Pseudomonas aeruginosa is an important opportunistic pathogen causing chronic airway infections, especially in cystic fibrosis (CF patients. The majority of the CF patients acquire P. aeruginosa during early childhood, and most of them develop chronic infections resulting in severe lung disease, which are rarely eradicated despite intensive antibiotic therapy. Current knowledge indicates that three major adaptive strategies, biofilm development, phenotypic diversification, and mutator phenotypes [driven by a defective mismatch repair system (MRS], play important roles in P. aeruginosa chronic infections, but the relationship between these strategies is still poorly understood. We have used the flow-cell biofilm model system to investigate the impact of the mutS associated mutator phenotype on development, dynamics, diversification and adaptation of P. aeruginosa biofilms. Through competition experiments we demonstrate for the first time that P. aeruginosa MRS-deficient mutators had enhanced adaptability over wild-type strains when grown in structured biofilms but not as planktonic cells. This advantage was associated with enhanced micro-colony development and increased rates of phenotypic diversification, evidenced by biofilm architecture features and by a wider range and proportion of morphotypic colony variants, respectively. Additionally, morphotypic variants generated in mutator biofilms showed increased competitiveness, providing further evidence for mutator-driven adaptive evolution in the biofilm mode of growth. This work helps to understand the basis for the specific high proportion and role of mutators in chronic infections, where P. aeruginosa develops in biofilm communities.
Pogan, Alin; Zumbrun, Kevin
2018-06-01
We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.
Analytic treatment of leading-order parton evolution equations: Theory and tests
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; McKay, Douglas W.
2009-01-01
We recently derived an explicit expression for the gluon distribution function G(x,Q 2 )=xg(x,Q 2 ) in terms of the proton structure function F 2 γp (x,Q 2 ) in leading-order (LO) QCD by solving the LO Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for the Q 2 evolution of F 2 γp (x,Q 2 ) analytically, using a differential-equation method. We showed that accurate experimental knowledge of F 2 γp (x,Q 2 ) in a region of Bjorken x and virtuality Q 2 is all that is needed to determine the gluon distribution in that region. We rederive and extend the results here using a Laplace-transform technique, and show that the singlet quark structure function F S (x,Q 2 ) can be determined directly in terms of G from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi gluon evolution equation. To illustrate the method and check the consistency of existing LO quark and gluon distributions, we used the published values of the LO quark distributions from the CTEQ5L and MRST2001 LO analyses to form F 2 γp (x,Q 2 ), and then solved analytically for G(x,Q 2 ). We find that the analytic and fitted gluon distributions from MRST2001LO agree well with each other for all x and Q 2 , while those from CTEQ5L differ significantly from each other for large x values, x > or approx. 0.03-0.05, at all Q 2 . We conclude that the published CTEQ5L distributions are incompatible in this region. Using a nonsinglet evolution equation, we obtain a sensitive test of quark distributions which holds in both LO and next-to-leading order perturbative QCD. We find in either case that the CTEQ5 quark distributions satisfy the tests numerically for small x, but fail the tests for x > or approx. 0.03-0.05--their use could potentially lead to significant shifts in predictions of quantities sensitive to large x. We encountered no problems with the MRST2001LO distributions or later CTEQ distributions. We suggest caution in the use of the CTEQ5 distributions.
International Nuclear Information System (INIS)
Oeien, A.H.
1980-09-01
For electrons in electric and magnetic fields which collide elastically with neutral atoms or molecules a minute evolution study is made using the multiple time scale method. In this study a set of quasi moment equations is used which is derived from the Boltzmann equation by taking appropriate quasi moments, i.e. velocity moments where the integration is performed only over velocity angles. In a systematic way the evolution in a transient regime is revealed where processes take place on time scales related to the electron-atom collision frequency and electron cyclotron frequency and how the evolution enters a regime where it is governed by a reduced transport equation is shown. This work has relevance to the theory of evolution of gases of charged particles in general and to non-neutral plasmas and partially ionized gases in particular. (Auth.)
On the classification of scalar evolution equations with non-constant separant
Hümeyra Bilge, Ayşe; Mizrahi, Eti
2017-01-01
The ‘separant’ of the evolution equation u t = F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order
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Ana Hranilovic
Full Text Available The yeast Lachancea thermotolerans (formerly Kluyveromyces thermotolerans is a species with remarkable, yet underexplored, biotechnological potential. This ubiquist occupies a range of natural and anthropic habitats covering a wide geographic span. To gain an insight into L. thermotolerans population diversity and structure, 172 isolates sourced from diverse habitats worldwide were analysed using a set of 14 microsatellite markers. The resultant clustering revealed that the evolution of L. thermotolerans has been driven by the geography and ecological niche of the isolation sources. Isolates originating from anthropic environments, in particular grapes and wine, were genetically close, thus suggesting domestication events within the species. The observed clustering was further validated by several means including, population structure analysis, F-statistics, Mantel's test and the analysis of molecular variance (AMOVA. Phenotypic performance of isolates was tested using several growth substrates and physicochemical conditions, providing added support for the clustering. Altogether, this study sheds light on the genotypic and phenotypic diversity of L. thermotolerans, contributing to a better understanding of the population structure, ecology and evolution of this non-Saccharomyces yeast.
Walsh, Matthew R.; Broyles, Whitnee; Beston, Shannon M.; Munch, Stephan B.
2016-01-01
Vertebrates exhibit extensive variation in relative brain size. It has long been assumed that this variation is the product of ecologically driven natural selection. Yet, despite more than 100 years of research, the ecological conditions that select for changes in brain size are unclear. Recent laboratory selection experiments showed that selection for larger brains is associated with increased survival in risky environments. Such results lead to the prediction that increased predation should favour increased brain size. Work on natural populations, however, foreshadows the opposite trajectory of evolution; increased predation favours increased boldness, slower learning, and may thereby select for a smaller brain. We tested the influence of predator-induced mortality on brain size evolution by quantifying brain size variation in a Trinidadian killifish, Rivulus hartii, from communities that differ in predation intensity. We observed strong genetic differences in male (but not female) brain size between fish communities; second generation laboratory-reared males from sites with predators exhibited smaller brains than Rivulus from sites in which they are the only fish present. Such trends oppose the results of recent laboratory selection experiments and are not explained by trade-offs with other components of fitness. Our results suggest that increased male brain size is favoured in less risky environments because of the fitness benefits associated with faster rates of learning and problem-solving behaviour. PMID:27412278
Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow
International Nuclear Information System (INIS)
Hammond, L A; Halliday, I; Care, C M; Stevens, A
2002-01-01
We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow
Destrade, M.
2010-12-08
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.
Destrade, M.; Goriely, A.; Saccomandi, G.
2010-01-01
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.
A New Fokker-Planck Approach for the Relaxation-driven Evolution of Galactic Nuclei
Vasiliev, Eugene
2017-10-01
We present an approach for simulating the collisional evolution of spherical isotropic stellar systems based on the one-dimensional Fokker-Planck equation. A novel aspect is that we use the phase volume as the argument of the distribution function instead of the traditionally used energy, which facilitates the solution. The publicly available code PhaseFlow implements a high-accuracy finite-element method for the Fokker-Planck equation, and can handle multiple-component systems, optionally with the central black hole and taking into account loss-cone effects and star formation. We discuss the energy balance in the general setting, and in application to the Bahcall-Wolf cusp around a central black hole, for which we derive a perturbative solution. We stress that the cusp is not a steady-state structure, but rather evolves in amplitude while retaining an approximately ρ \\propto {r}-7/4 density profile. Finally, we apply the method to the nuclear star cluster of the milky Way, and illustrate a possible evolutionary scenario in which a two-component system of lighter main-sequence stars and stellar-mass black holes develops a Bahcall-Wolf cusp in the heavier component and a weaker ρ \\propto {r}-3/2 cusp in the lighter, visible component, over the period of several Gyr. The present-day density profile is consistent with the recently detected mild cusp inside the central parsec, and is weakly sensitive to initial conditions.
On the Boussinesq-Burgers equations driven by dynamic boundary conditions
Zhu, Neng; Liu, Zhengrong; Zhao, Kun
2018-02-01
We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.
International Nuclear Information System (INIS)
Ablowitz, Mark J; Curtis, Christopher W
2011-01-01
The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.
Ablowitz, Mark J.; Curtis, Christopher W.
2011-05-01
The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.
A multiscale asymptotic analysis of time evolution equations on the complex plane
Energy Technology Data Exchange (ETDEWEB)
Braga, Gastão A., E-mail: gbraga@mat.ufmg.br [Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG (Brazil); Conti, William R. P., E-mail: wrpconti@gmail.com [Departamento de Ciências do Mar, Universidade Federal de São Paulo, Rua Dr. Carvalho de Mendonça 144, 11070-100 Santos, SP (Brazil)
2016-07-15
Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.
Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
International Nuclear Information System (INIS)
Thiele, U
2010-01-01
In the present contribution we review basic mathematical results for three physical systems involving self-organizing solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e. time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different systems. First, we discuss the linear stability of homogeneous steady states, i.e. flat films, and second the systematics of non-trivial steady states, i.e. drop/hole states for dewetting films and quantum-dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly unrelated physical systems mathematically, but does allow as well for discussing model extensions in a more unified way.
Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD
Energy Technology Data Exchange (ETDEWEB)
Block, Martin M. [Northwestern University, Department of Physics and Astronomy, Evanston, IL (United States); Durand, Loyal [University of Wisconsin, Department of Physics, Madison, WI (United States); Ha, Phuoc [Towson University, Department of Physics, Astronomy and Geosciences, Towson, MD (United States); McKay, Douglas W. [University of Kansas, Department of Physics and Astronomy, Lawrence, KS (United States)
2010-10-15
Using repeated Laplace transforms, we turn coupled, integral-differential singlet DGLAP equations into NLO (next-to-leading) coupled algebraic equations, which we then decouple. After two Laplace inversions we find new tools for pQCD: decoupled NLO analytic solutions F{sub s}(x,Q{sup 2})=F{sub s}(F{sub s0}(x),G{sub 0}(x)), G(x,Q{sup 2})=G(F{sub s0}(x), G{sub 0}(x)). F{sub s}, G are known NLO functions and F{sub s0}(x){identical_to}F{sub s}(x,Q{sub 0}{sup 2}), G{sub 0}(x){identical_to}G(x,Q{sub 0}{sup 2}) are starting functions for evolution beginning at Q{sup 2}=Q{sub 0}{sup 2}. We successfully compare our u and d non-singlet valence quark distributions with MSTW results (Martin et al., Eur. Phys. J. C 63:189, 2009). (orig.)
A transport equation for the evolution of shock amplitudes along rays
Directory of Open Access Journals (Sweden)
Giovanni Russo
1991-05-01
Full Text Available A new asymptotic method is derived for the study of the evolution of weak shocks in several dimension. The method is based on the Generalized Wavefront Expansion derived in [1]. In that paper the propagation of a shock into a known background was studied under the assumption that shock is weak, i.e. Mach Number =1+O(ε, ε ≪ 1, and that the perturbation of the field varies over a length scale O(ε. To the lowest order, the shock surface evolves along the rays associated with the unperturbed state. An infinite system of compatibility relations was derived for the jump in the field and its normal derivatives along the shock, but no valid criterion was found for a truncation of the system. Here we show that the infinite hierarchy is equivalent to a single equation that describes the evolution of the shock along the rays. We show that this method gives equivalent results to those obtained by Weakly Nonlinear Geometrical Optics [2].
El Mouden, C; André, J-B; Morin, O; Nettle, D
2014-02-01
Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes. © 2013 The Authors. Journal of Evolutionary Biology © 2013 European Society For Evolutionary Biology.
ORBITAL AND MASS RATIO EVOLUTION OF PROTOBINARIES DRIVEN BY MAGNETIC BRAKING
Energy Technology Data Exchange (ETDEWEB)
Zhao, Bo; Li, Zhi-Yun [Astronomy Department, University of Virginia, Charlottesville, VA 22904 (United States)
2013-01-20
The majority of stars reside in multiple systems, especially binaries. The formation and early evolution of binaries is a longstanding problem in star formation that is not yet fully understood. In particular, how the magnetic field observed in star-forming cores shapes the binary characteristics remains relatively unexplored. We demonstrate numerically, using an MHD version of the ENZO AMR hydro code, that a magnetic field of the observed strength can drastically change two of the basic quantities that characterize a binary system: the orbital separation and mass ratio of the two components. Our calculations focus on the protostellar mass accretion phase, after a pair of stellar 'seeds' have already formed. We find that in dense cores magnetized to a realistic level, the angular momentum of the material accreted by the protobinary is greatly reduced by magnetic braking. Accretion of strongly braked material shrinks the protobinary separation by a large factor compared to the non-magnetic case. The magnetic braking also changes the evolution of the mass ratio of unequal-mass protobinaries by producing material of low specific angular momentum that accretes preferentially onto the more massive primary star rather than the secondary. This is in contrast with the preferential mass accretion onto the secondary previously found numerically for protobinaries accreting from an unmagnetized envelope, which tends to drive the mass ratio toward unity. In addition, the magnetic field greatly modifies the morphology and dynamics of the protobinary accretion flow. It suppresses the traditional circumstellar and circumbinary disks that feed the protobinary in the non-magnetic case; the binary is fed instead by a fast collapsing pseudodisk whose rotation is strongly braked. The magnetic braking-driven inward migration of binaries from their birth locations may be constrained by high-resolution observations of the orbital distribution of deeply embedded protobinaries
Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood
2018-03-01
The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.
Supernova-driven outflows and chemical evolution of dwarf spheroidal galaxies.
Qian, Yong-Zhong; Wasserburg, G J
2012-03-27
We present a general phenomenological model for the metallicity distribution (MD) in terms of [Fe/H] for dwarf spheroidal galaxies (dSphs). These galaxies appear to have stopped accreting gas from the intergalactic medium and are fossilized systems with their stars undergoing slow internal evolution. For a wide variety of infall histories of unprocessed baryonic matter to feed star formation, most of the observed MDs can be well described by our model. The key requirement is that the fraction of the gas mass lost by supernova-driven outflows is close to unity. This model also predicts a relationship between the total stellar mass and the mean metallicity for dSphs in accord with properties of their dark matter halos. The model further predicts as a natural consequence that the abundance ratios [E/Fe] for elements such as O, Mg, and Si decrease for stellar populations at the higher end of the [Fe/H] range in a dSph. We show that, for infall rates far below the net rate of gas loss to star formation and outflows, the MD in our model is very sharply peaked at one [Fe/H] value, similar to what is observed in most globular clusters. This result suggests that globular clusters may be end members of the same family as dSphs.
Climate change-driven cliff and beach evolution at decadal to centennial time scales
Erikson, Li; O'Neill, Andrea; Barnard, Patrick; Vitousek, Sean; Limber, Patrick
2017-01-01
Here we develop a computationally efficient method that evolves cross-shore profiles of sand beaches with or without cliffs along natural and urban coastal environments and across expansive geographic areas at decadal to centennial time-scales driven by 21st century climate change projections. The model requires projected sea level rise rates, extrema of nearshore wave conditions, bluff recession and shoreline change rates, and cross-shore profiles representing present-day conditions. The model is applied to the ~470-km long coast of the Southern California Bight, USA, using recently available projected nearshore waves and bluff recession and shoreline change rates. The results indicate that eroded cliff material, from unarmored cliffs, contribute 11% to 26% to the total sediment budget. Historical beach nourishment rates will need to increase by more than 30% for a 0.25 m sea level rise (~2044) and by at least 75% by the year 2100 for a 1 m sea level rise, if evolution of the shoreline is to keep pace with rising sea levels.
Huang, Mugen; Luo, Jiaowan; Hu, Linchao; Zheng, Bo; Yu, Jianshe
2017-12-14
To suppress wild population of Aedes mosquitoes, the primary transmission vector of life-threatening diseases such as dengue, malaria, and Zika, an innovative strategy is to release male mosquitoes carrying the bacterium Wolbachia into natural areas to drive female sterility by cytoplasmic incompatibility. We develop a model of delay differential equations, incorporating the strong density restriction in the larval stage, to assess the delicate impact of life table parameters on suppression efficiency. Through mathematical analysis, we find the sufficient and necessary condition for global stability of the complete suppression state. This condition, combined with the experimental data for Aedes albopictus population in Guangzhou, helps us predict a large range of releasing intensities for suppression success. In particular, we find that if the number of released infected males is no less than four times the number of mosquitoes in wild areas, then the mosquito density in the peak season can be reduced by 95%. We introduce an index to quantify the dependence of suppression efficiency on parameters. The invariance of some quantitative properties of the index values under various perturbations of the same parameter justifies the applicability of this index, and the robustness of our modeling approach. The index yields a ranking of the sensitivity of all parameters, among which the adult mortality has the highest sensitivity and is considerably more sensitive than the natural larvae mortality. Copyright © 2017 Elsevier Ltd. All rights reserved.
Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
2018-04-01
This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.
Analytic solution to leading order coupled DGLAP evolution equations: A new perturbative QCD tool
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-01-01
We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)][M. M. Block, Eur. Phys. J. C 68, 683 (2010)] allow us to write fully decoupled solutions for the singlet structure function F s (x,Q 2 ) and G(x,Q 2 ) as F s (x,Q 2 )=F s (F s0 (x 0 ),G 0 (x 0 )) and G(x,Q 2 )=G(F s0 (x 0 ),G 0 (x 0 )), where the x 0 are the Bjorken x values at Q 0 2 . Here F s and G are known functions--found using LO DGLAP splitting functions--of the initial boundary conditions F s0 (x)≡F s (x,Q 0 2 ) and G 0 (x)≡G(x,Q 0 2 ), i.e., the chosen starting functions at the virtuality Q 0 2 . For both G(x) and F s (x), we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy--a computational fractional precision of O(10 -9 ). Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F s distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)], starting from their initial values at Q 0 2 =1 GeV 2 and 1.69 GeV 2 , respectively, using their choice of α s (Q 2 ). This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both G and F s satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of the starting functions on the evolved gluon and singlet structure functions, as functions of both Q
International Nuclear Information System (INIS)
Wu Jianping
2010-01-01
Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a (3+1)-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica. (general)
International Nuclear Information System (INIS)
Malmberg, T.
1993-09-01
The objective of this study is to derive and investigate thermodynamic restrictions for a particular class of internal variable models. Their evolution equations consist of two contributions: the usual irreversible part, depending only on the present state, and a reversible but path dependent part, linear in the rates of the external variables (evolution equations of ''mixed type''). In the first instance the thermodynamic analysis is based on the classical Clausius-Duhem entropy inequality and the Coleman-Noll argument. The analysis is restricted to infinitesimal strains and rotations. The results are specialized and transferred to a general class of elastic-viscoplastic material models. Subsequently, they are applied to several viscoplastic models of ''mixed type'', proposed or discussed in the literature (Robinson et al., Krempl et al., Freed et al.), and it is shown that some of these models are thermodynamically inconsistent. The study is closed with the evaluation of the extended Clausius-Duhem entropy inequality (concept of Mueller) where the entropy flux is governed by an assumed constitutive equation in its own right; also the constraining balance equations are explicitly accounted for by the method of Lagrange multipliers (Liu's approach). This analysis is done for a viscoplastic material model with evolution equations of the ''mixed type''. It is shown that this approach is much more involved than the evaluation of the classical Clausius-Duhem entropy inequality with the Coleman-Noll argument. (orig.) [de
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2017-11-01
Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines
International Nuclear Information System (INIS)
Konopel'chenko, B.G.
1983-01-01
New results in investigation of the group-theoretical and hamiltonian structure of the integrable evolution equations in 1+1 and 2+1 dimensions are briefly reviewed. Main general results, such as the form of integrable equations, Baecklund transfomations, symmetry groups, are turned out to have the same form for different spectral problems. The used generalized AKNS-method (the Ablowitz Kaup, Newell and Segur method) permits to prove that all nonlinear evolution equations considered are hamiltonians. The general condition of effective application of the ACNS mehtod to the concrete spectral problem is the possibility to calculate a recursion operator explicitly. The embedded representation is shown to be a fundamental object connected with different aspects of the inverse scattering problem
Directory of Open Access Journals (Sweden)
Kara B. De León
2017-10-01
Full Text Available Biofilms of sulfate-reducing bacteria (SRB are of particular interest as members of this group are culprits in corrosion of industrial metal and concrete pipelines as well as being key players in subsurface metal cycling. Yet the mechanism of biofilm formation by these bacteria has not been determined. Here we show that two supposedly identical wild-type cultures of the SRB Desulfovibrio vulgaris Hildenborough maintained in different laboratories have diverged in biofilm formation. From genome resequencing and subsequent mutant analyses, we discovered that a single nucleotide change within DVU1017, the ABC transporter of a type I secretion system (T1SS, was sufficient to eliminate biofilm formation in D. vulgaris Hildenborough. Two T1SS cargo proteins were identified as likely biofilm structural proteins, and the presence of at least one (with either being sufficient was shown to be required for biofilm formation. Antibodies specific to these biofilm structural proteins confirmed that DVU1017, and thus the T1SS, is essential for localization of these adhesion proteins on the cell surface. We propose that DVU1017 is a member of the lapB category of microbial surface proteins because of its phenotypic similarity to the adhesin export system described for biofilm formation in the environmental pseudomonads. These findings have led to the identification of two functions required for biofilm formation in D. vulgaris Hildenborough and focus attention on the importance of monitoring laboratory-driven evolution, as phenotypes as fundamental as biofilm formation can be altered.
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
International Nuclear Information System (INIS)
Tsuchida, Takayuki; Wolf, Thomas
2005-01-01
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
Energy Technology Data Exchange (ETDEWEB)
Tsuchida, Takayuki [Department of Physics, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337 (Japan); Wolf, Thomas [Department of Mathematics, Brock University, St Catharines, ON L2S 3A1 (Canada)
2005-09-02
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.
1982-12-01
1Muter.Te Motions Based on Ana lyzed Winds and wind-driven December 1982 Currents from. a Primitive Squat ion General a.OW -love"*..* Oean Circulation...mew se"$ (comeS.... do oISN..u am ae~ 00do OWaor NUN Fourier and Rotary Spc , Analysis Modeled Inertial and Subinrtial Motion 4 Primitive Equation
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Bauer, Bruno, S.; Siemon, Richard, E.
2008-10-22
We are pleased to report important progress in experimentally characterizing and numerically modeling the transformation into plasma of walls subjected to pulsed megagauss magnetic fields. Understanding this is important to Magnetized Target Fusion (MTF) because an important limitation to the metal liner approach to MTF comes from the strong eddy current heating on the surface of the metal liner. This has intriguing non-linear aspects when the magnetic field is in the megagauss regime as needed for MTF, and may limit the magnetic field in an MTF implosion. Many faculty, students, and staff have contributed to this work, and, implicitly or explicitly, to this report. Contributors include, in addition to the PIs, Andrey Esaulov, Stephan Fuelling, Irvin Lindemuth, Volodymyr Makhin, Ioana Paraschiv, Milena Angelova, Tom Awe, Tasha Goodrich, Arunkumar Prasadam, Andrew Oxner, Bruno Le Galloudec, Radu Presura, and Vladimir Ivanov. Highlights of the progress made during the grant include: • 12 articles published, and 44 conference and workshop presentations made, on a broad range of issues related to this project; • An ongoing experiment that uses the 1 MA, 100-ns Zebra z-pinch at UNR to apply 2 5 megagauss to a variety of metal surfaces, examining plasma formation and evolution; • Numerical simulation studies of the 1-MA Zebra, and potential Shiva Star and Atlas experiments that include realistic equations of state and radiation effects, using a variety of tables. • Collaboration with other groups doing simulations of this experiment at LANL, VNIIEF, SNL, and NumerEx leading to a successful international workshop at UNR in the spring of 2008.
International Nuclear Information System (INIS)
Bauer, Bruno S.; Siemon, Richard E.
2008-01-01
We are pleased to report important progress in experimentally characterizing and numerically modeling the transformation into plasma of walls subjected to pulsed megagauss magnetic fields. Understanding this is important to Magnetized Target Fusion (MTF) because an important limitation to the metal liner approach to MTF comes from the strong eddy current heating on the surface of the metal liner. This has intriguing non-linear aspects when the magnetic field is in the megagauss regime as needed for MTF, and may limit the magnetic field in an MTF implosion. Many faculty, students, and staff have contributed to this work, and, implicitly or explicitly, to this report. Contributors include, in addition to the PIs, Andrey Esaulov, Stephan Fuelling, Irvin Lindemuth, Volodymyr Makhin, Ioana Paraschiv, Milena Angelova, Tom Awe, Tasha Goodrich, Arunkumar Prasadam, Andrew Oxner, Bruno Le Galloudec, Radu Presura, and Vladimir Ivanov. Highlights of the progress made during the grant include: (1) 12 articles published, and 44 conference and workshop presentations made, on a broad range of issues related to this project; (2) An ongoing experiment that uses the 1 MA, 100-ns Zebra z-pinch at UNR to apply 2 5 megagauss to a variety of metal surfaces, examining plasma formation and evolution; (3) Numerical simulation studies of the 1-MA Zebra, and potential Shiva Star and Atlas experiments that include realistic equations of state and radiation effects, using a variety of tables; and (4) Collaboration with other groups doing simulations of this experiment at LANL, VNIIEF, SNL, and NumerEx leading to a successful international workshop at UNR in the spring of 2008.
Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C
Hanks, Thomas C.
2009-01-01
The diffusion equation is one of the three great partial differential equations of classical physics. It describes the flow or diffusion of heat in the presence of temperature gradients, fluid flow in porous media in the presence of pressure gradients, and the diffusion of molecules in the presence of chemical gradients. [The other two equations are the wave equation, which describes the propagation of electromagnetic waves (including light), acoustic (sound) waves, and elastic (seismic) waves radiated from earthquakes; and LaPlace’s equation, which describes the behavior of electric, gravitational, and fluid potentials, all part of potential field theory. The diffusion equation reduces to LaPlace’s equation at steady state, when the field of interest does not depend on t. Poisson’s equation is LaPlace’s equation with a source term.
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
International Nuclear Information System (INIS)
Yan Changshuo; Wang Jianmin
2010-01-01
High spatial resolution observations show that high-redshift galaxies are undergoing intensive evolution of dynamical structure and morphologies displayed by the Hα, Hβ, [O III], and [N II] images. It has been shown that supernova explosion (SNexp) of young massive stars during the star formation epoch, as kinetic feedback to host galaxies, can efficiently excite the turbulent viscosity. We incorporate the feedback into the dynamical equations through mass dropout and angular momentum transportation driven by the SNexp-excited turbulent viscosity. The empirical Kennicutt-Schmidt law is used for star formation rates (SFRs). We numerically solve the equations and show that there can be intensive evolution of structure of the gaseous disk. Secular evolution of the disk shows interesting characteristics: (1) high viscosity excited by SNexp can efficiently transport the gas from 10 kpc to ∼1 kpc forming a stellar disk whereas a stellar ring forms for the case with low viscosity; (2) starbursts trigger SMBH activity with a lag of ∼10 8 yr depending on SFRs, prompting the joint evolution of SMBHs and bulges; and (3) the velocity dispersion is as high as ∼100 km s -1 in the gaseous disk. These results are likely to vary with the initial mass function (IMF) that the SNexp rates rely on. Given the IMF, we use the GALAXEV code to compute the spectral evolution of stellar populations based on the dynamical structure. In order to compare the present models with the observed dynamical structure and images, we use the incident continuum from the simple stellar synthesis and CLOUDY to calculate emission line ratios of Hα, Hβ, [O III], and [N II], and Hα brightness of gas photoionized by young massive stars formed on the disks. The models can produce the main features of emission from star-forming galaxies. We apply the present model to two galaxies, BX 389 and BX 482 observed in the SINS high-z sample, which are bulge and disk-dominated, respectively. Two successive
International Nuclear Information System (INIS)
Oezis, Turgut; Aslan, Imail
2009-01-01
With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered. (general)
Meyer, Yves
2001-01-01
Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics invo...
Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
International Nuclear Information System (INIS)
Feng Qing-Hua; Zhang Yao-Ming; Meng Fan-Wei
2011-01-01
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. (general)
Rozhok, Andrii I; Salstrom, Jennifer L; DeGregori, James
2014-12-01
Age-dependent tissue decline and increased cancer incidence are widely accepted to be rate-limited by the accumulation of somatic mutations over time. Current models of carcinogenesis are dominated by the assumption that oncogenic mutations have defined advantageous fitness effects on recipient stem and progenitor cells, promoting and rate-limiting somatic evolution. However, this assumption is markedly discrepant with evolutionary theory, whereby fitness is a dynamic property of a phenotype imposed upon and widely modulated by environment. We computationally modeled dynamic microenvironment-dependent fitness alterations in hematopoietic stem cells (HSC) within the Sprengel-Liebig system known to govern evolution at the population level. Our model for the first time integrates real data on age-dependent dynamics of HSC division rates, pool size, and accumulation of genetic changes and demonstrates that somatic evolution is not rate-limited by the occurrence of mutations, but instead results from aged microenvironment-driven alterations in the selective/fitness value of previously accumulated genetic changes. Our results are also consistent with evolutionary models of aging and thus oppose both somatic mutation-centric paradigms of carcinogenesis and tissue functional decline. In total, we demonstrate that aging directly promotes HSC fitness decline and somatic evolution via non-cell-autonomous mechanisms.
International Nuclear Information System (INIS)
Gori, F.
2006-01-01
Mass conservation equation of non-renewable resources is employed to study the resources remaining in the reservoir according to the extraction policy. The energy conservation equation is transformed into an energy-capital conservation equation. The Hotelling rule is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is equal to unity. Mass and energy-capital conservation equations are then coupled and solved together. It is investigated the price evolution of extracted resources. The conclusion of the Hotelling rule for non-extracted resources, i.e. an exponential increase of the price of non-renewable resources at the rate of current interest, is then generalized. A new parameter, called 'Price Increase Factor', PIF, is introduced as the difference between the current interest rate of capital and the mass flow rate of extraction of non-renewable resources. The price of extracted resources can increase exponentially only if PIF is greater than zero or if the mass flow rate of extraction is lower than the current interest rate of capital. The price is constant if PIF is zero or if the mass flow rate of extraction is equal to the current interest rate. The price is decreasing with time if PIF is smaller than zero or if the mass flow rate of extraction is higher than the current interest rate. (author)
Equations for the non linear evolution of the resistive tearing modes in toroidal plasmas
International Nuclear Information System (INIS)
Edery, D.; Pellat, R.; Soule, J.L.
1979-09-01
Following the tokamak ordering, we simplify the resistive MHD equations in toroidal geometry. We obtain a closed system of non linear equations for two scalar potentials of the magnetic and velocity fields and for plasma density and temperature. If we expand these equations in the inverse of aspect ratio they are exact to the two first orders. Our formalism should correctly describe the mode coupling by curvature effects /1/ and the toroidal displacement of magnetic surfaces /2/. It provides a natural extension of the well known cylindrical model /3/ and is now being solved on computer
Directory of Open Access Journals (Sweden)
Bruno de Andrade
2009-01-01
Full Text Available We study the existence and uniqueness of almost automorphic (resp., pseudo-almost automorphic solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain.
Gardner, Andy; Smiseth, Per T
2011-01-22
In mammals, altricial birds and some invertebrates, parents care for their offspring by providing them with food and protection until independence. Although parental food provisioning is often essential for offspring survival and growth, very little is known about the conditions favouring the evolutionary innovation of this key component of care. Here, we develop a mathematical model for the evolution of parental food provisioning. We find that this evolutionary innovation is favoured when the efficiency of parental food provisioning is high relative to the efficiency of offspring self-feeding and/or parental guarding. We also explore the coevolution between food provisioning and other components of parental care, as well as offspring behaviour. We find that the evolution of food provisioning prompts evolutionary changes in other components of care by allowing parents to choose safer nest sites, and that it promotes the evolution of sibling competition, which in turn further drives the evolution of parental food provisioning. This mutual reinforcement of parental care and sibling competition suggests that evolution of parental food provisioning should show a unidirectional trend from no parental food provisioning to full parental food provisioning.
Recent evolutions in costing systems: A literature review of Time-Driven Activity-Based Costing
Siguenza Guzman, Lorena; Van den Abbeele, Alexandra; Vandewalle, Joos; Verhaaren, Henry; Cattrysse, Dirk
2013-01-01
This article provides a comprehensive literature review of Time-Driven Activity Based Costing (TDABC), a relatively new tool to improve the cost allocation to products and services. After a brief overview of traditional costing and activity based costing systems (ABC), a detailed description of the TDABC model is given and a comparison made between this methodology and its predecessor ABC. Thirty-six empirical contributions using TDABC over the period 2004-2012 were reviewed. The results and ...
Directory of Open Access Journals (Sweden)
Herb Kunze
2014-06-01
Full Text Available Let T be a set-valued contraction mapping on a general Banach space $\\mathcal{B}$. In the first part of this paper we introduce the evolution inclusion $\\dot x + x \\in Tx$ and study the convergence of solutions to this inclusion toward fixed points of T. Two cases are examined: (i T has a fixed point $\\bar y \\in \\mathcal{B}$ in the usual sense, i.e., $\\bar y = T \\bar y$ and (ii T has a fixed point in the sense of inclusions, i.e., $\\bar y \\in T \\bar y$. In the second part we extend this analysis to the case of set-valued evolution equations taking the form $\\dot x + x = Tx$. We also provide some applications to generalized fractal transforms.
Second order time evolution of the multigroup diffusion and P1 equations for radiation transport
International Nuclear Information System (INIS)
Olson, Gordon L.
2011-01-01
Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.
International Nuclear Information System (INIS)
Guidi, Leonardo F.; Marchetti, D.H.U.
2003-01-01
We establish a comparison between Rakib-Sivashinsky and Michelson-Sivashinsky quasilinear parabolic differential equations governing the weak thermal limit of flame front propagating in channels. For the former equation, we give a complete description of all steady solutions and present their local and global stability analysis. For the latter, bi-coalescent and interpolating unstable steady solutions are introduced and shown to be more numerous than the previous known coalescent solutions. These facts are argued to be responsible for the disagreement between the observed dynamics in numerical experiments and the exact (linear) stability analysis and give ingredients to construct quasi-stable solutions describing parabolic steadily propagating flame with centered tip
Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces
Directory of Open Access Journals (Sweden)
Xavier Carvajal Paredes
2010-11-01
Full Text Available In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq 2heta ge 2$ and the initial value problem associated with the nonlinear Schrodinger equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq heta geq 1$. Persistence property has been proved by approximation of the solutions and using a priori estimates.
Time evolution of tunneling in a thermal medium: Environment-driven excited tunneling
International Nuclear Information System (INIS)
Matsumoto, Sh.; Yoshimura, M.
2004-01-01
Time evolution of tunneling phenomena proceeding in a thermal medium is studied using a standard model of environmental interaction. A semiclassical probability formula for the particle motion in a metastable state of a one-dimensional system put in a thermal medium is combined with the formula of the quantum penetration factor through a potential barrier to derive the tunneling rate in the medium. The effect of environment, its influence on time evolution in particular, is clarified in our real-time formalism. A nonlinear resonance effect is shown to enhance the tunneling rate at finite times of order 2/η, with η the friction coefficient unless η is too small. In the linear approximation this effect has relevance to the parametric resonance. This effect enhances the possibility of early termination of the cosmological phase transition much prior to the typical Hubble time
Gardner, Andy; Smiseth, Per T.
2010-01-01
In mammals, altricial birds and some invertebrates, parents care for their offspring by providing them with food and protection until independence. Although parental food provisioning is often essential for offspring survival and growth, very little is known about the conditions favouring the evolutionary innovation of this key component of care. Here, we develop a mathematical model for the evolution of parental food provisioning. We find that this evolutionary innovation is favoured when th...
An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion
Messelmi, Farid
2017-12-01
We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.
Shao, Tao; Yang, Wenjin; Zhang, Cheng; Fang, Zhi; Zhou, Yixiao; Schamiloglu, Edl
2014-09-01
Current-voltage characteristics, discharge images, and optical spectra of atmospheric pressure plasma jets (APPJs) are studied using a microsecond pulse length generator producing repetitive output pulses with different polarities. The experimental results show that the APPJs excited by the pulses with positive polarity have longer plume, faster propagation speed, higher power, and more excited species, such as \\text{N}2 , O, He, \\text{N}2+ , than that with the negatively excited APPJs. The images taken using an intensified charge-coupled device show that the APPJs excited by pulses with positive polarity are characterized by a bullet-like structure, while the APPJs excited by pulses with negative polarity are continuous. The propagation speed of the APPJs driven by a microsecond pulse length generator is about tens of km/s, which is similar to the APPJs driven by a kHz frequency sinusoidal voltage source. The analysis shows that the space charge accumulation effect plays an important role during the discharge. The transient enhanced electric field induced by the accumulated ions between the needle-like electrode and the nozzle in the APPJs excited by pulses with negative polarity enhances electron field emission from the cathode, which is illustrated by the bright line on the time-integrated images. This makes the shape of the APPJ excited using pulses with negative polarity different from the bullet-like shape of the APPJs excited by pulses with positive polarity.
Ge, Cheng-Hao; Sun, Na; Kang, Qi; Ren, Long-Fei; Ahmad, Hafiz Adeel; Ni, Shou-Qing; Wang, Zhibin
2018-03-01
A distinct shift of bacterial community driven by organic matter (OM) and powder activated carbon (PAC) was discovered in the simultaneous anammox and denitrification (SAD) process which was operated in an anti-fouling submerged anaerobic membrane bio-reactor. Based on anammox performance, optimal OM dose (50 mg/L) was advised to start up SAD process successfully. The results of qPCR and high throughput sequencing analysis indicated that OM played a key role in microbial community evolutions, impelling denitrifiers to challenge anammox's dominance. The addition of PAC not only mitigated the membrane fouling, but also stimulated the enrichment of denitrifiers, accounting for the predominant phylum changing from Planctomycetes to Proteobacteria in SAD process. Functional genes forecasts based on KEGG database and COG database showed that the expressions of full denitrification functional genes were highly promoted in R C , which demonstrated the enhanced full denitrification pathway driven by OM and PAC under low COD/N value (0.11). Copyright © 2017 Elsevier Ltd. All rights reserved.
Dehydration-driven evolution of topological complexity in ethylamonium uranyl selenates
Energy Technology Data Exchange (ETDEWEB)
Gurzhiy, Vladislav V., E-mail: vladgeo17@mail.ru [Department of Crystallography, St. Petersburg State University, University Emb. 7/9, 199034 St. Petersburg (Russian Federation); Krivovichev, Sergey V. [Department of Crystallography, St. Petersburg State University, University Emb. 7/9, 199034 St. Petersburg (Russian Federation); Tananaev, Ivan G. [Far Eastern Federal University, Suhanova st. 8, 690950 Vladivostok (Russian Federation)
2017-03-15
Single crystals of four novel uranyl selenate and selenite-selenate oxysalts with protonated ethylamine molecules, (C{sub 2}H{sub 8}N){sub 2}[(UO{sub 2})(SeO{sub 4}){sub 2}(H{sub 2}O)](H{sub 2}O) (I), (C{sub 2}H{sub 8}N){sub 3}[(UO{sub 2})(SeO{sub 4}){sub 2}(HSeO{sub 4})] (II), (C{sub 2}H{sub 8}N)[(UO{sub 2})(SeO{sub 4})(HSeO{sub 3})] (III), and (C{sub 2}H{sub 8}N)(H{sub 3}O)[(UO{sub 2})(SeO{sub 4}){sub 2}(H{sub 2}O)] (IV) have been prepared by isothermal evaporation from aqueous solutions. Uranyl-containing 1D and 2D units have been investigated using topological approach and information-based complexity measurements that demonstrate the evolution of structural units and the increase of topological complexity with the decrease of H{sub 2}O content. - Graphical abstract: Single crystals of four novel uranyl selenate and selenite-selenate oxysalts with protonated ethylamine molecules have been prepared by isothermal evaporation from aqueous solutions. Structural analysis and information-based topological complexity calculations points to the possible sequence of crystalline phases formation, showing both topological and structural branches of evolution. - Highlights: • Single crystals of four novel uranyl oxysalts were prepared by evaporation method. • The graph theory was used for investigation of topologies of structural units. • Dehydration processes drives the evolution of topological complexity of 1D and 2D structural units.
Dark energy equation of state parameter and its evolution at low redshift
Energy Technology Data Exchange (ETDEWEB)
Tripathi, Ashutosh; Sangwan, Archana; Jassal, H.K., E-mail: ashutosh_tripathi@fudan.edu.cn, E-mail: archanakumari@iisermohali.ac.in, E-mail: hkjassal@iisermohali.ac.in [Indian Institute of Science Education and Research Mohali, SAS Nagar, Mohali 140306, Punjab (India)
2017-06-01
In this paper, we constrain dark energy models using a compendium of observations at low redshifts. We consider the dark energy as a barotropic fluid, with the equation of state a constant as well the case where dark energy equation of state is a function of time. The observations considered here are Supernova Type Ia data, Baryon Acoustic Oscillation data and Hubble parameter measurements. We compare constraints obtained from these data and also do a combined analysis. The combined observational constraints put strong limits on variation of dark energy density with redshift. For varying dark energy models, the range of parameters preferred by the supernova type Ia data is in tension with the other low redshift distance measurements.
Optical analogues of the Newton-Schrödinger equation and boson star evolution.
Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M; Faccio, Daniele
2016-11-14
Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.
Evolution of the earliest horses driven by climate change in the Paleocene-Eocene Thermal Maximum.
Secord, Ross; Bloch, Jonathan I; Chester, Stephen G B; Boyer, Doug M; Wood, Aaron R; Wing, Scott L; Kraus, Mary J; McInerney, Francesca A; Krigbaum, John
2012-02-24
Body size plays a critical role in mammalian ecology and physiology. Previous research has shown that many mammals became smaller during the Paleocene-Eocene Thermal Maximum (PETM), but the timing and magnitude of that change relative to climate change have been unclear. A high-resolution record of continental climate and equid body size change shows a directional size decrease of ~30% over the first ~130,000 years of the PETM, followed by a ~76% increase in the recovery phase of the PETM. These size changes are negatively correlated with temperature inferred from oxygen isotopes in mammal teeth and were probably driven by shifts in temperature and possibly high atmospheric CO(2) concentrations. These findings could be important for understanding mammalian evolutionary responses to future global warming.
Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation
International Nuclear Information System (INIS)
Nemirovskii, Sergey K.
2006-01-01
The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact powerlike solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l)∝l -5/2 obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection
Evolution of a network of vortex loops in He-II: exact solution of the rate equation.
Nemirovskii, Sergey K
2006-01-13
The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the "rate equation" for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact power-like solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l) proportional l(-5/2) obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection.
Morphological Evolution of Pit-Patterned Si(001) Substrates Driven by Surface-Energy Reduction
Salvalaglio, Marco; Backofen, Rainer; Voigt, Axel; Montalenti, Francesco
2017-09-01
Lateral ordering of heteroepitaxial islands can be conveniently achieved by suitable pit-patterning of the substrate prior to deposition. Controlling shape, orientation, and size of the pits is not trivial as, being metastable, they can significantly evolve during deposition/annealing. In this paper, we exploit a continuum model to explore the typical metastable pit morphologies that can be expected on Si(001), depending on the initial depth/shape. Evolution is predicted using a surface-diffusion model, formulated in a phase-field framework, and tackling surface-energy anisotropy. Results are shown to nicely reproduce typical metastable shapes reported in the literature. Moreover, long time scale evolutions of pit profiles with different depths are found to follow a similar kinetic pathway. The model is also exploited to treat the case of heteroepitaxial growth involving two materials characterized by different facets in their equilibrium Wulff's shape. This can lead to significant changes in morphologies, such as a rotation of the pit during deposition as evidenced in Ge/Si experiments.
Directory of Open Access Journals (Sweden)
Jin-Hua Xiao
Full Text Available Among the Chalcidoids, hymenopteran parasitic wasps that have diversified lifestyles, a partial mitochondrial genome has been reported only from Nasonia. This genome had many unusual features, especially a dramatic reorganization and a high rate of evolution. Comparisons based on more mitochondrial genomic data from the same superfamily were required to reveal weather these unusual features are peculiar to Nasonia or not. In the present study, we sequenced the nearly complete mitochondrial genomes from the species Philotrypesis. pilosa and Philotrypesis sp., both of which were associated with Ficus hispida. The acquired data included all of the protein-coding genes, rRNAs, and most of the tRNAs, and in P. pilosa the control region. High levels of nucleotide divergence separated the two species. A comparison of all available hymenopteran mitochondrial genomes (including a submitted partial genome from Ceratosolen solmsi revealed that the Chalcidoids had dramatic mitochondrial gene rearrangments, involved not only the tRNAs, but also several protein-coding genes. The AT-rich control region was translocated and inverted in Philotrypesis. The mitochondrial genomes also exhibited rapid rates of evolution involving elevated nonsynonymous mutations.
A model of the evolution of larval feeding rate in Drosophila driven by conflicting energy demands.
Mueller, Laurence D; Barter, Thomas T
2015-02-01
Energy allocation is believed to drive trade-offs in life history evolution. We develop a physiological and genetic model of energy allocation that drives evolution of feeding rate in a well-studied model system. In a variety of stressful environments Drosophila larvae adapt by altering their rate of feeding. Drosophila larvae adapted to high levels of ammonia, urea, and the presence of parasitoids evolve lower feeding rates. Larvae adapted to crowded conditions evolve higher feeding rates. Feeding rates should affect gross food intake, metabolic rates, and efficiency of food utilization. We develop a model of larval net energy intake as a function of feeding rates. We show that when there are toxic compounds in the larval food that require energy for detoxification, larvae can maximize their energy intake by slowing their feeding rates. While the reduction in feeding rates may increase development time and decrease competitive ability, we show that genotypes with lower feeding rates can be favored by natural selection if they have a sufficiently elevated viability in the toxic environment. This work shows how a simple phenotype, larval feeding rates, may be of central importance in adaptation to a wide variety of stressful environments via its role in energy allocation.
Strategy evolution driven by switching probabilities in structured multi-agent systems
Zhang, Jianlei; Chen, Zengqiang; Li, Zhiqi
2017-10-01
Evolutionary mechanism driving the commonly seen cooperation among unrelated individuals is puzzling. Related models for evolutionary games on graphs traditionally assume that players imitate their successful neighbours with higher benefits. Notably, an implicit assumption here is that players are always able to acquire the required pay-off information. To relax this restrictive assumption, a contact-based model has been proposed, where switching probabilities between strategies drive the strategy evolution. However, the explicit and quantified relation between a player's switching probability for her strategies and the number of her neighbours remains unknown. This is especially a key point in heterogeneously structured system, where players may differ in the numbers of their neighbours. Focusing on this, here we present an augmented model by introducing an attenuation coefficient and evaluate its influence on the evolution dynamics. Results show that the individual influence on others is negatively correlated with the contact numbers specified by the network topologies. Results further provide the conditions under which the coexisting strategies can be calculated analytically.
Mohanty, Bhaskar Chandra; Bector, Keerti; Laha, Ranjit
2018-03-01
Doping driven remarkable microstructural evolution of PbS thin films grown by a single-step chemical bath deposition process at 60 °C is reported. The undoped films were discontinuous with octahedral-shaped crystallites after 30 min of deposition, whereas Cu doping led to a distinctly different surface microstructure characterized by densely packed elongated crystallites. A mechanism, based on the time sequence study of microstructural evolution of the films, and detailed XRD and Raman measurements, has been proposed to explain the contrasting microstructure of the doped films. The incorporation of Cu forms an interface layer, which is devoid of Pb. The excess Cu ions in this interface layer at the initial stages of film growth strongly interact and selectively stabilize the charged {111} faces containing either Pb or S compared to the uncharged {100} faces that contain both Pb and S. This interaction interferes with the natural growth habit resulting in the observed surface features of the doped films. Concurrently, the Cu-doping potentially changed the optical properties of the films: A significant widening of the bandgap from 1.52 eV to 1.74 eV for increase in Cu concentration from 0 to 20% was observed, making it a highly potential absorber layer in thin film solar cells.
Matulla, Christoph; Hollósi, Brigitta; Andre, Konrad; Gringinger, Julia; Chimani, Barbara; Namyslo, Joachim; Fuchs, Tobias; Auerbach, Markus; Herrmann, Carina; Sladek, Brigitte; Berghold, Heimo; Gschier, Roland; Eichinger-Vill, Eva
2017-06-01
Road authorities, freight, and logistic industries face a multitude of challenges in a world changing at an ever growing pace. While globalization, changes in technology, demography, and traffic, for instance, have received much attention over the bygone decades, climate change has not been treated with equal care until recently. However, since it has been recognized that climate change jeopardizes many business areas in transport, freight, and logistics, research programs investigating future threats have been initiated. One of these programs is the Conference of European Directors of Roads' (CEDR) Transnational Research Programme (TRP), which emerged about a decade ago from a cooperation between European National Road Authorities and the EU. This paper presents findings of a CEDR project called CliPDaR, which has been designed to answer questions from road authorities concerning climate-driven future threats to transport infrastructure. Pertaining results are based on two potential future socio-economic pathways of mankind (one strongly economically oriented "A2" and one more balanced scenario "A1B"), which are used to drive global climate models (GCMs) producing global and continental scale climate change projections. In order to achieve climate change projections, which are valid on regional scales, GCM projections are downscaled by regional climate models. Results shown here originate from research questions raised by European Road Authorities. They refer to future occurrence frequencies of severely cold winter seasons in Fennoscandia, to particularly hot summer seasons in the Iberian Peninsula and to changes in extreme weather phenomena triggering landslides and rutting in Central Europe. Future occurrence frequencies of extreme winter and summer conditions are investigated by empirical orthogonal function analyses of GCM projections driven with by A2 and A1B pathways. The analysis of future weather phenomena triggering landslides and rutting events requires
Visible-Light-Driven Hydrogen Evolution Using Planarized Conjugated Polymer Photocatalysts.
Sprick, Reiner Sebastian; Bonillo, Baltasar; Clowes, Rob; Guiglion, Pierre; Brownbill, Nick J; Slater, Benjamin J; Blanc, Frédéric; Zwijnenburg, Martijn A; Adams, Dave J; Cooper, Andrew I
2016-01-26
Linear poly(p-phenylene)s are modestly active UV photocatalysts for hydrogen production in the presence of a sacrificial electron donor. Introduction of planarized fluorene, carbazole, dibenzo[b,d]thiophene or dibenzo[b,d]thiophene sulfone units greatly enhances the H 2 evolution rate. The most active dibenzo[b,d]thiophene sulfone co-polymer has a UV photocatalytic activity that rivals TiO 2 , but is much more active under visible light. The dibenzo[b,d]thiophene sulfone co-polymer has an apparent quantum yield of 2.3 % at 420 nm, as compared to 0.1 % for platinized commercial pristine carbon nitride.
International Nuclear Information System (INIS)
Colvin, Jeffrey D.; Jankowski, Alan F.; Kumar, Mukul; MoberlyChan, Warren J.; Reed, Bryan W.; Paisley, Dennis L.; Tierney, Thomas E.
2009-01-01
We previously reported [Colvin et al., J. Appl. Phys. 101, 084906 (2007)] on the microstructure morphology of pure Bi metal subjected to rapid laser-shock-driven melting and subsequent resolidification upon release of pressure, where the estimated effective undercooling rates were of the order of 10 9 -10 10 K/s. More recently, we repeated these experiments, but with a Bi/Zn alloy (Zn atomic fraction of 2%-4%) instead of elemental Bi and with a change in target design to suppress spall in the Bi/Zn samples. We observed a similar microstructure morphology in the two sets of experiments, with initially columnar grains recrystallizing to larger equiaxed grains. The Bi samples, however, exhibited micron-scale dendrites on the spall surfaces, whereas there were no dendritic structures anywhere in the nonspalled Bi/Zn, even down to the nanometer scale as observed by transmission electron microscopy. We present the simulations and the interferometry data that show that the samples in the two sets of experiments followed nearly identical hydrodynamic and thermodynamic paths apart from the presence of (probably partially liquid) spall in pure Bi. Simulations also show that the spall occurs right at the moving phase front and, hence, the spall itself cuts off the principal direction for latent heat dissipation across the phase boundary. We suggest that it is the liquid spall itself that creates the conditions for dendrite formation
Non-linear macro evolution of a dc driven micro atmospheric glow discharge
Energy Technology Data Exchange (ETDEWEB)
Xu, S. F.; Zhong, X. X., E-mail: xxzhong@sjtu.edu.cn [The State Key Laboratory on Fiber Optic Local Area, Communication Networks and Advanced Optical Communication Systems, Key Laboratory for Laser Plasmas and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China)
2015-10-15
We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge when the water acts as a cathode, different from the discharge when water behaves as an anode. Groups of snapshots of the micro discharge formed at different discharge currents are captured by an intensified charge-coupled device with controlled exposure time, and each group consisted of 256 images taken in succession. Edge detection methods are used to identify the water surface and then the total brightness is defined by adding up the signal counts over the area of the micro discharge. Motions of the water surface at different discharge currents show that the water surface lowers increasingly rapidly when the water acts as a cathode. In contrast, the water surface lowers at a constant speed when the water behaves as an anode. The light curves are similar to logistic growth curves, suggesting that a self-inhibition process occurs in the micro discharge. Meanwhile, the total brightness increases linearly during the same time when the water acts as an anode. Discharge-water interactions cause the micro discharge to evolve. The charged particle bomb process is probably responsible for the different behaviors of the micro discharges when the water acts as cathode and anode.
Soisson, F.; Becquart, C. S.; Castin, N.; Domain, C.; Malerba, L.; Vincent, E.
2010-11-01
Atomistic Kinetic Monte Carlo (AKMC) simulations are a powerful tool to study the microstructural and microchemical evolution of alloys controlled by diffusion processes, under irradiation and during thermal ageing. In the framework of the FP6 Perfect program, two main approaches have been applied to binary and multicomponent iron based alloys. The first one is based on a diffusion model which takes into account vacancy and self-interstitial jumps, using simple rigid lattice approximation and broken-bond models to compute the point-defect jump frequencies. The corresponding parameters are fitted on ab initio calculations of a few typical configurations and migration barriers. The second method uses empirical potentials to compute a much larger number of migration barriers, including atomic relaxations, and Artificial Intelligence regression methods to predict the other ones. It is somewhat less rapid than the first one, but significantly more than simulations using "on-the-fly" calculations of all the barriers. We review here the recent advances and perspectives concerning these techniques.
International Nuclear Information System (INIS)
Soisson, F.; Becquart, C.S.; Castin, N.; Domain, C.; Malerba, L.; Vincent, E.
2010-01-01
Atomistic Kinetic Monte Carlo (AKMC) simulations are a powerful tool to study the microstructural and microchemical evolution of alloys controlled by diffusion processes, under irradiation and during thermal ageing. In the framework of the FP6 Perfect program, two main approaches have been applied to binary and multicomponent iron based alloys. The first one is based on a diffusion model which takes into account vacancy and self-interstitial jumps, using simple rigid lattice approximation and broken-bond models to compute the point-defect jump frequencies. The corresponding parameters are fitted on ab initio calculations of a few typical configurations and migration barriers. The second method uses empirical potentials to compute a much larger number of migration barriers, including atomic relaxations, and Artificial Intelligence regression methods to predict the other ones. It is somewhat less rapid than the first one, but significantly more than simulations using 'on-the-fly' calculations of all the barriers. We review here the recent advances and perspectives concerning these techniques.
Evolution of Phototrophy in the Chloroflexi Phylum Driven by Horizontal Gene Transfer
Directory of Open Access Journals (Sweden)
Lewis M. Ward
2018-02-01
Full Text Available The evolutionary mechanisms behind the extant distribution of photosynthesis is a point of substantial contention. Hypotheses range from the presence of phototrophy in the last universal common ancestor and massive gene loss in most lineages, to a later origin in Cyanobacteria followed by extensive horizontal gene transfer into the extant phototrophic clades, with intermediate scenarios that incorporate aspects of both end-members. Here, we report draft genomes of 11 Chloroflexi: the phototrophic Chloroflexia isolate Kouleothrix aurantiaca as well as 10 genome bins recovered from metagenomic sequencing of microbial mats found in Japanese hot springs. Two of these metagenome bins encode photrophic reaction centers and several of these bins form a metabolically diverse, monophyletic clade sister to the Anaerolineae class that we term Candidatus Thermofonsia. Comparisons of organismal (based on conserved ribosomal and phototrophy (reaction center and bacteriochlorophyll synthesis protein phylogenies throughout the Chloroflexi demonstrate that two new lineages acquired phototrophy independently via horizontal gene transfer (HGT from different ancestral donors within the classically phototrophic Chloroflexia class. These results illustrate a complex history of phototrophy within this group, with metabolic innovation tied to HGT. These observations do not support simple hypotheses for the evolution of photosynthesis that require massive character loss from many clades; rather, HGT appears to be the defining mechanic for the distribution of phototrophy in many of the extant clades in which it appears.
Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times
Energy Technology Data Exchange (ETDEWEB)
Witzany, Vojtěch; Lämmerzahl, Claus, E-mail: vojtech.witzany@zarm.uni-bremen.de, E-mail: claus.laemmerzahl@zarm.uni-bremen.de [ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen (Germany)
2017-06-01
Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.
Discrete maximal regularity of time-stepping schemes for fractional evolution equations.
Jin, Bangti; Li, Buyang; Zhou, Zhi
2018-01-01
In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.
International Nuclear Information System (INIS)
Kawamura, Hiroyuki; Tanaka, Kazuhiro
2010-01-01
The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale μ with smaller interquark separations zt (z≤1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale ∼√(m b Λ QCD ) for t less than ∼1 GeV -1 , using the recently obtained operator product expansion of the DA as the input at μ∼1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at μ∼√(m b Λ QCD ) for the factorization formula by the compact integrals of the DA at μ∼1 GeV.
Camafort, Miquel; Booth-Rea, Guillermo; Pérez-Peña, Jose Vicente; Melki, Fetheddine; Gracia, Eulalia; Azañón, Jose Miguel; Ranero, César R.
2017-04-01
Active tectonics in North Africa is fundamentally driven by NW-SE directed slow convergence between the Nubia and Eurasia plates, leading to a region of thrust and strike-slip faulting. In this paper we analyze the morphometric characteristics of the little-studied northern Tunisia sector. The study aimed at identifying previously unknown active tectonic structures, and to further understand the mechanisms that drive the drainage evolution in this region of slow convergence. The interpretation of morphometric data was supported with a field campaign of a selection of structures. The analysis indicates that recent fluvial captures have been the main factor rejuvenating drainage catchments. The Medjerda River, which is the main catchment in northern Tunisia, has increased its drainage area during the Quaternary by capturing adjacent axial valleys to the north and south of its drainage divide. These captures are probably driven by gradual uplift of adjacent axial valleys by reverse/oblique faults or associated folds like El Alia-Teboursouk and Dkhila faults. Our fieldwork found that these faults cut Holocene colluvial fans containing seismites like clastic dikes and sand volcanoes, indicating recent seismogenic faulting. The growth and stabilization of the axial Medjerda River against the natural tendency of transverse drainages might be caused by a combination of dynamic topography and transpressive tectonics. The orientation of the large axial Medjerda drainage that runs from eastern Algeria towards northeastern Tunisia into the Gulf of Tunis, might be the associated to negative buoyancy caused by the underlying Nubia slab at its mouth, together with uplift of the Medjerda headwaters along the South Atlassic dextral transfer zone.
Directory of Open Access Journals (Sweden)
Jinliang Xu
2013-06-01
Full Text Available This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF.
Piontkivska, Helen; Matos, Luis F; Paul, Sinu; Scharfenberg, Brian; Farmerie, William G; Miyamoto, Michael M; Wayne, Marta L
2016-10-05
Sigma virus (DMelSV) is ubiquitous in natural populations of Drosophila melanogaster. Host-mediated, selective RNA editing of adenosines to inosines (ADAR) may contribute to control of viral infection by preventing transcripts from being transported into the cytoplasm or being translated accurately; or by increasing the viral genomic mutation rate. Previous PCR-based studies showed that ADAR mutations occur in DMelSV at low frequency. Here we use SOLiD TM deep sequencing of flies from a single host population from Athens, GA, USA to comprehensively evaluate patterns of sequence variation in DMelSV with respect to ADAR. GA dinucleotides, which are weak targets of ADAR, are strongly overrepresented in the positive strand of the virus, consistent with selection to generate ADAR resistance on this complement of the transient, double-stranded RNA intermediate in replication and transcription. Potential ADAR sites in a worldwide sample of viruses are more likely to be "resistant" if the sites do not vary among samples. Either variable sites are less constrained and hence are subject to weaker selection than conserved sites, or the variation is driven by ADAR. We also find evidence of mutations segregating within hosts, hereafter referred to as hypervariable sites. Some of these sites were variable only in one or two flies (i.e., rare); others were shared by four or even all five of the flies (i.e., common). Rare and common hypervariable sites were indistinguishable with respect to susceptibility to ADAR; however, polymorphism in rare sites were more likely to be consistent with the action of ADAR than in common ones, again suggesting that ADAR is deleterious to the virus. Thus, in DMelSV, host mutagenesis is constraining viral evolution both within and between hosts. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Directory of Open Access Journals (Sweden)
Sicard Delphine
2009-12-01
Full Text Available Abstract Background Variation of resource supply is one of the key factors that drive the evolution of life-history strategies, and hence the interactions between individuals. In the yeast Saccharomyces cerevisiae, two life-history strategies related to different resource utilization have been previously described in strains from different industrial origins. In this work, we analyzed metabolic traits and life-history strategies in a broader collection of yeast strains sampled in various ecological niches (forest, human body, fruits, laboratory and industrial environments. Results By analysing the genetic and plastic variation of six life-history and three metabolic traits, we showed that S. cerevisiae populations harbour different strategies depending on their ecological niches. On one hand, the forest and laboratory strains, referred to as extreme "ants", reproduce quickly, reach a large carrying capacity and a small cell size in fermentation, but have a low reproduction rate in respiration. On the other hand, the industrial strains, referred to as extreme "grasshoppers", reproduce slowly, reach a small carrying capacity but have a big cell size in fermentation and a high reproduction rate in respiration. "Grasshoppers" have usually higher glucose consumption rate than "ants", while they produce lower quantities of ethanol, suggesting that they store cell resources rather than secreting secondary products to cross-feed or poison competitors. The clinical and fruit strains are intermediate between these two groups. Conclusions Altogether, these results are consistent with a niche-driven evolution of S. cerevisiae, with phenotypic convergence of populations living in similar habitat. They also revealed that competition between strains having contrasted life-history strategies ("ants" and "grasshoppers" seems to occur at low frequency or be unstable since opposite life-history strategies appeared to be maintained in distinct ecological niches.
MacArthur, Iain; Anastasi, Elisa; Alvarez, Sonsiray; Scortti, Mariela; Vázquez-Boland, José A
2017-05-01
The conjugative virulence plasmid is a key component of the Rhodococcus equi accessory genome essential for pathogenesis. Three host-associated virulence plasmid types have been identified the equine pVAPA and porcine pVAPB circular variants, and the linear pVAPN found in bovine (ruminant) isolates. We recently characterized the R. equi pangenome (Anastasi E, et al. 2016. Pangenome and phylogenomic analysis of the pathogenic actinobacterium Rhodococcus equi. Genome Biol Evol. 8:3140-3148.) and we report here the comparative analysis of the virulence plasmid genomes. Plasmids within each host-associated type were highly similar despite their diverse origins. Variation was accounted for by scattered single nucleotide polymorphisms and short nucleotide indels, while larger indels-mostly in the plasticity region near the vap pathogencity island (PAI)-defined plasmid genomic subtypes. Only one of the plasmids analyzed, of pVAPN type, was exceptionally divergent due to accumulation of indels in the housekeeping backbone. Each host-associated plasmid type carried a unique PAI differing in vap gene complement, suggesting animal host-specific evolution of the vap multigene family. Complete conservation of the vap PAI was observed within each host-associated plasmid type. Both diversity of host-associated plasmid types and clonality of specific chromosomal-plasmid genomic type combinations were observed within the same R. equi phylogenomic subclade. Our data indicate that the overall strong conservation of the R. equi host-associated virulence plasmids is the combined result of host-driven selection, lateral transfer between strains, and geographical spread due to international livestock exchanges. © The Author(s) 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Energy Technology Data Exchange (ETDEWEB)
Benuzzi, A
1997-12-15
This work is dedicated to shock waves and their applications to the study of the equation of state of compressed matter.This document is divided into 6 chapters: 1) laser-produced plasmas and abrasion processes, 2) shock waves and the equation of state, 3) relative measuring of the equation of state, 4) comparison between direct and indirect drive to compress the target, 5) the measurement of a new parameter: the shock temperature, and 6) control and measurement of the pre-heating phase. In this work we have reached relevant results, we have shown for the first time the possibility of generating shock waves of very high quality in terms of spatial distribution, time dependence and of negligible pre-heating phase with direct laser radiation. We have shown that the shock pressure stays unchanged as time passes for targets whose thickness is over 10 {mu}m. A relative measurement of the equation of state has been performed through the simultaneous measurement of the velocity of shock waves passing through 2 different media. The great efficiency of the direct drive has allowed us to produce pressures up to 40 Mbar. An absolute measurement of the equation of state requires the measurement of 2 parameters, we have then performed the measurement of the colour temperature of an aluminium target submitted to laser shocks. A simple model has been developed to infer the shock temperature from the colour temperature. The last important result is the assessment of the temperature of the pre-heating phase that is necessary to know the media in which the shock wave propagates. The comparison of the measured values of the reflectivity of the back side of the target with the computed values given by an adequate simulation has allowed us to deduce the evolution of the temperature of the pre-heating phase. (A.C.)
Cafaro, Carlo; Alsing, Paul M
2018-04-01
The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.
Cafaro, Carlo; Alsing, Paul M.
2018-04-01
The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.
On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2
International Nuclear Information System (INIS)
Troudet, T.; Paris-11 Univ., 91 - Orsay
1986-01-01
We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)
Citrin, J.; Bourdelle, C.; Casson, F. J.; Angioni, C.; Bonanomi, N.; Camenen, Y.; Garbet, X.; Garzotti, L.; Görler, T.; Gürcan, O.; Koechl, F.; Imbeaux, F.; Linder, O.; van de Plassche, K.; Strand, P.; Szepesi, G.; Contributors, JET
2017-12-01
Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in the quasilinear gyrokinetic transport model QuaLiKiz (Bourdelle et al 2016 Plasma Phys. Control. Fusion 58 014036), which employs an approximated solution of the mode structures to significantly speed up computation time compared to full linear gyrokinetic solvers. Optimisation of the dispersion relation solution algorithm within integrated modelling applications leads to flux calculations × {10}6-7 faster than local nonlinear simulations. This allows tractable simulation of flux-driven dynamic profile evolution including all transport channels: ion and electron heat, main particles, impurities, and momentum. Furthermore, QuaLiKiz now includes the impact of rotation and temperature anisotropy induced poloidal asymmetry on heavy impurity transport, important for W-transport applications. Application within the JETTO integrated modelling code results in 1 s of JET plasma simulation within 10 h using 10 CPUs. Simultaneous predictions of core density, temperature, and toroidal rotation profiles for both JET hybrid and baseline experiments are presented, covering both ion and electron turbulence scales. The simulations are successfully compared to measured profiles, with agreement mostly in the 5%-25% range according to standard figures of merit. QuaLiKiz is now open source and available at www.qualikiz.com.
A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics
Halpern, Federico
2017-10-01
The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.
International Nuclear Information System (INIS)
Marczynski, Slawomir
2011-01-01
The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form ν∂a(τ)/∂τ=a(τ) -a 2 (τ- 1) a(τ- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.
Piontkivska, Helen; Matos, Luis F.; Paul, Sinu; Scharfenberg, Brian; Farmerie, William G.; Miyamoto, Michael M.; Wayne, Marta L.
2016-01-01
Abstract Sigma virus (DMelSV) is ubiquitous in natural populations of Drosophila melanogaster. Host-mediated, selective RNA editing of adenosines to inosines (ADAR) may contribute to control of viral infection by preventing transcripts from being transported into the cytoplasm or being translated accurately; or by increasing the viral genomic mutation rate. Previous PCR-based studies showed that ADAR mutations occur in DMelSV at low frequency. Here we use SOLiDTM deep sequencing of flies from a single host population from Athens, GA, USA to comprehensively evaluate patterns of sequence variation in DMelSV with respect to ADAR. GA dinucleotides, which are weak targets of ADAR, are strongly overrepresented in the positive strand of the virus, consistent with selection to generate ADAR resistance on this complement of the transient, double-stranded RNA intermediate in replication and transcription. Potential ADAR sites in a worldwide sample of viruses are more likely to be “resistant” if the sites do not vary among samples. Either variable sites are less constrained and hence are subject to weaker selection than conserved sites, or the variation is driven by ADAR. We also find evidence of mutations segregating within hosts, hereafter referred to as hypervariable sites. Some of these sites were variable only in one or two flies (i.e., rare); others were shared by four or even all five of the flies (i.e., common). Rare and common hypervariable sites were indistinguishable with respect to susceptibility to ADAR; however, polymorphism in rare sites were more likely to be consistent with the action of ADAR than in common ones, again suggesting that ADAR is deleterious to the virus. Thus, in DMelSV, host mutagenesis is constraining viral evolution both within and between hosts. PMID:27614234
Bindi, D.; Cotton, F.; Kotha, S. R.; Bosse, C.; Stromeyer, D.; Grünthal, G.
2017-09-01
We present a ground motion prediction equation (GMPE) for probabilistic seismic hazard assessments (PSHA) in low-to-moderate seismicity areas, such as Germany. Starting from the NGA-West2 flat-file (Ancheta et al. in Earthquake Spectra 30:989-1005, 2014), we develop a model tailored to the hazard application in terms of data selection and implemented functional form. In light of such hazard application, the GMPE is derived for hypocentral distance (along with the Joyner-Boore one), selecting recordings at sites with vs30 ≥ 360 m/s, distances within 300 km, and magnitudes in the range 3 to 8 (being 7.4 the maximum magnitude for the PSHA in the target area). Moreover, the complexity of the considered functional form is reflecting the availability of information in the target area. The median predictions are compared with those from the NGA-West2 models and with one recent European model, using the Sammon's map constructed for different scenarios. Despite the simplification in the functional form, the assessed epistemic uncertainty in the GMPE median is of the order of those affecting the NGA-West2 models for the magnitude range of interest of the hazard application. On the other hand, the simplification of the functional form led to an increment of the apparent aleatory variability. In conclusion, the GMPE developed in this study is tailored to the needs for applications in low-to-moderate seismic areas and for short return periods (e.g., 475 years); its application in studies where the hazard is involving magnitudes above 7.4 and for long return periods is not advised.
Venturi, D.; Karniadakis, G. E.
2012-08-01
By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.
Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef
2013-01-01
Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.
Liebetrau, V.; Augustin, N.; Kutterolf, S.; Schmidt, M.; Eisenhauer, A.; Garbe-Schönberg, D.; Weinrebe, W.
2014-10-01
Continuous surface cores of cold-seep carbonates were recovered offshore Pacific Nicaragua and Costa Rica from 800 to 1,500-m water depths (Meteor 66/3) in order to decipher their evolution and methane enriched fluid emanation in contrasting geological settings. Cores from the mounds Iguana, Perezoso, Baula V and from the Jaco Scarp escarpment were used for a multi-method approach. For both settings aragonite was revealed as dominant authigenic carbonate phase in vein fillings and matrix cementation, followed by Mg-calcite as second most abundant. This common precipitation process of CaCO3 polymorphs could be ascribed as indirectly driven by chemical changes of the advecting pore water due to anaerobic oxidation of methane. A more direct influence of seep-related microbial activity on the authigenic mineral assemblage in both settings is probably reflected by the observed minor amounts of dolomite and a dolomite-like CaMg carbonate (MgCO3 ~ 42 %). δ13C data of Jaco Scarp samples are significantly lower (-43 to -56 ‰ PDB) than for mound samples (-22 to -36 ‰ PDB), indicating differences in fluid composition and origin. Noteworthy, δ18O values of Scarp samples correlate most closely with the ocean signature at their time of formation. Documenting the archive potential, a high resolution case study of a mound core implies at least 40 changes in fluid supply within a time interval of approximately 14 ky. As most striking difference, the age data indicate a late-stage downward-progressing cementation front for all three mound cap structures (approx. 2-5 cm/ky), but a significantly faster upward carbonate buildup in the bulging sediments on top of the scarp environment (approx. 120 cm/ky). The latter data set leads to the hypothesis of chemoherm carbonate emplacement in accord with reported sedimentation rates until decompression of the advective fluid system, probably caused by the Jaco Scarp landslide and dating this to approximately 13,000 years ago.
Direct Numerical Simulations of turbulent flow in a driven cavity
Verstappen, R.; Wissink, J.G.; Cazemier, W.; Veldman, A.E.P.
Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Auzinger, Winfried; Hofstä tter, Harald; Ketcheson, David I.; Koch, Othmar
2016-01-01
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
Auzinger, Winfried
2016-07-28
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
A nonlinear bounce kinetic equation for trapped electrons
International Nuclear Information System (INIS)
Gang, F.Y.
1990-03-01
A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs
Energy Technology Data Exchange (ETDEWEB)
Winckler, N., E-mail: n.winckler@gsi.de [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Rybalchenko, A. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Shevelko, V.P. [P.N. Lebedev Physical Institute, 119991 Moscow (Russian Federation); Al-Turany, M. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); CERN, European Organization for Nuclear Research, 1211 Geneve 23 (Switzerland); Kollegger, T. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Stöhlker, Th. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Helmholtz-Institute Jena, D-07743 Jena (Germany); Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, D-07743 Jena (Germany)
2017-02-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Winckler, N; Shevelko, V P; Al-Turany, M; Kollegger, T; Stöhlker, Th
2017-01-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Directory of Open Access Journals (Sweden)
Chris N Bayer
Full Text Available Incomprehension and denial of the theory of evolution among high school students has been observed to also occur when teachers are not equipped to deliver a compelling case also for human evolution based on fossil evidence. This paper assesses the outcomes of a novel inquiry-based paleoanthropology lab teaching human evolution to high-school students. The inquiry-based Be a Paleoanthropologist for a Day lab placed a dozen hominin skulls into the hands of high-school students. Upon measuring three variables of human evolution, students explain what they have observed and discuss findings. In the 2013/14 school year, 11 biology classes in 7 schools in the Greater New Orleans area participated in this lab. The interviewed teacher cohort unanimously agreed that the lab featuring hominin skull replicas and stimulating student inquiry was a pedagogically excellent method of delivering the subject of human evolution. First, the lab's learning path of transforming facts to data, information to knowledge, and knowledge to acceptance empowered students to themselves execute part of the science that underpins our understanding of deep time hominin evolution. Second, although challenging, the hands-on format of the lab was accessible to high-school students, most of whom were readily able to engage the lab's scientific process. Third, the lab's exciting and compelling pedagogy unlocked higher order thinking skills, effectively activating the cognitive, psychomotor and affected learning domains as defined in Bloom's taxonomy. Lastly, the lab afforded students a formative experience with a high degree of retention and epistemic depth. Further study is warranted to gauge the degree of these effects.
Bayer, Chris N; Luberda, Michael
2016-01-01
Incomprehension and denial of the theory of evolution among high school students has been observed to also occur when teachers are not equipped to deliver a compelling case also for human evolution based on fossil evidence. This paper assesses the outcomes of a novel inquiry-based paleoanthropology lab teaching human evolution to high-school students. The inquiry-based Be a Paleoanthropologist for a Day lab placed a dozen hominin skulls into the hands of high-school students. Upon measuring three variables of human evolution, students explain what they have observed and discuss findings. In the 2013/14 school year, 11 biology classes in 7 schools in the Greater New Orleans area participated in this lab. The interviewed teacher cohort unanimously agreed that the lab featuring hominin skull replicas and stimulating student inquiry was a pedagogically excellent method of delivering the subject of human evolution. First, the lab's learning path of transforming facts to data, information to knowledge, and knowledge to acceptance empowered students to themselves execute part of the science that underpins our understanding of deep time hominin evolution. Second, although challenging, the hands-on format of the lab was accessible to high-school students, most of whom were readily able to engage the lab's scientific process. Third, the lab's exciting and compelling pedagogy unlocked higher order thinking skills, effectively activating the cognitive, psychomotor and affected learning domains as defined in Bloom's taxonomy. Lastly, the lab afforded students a formative experience with a high degree of retention and epistemic depth. Further study is warranted to gauge the degree of these effects.
Shige, S.; Miyasaka, K.; Shi, W.; Soga, Y.; Sato, M.; Sievers, A. J.
2018-02-01
Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping an LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum the LSM can be continuously converted into ILMs and vice versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.
Nakagawa, Y.
1981-01-01
The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.
International Nuclear Information System (INIS)
Arvieu, R.; Carbonell, J.; Gignoux, C.; Mangin-Brinet, M.; Rozmej, P.
1997-01-01
The time evolution of coherent rotational wave packets associated to a diatomic molecule or to a deformed nucleus has been studied. Assuming a rigid body dynamics the J(J+1) law leads to a mechanism of cloning: the way function is divided into wave packets identical to the initial one at specific time. Applications are studied for a nuclear wave packed formed by Coulomb excitation. Exact boundary conditions at finite distance for the solution of the time-dependent Schroedinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples. (authors)
Lemke, Raymond
2015-06-01
The focus of this talk is on magnetically driven, liner implosion experiments on the Z machine (Z) in which a solid, metal tube is shocklessly compressed to multi-megabar pressure. The goal of the experiments is to collect velocimetry data that can be used in conjunction with a new optimization based analysis technique to infer the principal isentrope of the tube material over a range of pressures. For the past decade, shock impact and ramp loading experiments on Z have used planar platforms exclusively. While producing state-of-the-art results for material science, it is difficult to produce drive pressures greater than 6 Mbar in the divergent planar geometry. In contrast, a cylindrical liner implosion is convergent; magnetic drive pressures approaching 50 Mbar are possible with the available current on Z (~ 20 MA). In our cylindrical experiments, the liner comprises an inner tube composed of the sample material (e.g., Ta) of unknown equation of state, and an outer tube composed of aluminum (Al) that serves as the current carrying cathode. Internal to the sample are fielded multiple PDV (Photonic Doppler Velocimetry) probes that measure velocity of the inner free surface of the imploding sample. External to the composite liner, at much larger radius, is an Al tube that is the return current anode. VISAR (velocity interferometry system for any reflector) probes measure free surface velocity of the exploding anode. Using the latter, MHD and optimization codes are employed to solve an inverse problem that yields the current driving the liner implosion. Then, the drive current, PDV velocity, MHD and optimization codes, are used to solve another inverse problem that yields pressure vs. density on approximately the principal isentrope of the sample material. Results for Ta, Re, and Cu compressed to ~ 10 Mbar are presented. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin
Czech Academy of Sciences Publication Activity Database
Walch, S.; Girichidis, P.; Naab, T.; Gatto, A.; Glover, S.C.O.; Wünsch, Richard; Klessen, R.S.; Clark, P.C.; Peters, T.; Derigs, D.; Baczynski, C.
2015-01-01
Roč. 454, č. 1 (2015), s. 238-268 ISSN 0035-8711 R&D Projects: GA ČR GAP209/12/1795 Institutional support: RVO:67985815 Keywords : magnetodydrodynamics * ISM clouds * ISM evolution Subject RIV: BN - Astronomy , Celestial Mechanics, Astrophysics Impact factor: 4.952, year: 2015
Changsheng, LI; Frolking, Steve; Frolking, Tod A.
1992-01-01
Simulations of N2O and CO2 emissions from soils were conducted with a rain-event driven, process-oriented model (DNDC) of nitrogen and carbon cycling processes in soils. The magnitude and trends of simulated N2O (or N2O + N2) and CO2 emissions were consistent with the results obtained in field experiments. The successful simulation of these emissions from the range of soil types examined demonstrates that the DNDC will be a useful tool for the study of linkages among climate, soil-atmosphere interactions, land use, and trace gas fluxes.
Fritzsch, Bernd; Straka, Hans
2014-01-01
Among the major distance senses of vertebrates, the ear is unique in its complex morphological changes during evolution. Conceivably, these changes enable the ear to adapt toward sensing various physically well-characterized stimuli. This review develops a scenario that integrates sensory cell with organ evolution. We propose that molecular and cellular evolution of the vertebrate hair cells occurred prior to the formation of the vertebrate ear. We previously proposed that the genes driving hair cell differentiation, were aggregated in the otic region through developmental re-patterning that generated a unique vertebrate embryonic structure, the otic placode. In agreement with the presence of graviceptive receptors in many vertebrate outgroups, it is likely that the vertebrate ear originally functioned as a simple gravity-sensing organ. Based on the rare occurrence of angular acceleration receptors in vertebrate outgroups, we further propose that the canal system evolved with a more sophisticated ear morphogenesis. This evolving morphogenesis obviously turned the initial otocyst into a complex set of canals and recesses, harboring multiple sensory epithelia each adapted to the acquisition of a specific aspect of a given physical stimulus. As support for this evolutionary progression, we provide several details of the molecular basis of ear development. PMID:24281353
Yager-Elorriaga, D. A.; Lau, Y. Y.; Zhang, P.; Campbell, P. C.; Steiner, A. M.; Jordan, N. M.; McBride, R. D.; Gilgenbach, R. M.
2018-05-01
In this paper, we present experimental results on axially magnetized (Bz = 0.5 - 2.0 T), thin-foil (400 nm-thick) cylindrical liner-plasmas driven with ˜600 kA by the Michigan Accelerator for Inductive Z-Pinch Experiments, which is a linear transformer driver at the University of Michigan. We show that: (1) the applied axial magnetic field, irrespective of its direction (e.g., parallel or anti-parallel to the flow of current), reduces the instability amplitude for pure magnetohydrodynamic (MHD) modes [defined as modes devoid of the acceleration-driven magneto-Rayleigh-Taylor (MRT) instability]; (2) axially magnetized, imploding liners (where MHD modes couple to MRT) generate m = 1 or m = 2 helical modes that persist from the implosion to the subsequent explosion stage; (3) the merging of instability structures is a mechanism that enables the appearance of an exponential instability growth rate for a longer than expected time-period; and (4) an inverse cascade in both the axial and azimuthal wavenumbers, k and m, may be responsible for the final m = 2 helical structure observed in our experiments. These experiments are particularly relevant to the magnetized liner inertial fusion program pursued at Sandia National Laboratories, where helical instabilities have been observed.
THE TRANSITION MASS-LOSS RATE: CALIBRATING THE ROLE OF LINE-DRIVEN WINDS IN MASSIVE STAR EVOLUTION
Energy Technology Data Exchange (ETDEWEB)
Vink, Jorick S.; Graefener, Goetz, E-mail: jsv@arm.ac.uk [Armagh Observatory, College Hill, BT61 9DG Armagh (United Kingdom)
2012-06-01
A debate has arisen regarding the importance of stationary versus eruptive mass loss for massive star evolution. The reason is that stellar winds have been found to be clumped, which results in the reduction of unclumped empirical mass-loss rates. Most stellar evolution models employ theoretical mass-loss rates which are already reduced by a moderate factor of {approx_equal}2-3 compared to non-corrected empirical rates. A key question is whether these reduced rates are of the correct order of magnitude, or if they should be reduced even further, which would mean that the alternative of eruptive mass loss becomes necessary. Here we introduce the transition mass-loss rate M-dot{sub trans} between O and Wolf-Rayet stars. Its novelty is that it is model independent. All that is required is postulating the spectroscopic transition point in a given data set, and determining the stellar luminosity, which is far less model dependent than the mass-loss rate. The transition mass-loss rate is subsequently used to calibrate stellar wind strength by its application to the Of/WNh stars in the Arches cluster. Good agreement is found with two alternative modeling/theoretical results, suggesting that the rates provided by current theoretical models are of the right order of magnitude in the {approx}50 M{sub Sun} mass range. Our results do not confirm the specific need for eruptive mass loss as luminous blue variables, and current stellar evolution modeling for Galactic massive stars seems sound. Mass loss through alternative mechanisms might still become necessary at lower masses, and/or metallicities, and the quantification of alternative mass loss is desirable.
THE TRANSITION MASS-LOSS RATE: CALIBRATING THE ROLE OF LINE-DRIVEN WINDS IN MASSIVE STAR EVOLUTION
International Nuclear Information System (INIS)
Vink, Jorick S.; Gräfener, Götz
2012-01-01
A debate has arisen regarding the importance of stationary versus eruptive mass loss for massive star evolution. The reason is that stellar winds have been found to be clumped, which results in the reduction of unclumped empirical mass-loss rates. Most stellar evolution models employ theoretical mass-loss rates which are already reduced by a moderate factor of ≅2-3 compared to non-corrected empirical rates. A key question is whether these reduced rates are of the correct order of magnitude, or if they should be reduced even further, which would mean that the alternative of eruptive mass loss becomes necessary. Here we introduce the transition mass-loss rate M-dot trans between O and Wolf-Rayet stars. Its novelty is that it is model independent. All that is required is postulating the spectroscopic transition point in a given data set, and determining the stellar luminosity, which is far less model dependent than the mass-loss rate. The transition mass-loss rate is subsequently used to calibrate stellar wind strength by its application to the Of/WNh stars in the Arches cluster. Good agreement is found with two alternative modeling/theoretical results, suggesting that the rates provided by current theoretical models are of the right order of magnitude in the ∼50 M ☉ mass range. Our results do not confirm the specific need for eruptive mass loss as luminous blue variables, and current stellar evolution modeling for Galactic massive stars seems sound. Mass loss through alternative mechanisms might still become necessary at lower masses, and/or metallicities, and the quantification of alternative mass loss is desirable.
Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fouokeng, Georges Collince; Fai, Lukong Cornelius
2018-04-01
The effects of 1/f^{α } (α =1,2) noise stemming from one or a collection of random bistable fluctuators (RBFs), on the evolution of entanglement, of three non-interacting qubits are investigated. Three different initial configurations of the qubits are analyzed in detail: the Greenberger-Horne-Zeilinger (GHZ)-type states, W-type states and mixed states composed of a GHZ state and a W state (GHZ-W). For each initial configuration, the evolution of entanglement is investigated for three different qubit-environment (Q-E) coupling setups, namely independent environments, mixed environments and common environment coupling. With the help of tripartite negativity and suitable entanglement witnesses, we show that the evolution of entanglement is extremely influenced not only by the initial configuration of the qubits, the spectrum of the environment and the Q-E coupling setup considered, but also by the number of RBF modeling the environment. Indeed, we find that the decay of entanglement is accelerated when the number of fluctuators modeling the environment is increased. Furthermore, we find that entanglement can survive indefinitely to the detrimental effects of noise even for increasingly larger numbers of RBFs. On the other hand, we find that the proficiency of the tripartite entanglement witnesses to detect entanglement is weaker than that of the tripartite negativity and that the symmetry of the initial states is broken when the qubits are coupled to the noise in mixed environments. Finally, we find that the 1 / f noise is more harmful to the survival of entanglement than the 1/f2 noise and that the mixed GHZ-W states followed by the GHZ-type states preserve better entanglement than the W-type ones.
Directory of Open Access Journals (Sweden)
Jianhua Sui
2008-11-01
Full Text Available Phylogenetic analyses have provided strong evidence that amino acid changes in spike (S protein of animal and human SARS coronaviruses (SARS-CoVs during and between two zoonotic transfers (2002/03 and 2003/04 are the result of positive selection. While several studies support that some amino acid changes between animal and human viruses are the result of inter-species adaptation, the role of neutralizing antibodies (nAbs in driving SARS-CoV evolution, particularly during intra-species transmission, is unknown. A detailed examination of SARS-CoV infected animal and human convalescent sera could provide evidence of nAb pressure which, if found, may lead to strategies to effectively block virus evolution pathways by broadening the activity of nAbs. Here we show, by focusing on a dominant neutralization epitope, that contemporaneous- and cross-strain nAb responses against SARS-CoV spike protein exist during natural infection. In vitro immune pressure on this epitope using 2002/03 strain-specific nAb 80R recapitulated a dominant escape mutation that was present in all 2003/04 animal and human viruses. Strategies to block this nAb escape/naturally occurring evolution pathway by generating broad nAbs (BnAbs with activity against 80R escape mutants and both 2002/03 and 2003/04 strains were explored. Structure-based amino acid changes in an activation-induced cytidine deaminase (AID "hot spot" in a light chain CDR (complementarity determining region alone, introduced through shuffling of naturally occurring non-immune human VL chain repertoire or by targeted mutagenesis, were successful in generating these BnAbs. These results demonstrate that nAb-mediated immune pressure is likely a driving force for positive selection during intra-species transmission of SARS-CoV. Somatic hypermutation (SHM of a single VL CDR can markedly broaden the activity of a strain-specific nAb. The strategies investigated in this study, in particular the use of structural
Ulibarri, Z.; Munsat, T.; Dee, R.; Horanyi, M.; James, D.; Kempf, S.; Nagle, M.; Sternovsky, Z.
2017-12-01
Although ice is prevalent in the solar system and the long-term evolution of many airless icy bodies is affected by hypervelocity micrometeoroid bombardment, there has been little experimental investigation into these impact phenomena, especially at the impact speeds encountered in space. For example, there is little direct information about how dust impacts alter the local chemistry, and dust impacts may be an important mechanism for creating complex organic molecules necessary for life. Laser ablation and light-gas gun experiments simulating dust impacts have successfully created amino acid precursors from base components in ice surfaces. Additionally, the Cassini mission revealed CO2 deposits in icy satellites of Saturn, which may have been created by dust impacts. With the creation of a cryogenically cooled ice target for the dust accelerator facility at the NASA SSERVI-funded Institute for Modeling Plasma, Atmospheres, and Cosmic Dust (IMPACT), it is now possible to study the effects of micrometeoroid impacts in a controlled environment under conditions and at energies typically encountered in nature. Complex ice-target mixtures are created with a flash-freezing target which allows for homogeneous mixtures to be frozen in place even with salt mixtures that otherwise would form inhomogeneous ice surfaces. Coupled with the distinctive capabilities of the IMPACT dust facility, highly valuable data concerning the evolution of icy bodies under hypervelocity bombardment and the genesis of complex organic chemistry on these icy bodies can be gathered in unique and tightly controlled experiments. Results from recent and ongoing investigations will be presented.
Lyu, Mengjie; Liu, Youwen; Zhi, Yuduo; Xiao, Chong; Gu, Bingchuan; Hua, Xuemin; Fan, Shaojuan; Lin, Yue; Bai, Wei; Tong, Wei; Zou, Youming; Pan, Bicai; Ye, Bangjiao; Xie, Yi
2015-12-02
Fabricating a flexible room-temperature ferromagnetic resistive-switching random access memory (RRAM) device is of fundamental importance to integrate nonvolatile memory and spintronics both in theory and practice for modern information technology and has the potential to bring about revolutionary new foldable information-storage devices. Here, we show that a relatively low operating voltage (+1.4 V/-1.5 V, the corresponding electric field is around 20,000 V/cm) drives the dual vacancies evolution in ultrathin SnO2 nanosheets at room temperature, which causes the reversible transition between semiconductor and half-metal, accompanyied by an abrupt conductivity change up to 10(3) times, exhibiting room-temperature ferromagnetism in two resistance states. Positron annihilation spectroscopy and electron spin resonance results show that the Sn/O dual vacancies in the ultrathin SnO2 nanosheets evolve to isolated Sn vacancy under electric field, accounting for the switching behavior of SnO2 ultrathin nanosheets; on the other hand, the different defect types correspond to different conduction natures, realizing the transition between semiconductor and half-metal. Our result represents a crucial step to create new a information-storage device realizing the reversible transition between semiconductor and half-metal with flexibility and room-temperature ferromagnetism at low energy consumption. The as-obtained half-metal in the low-resistance state broadens the application of the device in spintronics and the semiconductor to half-metal transition on the basis of defects evolution and also opens up a new avenue for exploring random access memory mechanisms and finding new half-metals for spintronics.
Directory of Open Access Journals (Sweden)
Brown Scott
2010-07-01
Full Text Available Abstract Background Interleukin-4 (IL4 is a secreted immunoregulatory cytokine critically involved in host protection from parasitic helminths 1. Reasoning that helminths may have evolved mechanisms to antagonize IL4 to maximize their dispersal, we explored mammalian IL4 evolution. Results This analysis revealed evidence of diversifying selection at 15 residues, clustered in epitopes responsible for IL4 binding to its Type I and Type II receptors. Such a striking signature of selective pressure suggested either recurrent episodes of pathogen antagonism or ligand/receptor co-evolution. To test the latter possibility, we performed detailed functional analysis of IL4 allotypes expressed by Mus musculus musculus and Mus musculus castaneus, which happen to differ at 5 residues (including three at positively selected sites in and adjacent to the site 1 epitope that binds the IL4Rα subunit shared by the Type I and Type II IL4 receptors. We show that this intra-species variation affects the ability of IL4 neither to bind IL4 receptor alpha (IL4Rα nor to signal biological responses through its Type I receptor. Conclusions Our results -- reminiscent of clustered positively selected sites revealing functionally important residues at host-virus interaction interfaces -- are consistent with IL4 having evolved to avoid recurrent pathogen antagonism, while maintaining the capacity to bind and signal through its cognate receptor. This work exposes what may be a general feature of evolutionary conflicts fought by pathogen antagonists at host protein-protein interaction interfaces involved in immune signaling: the emergence of receptor-binding ligand epitopes capable of buffering amino acid variation.
Mukhopadhyay, Mala; Hazra, S
2018-01-03
Structures of Langmuir-Schaefer (LS) monolayers of thiol-coated Au-nanoparticles (DT-AuNPs) deposited on H-terminated and OTS self-assembled Si substrates (of different hydrophobic strength and stability) and their evolution with time under ambient conditions, which plays an important role for their practical use as 2D-nanostructures over large areas, were investigated using the X-ray reflectivity technique. The strong effect of substrate surface energy (γ) on the initial structures and the competitive role of room temperature thermal energy (kT) and the change in interfacial energy (Δγ) at ambient conditions on the evolution and final structures of the DT-AuNP LS monolayers are evident. The strong-hydrophobic OTS-Si substrate, during transfer, seems to induce strong attraction towards hydrophobic DT-AuNPs on hydrophilic (repulsive) water to form vertically compact partially covered (with voids) monolayer structures (of perfect monolayer thickness) at low pressure and nearly covered buckled monolayer structures (of enhanced monolayer thickness) at high pressure. After transfer, the small kT-energy (in absence of repulsive water) probably fluctuates the DT-AuNPs to form vertically expanded monolayer structures, through systematic exponential growth with time. The effect is prominent for the film deposited at low pressure, where the initial film-coverage and film-thickness are low. On the other hand, the weak-hydrophobic H-Si substrate, during transfer, appears to induce optimum attraction towards DT-AuNPs to better mimic the Langmuir monolayer structures on it. After transfer, the change in the substrate surface nature, from weak-hydrophobic to weak-hydrophilic with time (i.e. Δγ-energy, apart from the kT-energy), enhances the size of the voids and weakens the monolayer/bilayer structure to form a similar expanded monolayer structure, the thickness of which is probably optimized by the available thermal energy.
International Nuclear Information System (INIS)
Zaleśny, Jarosław; Galant, Grzegorz; Berczyński, Paweł; Berczyński, Stefan; Lisak, Mietek
2011-01-01
In this paper the Berk-Breizman (BB) model of plasma wave instability arising on the stability threshold is considered. An interesting although physically unacceptable feature of the model is the explosive behaviour occurring in the regime of small values of the collision frequency parameter. We present an analytical description of the explosive solution, based on a fitting to the numerical solution of the BB equation with the collision parameter equal to zero. We find that the chaotic behaviour taking place for small but non-zero values of the collision parameter is absent in this case; therefore, chaotic behaviour seems to be an independent phenomenon not directly related to the blow-up regime. The time and the velocity dependence of the distribution function are found numerically and plotted to better understand what actually happens in the model. It allows us to obtain a good qualitative understanding of the time evolution of the mode amplitude including the linear growth of the amplitude, reaching its maximum and then decreasing towards the zero value. Nevertheless, we have no satisfactory physical explanation of the amplitude evolution when the amplitude vanishes at some time and then revives but with an opposite phase.
Directory of Open Access Journals (Sweden)
Zhiqian Yi
2015-09-01
Full Text Available Marine diatoms have recently gained much attention as they are expected to be a promising resource for sustainable production of bioactive compounds such as carotenoids and biofuels as a future clean energy solution. To develop photosynthetic cell factories, it is important to improve diatoms for value-added products. In this study, we utilized UVC radiation to induce mutations in the marine diatom Phaeodactylum tricornutum and screened strains with enhanced accumulation of neutral lipids and carotenoids. Adaptive laboratory evolution (ALE was also used in parallel to develop altered phenotypic and biological functions in P. tricornutum and it was reported for the first time that ALE was successfully applied on diatoms for the enhancement of growth performance and productivity of value-added carotenoids to date. Liquid chromatography-mass spectrometry (LC-MS was utilized to study the composition of major pigments in the wild type P. tricornutum, UV mutants and ALE strains. UVC radiated strains exhibited higher accumulation of fucoxanthin as well as neutral lipids compared to their wild type counterpart. In addition to UV mutagenesis, P. tricornutum strains developed by ALE also yielded enhanced biomass production and fucoxanthin accumulation under combined red and blue light. In short, both UV mutagenesis and ALE appeared as an effective approach to developing desired phenotypes in the marine diatoms via electromagnetic radiation-induced oxidative stress.
Bianucci, Marco
2018-05-01
Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.
International Nuclear Information System (INIS)
Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.
2011-01-01
We recently derived explicit solutions of the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations for the Q 2 evolution of the singlet structure function F s (x,Q 2 ) and the gluon distribution G(x,Q 2 ) using very efficient Laplace transform techniques. We apply our results here to a study of the HERA data on deep inelastic ep scattering as recently combined by the H1 and ZEUS groups. We use initial distributions F 2 γp (x,Q 0 2 ) and G(x,Q 0 2 ) determined for x s (x,Q 0 2 ) from F 2 γp (x,Q 0 2 ) using small nonsinglet quark distributions taken from either the CTEQ6L or the MSTW2008LO analyses, evolve F s and G to arbitrary Q 2 , and then convert the results to individual quark distributions. Finally, we show directly from a study of systematic trends in a comparison of the evolved F 2 γp (x,Q 2 ) with the HERA data that the assumption of leading-order DGLAP evolution is inconsistent with those data.
International Nuclear Information System (INIS)
Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A
2015-01-01
This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3–9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects. (paper)
Directory of Open Access Journals (Sweden)
Michael P Walsh
2009-06-01
the first genomic, bioinformatic, and biological descriptions of the molecular evolution events engendering an emerging pathogenic adenovirus.
Tian, Lin; Xian, Xiaozhai; Cui, Xingkai; Tang, Hua; Yang, Xiaofei
2018-02-01
Semiconductor-based photocatalysis has been considered as one of the most effective techniques to achieve the conversion of clean and sustainable sunlight to solar fuel, in which the construction of novel solar-driven photocatalytic systems is the key point. Here, we report initially the synthesis of modified graphitic carbon nitride (g-C3N4) nanorods via the calcination of intermediates obtained from the co-polymerization of precursors, and the in-situ hybridization of Ag3PO4 with as-prepared modified g-C3N4 to produce g-C3N4 nanorod/Ag3PO4 composite materials. The diameter of modified rod-like g-C3N4 materials is determined to be around 1 μm. Subsequently the morphological features, crystal and chemical structures of the assembled g-C3N4 nanorod/Ag3PO4 composites were systematically investigated by SEM, XRD, XPS, UV-vis diffuse reflectance spectra (DRS). Furthermore, the use of as-prepared composite materials as the catalyst for photocatalytic oxygen evolution from water splitting was studied. The oxygen-generating results showed that the composite photocatalyst modified with 600 mg rod-like g-C3N4 demonstrates 2.5 times higher efficiency than that of bulk Ag3PO4. The mechanism behind the enhancement in the oxygen-evolving activity is proposed on the basis of in-situ electron spin resonance (ESR) measurement as well as theoretical analysis. The study provides new insights into the design and development of new photocatalytic composite materials for energy and environmental applications.
Pollman, C. D.; Swain, E. B.; Bael, D.; Myrbo, A.; Monson, P.; Shore, M. D.
2017-11-01
The generation of elevated concentrations of sulfide in sediment pore waters that are toxic to rooted macrophytes is problematic in both marine and freshwaters. In marine waters, biogeochemical conditions that lead to toxic levels of sulfide generally relate to factors that affect oxygen dynamics or the sediment iron concentration. In freshwaters, increases in surface water sulfate have been implicated in decline of Zizania palustris (wild rice), which is important in wetlands across the Great Lakes region of North America. We developed a structural equation (SE) model to elucidate key variables that govern the evolution of sulfide in pore waters in shallow aquatic habitats that are potentially capable of supporting wild rice. The conceptual basis for the model is the hypothesis that dissimilatory sulfate reduction is limited by the availability of both sulfate and total organic carbon (TOC) in the sediment. The conceptual model also assumes that pore water sulfide concentrations are constrained by the availability of pore water iron and that sediment iron supports the supply of dissolved iron to the pore water. A key result from the SE model is that variations in three external variables (sulfate, sediment TOC, and sediment iron) contribute nearly equally to the observed variations in pore water sulfide. As a result, management efforts to mitigate against the toxic effects of pore water sulfide on macrophytes such as wild rice should approach defining a protective sulfate threshold as an exercise tailored to the geochemistry of each site that quantitatively considers the effects of ambient concentrations of sediment Fe and TOC.
Pelinovsky, Efim; Chaikovskaia, Natalya; Rodin, Artem
2015-04-01
The paper presents the analysis of the formation and evolution of shock wave in shallow water with no restrictions on its amplitude in the framework of the nonlinear shallow water equations. It is shown that in the case of large-amplitude waves appears a new nonlinear effect of reflection from the shock front of incident wave. These results are important for the assessment of coastal flooding by tsunami waves and storm surges. Very often the largest number of victims was observed on the coastline where the wave moved breaking. Many people, instead of running away, were just looking at the movement of the "raging wall" and lost time. This fact highlights the importance of researching the problem of security and optimal behavior of people in situations with increased risk. Usually there is uncertainty about the exact time, when rogue waves will impact. This fact limits the ability of people to adjust their behavior psychologically to the stressful situations. It concerns specialists, who are busy both in the field of flying activity and marine service as well as adults, young people and children, who live on the coastal zone. The rogue wave research is very important and it demands cooperation of different scientists - mathematicians and physicists, as well as sociologists and psychologists, because the final goal of efforts of all scientists is minimization of the harm, brought by rogue waves to humanity.
Lin, Pei-Chun; Yu, Chun-Chang; Chen, Charlie Chung-Ping
2015-01-01
As one of the critical stages of a very large scale integration fabrication process, postexposure bake (PEB) plays a crucial role in determining the final three-dimensional (3-D) profiles and lessening the standing wave effects. However, the full 3-D chemically amplified resist simulation is not widely adopted during the postlayout optimization due to the long run-time and huge memory usage. An efficient simulation method is proposed to simulate the PEB while considering standing wave effects and resolution enhancement techniques, such as source mask optimization and subresolution assist features based on the Sylvester equation and Abbe-principal component analysis method. Simulation results show that our algorithm is 20× faster than the conventional Gaussian convolution method.
Energy Technology Data Exchange (ETDEWEB)
Arvieu, R.; Carbonell, J.; Gignoux, C.; Mangin-Brinet, M. [Inst. des Sciences Nucleaires, Grenoble-1 Univ., 38 (France); Rozmej, P. [Uniwersytet Marii Curie-Sklodowskiej, Lublin (Poland)
1997-12-31
The time evolution of coherent rotational wave packets associated to a diatomic molecule or to a deformed nucleus has been studied. Assuming a rigid body dynamics the J(J+1) law leads to a mechanism of cloning: the way function is divided into wave packets identical to the initial one at specific time. Applications are studied for a nuclear wave packed formed by Coulomb excitation. Exact boundary conditions at finite distance for the solution of the time-dependent Schroedinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples. (authors) 3 refs.
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
International Nuclear Information System (INIS)
Long, K.A.; Tahir, N.A.
1986-01-01
In a previous paper by Long and Tahir [Phys. Fluids 29, 275 (1986)], the motion of plane targets irradiated by ion beams whose energy deposition was assumed to be independent of the ion energy, and the temperature and density of the plasma, was analyzed. In this paper, the analytic solution is extended in order to include the effects of a temperature-and density-dependent energy deposition as a result of electron excitation, an improved equation of state, thermal ionization, a pulse shape, and radiation losses. The change in the energy deposition with temperature and density leads to range shortening and an increased power deposition in the target. It is shown how the analytic theory can be used to analyze experiments to measure the enhanced energy deposition. In order to further analyze experiments, numerical simulations are presented which include the plasma-induced effects on the energy deposition. It is shown that since the change in the range is due to both decrease in density and the increase in temperature, it is not possible to separate these two effects in present experiments. Therefore, the experiments which measure the time-dependent energy of the ions emerging from the back side of a plane target do not as yet measure the energy loss as a function of the density and temperature of the plasma or of the energy of the ion, but only an averaged loss over certain ranges of these physical quantities
Learning partial differential equations via data discovery and sparse optimization.
Schaeffer, Hayden
2017-01-01
We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.
Iterative Splitting Methods for Differential Equations
Geiser, Juergen
2011-01-01
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
The effect of sheared toroidal rotation on pressure driven magnetic islands in toroidal plasmas
Energy Technology Data Exchange (ETDEWEB)
Hegna, C. C. [Departments of Engineering Physics and Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)
2016-05-15
The impact of sheared toroidal rotation on the evolution of pressure driven magnetic islands in tokamak plasmas is investigated using a resistive magnetohydrodynamics model augmented by a neoclassical Ohm's law. Particular attention is paid to the asymptotic matching data as the Mercier indices are altered in the presence of sheared flow. Analysis of the nonlinear island Grad-Shafranov equation shows that sheared flows tend to amplify the stabilizing pressure/curvature contribution to pressure driven islands in toroidal tokamaks relative to the island bootstrap current contribution. As such, sheared toroidal rotation tends to reduce saturated magnetic island widths.
Internally driven inertial waves in geodynamo simulations
Ranjan, A.; Davidson, P. A.; Christensen, U. R.; Wicht, J.
2018-05-01
Inertial waves are oscillations in a rotating fluid, such as the Earth's outer core, which result from the restoring action of the Coriolis force. In an earlier work, it was argued by Davidson that inertial waves launched near the equatorial regions could be important for the α2 dynamo mechanism, as they can maintain a helicity distribution which is negative (positive) in the north (south). Here, we identify such internally driven inertial waves, triggered by buoyant anomalies in the equatorial regions in a strongly forced geodynamo simulation. Using the time derivative of vertical velocity, ∂uz/∂t, as a diagnostic for traveling wave fronts, we find that the horizontal movement in the buoyancy field near the equator is well correlated with a corresponding movement of the fluid far from the equator. Moreover, the azimuthally averaged spectrum of ∂uz/∂t lies in the inertial wave frequency range. We also test the dispersion properties of the waves by computing the spectral energy as a function of frequency, ϖ, and the dispersion angle, θ. Our results suggest that the columnar flow in the rotation-dominated core, which is an important ingredient for the maintenance of a dipolar magnetic field, is maintained despite the chaotic evolution of the buoyancy field on a fast timescale by internally driven inertial waves.
Two-dimensional simulations of magnetically-driven instabilities
International Nuclear Information System (INIS)
Peterson, D.; Bowers, R.; Greene, A.E.; Brownell, J.
1986-01-01
A two-dimensional Eulerian MHD code is used to study the evolution of magnetically-driven instabilities in cylindrical geometry. The code incorporates an equation of state, resistivity, and radiative cooling model appropriate for an aluminum plasma. The simulations explore the effects of initial perturbations, electrical resistivity, and radiative cooling on the growth and saturation of the instabilities. Comparisons are made between the 2-D simulations, previous 1-D simulations, and results from the Pioneer experiments of the Los Alamos foil implosion program
Parente, Stephen T; Feldman, Roger
2008-08-01
Using results from peer-reviewed empirical analyses we describe the development and impact of the consumer-driven health plan market over the last 5 years. The results of these analyses show that consumers are responding to the financial incentives of these new health insurance benefits. Although the results may not always be what the consumer-driven health plan developers intended, there is clear evidence of 'consumerism', where individuals act in a way that generally increases their access to healthcare or investments, if the opportunity is present. Just as Medicare Part D enrollment demonstrated consumers could identify differences in prescription drug plans and make rational choices, so too are prospective patients able to function as consumers in the medical marketplace when give the opportunity.
Ding, Qi
2015-09-21
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Silicon micropyramids with n+pp+ junctions are demonstrated to be efficient absorbers for integrated solar-driven hydrogen production systems enabling significant improvements in both photocurrent and onset potential. When conformally coated with MoSxCly, a catalyst that has excellent catalytic activity and high optical transparency, the highest photocurrent density for Si-based photocathodes with earth-abundant catalysts is achieved.
The AGL equation from the dipole picture
International Nuclear Information System (INIS)
Gay Ducati, M.B.; Goncalves, V.P.
1999-01-01
The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to a unitarized gluon distribution in the small x regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this paper that the AGL equation and, consequently, the GLR equation, can also be obtained from the dipole picture in the double logarithmic limit, using an evolution equation, recently proposed, which includes all multiple pomeron exchanges in the leading logarithmic approximation. Our conclusion is that the AGL equation is a good candidate for a unitarized evolution equation at small x in the DLA limit
Pijning, Tjaard; Bai, Yuxiang; Gangoiti Muñecas, Joana; Dijkhuizen, Lubbert
2016-01-01
The human diet has been subject to dramatic changes due to food processing and refining. However, whether this affected the evolution of enzymes in human microbiota is largely unknown. It was proposed that glycoside hydrolase family 70 (GH70) glucansucrases (GS) from Lactobacilli, which synthesize
Bai, Yuxiang; Gangoiti, Joana; Dijkstra, Bauke W; Dijkhuizen, Lubbert; Pijning, Tjaard
2017-01-01
Food processing and refining has dramatically changed the human diet, but little is known about whether this affected the evolution of enzymes in human microbiota. We present evidence that glycoside hydrolase family 70 (GH70) glucansucrases from lactobacilli, synthesizing α-glucan-type extracellular
International Nuclear Information System (INIS)
Freedhoff, Helen
2004-01-01
We study an aggregate of N identical two-level atoms (TLA's) coupled by the retarded interatomic interaction, using the Lehmberg-Agarwal master equation. First, we calculate the entangled eigenstates of the system; then, we use these eigenstates as a basis set for the projection of the master equation. We demonstrate that in this basis the equations of motion for the level populations, as well as the expressions for the emission and absorption spectra, assume a simple mathematical structure and allow for a transparent physical interpretation. To illustrate the use of the general theory in emission processes, we study an isosceles triangle of atoms, and present in the long wavelength limit the (cascade) emission spectrum for a hexagon of atoms fully excited at t=0. To illustrate its use for absorption processes, we tabulate (in the same limit) the biexciton absorption frequencies, linewidths, and relative intensities for polygons consisting of N=2,...,9 TLA's
EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.
A data-driven approach for modeling post-fire debris-flow volumes and their uncertainty
Friedel, Michael J.
2011-01-01
This study demonstrates the novel application of genetic programming to evolve nonlinear post-fire debris-flow volume equations from variables associated with a data-driven conceptual model of the western United States. The search space is constrained using a multi-component objective function that simultaneously minimizes root-mean squared and unit errors for the evolution of fittest equations. An optimization technique is then used to estimate the limits of nonlinear prediction uncertainty associated with the debris-flow equations. In contrast to a published multiple linear regression three-variable equation, linking basin area with slopes greater or equal to 30 percent, burn severity characterized as area burned moderate plus high, and total storm rainfall, the data-driven approach discovers many nonlinear and several dimensionally consistent equations that are unbiased and have less prediction uncertainty. Of the nonlinear equations, the best performance (lowest prediction uncertainty) is achieved when using three variables: average basin slope, total burned area, and total storm rainfall. Further reduction in uncertainty is possible for the nonlinear equations when dimensional consistency is not a priority and by subsequently applying a gradient solver to the fittest solutions. The data-driven modeling approach can be applied to nonlinear multivariate problems in all fields of study.
Polygons of differential equations for finding exact solutions
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given
Kumar, Suneel; Reddy, Nagappagari Lakshmana; Kushwaha, Himmat Singh; Kumar, Ashish; Shankar, Muthukonda Venkatakrishnan; Bhattacharyya, Kaustava; Halder, Aditi; Krishnan, Venkata
2017-09-22
The development of noble metal-free catalysts for hydrogen evolution is required for energy applications. In this regard, ternary heterojunction nanocomposites consisting of ZnO nanoparticles anchored on MoS 2 -RGO (RGO=reduced graphene oxide) nanosheets as heterogeneous catalysts show highly efficient photocatalytic H 2 evolution. In the photocatalytic process, the catalyst dispersed in an electrolytic solution (S 2- and SO 3 2- ions) exhibits an enhanced rate of H 2 evolution, and optimization experiments reveal that ZnO with 4.0 wt % of MoS 2 -RGO nanosheets gives the highest photocatalytic H 2 production of 28.616 mmol h -1 g cat -1 under sunlight irradiation; approximately 56 times higher than that on bare ZnO and several times higher than those of other ternary photocatalysts. The superior catalytic activity can be attributed to the in situ generation of ZnS, which leads to improved interfacial charge transfer to the MoS 2 cocatalyst and RGO, which has plenty of active sites available for photocatalytic reactions. Recycling experiments also proved the stability of the optimized photocatalyst. In addition, the ternary nanocomposite displayed multifunctional properties for hydrogen evolution activity under electrocatalytic and photoelectrocatalytic conditions owing to the high electrode-electrolyte contact area. Thus, the present work provides very useful insights for the development of inexpensive, multifunctional catalysts without noble metal loading to achieve a high rate of H 2 generation. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space
International Nuclear Information System (INIS)
Rodriguez D, R.
2007-01-01
In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)
Optical Bloch equations with multiply connected states
International Nuclear Information System (INIS)
Stacey, D N; Lucas, D M; Allcock, D T C; Szwer, D J; Webster, S C
2008-01-01
The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. The case considered is that for which the time scale of interest in the problem is long compared with that set by the differences in detuning of the radiation fields stimulating via the different routes. It is shown that the Bloch equations then reduce to the standard form of linear differential equations with constant coefficients. The theory is applied to a two-state system driven by two lasers with different intensities and frequencies and to a three-state Λ-system with one laser driving one transition and two driving the second. It is also shown that the theory reproduces well the observed response of a cold 40 Ca + ion when subject to a single laser frequency driving the 4S 1/2 -4P 1/2 transition and a laser with two strong sidebands driving 3D 3/2 -4P 1/2
International Nuclear Information System (INIS)
Gori, F.
2006-01-01
The time evolution of the price of resources sold to the market and of the price difference, between sold and extracted resources, is investigated in case of no accumulation of the resources; i.e. when the resources are extracted and sold to the market at the same mass flow rate. The price evolution of sold resources varies with time according to the relation between the price increase factor, PIF, of sold and extracted resources. The price evolutions of sold resources and price difference are investigated according to the relation between extraction rate and interest rate of extracted and sold resources. The price of sold resources and the price difference increase with time if the PIF of sold resources is greater than the PIF of extracted resources and the initial price is greater than the critical price of sold resources, which depends on the initial price of extracted resources and the interest rate of non-extracted and extracted resources. The price of sold resources and the price difference decrease with time if the PIF of sold resources is greater than the PIF of extracted resources and the initial price is smaller than the critical price of sold resources. The other cases are discussed extensively in the paper. (author)
Energy Technology Data Exchange (ETDEWEB)
Chen, Wen-Cong [School of Physics and Electrical Information, Shangqiu Normal University, Shangqiu 476000 (China); Podsiadlowski, Philipp, E-mail: chenwc@pku.edu.cn [Department of Physics, University of Oxford, Oxford OX1 3RH (United Kingdom)
2016-10-20
It is generally believed that ultracompact X-ray binaries (UCXBs) evolved from binaries consisting of a neutron star accreting from a low-mass white dwarf (WD) or helium star where mass transfer is driven by gravitational radiation. However, the standard WD evolutionary channel cannot produce the relatively long-period (40–60 minutes) UCXBs with a high time-averaged mass-transfer rate. In this work, we explore an alternative evolutionary route toward UCXBs, where the companions evolve from intermediate-mass Ap/Bp stars with an anomalously strong magnetic field (100–10,000 G). Including the magnetic braking caused by the coupling between the magnetic field and an irradiation-driven wind induced by the X-ray flux from the accreting component, we show that intermediate-mass X-ray binaries (IMXBs) can evolve into UCXBs. Using the MESA code, we have calculated evolutionary sequences for a large number of IMXBs. The simulated results indicate that, for a small wind-driving efficiency f = 10{sup −5}, the anomalous magnetic braking can drive IMXBs to an ultra-short period of 11 minutes. Comparing our simulated results with the observed parameters of 15 identified UCXBs, the anomalous magnetic braking evolutionary channel can account for the formation of seven and eight sources with f = 10{sup −3}, and 10{sup −5}, respectively. In particular, a relatively large value of f can fit three of the long-period, persistent sources with a high mass-transfer rate. Though the proportion of Ap/Bp stars in intermediate-mass stars is only 5%, the lifetime of the UCXB phase is ≳2 Gyr, producing a relatively high number of observable systems, making this an alternative evolutionary channel for the formation of UCXBs.
Porretta, Daniele; Urbanelli, Sandra
2012-04-01
How natural selection might be involved in speciation remains a fundamental question in evolutionary biology. When two or more species co-occur in the same areas, natural selection may favor divergence in mating traits. By acting in sympatric but not allopatric populations, natural selection can also affect mate choice within species and ultimately initiate speciation among conspecific populations. Here, we address this potential effect in the sea rock-pool beetles Ochthebius quadricollis and O. urbanelliae. The two species, which inhabit the Mediterranean coasts, co-occurr syntopically in an area along the Italian Tyrrhenian coast and completed reproductive isolation by reinforcement. In this article, through mating trials under laboratory conditions between conspecific populations, we found in O. quadricollis no deviations from random mating. Conversely, in O. urbanelliae, we found a clear pattern of premating isolation between the reinforced populations sympatric with O. quadricollis and those nonreinforced allopatric. This pattern is consistent with the view that natural selection, which completed the reproductive isolation between the two species in sympatry, led incidentally also to partial premating reproductive isolation (I(PSI) estimator from 0.683 to 0.792) between conspecific populations of O. urbanelliae. This case study supports an until recently underappreciated role of natural selection resulting from species interactions in initiating speciation. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.
Cui, Xingkai; Yang, Xiaofei; Xian, Xiaozhai; Tian, Lin; Tang, Hua; Liu, Qinqin
2018-04-01
Oxygen evolution has been considered as the rate-determining step in photocatalytic water splitting due to its sluggish four-electron half-reaction rate, the development of oxygen-evolving photocatalysts with well-defined morphologies and superior interfacial contact is highly important for achieving high-performance solar water splitting. Herein, we report the fabrication of Ag3PO4/MoS2 nanocomposites and, for the first time, their use in photocatalytic water splitting into oxygen under LED light illumination. Ag3PO4 nanoparticles were found to be anchored evenly on the surface of MoS2 nanosheets, confirming an efficient hybridization of two semiconductor materials. A maximum oxygen-generating rate of 201.6 mol L-1 g-1 h-1 was determined when 200 mg MoS2 nanosheets were incorporated into Ag3PO4 nanoparticles, which is around 5 times higher than that of bulk Ag3PO4. Obvious enhancements in light-harvesting property, as well as electron-hole separation and charge transportation are revealed by the combination of different characterizations. ESR analysis verified that more active oxygen-containing radicals generate over illuminated Ag3PO4/MoS2 composite photocatalysts rather than irradiated Ag3PO4. The improvement in oxygen evolution performance of Ag3PO4/MoS2 composite photocatalysts is ascribed to wide spectra response in the visible-light region, more efficient charge separation and enhanced oxidation capacity in the valence band (VB). This study provides new insights into the design and development of novel composite photocatalytic materials for solar-to-fuel conversion.
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Li, Ni; Zhou, Jing; Sheng, Ziqiong; Xiao, Wei
2018-02-01
Construction of two-dimensional/two-dimensional (2D/2D) hybrid with well-defined composition and microstructure is a general protocol to achieve high-performance catalysts. We herein report preparation of g-C3N4-MoS2 hybrid by pyrolysis of affordable melamine and (NH4)2MoS4 in molten LiCl-NaCl-KCl at 550 °C. Molten salts are confirmed as ideal reaction media for formation of homogeneous hybrid. Characterizations suggest a strong interaction between g-C3N4 and MoS2 in the hybrid, which results in an enhanced visible-light-driven photocatalytic hydrogen generation of the hybrid with an optimal g-C3N4/MoS2 ratio. The present study highlights the merits of molten salt methods on preparation of 2D photocatalysts and provides a rational design of 2D/2D hybrid catalysts for advanced environmental and energy applications.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Attractors for equations of mathematical physics
Chepyzhov, Vladimir V
2001-01-01
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti
Directory of Open Access Journals (Sweden)
Jiale Xie
2018-05-01
Full Text Available To achieve accurate state-of-charge (SoC estimation for LiFePO4 (lithium iron phosphate batteries under harsh conditions, this paper resorts to the Peukert’s law to accommodate different temperatures and load excitations. By analyzing battery heat generation and dissipation, a thermal evolution model (TEM is elaborated and exploited for on-line parameter identification of the equivalent circuit model (ECM. Then, a SoC estimation framework is proposed based on the Adaptive Extended Kalman Filter (AEKF algorithm. Experimental results on a LiFePO4 pack subject to the Federal Urban Driving Schedule (FUDS profile under different temperatures and initial states suggest that the proposed SoC estimator provides good robustness and accuracy against changing temperature and highly dynamic loads.
Nutz, Alexis; Schuster, Mathieu; Boës, Xavier; Rubino, Jean-Loup
2017-01-01
Lakes act as major archives for continental paleoenvironments, particularly when the evolution of lake levels over time serves as a guide for understanding regional paleohydrology and paleoclimate. In this paper, two sections from the Nachukui Formation (Turkana Depression, East African Rift System) provide a complete record of lake level variability and then paleohydrology for Lake Turkana between 1.95 and 1.72 Ma. This period corresponds to a key time during which important human evolutionary and technological innovations have occurred in East Africa and in the Turkana area. Based on sedimentary facies and sequence analyses on coastal deposits, one long-term regressive-transgressive cycle is identified between 1.95 and 1.72 Ma. Superimposed on this trend, five higher-frequency cycles of lake level change are identified between 1.87 and 1.76 Ma. Origins of these periodicities are attributed to orbital forcings. The extents of bathymetry change and shoreline migration during these periods are explored, suggesting that the period between 1.87 and 1.76 Ma was relatively dry and that climate experienced a relatively low variability. This finding differs strongly from most of the previous paleoenvironmental investigations in the region that argue high climate variability during a relatively wet period. This work emphasizes the importance of using sequence stratigraphy for analyzing lacustrine deposits.
The forced nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
International Nuclear Information System (INIS)
Piattella, O.F.; Rodrigues, D.C.; Fabris, J.C.; Pacheco, J.A. de Freitas
2013-01-01
We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ 1D 2 ) 3/2 remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ''observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: λ J = (5π/G) 1/2 Q −1/3 ρ dm −1/6 . The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10 −6 M ⊙
Directory of Open Access Journals (Sweden)
H. Meftah
2010-03-01
Full Text Available In this paper, direct numerical simulation databases have been generated to analyze the impact of the propagation of a spray flame on several subgrid scales (SGS models dedicated to the closure of the transport equations of the subgrid fluctuations of the mixture fraction Z and the progress variable c. Computations have been carried out starting from a previous inert database [22] where a cold flame has been ignited in the center of the mixture when the droplet segregation and evaporation rate were at their highest levels. First, a RANS analysis has shown a brutal increase of the mixture fraction fluctuations due to the fuel consumption by the flame. Indeed, local vapour mass fraction reaches then a minimum value, far from the saturation level. It leads to a strong increase of the evaporation rate, which is also accompanied by a diminution of the oxidiser level. In a second part of this paper, a detailed evaluation of the subgrid models allowing to close the variance and the dissipation rates of the mixture fraction and the progress variable has been carried out. Models that have been selected for their efficiency in inert flows have shown a very good behaviour in the framework of reactive flows.
Antishadowing effects in the unitarized BFKL equation
International Nuclear Information System (INIS)
Ruan Jianhong; Shen Zhenqi; Yang Jifeng; Zhu Wei
2007-01-01
A unitarized BFKL equation incorporating shadowing and antishadowing corrections of the gluon recombination is proposed. This equation reduces to the Balitsky-Kovchegov evolution equation near the saturation limit. We find that the antishadowing effects have a sizable influence on the gluon distribution function in the preasymptotic regime
Antishadowing effects in the unitarized BFKL equation
Energy Technology Data Exchange (ETDEWEB)
Ruan Jianhong [Department of Physics, East China Normal University, Shanghai 200062 (China); Shen Zhenqi [Department of Physics, East China Normal University, Shanghai 200062 (China); Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China); Zhu Wei [Department of Physics, East China Normal University, Shanghai 200062 (China)]. E-mail: weizhu@mail.ecnu.edu.cn
2007-01-01
A unitarized BFKL equation incorporating shadowing and antishadowing corrections of the gluon recombination is proposed. This equation reduces to the Balitsky-Kovchegov evolution equation near the saturation limit. We find that the antishadowing effects have a sizable influence on the gluon distribution function in the preasymptotic regime.
Directory of Open Access Journals (Sweden)
Analiza M. Silva
2013-01-01
Full Text Available Simple methods to assess both fat (FM and fat-free mass (FFM are required in paediatric populations. Several bioelectrical impedance instruments (BIAs and anthropometric equations have been developed using different criterion methods (multicomponent models for assessing FM and FFM. Through childhood, FFM density increases while FFM hydration decreases until reaching adult values. Therefore, multicomponent models should be used as the gold standard method for developing simple techniques because two-compartment models (2C model rely on the assumed adult values of FFM density and hydration (1.1 g/cm3 and 73.2%, respectively. This study will review BIA and/or anthropometric-based equations for assessing body composition in paediatric populations. We reviewed English language articles from MEDLINE (1985–2012 with the selection of predictive equations developed for assessing FM and FFM using three-compartment (3C and 4C models as criterion. Search terms included children, adolescent, childhood, adolescence, 4C model, 3C model, multicomponent model, equation, prediction, DXA, BIA, resistance, anthropometry, skinfold, FM, and FFM. A total of 14 studies (33 equations were selected with the majority developed using DXA as the criterion method with a limited number of studies providing cross-validation results. Overall, the selected equations are useful for epidemiological studies, but some concerns still arise on an individual basis.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Energy Technology Data Exchange (ETDEWEB)
Postnikov, S. [Nuclear Theory Center, Indiana University, Bloomington, IN (United States); Dainotti, M. G. [Physics Department, Stanford University, Via Pueblo Mall 382, Stanford, CA (United States); Hernandez, X. [Instituto de Astronomía, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Capozziello, S., E-mail: spostnik@indiana.edu, E-mail: mdainott@stanford.edu, E-mail: dainotti@oa.uj.edu.pl, E-mail: xavier@astros.unam.mx, E-mail: capozziello@na.infn.it [Dipartimento di Fisica, Universitá di Napoli " Federico II," Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy)
2014-03-10
We study the dark energy equation of state as a function of redshift in a nonparametric way, without imposing any a priori w(z) (ratio of pressure over energy density) functional form. As a check of the method, we test our scheme through the use of synthetic data sets produced from different input cosmological models that have the same relative errors and redshift distribution as the real data. Using the luminosity-time L{sub X} -T{sub a} correlation for gamma-ray burst (GRB) X-ray afterglows (the Dainotti et al. correlation), we are able to utilize GRB samples from the Swift satellite as probes of the expansion history of the universe out to z ≈ 10. Within the assumption of a flat Friedmann-Lemaître-Robertson-Walker universe and combining supernovae type Ia (SNeIa) data with baryonic acoustic oscillation constraints, the resulting maximum likelihood solutions are close to a constant w = –1. If one imposes the restriction of a constant w, we obtain w = –0.99 ± 0.06 (consistent with a cosmological constant) with the present-day Hubble constant as H {sub 0} = 70.0 ± 0.6km s{sup –1} Mpc{sup –1} and density parameter as Ω{sub Λ0} = 0.723 ± 0.025, while nonparametric w(z) solutions give us a probability map that is centered at H {sub 0} = 70.04 ± 1km s{sup –1} Mpc{sup –1} and Ω{sub Λ0} = 0.724 ± 0.03. Our chosen GRB data sample with a full correlation matrix allows us to estimate the amount, as well as quality (errors), of data needed to constrain w(z) in the redshift range extending an order of magnitude beyond the farthest SNeIa measured.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Diffusive smoothing of surfzone bathymetry by gravity-driven sediment transport
Moulton, M. R.; Elgar, S.; Raubenheimer, B.
2012-12-01
Gravity-driven sediment transport often is assumed to have a small effect on the evolution of nearshore morphology. Here, it is shown that down-slope gravity-driven sediment transport is an important process acting to smooth steep bathymetric features in the surfzone. Gravity-driven transport can be modeled as a diffusive term in the sediment continuity equation governing temporal (t) changes in bed level (h): ∂h/∂t ≈ κ ▽2h, where κ is a sediment diffusion coefficient that is a function of the bed shear stress (τb) and sediment properties, such as the grain size and the angle of repose. Field observations of waves, currents, and the evolution of large excavated holes (initially 10-m wide and 2-m deep, with sides as steep as 35°) in an energetic surfzone are consistent with diffusive smoothing by gravity. Specifically, comparisons of κ estimated from the measured bed evolution with those estimated with numerical model results for several transport theories suggest that gravity-driven sediment transport dominates the bed evolution, with κ proportional to a power of τb. The models are initiated with observed bathymetry and forced with observed waves and currents. The diffusion coefficients from the measurements and from the model simulations were on average of order 10-5 m2/s, implying evolution time scales of days for features with length scales of 10 m. The dependence of κ on τb varies for different transport theories and for high and low shear stress regimes. The US Army Corps of Engineers Field Research Facility, Duck, NC provided excellent logistical support. Funded by a National Security Science and Engineering Faculty Fellowship, a National Defense Science and Engineering Graduate Fellowship, and the Office of Naval Research.
Effective equations for the quantum pendulum from momentous quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.
2010-01-01
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when
From current-driven to neoclassically driven tearing modes.
Reimerdes, H; Sauter, O; Goodman, T; Pochelon, A
2002-03-11
In the TCV tokamak, the m/n = 2/1 island is observed in low-density discharges with central electron-cyclotron current drive. The evolution of its width has two distinct growth phases, one of which can be linked to a "conventional" tearing mode driven unstable by the current profile and the other to a neoclassical tearing mode driven by a perturbation of the bootstrap current. The TCV results provide the first clear observation of such a destabilization mechanism and reconcile the theory of conventional and neoclassical tearing modes, which differ only in the dominant driving term.
Stellar structure and evolution
International Nuclear Information System (INIS)
Kippernhahn, R.; Weigert, A.
1990-01-01
This book introduces the theory of the internal structure of stars and their evolution in time. It presents the basic physics of stellar interiors, methods for solving the underlying equations, and the most important results necessary for understanding the wide variety of stellar types and phenomena. The evolution of stars is discussed from their birth through normal evolution to possibly spectacular final stages. Chapters on stellar oscillations and rotation are included
Classical and quantum dynamics of driven elliptical billiards
Energy Technology Data Exchange (ETDEWEB)
Lenz, Florian
2009-12-09
Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)
Classical and quantum dynamics of driven elliptical billiards
International Nuclear Information System (INIS)
Lenz, Florian
2009-01-01
Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Ion transfer through solvent polymeric membranes driven by an exponential current flux.
Molina, A; Torralba, E; González, J; Serna, C; Ortuño, J A
2011-03-21
General analytical equations which govern ion transfer through liquid membranes with one and two polarized interfaces driven by an exponential current flux are derived. Expressions for the transient and stationary E-t, dt/dE-E and dI/dE-E curves are obtained, and the evolution from transient to steady behaviour has been analyzed in depth. We have also shown mathematically that the voltammetric and stationary chronopotentiometric I(N)-E curves are identical (with E being the applied potential for voltammetric techniques and the measured potential for chronopotentiometric techniques), and hence, their derivatives provide identical information.
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
Interactive music composition driven by feature evolution.
Kaliakatsos-Papakostas, Maximos A; Floros, Andreas; Vrahatis, Michael N
2016-01-01
Evolutionary music composition is a prominent technique for automatic music generation. The immense adaptation potential of evolutionary algorithms has allowed the realisation of systems that automatically produce music through feature and interactive-based composition approaches. Feature-based composition employs qualitatively descriptive music features as fitness landmarks. Interactive composition systems on the other hand, derive fitness directly from human ratings and/or selection. The paper at hand introduces a methodological framework that combines the merits of both evolutionary composition methodologies. To this end, a system is presented that is organised in two levels: the higher level of interaction and the lower level of composition. The higher level incorporates the particle swarm optimisation algorithm, along with a proposed variant and evolves musical features according to user ratings. The lower level realizes feature-based music composition with a genetic algorithm, according to the top level features. The aim of this work is not to validate the efficiency of the currently utilised setup in each level, but to examine the convergence behaviour of such a two-level technique in an objective manner. Therefore, an additional novelty in this work concerns the utilisation of artificial raters that guide the system through the space of musical features, allowing the exploration of its convergence characteristics: does the system converge to optimal melodies, is this convergence fast enough for potential human listeners and is the trajectory to convergence "interesting' and "creative" enough? The experimental results reveal that the proposed methodological framework represents a fruitful and robust, novel approach to interactive music composition.
Leadership-driven innovation & evolution of societies
Coccia, M.
2014-01-01
The fundamental problem in the field of the economics of innovation is which economic subjects are the sources of radical innovations and high technological performances. The study here confronts this problem by developing a theoretical framework underpinned in the concept of purposeful system
About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models
De La Sen, M.
2008-01-01
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/592950 This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called ...
A generalized advection dispersion equation
Indian Academy of Sciences (India)
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
A solvable two-species catalysis-driven aggregation model
Ke Jian Hong
2003-01-01
We study the kinetics of a two-species catalysis-driven aggregation system, in which an irreversible aggregation between any two clusters of one species occurs only with the catalytic action of another species. By means of a generalized mean-field rate equation, we obtain the asymptotic solutions of the cluster mass distributions in a simple process with a constant rate kernel. For the case without any consumption of the catalyst, the cluster mass distribution of either species always approaches a conventional scaling law. However, the evolution behaviour of the system in the case with catalyst consumption is complicated and depends crucially on the relative data of the initial concentrations of the two species.
Hilbert space methods in partial differential equations
Showalter, Ralph E
1994-01-01
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoî t
2011-01-01
simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.
Magnaudet, Jacques; Tchoufag, Joel; Fabre, David
2015-11-01
Gravity/buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Using a weakly nonlinear expansion of the full set of governing equations, we derive a new generic reduced-order model of this class of phenomena based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (eg. fluttering or spiraling) and characteristics (eg. frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.
Tchoufag, Joël; Fabre, David; Magnaudet, Jacques
2015-09-01
Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.
Integrable systems of partial differential equations determined by structure equations and Lax pair
International Nuclear Information System (INIS)
Bracken, Paul
2010-01-01
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Perturbation theory for continuous stochastic equations
International Nuclear Information System (INIS)
Chechetkin, V.R.; Lutovinov, V.S.
1987-01-01
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)
Singularities in the nonisotropic Boltzmann equation
International Nuclear Information System (INIS)
Garibotti, C.R.; Martiarena, M.L.; Zanette, D.
1987-09-01
We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs
Statistical Methods for Stochastic Differential Equations
Kessler, Mathieu; Sorensen, Michael
2012-01-01
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp
FDTD for Hydrodynamic Electron Fluid Maxwell Equations
Directory of Open Access Journals (Sweden)
Yingxue Zhao
2015-05-01
Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.
Toward making the constraint hypersurface an attractor in free evolution
International Nuclear Information System (INIS)
Fiske, David R.
2004-01-01
When constructing numerical solutions to systems of evolution equations subject to a constraint, one must decide what role the constraint equations will play in the evolution system. In one popular choice, known as free evolution, a simulation is treated as a Cauchy problem, with the initial data constructed to satisfy the constraint equations. This initial data are then evolved via the evolution equations with no further enforcement of the constraint equations. The evolution, however, via the discretized evolution equations introduce constraint violating modes at the level of truncation error, and these constraint violating modes will behave in a formalism dependent way. This paper presents a generic method for incorporating the constraint equations into the evolution equations so that the off-constraint dynamics are biased toward the constraint satisfying solutions
Quantum adiabatic Markovian master equations
International Nuclear Information System (INIS)
Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A
2012-01-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)
International Nuclear Information System (INIS)
Fox, Ronald F.; Vela-Arevalo, Luz V.
2002-01-01
The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances
Information-Driven Inspections
International Nuclear Information System (INIS)
Laughter, Mark D.; Whitaker, J. Michael; Lockwood, Dunbar
2010-01-01
New uranium enrichment capacity is being built worldwide in response to perceived shortfalls in future supply. To meet increasing safeguards responsibilities with limited resources, the nonproliferation community is exploring next-generation concepts to increase the effectiveness and efficiency of safeguards, such as advanced technologies to enable unattended monitoring of nuclear material. These include attribute measurement technologies, data authentication tools, and transmission and security methods. However, there are several conceptual issues with how such data would be used to improve the ability of a safeguards inspectorate such as the International Atomic Energy Agency (IAEA) to reach better safeguards conclusions regarding the activities of a State. The IAEA is pursuing the implementation of information-driven safeguards, whereby all available sources of information are used to make the application of safeguards more effective and efficient. Data from continuous, unattended monitoring systems can be used to optimize on-site inspection scheduling and activities at declared facilities, resulting in fewer, better inspections. Such information-driven inspections are the logical evolution of inspection planning - making use of all available information to enhance scheduled and randomized inspections. Data collection and analysis approaches for unattended monitoring systems can be designed to protect sensitive information while enabling information-driven inspections. A number of such inspections within a predetermined range could reduce inspection frequency while providing an equal or greater level of deterrence against illicit activity, all while meeting operator and technology holder requirements and reducing inspector and operator burden. Three options for using unattended monitoring data to determine an information-driven inspection schedule are to (1) send all unattended monitoring data off-site, which will require advances in data analysis techniques to
Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet
Energy Technology Data Exchange (ETDEWEB)
Cunha, R. O. [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Centro Interdisciplinar de Ciências da Natureza, Universidade Federal da Integração Latino-Americana, 85867-970 Foz do Iguaçu, PR (Brazil); Holanda, J.; Azevedo, A.; Rezende, S. M., E-mail: rezende@df.ufpe.br [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Vilela-Leão, L. H. [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Centro Acadêmico do Agreste, Universidade Federal de Pernambuco, 55002-970 Caruaru, PE (Brazil); Rodríguez-Suárez, R. L. [Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago (Chile)
2015-05-11
We report an investigation of the dynamics of the three-magnon splitting process associated with the ferromagnetic resonance (FMR) in films of the insulating ferrimagnet yttrium iron garnet (YIG). The experiments are performed with a 6 μm thick YIG film close to a microstrip line fed by a microwave generator operating in the 2–6 GHz range. The magnetization precession is driven by the microwave rf magnetic field perpendicular to the static magnetic field, and its dynamics is observed by monitoring the amplitude of the FMR absorption peak. The time evolution of the amplitude reveals that if the frequency is lowered below a critical value of 3.3 GHz, the FMR mode pumps two magnons with opposite wave vectors that react back on the FMR, resulting in a nonlinear dynamics of the magnetization. The results are explained by a model with coupled nonlinear equations describing the time evolution of the magnon modes.
Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable
Energy Technology Data Exchange (ETDEWEB)
Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1968-07-01
In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)
Hyperbolicity and constrained evolution in linearized gravity
International Nuclear Information System (INIS)
Matzner, Richard A.
2005-01-01
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them (unconstrained evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly 'more correct' to introduce a scheme which actively maintains the constraints by solution (constrained evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations
Theory of neoclassical ion temperature-gradient-driven turbulence
Kim, Y. B.; Diamond, P. H.; Biglari, H.; Callen, J. D.
1991-02-01
The theory of collisionless fluid ion temperature-gradient-driven turbulence is extended to the collisional banana-plateau regime. Neoclassical ion fluid evolution equations are developed and utilized to investigate linear and nonlinear dynamics of negative compressibility ηi modes (ηi≡d ln Ti/d ln ni). In the low-frequency limit (ωB2p. As a result of these modifications, growth rates are dissipative, rather than sonic, and radial mode widths are broadened [i.e., γ˜k2∥c2s(ηi -(2)/(3) )/μi, Δx˜ρs(Bt/Bp) (1+ηi)1/2, where k∥, cs, and ρs are the parallel wave number, sound velocity, and ion gyroradius, respectively]. In the limit of weak viscous damping, enhanced neoclassical polarization persists and broadens radial mode widths. Linear mixing length estimates and renormalized turbulence theory are used to determine the ion thermal diffusivity in both cases. In both cases, a strong favorable dependence of ion thermal diffusivity on Bp (and hence plasma current) is exhibited. Furthermore, the ion thermal diffusivity for long wavelength modes exhibits favorable density scaling. The possible role of neoclassical ion temperature-gradient-driven modes in edge fluctuations and transport in L-phase discharges and the L to H transition is discussed.
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Numerical Methods for Partial Differential Equations
Guo, Ben-yu
1987-01-01
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
International Nuclear Information System (INIS)
Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
2016-01-01
We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g 1 structure function. These evolution equations resum powers of α s ln 2 (1/x) in the polarization-dependent evolution along with the powers of α s ln (1/x) in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c N f limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for the g 1 structure function derived previously by Bartels, Ermolaev and Ryskin http://dx.doi.org/10.1007/s002880050285.
Differential equations, mechanics, and computation
Palais, Richard S
2009-01-01
This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.
Generalized equations of gravitational field
International Nuclear Information System (INIS)
Stanyukovich, K.P.; Borisova, L.B.
1985-01-01
Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)
Nonadiabatic quantum Vlasov equation for Schwinger pair production
International Nuclear Information System (INIS)
Kim, Sang Pyo; Schubert, Christian
2011-01-01
Using Lewis-Riesenfeld theory, we derive an exact nonadiabatic master equation describing the time evolution of the QED Schwinger pair-production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov-type integral equation, or as a third-order differential equation. In the last version it relates to the Korteweg-de Vries equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of timelike delta function pulse fields is also briefly considered.
Wilds, Roy; Kauffman, Stuart A.; Glass, Leon
2008-09-01
We study the evolution of complex dynamics in a model of a genetic regulatory network. The fitness is associated with the topological entropy in a class of piecewise linear equations, and the mutations are associated with changes in the logical structure of the network. We compare hill climbing evolution, in which only mutations that increase the fitness are allowed, with neutral evolution, in which mutations that leave the fitness unchanged are allowed. The simple structure of the fitness landscape enables us to estimate analytically the rates of hill climbing and neutral evolution. In this model, allowing neutral mutations accelerates the rate of evolutionary advancement for low mutation frequencies. These results are applicable to evolution in natural and technological systems.
Effects of electron cyclotron current drive on the evolution of double tearing mode
International Nuclear Information System (INIS)
Sun, Guanglan; Dong, Chunying; Duan, Longfang
2015-01-01
The effects of electron cyclotron current drive (ECCD) on the double tearing mode (DTM) in slab geometry are investigated by using two-dimensional compressible magnetohydrodynamics equations. It is found that, mainly, the double tearing mode is suppressed by the emergence of the secondary island, due to the deposition of driven current on the X-point of magnetic island at one rational surface, which forms a new non-complete symmetric magnetic topology structure (defined as a non-complete symmetric structure, NSS). The effects of driven current with different parameters (magnitude, initial time of deposition, duration time, and location of deposition) on the evolution of DTM are analyzed elaborately. The optimal magnitude or optimal deposition duration of driven current is the one which makes the duration of NSS the longest, which depends on the mutual effect between ECCD and the background plasma. Moreover, driven current introduced at the early Sweet-Parker phase has the best suppression effect; and the optimal moment also exists, depending on the duration of the NSS. Finally, the effects varied by the driven current disposition location are studied. It is verified that the favorable location of driven current is the X-point which is completely different from the result of single tearing mode
Effects of electron cyclotron current drive on the evolution of double tearing mode
Energy Technology Data Exchange (ETDEWEB)
Sun, Guanglan, E-mail: sunguanglan@nciae.edu.cn; Dong, Chunying [Basic Science Section, North China Institute of Aerospace Engineering, Langfang 065000 (China); Duan, Longfang [School of Computer and Remote Sensing Information Technology, North China Institute of Aerospace Engineering, Langfang 065000 (China)
2015-09-15
The effects of electron cyclotron current drive (ECCD) on the double tearing mode (DTM) in slab geometry are investigated by using two-dimensional compressible magnetohydrodynamics equations. It is found that, mainly, the double tearing mode is suppressed by the emergence of the secondary island, due to the deposition of driven current on the X-point of magnetic island at one rational surface, which forms a new non-complete symmetric magnetic topology structure (defined as a non-complete symmetric structure, NSS). The effects of driven current with different parameters (magnitude, initial time of deposition, duration time, and location of deposition) on the evolution of DTM are analyzed elaborately. The optimal magnitude or optimal deposition duration of driven current is the one which makes the duration of NSS the longest, which depends on the mutual effect between ECCD and the background plasma. Moreover, driven current introduced at the early Sweet-Parker phase has the best suppression effect; and the optimal moment also exists, depending on the duration of the NSS. Finally, the effects varied by the driven current disposition location are studied. It is verified that the favorable location of driven current is the X-point which is completely different from the result of single tearing mode.
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Taylor dispersion in wind-driven current
Li, Gang; Wang, Ping; Jiang, Wei-Quan; Zeng, Li; Li, Zhi; Chen, G. Q.
2017-12-01
Taylor dispersion associated with wind-driven currents in channels, shallow lakes and estuaries is essential to hydrological environmental management. For solute dispersion in a wind-driven current, presented in this paper is an analytical study of the evolution of concentration distribution. The concentration moments are intensively derived for an accurate presentation of the mean concentration distribution, up to the effect of kurtosis. The vertical divergence of concentration is then deduced by Gill's method of series expansion up to the fourth order. Based on the temporal evolution of the vertical concentration distribution, the dispersion process in the wind-driven current is concretely characterized. The uniform shear leads to a special symmetrical distribution of mean concentration free of skewness. The non-uniformity of vertical concentration is caused by convection and smeared out gradually by the effect of diffusion, but fails to disappear even at large times.
Monge-Ampere equations and tensorial functors
International Nuclear Information System (INIS)
Tunitsky, Dmitry V
2009-01-01
We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.
Pseudodifferential equations over non-Archimedean spaces
Zúñiga-Galindo, W A
2016-01-01
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Constrained evolution in numerical relativity
Anderson, Matthew William
The strongest potential source of gravitational radiation for current and future detectors is the merger of binary black holes. Full numerical simulation of such mergers can provide realistic signal predictions and enhance the probability of detection. Numerical simulation of the Einstein equations, however, is fraught with difficulty. Stability even in static test cases of single black holes has proven elusive. Common to unstable simulations is the growth of constraint violations. This work examines the effect of controlling the growth of constraint violations by solving the constraints periodically during a simulation, an approach called constrained evolution. The effects of constrained evolution are contrasted with the results of unconstrained evolution, evolution where the constraints are not solved during the course of a simulation. Two different formulations of the Einstein equations are examined: the standard ADM formulation and the generalized Frittelli-Reula formulation. In most cases constrained evolution vastly improves the stability of a simulation at minimal computational cost when compared with unconstrained evolution. However, in the more demanding test cases examined, constrained evolution fails to produce simulations with long-term stability in spite of producing improvements in simulation lifetime when compared with unconstrained evolution. Constrained evolution is also examined in conjunction with a wide variety of promising numerical techniques, including mesh refinement and overlapping Cartesian and spherical computational grids. Constrained evolution in boosted black hole spacetimes is investigated using overlapping grids. Constrained evolution proves to be central to the host of innovations required in carrying out such intensive simulations.
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
Methylome evolution in plants.
Vidalis, Amaryllis; Živković, Daniel; Wardenaar, René; Roquis, David; Tellier, Aurélien; Johannes, Frank
2016-12-20
Despite major progress in dissecting the molecular pathways that control DNA methylation patterns in plants, little is known about the mechanisms that shape plant methylomes over evolutionary time. Drawing on recent intra- and interspecific epigenomic studies, we show that methylome evolution over long timescales is largely a byproduct of genomic changes. By contrast, methylome evolution over short timescales appears to be driven mainly by spontaneous epimutational events. We argue that novel methods based on analyses of the methylation site frequency spectrum (mSFS) of natural populations can provide deeper insights into the evolutionary forces that act at each timescale.
Geometry of the isotropic oscillator driven by the conformal mode
Energy Technology Data Exchange (ETDEWEB)
Galajinsky, Anton [Tomsk Polytechnic University, School of Physics, Tomsk (Russian Federation)
2018-01-15
Geometrization of a Lagrangian conservative system typically amounts to reformulating its equations of motion as the geodesic equations in a properly chosen curved spacetime. The conventional methods include the Jacobi metric and the Eisenhart lift. In this work, a modification of the Eisenhart lift is proposed which describes the isotropic oscillator in arbitrary dimension driven by the one-dimensional conformal mode. (orig.)
Dilation of non-quasifree dissipative evolution
Energy Technology Data Exchange (ETDEWEB)
Varilly, J C [Costa Rica Univ., San Jose. Escuela de Matematica
1981-03-01
A semigroup evolution for the 1/2-spin which admits a conservative dilation is known to be governed by a Bloch equation in a standard form. Here we construct a conservative dilation directly from the Bloch equation, thus yielding an example of a dilation scheme for an evolution which is not quasifree. Moreover, we show that this conservative evolution is never ergodic in the non-quasifree case.
Dynamics of the driven Goodwin business cycle equation
International Nuclear Information System (INIS)
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2015-01-01
We study dynamics of the Goodwin nonlinear accelerator business cycle model with periodic forced autonomous investment I a (t) = a(1 – cos ωt), where a and ω are the amplitude and the frequency of investment. We give examples of the parameters a and ω when the chaotic oscillations of income are possible. We find the critical values of amplitude a cr (ω): if a > a cr (ω) the period of the income equals to the driving period T=2π/ω
Minimal length, Friedmann equations and maximum density
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel [Center for Theoretical Physics, British University of Egypt,Sherouk City 11837, P.O. Box 43 (Egypt); Department of Physics, Faculty of Science, Ain Shams University,Cairo, 11566 (Egypt); Ali, Ahmed Farag [Centre for Fundamental Physics, Zewail City of Science and Technology,Sheikh Zayed, 12588, Giza (Egypt); Department of Physics, Faculty of Science, Benha University,Benha, 13518 (Egypt)
2014-06-16
Inspired by Jacobson’s thermodynamic approach, Cai et al. have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation http://dx.doi.org/10.1103/PhysRevD.75.084003 of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ,a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p=ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
On Rank Driven Dynamical Systems
Veerman, J. J. P.; Prieto, F. J.
2014-08-01
We investigate a class of models related to the Bak-Sneppen (BS) model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of "complex behavior" such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in are associated to agents located at the vertices of a graph . Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses. We consider two cases: The exogenous case where the new fitnesses are taken from an a priori fixed distribution, and the endogenous case where the new fitnesses are taken from the current distribution as it evolves. We approximate the dynamics by making a simplifying independence assumption. We use Order Statistics and Dynamical Systems to define a rank-driven dynamical system that approximates the evolution of the distribution of the fitnesses in these rank-driven models, as well as in the BS model. For this simplified model we can find the limiting marginal distribution as a function of the initial conditions. Agreement with experimental results of the BS model is excellent.
New application of Exp-function method for improved Boussinesq equation
Energy Technology Data Exchange (ETDEWEB)
Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Department of Physics, Faculty of Education for Girls, Science Departments, King Khalid University, Bisha (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com; Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College (Bisha), King Khalid University, Bisha, PO Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com; El-Basyony, S.T. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)
2007-10-01
The Exp-function method is used to obtain generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computation method, namely, the improved Boussinesq equation. The method is straightforward and concise, and its applications is promising for other nonlinear evolution equations in mathematical physics.
A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
Sudao, Bilige; Wang, Xiaomin
2015-01-01
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
CIME course on Control of Partial Differential Equations
Alabau-Boussouira, Fatiha; Glass, Olivier; Le Rousseau, Jérôme; Zuazua, Enrique
2012-01-01
The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a fri...
Hamilton-Jacobi-Bellman equations for quantum control | Ogundiran ...
African Journals Online (AJOL)
The aim of this work is to study Hamilton-Jacobi-Bellman equation for quantum control driven by quantum noises. These noises are annhihilation, creation and gauge processes. We shall consider the solutions of Hamilton-Jacobi-Bellman equation via the Hamiltonian system measurable in time. JONAMP Vol. 11 2007: pp.
COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.
New variational principles for locating periodic orbits of differential equations.
Boghosian, Bruce M; Fazendeiro, Luis M; Lätt, Jonas; Tang, Hui; Coveney, Peter V
2011-06-13
We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.
Exact soliton-like solutions of perturbed phi4-equation
International Nuclear Information System (INIS)
Gonzalez, J.A.
1986-05-01
Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)
Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus
2014-01-01
Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.
Semiclassical evolution of dissipative Markovian systems
International Nuclear Information System (INIS)
Ozorio de Almeida, A M; Rios, P de M; Brodier, O
2009-01-01
A semiclassical approximation for an evolving density operator, driven by a 'closed' Hamiltonian operator and 'open' Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra 'open' term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further 'small-chord' approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions
Kinetic equation solution by inverse kinetic method
International Nuclear Information System (INIS)
Salas, G.
1983-01-01
We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
The equations icons of knowledge
Bais, Sander
2005-01-01
For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Trajectory attractors of equations of mathematical physics
International Nuclear Information System (INIS)
Vishik, Marko I; Chepyzhov, Vladimir V
2011-01-01
In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.
Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos
2017-09-01
The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.
A kinetic equation for irreversible aggregation
International Nuclear Information System (INIS)
Zanette, D.H.
1990-09-01
We introduce a kinetic equation for describing irreversible aggregation in the ballistic regime, including velocity distributions. The associated evolution for the macroscopic quantities is studied, and the general solution for Maxwell interaction models is obtained in the Fourier representation. (author). 23 refs
Integrable boundary conditions and modified Lax equations
International Nuclear Information System (INIS)
Avan, Jean; Doikou, Anastasia
2008-01-01
We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding 'transfer' matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix and the boundary matrix
Model-driven software migration a methodology
Wagner, Christian
2014-01-01
Today, reliable software systems are the basis of any business or company. The continuous further development of those systems is the central component in software evolution. It requires a huge amount of time- man power- as well as financial resources. The challenges are size, seniority and heterogeneity of those software systems. Christian Wagner addresses software evolution: the inherent problems and uncertainties in the process. He presents a model-driven method which leads to a synchronization between source code and design. As a result the model layer will be the central part in further e
Vlasov dynamics of periodically driven systems
Banerjee, Soumyadip; Shah, Kushal
2018-04-01
Analytical solutions of the Vlasov equation for periodically driven systems are of importance in several areas of plasma physics and dynamical systems and are usually approximated using ponderomotive theory. In this paper, we derive the plasma distribution function predicted by ponderomotive theory using Hamiltonian averaging theory and compare it with solutions obtained by the method of characteristics. Our results show that though ponderomotive theory is relatively much easier to use, its predictions are very restrictive and are likely to be very different from the actual distribution function of the system. We also analyse all possible initial conditions which lead to periodic solutions of the Vlasov equation for periodically driven systems and conjecture that the irreducible polynomial corresponding to the initial condition must only have squares of the spatial and momentum coordinate. The resulting distribution function for other initial conditions is aperiodic and can lead to complex relaxation processes within the plasma.
New exact solutions to the generalized KdV equation with ...
Indian Academy of Sciences (India)
is reduced to an ordinary differential equation with constant coefficients ... Application to generalized KdV equation with generalized evolution ..... [12] P F Byrd and M D Friedman, Handbook of elliptic integrals for engineers and physicists.
Equation of motion for estimation fidelity of monitored oscillating qubits
CSIR Research Space (South Africa)
Bassa, H
2017-08-01
Full Text Available We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of discrete, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation fidelity from a...
Final state dipole showers and the DGLAP equation
International Nuclear Information System (INIS)
Nagy, Zoltan; Soper, Davison E.
2009-01-01
We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a recent paper of Dokshitzer and Marchesini that raised troubling issues about whether a dipole based shower could give the DGLAP equation for the quark energy distribution.
A multi-frequency approach to free electron lasers driven by short electron bunches
International Nuclear Information System (INIS)
Piovella, Nicola
1997-01-01
A multi-frequency model for free electron lasers (FELs), based on the Fourier decomposition of the radiation field coupled with the beam electrons, is discussed. We show that the multi-frequency approach allows for an accurate description of the evolution of the radiation spectrum, also when the FEL is driven by short electron bunches, of arbitrary longitudinal profile. We derive from the multi-frequency model, by averaging over one radiation period, the usual FEL equations modelling the slippage between radiation and particles and describing the super-radiant regime in high-gain FELs. As an example of application of the multi-frequency model, we discuss the coherent spontaneous emission (CSE) from short electron bunches
Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation
International Nuclear Information System (INIS)
Pandir, Yusuf; Gurefe, Yusuf; Misirli, Emine
2013-01-01
In this paper, we study the Kadomtsev-Petviashvili equation with generalized evolution and derive some new results using the approach called the trial equation method. The obtained results can be expressed by the soliton solutions, rational function solutions, elliptic function solutions and Jacobi elliptic function solutions. In the discussion, we give a new version of the trial equation method for nonlinear differential equations.
The evolution of Saccharomycotina yeasts
Associations between traits are prevalent in nature, occurring across a diverse range of taxa and traits. The evolution of trait correlations can be driven by factors intrinsic or extrinsic to an organism, but few studies, especially in microbes, have simultaneously investigated both across a broad ...
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
A simple model for binary star evolution
International Nuclear Information System (INIS)
Whyte, C.A.; Eggleton, P.P.
1985-01-01
A simple model for calculating the evolution of binary stars is presented. Detailed stellar evolution calculations of stars undergoing mass and energy transfer at various rates are reported and used to identify the dominant physical processes which determine the type of evolution. These detailed calculations are used to calibrate the simple model and a comparison of calculations using the detailed stellar evolution equations and the simple model is made. Results of the evolution of a few binary systems are reported and compared with previously published calculations using normal stellar evolution programs. (author)
Analysis of directly driven ICF targets
International Nuclear Information System (INIS)
Velarde, G.; Aragones, J.M.; Gago, J.A.
1986-01-01
The current capabilities at DENIM for the analysis of directly driven targets are presented. These include theoretical, computational and applied physical studies and developments of detailed simulation models for the most relevant processes in ICF. The simulation of directly driven ICF targets is carried out with the one-dimensional NORCLA code developed at DENIM. This code contains two main segments: NORMA and CLARA, able to work fully coupled and in an iterative manner. NORMA solves the hydrodynamic equations in a lagrangian mesh. It has modular programs couple to it to treat the laser or particle beam interaction with matter. Equations of state, opacities and conductivities are taken from a DENIM atomic data library, generated externally with other codes that will also be explained in this work. CLARA solves the transport equation for neutrons, as well as for charged particles, and suprathermal electrons using discrete ordinates and finite element methods in the computational procedure. Parametric calculations of multilayered single-shell targets driven by heavy ion beams are also analyzed. Finally, conclusions are focused on the ongoing developments in the areas of interest such as: radiation transport, atomic physics, particle in cell method, charged particle transport, two-dimensional calculations and instabilities. (author)
A new formulation of equations of compressible fluids by analogy with Maxwell's equations
International Nuclear Information System (INIS)
Kambe, Tsutomu
2010-01-01
A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.
Antonyuk, Boris P
2009-01-01
This book deals with influencing the properties of solids by light-driven electron transport. The theoretical basis of these effects, light-driven ordering and self-organisation, as well as optical motors are presented. With light as a tool, new ways to produce materials are opened.
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Simulation of electrically driven jet using Chebyshev collocation method
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations(PDEs).Following the method of lines,the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations(DAEs).By differentiating constrains in DAEs twice,the system is transformed into a set of ordinary differential equations(ODEs) with invariants.Then the implicit differential equations solver "ddaskr" is used to solve the ODEs and ...
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Directory of Open Access Journals (Sweden)
Karen Kearns
2005-10-01
Full Text Available This is a case study of the evolution of how a successful knowledge management initiative was achieved in a corporate learning organization. The initiative was centered on providing training tools and documentation of automated laboratory workstations that are utilized by scientists in a drug discovery environment. The case study will address the software tools, processes for content building, and the organizational dynamics that either assisted or blocked the progression of the initiative. Over a four-year period three distinct efforts were implemented, each differed in the particular software tools and focus of the initiatives. This presentation will compare and contrast the elements that provided barriers to success in the first two initiatives and the mechanisms and focus used in the third initiative that proved successful, scalable, and sustainable.
Transitional inertialess instabilities in driven multilayer channel flows
Papaefthymiou, Evangelos; Papageorgiou, Demetrios
2016-11-01
We study the nonlinear stability of viscous, immiscible multilayer flows in channels driven both by a pressure gradient and/or gravity in a slightly inclined channel. Three fluid phases are present with two internal interfaces. Novel weakly nonlinear models of coupled evolution equations are derived and we concentrate on inertialess flows with stably stratified fluids, with and without surface tension. These are 2 × 2 systems of second-order semilinear parabolic PDEs that can exhibit inertialess instabilities due to resonances between the interfaces - mathematically this is manifested by a transition from hyperbolic to elliptic behavior of the nonlinear flux functions. We consider flows that are linearly stable (i.e the nonlinear fluxes are hyperbolic initially) and use the theory of nonlinear systems of conservation laws to obtain a criterion (which can be verified easily) that can predict nonlinear stability or instability (i.e. nonlinear fluxes encounter ellipticity as they evolve spatiotemporally) at large times. In the former case the solution decays asymptotically to its base state, and in the latter nonlinear traveling waves emerge. EPSRC Grant Numbers EP/K041134 and EP/L020564.
Relations between nonlinear Riccati equations and other equations in fundamental physics
International Nuclear Information System (INIS)
Schuch, Dieter
2014-01-01
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
International Nuclear Information System (INIS)
Green, B I; Vedula, Prakash
2013-01-01
An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
International Nuclear Information System (INIS)
Zheng, Lin; Zheng, Song; Zhai, Qinglan
2016-01-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Energy Technology Data Exchange (ETDEWEB)
Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)
2016-02-05
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
The Approach to Equilibrium: Detailed Balance and the Master Equation
Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.
2011-01-01
The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…
A note on the three dimensional sine--Gordon equation
Shariati, Ahmad
1996-01-01
Using a simple ansatz for the solutions of the three dimensional generalization of the sine--Gordon and Toda model introduced by Konopelchenko and Rogers, a class of solutions is found by elementary methods. It is also shown that these equations are not evolution equations in the sense that solution to the initial value problem is not unique.
Perfect fluid cosmological Universes: One equation of state and the ...
Indian Academy of Sciences (India)
Anadijiban Das
2018-01-04
Jan 4, 2018 ... equation of state, one may calculate the geometric vari- ables, such as the ... connected by any analytic function ψ, the evolutions equations, mainly ... [3] J E Marsden and A J Tromba, Vector calculus, 3rd edn. (W. H. Freeman ...
A Hamiltonian structure for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1991-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)
From the Hartree dynamics to the Vlasov equation
DEFF Research Database (Denmark)
Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara
2016-01-01
We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...
Effective Schroedinger equations on submanifolds
Energy Technology Data Exchange (ETDEWEB)
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
New exact solutions of the mBBM equation
International Nuclear Information System (INIS)
Zhang Zhe; Li Desheng
2013-01-01
The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)
Gaševic, Dragan; Djuric, Dragan; Devedžic, Vladan
A relevant initiative from the software engineering community called Model Driven Engineering (MDE) is being developed in parallel with the Semantic Web (Mellor et al. 2003a). The MDE approach to software development suggests that one should first develop a model of the system under study, which is then transformed into the real thing (i.e., an executable software entity). The most important research initiative in this area is the Model Driven Architecture (MDA), which is Model Driven Architecture being developed under the umbrella of the Object Management Group (OMG). This chapter describes the basic concepts of this software engineering effort.
International Nuclear Information System (INIS)
Wang Qi; Chen Yong; Zhang Hongqing
2005-01-01
In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation