Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
Asymptotic stability of an Euler-Bernoulli beam coupled to non-linear spring-damper systems
Gorrec, Yann Le; Zwart, Hans; Ramirez, Hector
2017-01-01
The stability of an undamped Euler Bernoulli beam connected to non-linear mass spring damper systems is addressed. It is shown that under mild assumptions on the local behaviour of the non-linear springs and dampers the solutions exist and the system is globally asymptotically stable.
ASYMPIOTIC SOLUTIONS OF THE NON-LINEAR WAVE EQUAION
African Journals Online (AJOL)
MIS
1983-09-01
Sep 1, 1983 ... we scale both x and t by introducing the fast variables. = t, X = x. (2.2a) and the slow variables. T. = εt, X = εX. (2.2b). The derivatives now become ut = u + εuT and ux = ux + εuX and the solution of the nonlinear wave equation (1.1) is sought in the form of a uniformly valid asymptotic expansion in powers of ε.
Positive non-symmetric solutions of a non-linear boundary value problem
Directory of Open Access Journals (Sweden)
Samuel Peres
2013-11-01
Full Text Available This paper deals with a non-linear second order ordinary differential equation with symmetric non-linear boundary conditions, where both of the non-linearities are of power type. It provides results concerning the existence and multiplicity of positive non-symmetric solutions for values of parameters not considered before. The main tool is the shooting method.
Application of the full reduction technique for solution of equations with vector form non-linearity
Saliuk, D. A.
2013-12-01
We consider making use of the full reduction algorithm for solving the equations with a vector non-linearity. The solutions of such the equations describe the planetary scale non-linear vortex structures of the Earth atmosphere, ionosphere and magnetosphere. We present the modification of full reduction technique for Charney-Obukhov equation with periodic boundary conditions. This technique allows to reduce significantly calculation time and to apply much more detailed spatial grid for studying non-linear processes in the near-Earth space.
Some examples of non-linear systems and characteristics of their solutions
CSIR Research Space (South Africa)
Greben, JM
2006-07-01
Full Text Available -linear structure of the equations, a structure which is dictated by the symmetries of physics. A central theme in these non-linear solutions is that the magnitude of the driving term (or the initial cause in more mundane language), is of little influence...
Numerical solution of two-dimensional non-linear partial differential ...
African Journals Online (AJOL)
differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be solved at each time level. To linearize the resulting system of difference equations, Newton ...
Global search of non-linear systems periodic solutions: A rotordynamics application
Sarrouy, E.; Thouverez, F.
2010-08-01
Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions—where T is known—of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Terras, V. [CNRS, ENS Lyon (France). Lab. de Physique
2010-12-15
We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schroedinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics. (orig.)
Asymptotically periodic solutions of Volterra integral equations
Directory of Open Access Journals (Sweden)
Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Asymptotic Methods for Solitary Solutions and Compactons
Directory of Open Access Journals (Sweden)
Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
Phantom solution in a non-linear Israel-Stewart theory
Cruz, Miguel; Cruz, Norman; Lepe, Samuel
2017-06-01
In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.
Phantom solution in a non-linear Israel–Stewart theory
Directory of Open Access Journals (Sweden)
Miguel Cruz
2017-06-01
Full Text Available In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel–Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p=ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than −1 and constant in time.
(19)F labelled glycosaminoglycan probes for solution NMR and non-linear (CARS) microscopy.
Lima, Marcelo A; Cavalheiro, Renan P; M Viana, Gustavo; Meneghetti, Maria C Z; Rudd, Timothy R; Skidmore, Mark A; Powell, Andrew K; Yates, Edwin A
2017-06-01
Studying polysaccharide-protein interactions under physiological conditions by conventional techniques is challenging. Ideally, macromolecules could be followed by both in vitro spectroscopy experiments as well as in tissues using microscopy, to enable a proper comparison of results over these different scales but, often, this is not feasible. The cell surface and extracellular matrix polysaccharides, glycosaminoglycans (GAGs) lack groups that can be detected selectively in the biological milieu. The introduction of (19)F labels into GAG polysaccharides is explored and the interaction of a labelled GAG with the heparin-binding protein, antithrombin, employing (19)F NMR spectroscopy is followed. Furthermore, the ability of (19)F labelled GAGs to be imaged using CARS microscopy is demonstrated. (19)F labelled GAGs enable both (19)F NMR protein-GAG binding studies in solution at the molecular level and non-linear microscopy at a microscopic scale to be conducted on the same material, essentially free of background signals.
Naumis, Gerardo G.; Lopez-Rodriguez, Francisco J.
2008-01-01
We find the exact solution of graphene s carriers under electromagnetic radiation. To obtain such solution, we combine Floquet theory with a trial solution. Then the energy spectrum is obtained without using any approximation. Using such results, we prove that the energy spectrum presents a gap opening which depends on de radiation frequency and electric wave intensity, whereas the current shows a strongly non-linear behaviour.
Solitons on nanotubes and fullerenes as solutions of a modified non-linear Schroedinger equation
Brihaye, Yves; Hartmann, Betti
2004-01-01
Fullerenes and nanotubes consist of a large number of carbon atoms sitting on the sites of a regular lattice. For pratical reasons it is often useful to approximate the equations on this lattice in terms of the continuous equation. At the moment, the best candidate for such an equation is the modified non-linear Schroedinger equation. In this paper, we study the modified non-linear Schroedinger equation, which arises as continuous equation in a system describing an excitation on a hexagonal l...
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
Asymptotic behaviour as t\\to \\infty of the solutions of the generalized Korteweg-de Vries equation
Naumkin, P. I.; Shishmarev, I. A.
1996-06-01
Asymptotic formulae representing for large time the solution of the Cauchy problem are obtained for the generalized Korteweg-de Vries equation with non-linear term to an integer power greater than three. The error terms are estimated. The method is based on the perturbation theory with respect to a parameter characterizing the smallness of the initial data.
On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media
Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo
2013-04-01
A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.
Directory of Open Access Journals (Sweden)
G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Asymptotic Solutions of Serial Radial Fuel Shuffling
Directory of Open Access Journals (Sweden)
Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
An asymptotic solution of large-$N$ $QCD$
Bochicchio, Marco
2014-01-01
We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-poin...
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Hagedorn, Peter
1982-01-01
Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.
Directory of Open Access Journals (Sweden)
Eusebio Eduardo Hernández Martinez
2013-01-01
Full Text Available In robotics, solving the direct kinematics problem (DKP for parallel robots is very often more difficult and time consuming than for their serial counterparts. The problem is stated as follows: given the joint variables, the Cartesian variables should be computed, namely the pose of the mobile platform. Most of the time, the DKP requires solving a non-linear system of equations. In addition, given that the system could be non-convex, Newton or Quasi-Newton (Dogleg based solvers get trapped on local minima. The capacity of such kinds of solvers to find an adequate solution strongly depends on the starting point. A well-known problem is the selection of such a starting point, which requires a priori information about the neighbouring region of the solution. In order to circumvent this issue, this article proposes an efficient method to select and to generate the starting point based on probabilistic learning. Experiments and discussion are presented to show the method performance. The method successfully avoids getting trapped on local minima without the need for human intervention, which increases its robustness when compared with a single Dogleg approach. This proposal can be extended to other structures, to any non-linear system of equations, and of course, to non-linear optimization problems.
Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.
2018-01-01
The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.
An asymptotic solution of large-N QCD
Directory of Open Access Journals (Sweden)
Bochicchio Marco
2014-01-01
Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
An asymptotic solution of large-N QCD
Bochicchio, Marco
2014-11-01
We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
Asymptotic behaviour of solutions of a nonlinear transport equation
C.J. van Duijn (Hans); M.A. Peletier (Mark)
1996-01-01
textabstractWe investigate the asymptotic behaviour of solutions of the convection- diffusion equation $$ b(u)_t + divleft( u q - n u right) = 0 qquad hbox{for r = |x| > e quadhbox{andquad t>0, $$ where $q=l/r, er $, $l>0$. The asymptotic limits that we consider are $ttoinfty$ and $e downto0$. We
On oscillation and asymptotic behaviour of solutions of forced first ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 111; Issue 3. On Oscillation and Asymptotic Behaviour of Solutions of Forced First Order Neutral Differential Equations. N Parhi R N Rath. Volume 111 Issue 3 August 2001 pp ... Keywords. Oscillation; nonoscillation; neutral equations; asymptotic behaviour.
Programmable Solution for Solving Non-linearity Characteristics of Smart Sensor Applications
Directory of Open Access Journals (Sweden)
S. Khan
2007-10-01
Full Text Available This paper presents a simple but programmable technique to solve the problem of non-linear characteristics of sensors used in more sensitive applications. The nonlinearity of the output response becomes a very sensitive issue in cases where a proportional increase in the physical quantity fails to bring about a proportional increase in the signal measured. The nonlinearity is addressed by using the interpolation method on the characteristics of a given sensor, approximating it to a set of tangent lines, the tangent points of which are recognized in the code of the processor by IF-THEN code. The method suggested here eliminates the use of external circuits for interfacing, and eases the programming burden on the processor at the cost of proportionally reduced memory requirements. The mathematically worked out results are compared with the simulation and experimental results for an IR sensor selected for the purpose and used for level measurement. This work will be of paramount importance and significance in applications where the controlled signal is required to follow the input signal precisely particularly in sensitive robotic applications.
Three dimensional magnetic solutions in massive gravity with (non)linear field
Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Momennia, M.
2017-12-01
The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Directory of Open Access Journals (Sweden)
H. M. Abdelhafez
2016-03-01
Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.
Existence of entire solutions of some non-linear differential-difference equations.
Chen, Minfeng; Gao, Zongsheng; Du, Yunfei
2017-01-01
In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m, n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].
Symmetry and Numerical Solutions for Systems of Non-linear Reaction Diffusion Equations
KUMAR,SANJEEV; Singh, Ravendra
2007-01-01
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion equation with respect to one-dimensional Algebra is carried out in this work. Some classes of analytical and numerical solutions are obtained and expressed using suitable graphs.
Approximate solution of the non-linear diffusion equation of multiple orders
Directory of Open Access Journals (Sweden)
Wu Fei
2016-01-01
Full Text Available In this paper, fractional diffusion equation of multiple orders is approximately solved. The equation is given in the equivalent integral form. The Adomian polynomial is adopted and analytical solutions are obtained. The result contains two parameters that can have more space for fitting the experiment data.
An Efficient Implementation of Non-Linear Limit State Analysis Based on Lower-Bound Solutions
DEFF Research Database (Denmark)
Damkilde, Lars; Schmidt, Lotte Juhl
2005-01-01
Limit State analysis has been used in design for decades e.g. the yield line theory for concrete slabs or slip line solutions in geotechnics. In engineering practice manual methods have been dominating but in recent years the interest in numerical methods has been increasing. In this respect...... it is mandatory to formulate the methods using the well-known finite element concept in order to interface with other types of analysis....
ZHU, C. S.; ROBB, D. A.; EWINS, D. J.
2002-05-01
The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.
Self-similar shock wave solutions of the non-linear Maxwell equations
Barna, I F
2013-01-01
In our study we consider nonlinear, power-law field-dependent electrical permitivity and magnetic permeability and investigate the time-dependent Maxwell equations with the self-similar Ansatz. This is a first-order hyperbolic PDE system which can conserve non-continuous initial conditions describing electromagnetic shock-waves. Besides shock-waves other interesting solutions (e.g. with localized compact support) can be found with delicate physical properties. Such phenomena may happen in complex materials induced by the planned powerful Extreme Light Infrastructure(ELI) laser pulses.
Asymptotic shape of solutions to nonlinear eigenvalue problems
Directory of Open Access Journals (Sweden)
Tetsutaro Shibata
2005-03-01
Full Text Available We consider the nonlinear eigenvalue problem $$ -u''(t = f(lambda, u(t, quad u mbox{greater than} 0, quad u(0 = u(1 = 0, $$ where $lambda > 0$ is a parameter. It is known that under some conditions on $f(lambda, u$, the shape of the solutions associated with $lambda$ is almost `box' when $lambda gg 1$. The purpose of this paper is to study precisely the asymptotic shape of the solutions as $lambda o infty$ from a standpoint of $L^1$-framework. To do this, we establish the asymptotic formulas for $L^1$-norm of the solutions as $lambda o infty$.
Asymptotics of solutions to semilinear stochastic wave equations
Chow, Pao-Liu
2006-01-01
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution, in mean-square and the almost sure sense, are studied. Then...
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
Abstract. In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute ...
The Asymptotic Solution for the Steady Variable-Viscosity Free ...
African Journals Online (AJOL)
Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in ...
Uniqueness and asymptotic stability properties of the critical solution ...
African Journals Online (AJOL)
In this research, the Volterra prey/predator model system is modified by introducing time-lag functions f (t - h) into the state parameters to account for the ... The asymptotic stability properties of the critical solution are investigated using the quadratic matrix equation and symmetric linear matrix inequality test. Results obtained ...
Asymptotic solutions of diffusion models for risk reserves
Directory of Open Access Journals (Sweden)
S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Solution branches for nonlinear problems with an asymptotic oscillation property
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Lin Gong
2015-10-01
Full Text Available In this article we employ an oscillatory condition on the nonlinear term, to prove the existence of a connected component of solutions of a nonlinear problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions to the nonlinear problem for all parameter values in that interval.
Precise asymptotic behavior of solutions to damped simple pendulum equations
Directory of Open Access Journals (Sweden)
Tetsutaro Shibata
2009-11-01
Full Text Available We consider the simple pendulum equation $$displaylines{ -u''(t + epsilon f(u'(t = lambdasin u(t, quad t in I:=(-1, 1,cr u(t > 0, quad t in I, quad u(pm 1 = 0, }$$ where $0 < epsilon le 1$, $lambda > 0$, and the friction term is either $f(y = pm|y|$ or $f(y = -y$. Note that when $f(y = -y$ and $epsilon = 1$, we have well known original damped simple pendulum equation. To understand the dependance of solutions, to the damped simple pendulum equation with $lambda gg 1$, upon the term $f(u'(t$, we present asymptotic formulas for the maximum norm of the solutions. Also we present an asymptotic formula for the time at which maximum occurs, for the case $f(u = -u$.
Diamond, Jared M.
1966-01-01
1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254
Brem, Gerrit; Brouwers, J.J.H.
1990-01-01
In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...
Asymptotic shape of solutions to the perturbed simple pendulum problems
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Tetsutaro Shibata
2007-05-01
Full Text Available We consider the positive solution of the perturbed simple pendulum problem $$ u''(r + frac{N-1}{r}u'(r - g(u(t + lambda sin u(r = 0, $$ with $0 < r < R$, $ u'(0 = u(R = 0$. To understand well the shape of the solution $u_lambda$ when $lambda gg 1$, we establish the leading and second terms of $Vert u_lambdaVert_q$ ($1 le q < infty$ with the estimate of third term as $lambda o infty$. We also obtain the asymptotic formula for $u_lambda'(R$ as $lambda o infty$.
On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model
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Attila Dénes
2016-09-01
Full Text Available We make more realistic our model [Nonlinear Anal. 73(2010, 650-659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka-Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original non-autonomous system "rolls up"' onto a cycle of the limiting Lotka-Volterra equation as $t\\to\\infty$, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.
Thermodynamical description of stationary, asymptotically flat solutions with conical singularities
Herdeiro, Carlos; Rebelo, Carmen
2010-01-01
We examine the thermodynamical properties of a number of asymptotically flat, stationary (but not static) solutions having conical singularities, with both connected and non-connected event horizons, using the thermodynamical description recently proposed in arXiv:0912.3386 [gr-qc]. The examples considered are the double-Kerr solution, the black ring rotating in either S^2 or S^1 and the black Saturn, where the balance condition is not imposed for the latter two solutions. We show that not only the Bekenstein-Hawking area law is recovered from the thermodynamical description but also the thermodynamical angular momentum is the ADM angular momentum. We also analyse the thermodynamical stability and show that, for all these solutions, either the isothermal moment of inertia or the specific heat at constant angular momentum is negative, at any point in parameter space. Therefore, all these solutions are thermodynamically unstable in the grand canonical ensemble.
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
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Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations
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Josef Diblík
2011-01-01
Full Text Available A linear Volterra difference equation of the form x(n+1=a(n+b(nx(n+∑i=0nK(n,ix(i, where x:N0→R, a:N0→R, K:N0×N0→R and b:N0→R∖{0} is ω-periodic, is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on ∏j=0ω-1b(j is assumed. The results generalize some of the recent results.
Asymptotics of weakly collapsing solutions of nonlinear Schroedinger equation
Ovchinnikov, Yu N
2001-01-01
One studied possible types of asymptotic behavior of weakly collapsing solution of the 3-rd nonlinear Schroedinger equation. It is shown that within left brace A, C sub 1 right brace parameter space there are two neighboring lines along which the amplitude of oscillation terms is exponentially small as to C sub 1 parameter. The same lines locates values of left brace A, C sub 1 right brace parameters at which the energy is equal to zero. With increase of C sub 1 parameter the accuracy of numerical determination of points with zero energy drops abruptly
Energy Technology Data Exchange (ETDEWEB)
Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.
Periodic Solutions and S-Asymptotically Periodic Solutions to Fractional Evolution Equations
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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.
Solution of internal erosion equations by asymptotic expansion
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Dubujet P.
2012-07-01
Full Text Available One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.
Ground state solutions for asymptotically periodic Schrodinger equations with critical growth
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Hui Zhang
2013-10-01
Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... to a single ordinary differential equation for the variable $y=E^2$, where $E$ is the electric field intensity. The differential equation has solutions $y=y(\\xi)$, where $\\xi=z-st$ is the traveling wave variable and $s$ is the velocity of the wave. These solutions exhibit new phenomena not obtainable...... by the NLS approximation. The characteristics of the solutions depends on the values of the wave velocity $s$ and the energy integration constant $\\epsilon$. Both smooth periodic traveling waves and non-smooth solutions in which the electric field gradient diverges (i.e. solutions in which $|E...
Banerjee, Ayan; Jotania, Kanti; Sharma, Ranjan; Rahaman, Mosiur
2014-01-01
Gravitational analyzes in lower dimensions has become a field of active research interest ever since Banados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69, 1849, 1992) proved the existence of a black hole solution in (2 + 1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2 + 1)-dimensional anisotropic star in anti-de Sitter background space-time which have been obtained by assuming that the equation of state (EOS) describing the material composition of the star could either be linear or non-linear in nature. By matching the interior solution to the BTZ exterior metric with zero spin, we have demonstrated that the solutions provided here are regular and well-behaved at the stellar interior.
Banerjee, Ayan; Rahaman, Farook; Jotania, Kanti; Sharma, Ranjan; Rahaman, Mosiur
2015-02-01
Gravitational analyzes in lower dimensions has become a field of active research interest ever since Bañados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69:1849, 1992) proved the existence of a black hole solution in (2+1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2+1)-dimensional anisotropic star in anti-de Sitter background space-time which have been obtained by assuming that the equation of state (EOS) describing the material composition of the star could either be linear or non-linear in nature. By matching the interior solution to the BTZ exterior metric with zero spin, we have demonstrated that the solutions provided here are regular and well-behaved at the stellar interior.
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption....
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Asymptotic Solution of the Theory of Shells Boundary Value Problem
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I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
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Vladimir V. Varlamov
1999-01-01
classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
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Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Energy Technology Data Exchange (ETDEWEB)
Valat, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1960-12-15
Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de
Graffi, Dario
2011-01-01
L. Cesari: Non-linear analysis.- J.K. Hale: Oscillations in neutral functional differential equations.- M. Jean: Elements de la theorie des equations differentielles avec commandes.- J. Mawhin: Un apercu des recherches belges en theorie des equations differentielles ordinaires dans le champ reel entre 1967 et 1972.- Yu A. Mitropol'skii: Certains aspects des progres de la methode de centrage.- Th. Vogel: Quelques problemes non lineaires en physique mathematique.
Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation
Zakharov, Sergei V.
2015-01-01
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
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Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Asymptotic Solutions of Time-Space Fractional Coupled Systems by Residual Power Series Method
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Wenjin Li
2017-01-01
Full Text Available This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application.
Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis
Harada, Tomohiro; Maeda, Hideki; Carr, B. J.
2008-01-01
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure (γ>1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically “quasi-Friedmann,” in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.
Ashrafi, Motahare; Arab Chamjangali, Mansour; Bagherian, Ghadamali; Goudarzi, Nasser
2017-01-01
The performance of the Nano-magnetite Fe3O4 impregnated onto walnut shell (Fe3O4-WNS), which possessed the adsorption features of walnut shell and the magnetic property of Fe3O4, was investigated for the elimination of the methyl violet and Rhodamine 6G from contaminated aqueous solutions. The effects of different experimental variables on the removal efficiency of the cited dyes were examined. Then these variables were used as the inputs to generate linear and non-linear models such as the multiple linear regression, random forest, and artificial neural network to predict the removal efficiency of these dye species at different experimental conditions. The validation studies of these models were performed using the test set, which was not present in the modeling procedure. It was found that ANN had a higher ability to predict the adsorption process under different experimental conditions, and could be applied for the development of an automated dye wastewater removal plant. Also the maximum adsorption capacity (qmax) indicated that the qmax value for Fe3O4-WNS for removal of cationic dyes was comparable or better than that for some reported adsorbents. Also it should be cited that exhausted Fe3O4-WNS was regenerated using dishwashing liquid, and reused for removal of the cited dye species from aqueous solutions.
Ashrafi, Motahare; Arab Chamjangali, Mansour; Bagherian, Ghadamali; Goudarzi, Nasser
2017-01-15
The performance of the Nano-magnetite Fe3O4 impregnated onto walnut shell (Fe3O4-WNS), which possessed the adsorption features of walnut shell and the magnetic property of Fe3O4, was investigated for the elimination of the methyl violet and Rhodamine 6G from contaminated aqueous solutions. The effects of different experimental variables on the removal efficiency of the cited dyes were examined. Then these variables were used as the inputs to generate linear and non-linear models such as the multiple linear regression, random forest, and artificial neural network to predict the removal efficiency of these dye species at different experimental conditions. The validation studies of these models were performed using the test set, which was not present in the modeling procedure. It was found that ANN had a higher ability to predict the adsorption process under different experimental conditions, and could be applied for the development of an automated dye wastewater removal plant. Also the maximum adsorption capacity (qmax) indicated that the qmax value for Fe3O4-WNS for removal of cationic dyes was comparable or better than that for some reported adsorbents. Also it should be cited that exhausted Fe3O4-WNS was regenerated using dishwashing liquid, and reused for removal of the cited dye species from aqueous solutions. Copyright © 2016 Elsevier B.V. All rights reserved.
Convergence of hybrid methods for solving non-linear partial ...
African Journals Online (AJOL)
This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...
Asymptotic behavior of solutions to a system of Schrodinger equations
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Xavier Carvajal
2017-07-01
Full Text Available This article concerns the behaviour of solutions to a coupled system of Schrodinger equations that has applications in many physical problems, especially in nonlinear optics. In particular, when the solution exists globally, we obtain the growth of the solutions in the energy space. Finally, some conditions are also obtained for having blow-up in this space.
Non-linear modelling of breast tissue.
Whiteley, Jonathan P; Gavaghan, David J; Chapman, S Jonathan; Brady, J Michael
2007-09-01
Previous approaches to modelling the large deformation of breast tissue, as occurs, e.g. in imaging using magnetic resonance imaging or mammography, include using linear elasticity and pseudo-non-linear elasticity, in which case the non-linear deformation is approximated by a series of small linear isotropic deformations, with the (constant) Young's modulus of each linear deformation an exponential function of the total non-linear strain. In this paper, these two approaches are compared to the solution of the full non-linear elastic problem for tissue with an exponential relationship between stress and strain. Having formulated each model and related the coefficients between the models, numerical simulations are performed on a block of incompressible material. These demonstrate that the simpler models may not be appropriate even in the case of modelling deformations of the human breast under gravity.
On oscillation and asymptotic behaviour of solutions of forced first ...
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
In most of our results, the assumptions are stronger than (1). It seems that it is possible to obtain an example of a neutral differential equation in the critical case such that (1) holds but the equation admits a nonoscillatory solution which does not tend to zero as t → ∞. A similar example is obtained in the discrete case by Yu ...
Asymptotic expansion of unsteady gravity flow of a power-law fluid ...
African Journals Online (AJOL)
We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...
Asymptotic stability of multi-soliton solutions for nonlinear Schroedinger eqations
Perelman, G.
2003-01-01
We consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for large time the asymptotics of the solution is given by a sum of solitons with slightly modified parameters and a small dispersive term.
Mikhailov, E. A.; Teplyakov, I. O.
2017-11-01
The flow generated in the conductive medium with the electromagnetic force appearing when non-uniform electric current interacts with the own magnetic field was considered. The problem was solved analytically using Stokes approximation in a hemispherical geometry. Also numerical solution was obtained and comparing with the oldest mode of analytical one was carried out. The numerical and asymptotic results are quite similar.
Directory of Open Access Journals (Sweden)
Yan-Tao Bian
2014-04-01
Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \
High-frequency asymptotics of solutions of ODE in a Banach space
Sazonov, L. I.
2017-12-01
We construct and justify high-frequency asymptotic expansions of solutions for some class of linear ODE in a Banach space. In particular, we obtain new results in the case when the averaged ODE are degenerate. The author is deceased. The editors are grateful to A. B. Morgulis, who finished the paper after the author’s death.
Asymptotic behavior of solutions to a degenerate quasilinear parabolic equation with a gradient term
Directory of Open Access Journals (Sweden)
Huilai Li
2015-12-01
Full Text Available This article concerns the asymptotic behavior of solutions to the Cauchy problem of a degenerate quasilinear parabolic equations with a gradient term. A blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at infinity.
ASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs
Energy Technology Data Exchange (ETDEWEB)
Leonid Kunyansky, PhD
2008-11-26
The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems of photonic crystals theory. The results we obtained lie in three areas: (1) asymptotically fast, high-order algorithms for the solution of eigenvalue problems of photonics, (2) fast, high-order algorithms for the solution of acoustic and electromagnetic scattering problems in the inhomogeneous media, and (3) inversion formulas and fast algorithms for the inverse source problem for the acoustic wave equation, with applications to thermo- and opto- acoustic tomography.
Directory of Open Access Journals (Sweden)
H. Ullah
2015-01-01
Full Text Available The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM. The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.
Tables of generalized Airy functions for the asymptotic solution of the differential equation
Nosova, L N
1965-01-01
Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.
On the asymptotic behaviour of 2D stationary Navier-Stokes solutions with symmetry conditions
Decaster, Agathe; Iftimie, Dragoş
2017-10-01
We consider the 2D stationary incompressible Navier-Stokes equations in ℝ2. Under suitable symmetry, smallness and decay at infinity conditions on the forcing we determine the behaviour at infinity of the solutions. Moreover, when the forcing is small, satisfies suitable symmetry conditions and decays at infinity like a vector field homogeneous of degree -3, we show that there exists a unique small solution whose asymptotic behaviour at infinity is homogeneous of degree -1.
Existence and asymptotic behavior of solutions for Henon equations in hyperbolic spaces
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Haiyang He
2013-09-01
Full Text Available In this article, we consider the existence and asymptotic behavior of solutions for the Henon equation $$\\displaylines{ -\\Delta_{\\mathbb{B}^N}u=(d(x^{\\alpha}|u|^{p-2}u, \\quad x\\in \\Omega\\cr u=0 \\quad x\\in \\partial \\Omega, }$$ where $\\Delta_{\\mathbb{B}^N}$ denotes the Laplace Beltrami operator on the disc model of the Hyperbolic space $\\mathbb{B}^N$, $d(x=d_{\\mathbb{B}^N}(0,x$, $\\Omega \\subset \\mathbb{B}^N$ is geodesic ball with radius $1$, $\\alpha>0, N\\geq 3$. We study the existence of hyperbolic symmetric solutions when $2
asymptotic behavior of the ground state solution when p tends to the critical exponent $2^* =\\frac{2N}{N-2}$ with $N\\geq 3$.
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Jafar Biazar
2015-01-01
Full Text Available We combine the Adomian decomposition method (ADM and Adomian’s asymptotic decomposition method (AADM for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.
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M. Farooq
Full Text Available This article studies MHD double stratified stagnation point flow of Carreau fluid towards a non linear stretchable surface with radiation. Features of heat and mass transfer are evaluated by using convective boundary conditions. Resulting nonlinear problems are solved and studied for the velocity, temperature and concentration fields. Heat and mass transfer rates in addition to skin friction are discussed. Besides this for the verification of the present findings, the results of presented analysis have been compared with the available works in particular situations and reasonable agreement is noted. Keywords: Convective boundary condition, Thermal radiation, Double stratification, Stagnation point flow
Asymptotic behaviour of solutions for porous medium equation with periodic absorption
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Yin Jingxue
2001-01-01
Full Text Available This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be attracted into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is unstable. We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is stable.
On the Asymptotic Behavior of Positive Solutions of Certain Fractional Differential Equations
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Said R. Grace
2015-01-01
Full Text Available This paper deals with the asymptotic behavior of positive solutions of certain forced fractional differential equations of the form DcαCyt=et+ft, xt, c>1, α∈0,1, where yt=atx′t′, c0=y(c/Γ(1 =yc, and c0 is a real constant. From the obtained results, we derive a technique which can be applied to some related fractional differential equations.
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Qiong Liu
2012-01-01
Full Text Available We study the following fourth-order elliptic equations: Δ2+Δ=(,,∈Ω,=Δ=0,∈Ω, where Ω⊂ℝ is a bounded domain with smooth boundary Ω and (, is asymptotically linear with respect to at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.
Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations
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Aimin Liu
2014-01-01
Full Text Available This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations dxt=Atxt+Ft,xt,xtdt+H(t,xt,xt∘dW(t. A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup {Tt}t≥0 is essentially removed, which is generated by the linear densely defined operator A∶D(A⊂L2(ℙ,ℍ→L2(ℙ,ℍ, only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.
Pulse Propagation in a Non-Linear Medium
Edah, Gaston; Adanhounmè, Villévo; Kanfon, Antonin; Guédjé, François; Hounkonnou, Mahouton Norbert
2015-02-01
This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium.
Asymptotic behavior of solutions to nonlinear initial-value fractional differential problems
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Mohammed D. Kassim
2016-10-01
Full Text Available We study the boundedness and asymptotic behavior of solutions for a class of nonlinear fractional differential equations. These equations involve two Riemann-Liouville fractional derivatives of different orders. We determine fairly large classes of nonlinearities and appropriate underlying spaces where solutions are bounded, exist globally and decay to zero as a power type function. Our results are obtained by using generalized versions of Gronwall-Bellman inequality, appropriate regularization techniques and several properties of fractional derivatives. Three examples are given to illustrate our results.
Ritchie, R.H.; Sakakura, A.Y.
1956-01-01
The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.
Asymptotics for the multiple pole solutions of the nonlinear Schrödinger equation
Schiebold, Cornelia
2017-07-01
Multiple pole solutions consist of groups of weakly bound solitons. For the (focusing) nonlinear Schrödinger equation the double pole solution was constructed by Zakharov and Shabat. In the sequel particular cases have been discussed in the literature, but it has remained an open problem to understand multiple pole solutions in their full complexity. In the present work this problem is solved, in the sense that a rigorous and complete asymptotic description of the multiple pole solutions is given. More precisely, the asymptotic paths of the solitons are determined and their position- and phase-shifts are computed explicitly. As a corollary we generalize the conservation law known for the N-solitons. In the special case of one wave packet, our result confirms a conjecture of Olmedilla. Our method stems from an operator theoretic approach to integrable systems. To facilitate comparison with the literature, we also establish the link to the construction of multiple pole solutions via the inverse scattering method. The work is rounded off by many examples and Mathematica plots and a detailed discussion of the transition to the next level of degeneracy.
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Nita Jain
2015-09-01
Full Text Available The work presented in this paper is focused on deductive group-theoretic transformations to develop the similarity solution of steady, laminar, incompressible quasi three dimensional boundary layer flow governing power law fluid. The application of one-parameter group reduces the number of independent variables to one and consequently the system of governing, highly non-linear partial differential equations reduces to a self similar, non-linear ordinary differential equation with appropriate auxiliary conditions. The numerical solution for a power law fluid considered for small cross flow is obtained systematically using MSABC in dimensionless form.
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Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
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Alok Dhaundiyal
2016-10-01
Full Text Available This article focuses on the influence of relevant parameters of biomass pyrolysis on the numerical solution of the isothermal nth-order distributed activation energy model (DAEM using the Rayleigh distribution as the initial distribution function F(E of the activation energies. In this study, the integral upper limit, the frequency factor, the reaction order and the scale parameters are investigated. This paper also derived the asymptotic approximation for the DAEM. The influence of these parameters is used to calculate the kinetic parameters of the isothermal nth-order DAEM with the help of thermo-analytical results of TGA/DTG analysis.
Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball
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Habib Maagli
2013-04-01
Full Text Available In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem $$displaylines{ -Delta u=a(xu^{sigma }quadext{in }D, cr lim _{|x|o 1}u(x= lim_{|x|o infty}u(x =0. }$$ Here D is the complement of the closed unit ball of $mathbb{R} ^n$ ($ngeq 3$, $sigma<1$ and the function a is a nonnegative function in $C_{m loc}^{gamma}(D$, $0
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Fazle Mabood
2015-01-01
Full Text Available The heat flow patterns profiles are required for heat transfer simulation in each type of the thermal insulation. The exothermic reaction models in porous medium can prescribe the problems in the form of nonlinear ordinary differential equations. In this research, the driving force model due to the temperature gradients is considered. A governing equation of the model is restricted into an energy balance equation that provides the temperature profile in conduction state with constant heat source on the steady state. The proposed optimal homotopy asymptotic method (OHAM is used to compute the solutions of the exothermic reactions equation.
Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
Chesler, Paul M.; Yaffe, Laurence G.
2014-07-01
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.
Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus
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Safa Dridi
2015-01-01
Full Text Available In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \\[-\\Delta u=q(xu^{\\sigma }\\;\\text{in}\\;\\Omega,\\quad u_{|\\partial\\Omega}=0.\\] Here \\(\\Omega\\ is an annulus in \\(\\mathbb{R}^{n}\\, \\(n\\geq 3\\, \\(\\sigma \\lt 1\\ and \\(q\\ is a positive function in \\(\\mathcal{C}_{loc}^{\\gamma }(\\Omega \\, \\(0\\lt\\gamma \\lt 1\\, satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.
Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
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Anna Kisiolek
2005-01-01
Full Text Available We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1+pnf(xn−k=hn. We show that there exists a solution (xn, which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj+b‖=o(1, a,b∈ℝ. In this paper, we extend the results of Agarwal (1992, Dawidowski et al. (2001, Drozdowicz and Popenda (1987, M. Migda (2001, and M. Migda and J. Migda (1988. We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
An Asymptotic Theory for the Re-Equilibration of a Micellar Surfactant Solution
Griffiths, I. M.
2012-01-01
Micellar surfactant solutions are characterized by a distribution of aggregates made up predominantly of premicellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale reequilibration following a system dilution, known as the t1 and t2 processes, whose dynamics may be described by the Becker-Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes.© 2012 Society for Industrial and Applied Mathematics.
Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations
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Després, Bruno, E-mail: despres@ann.jussieu.fr [Laboratory Jacques Louis Lions, University Pierre et Marie Curie, Paris VI, Boîte courrier 187, 75252 Paris Cedex 05 (France); Weder, Ricardo, E-mail: weder@unam.mx [Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, DF 01000 (Mexico)
2016-03-22
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of an upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Després, L.M. Imbert-Gérard and R. Weder (2014) [15], where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas. - Highlights: • The upper-hybrid resonance in the cold plasma model is considered. • The long-time asymptotic of the solutions to Maxwell's equations is studied. • A method based in a singular limiting absorption principle is proposed.
Banerjee, Ayan; Rahaman, Farook; Jotania, Kanti; Sharma, Ranjan; Rahaman, Mosiur
2014-01-01
Gravitational analyzes in lower dimensions has become a field of active research interest ever since Banados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69, 1849, 1992) proved the existence of a black hole solution in (2 + 1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2 + 1)-dimensional anisotropic star in anti-de ...
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... property of the suspension is studied and it demonstrated that significant part of the variation can be predicted from the dissipated power....
Asymptotic solutions of glass temperature profiles during steady optical fibre drawing
Taroni, M.
2013-03-12
In this paper we derive realistic simplified models for the high-speed drawing of glass optical fibres via the downdraw method that capture the fluid dynamics and heat transport in the fibre via conduction, convection and radiative heating. We exploit the small aspect ratio of the fibre and the relative orders of magnitude of the dimensionless parameters that characterize the heat transfer to reduce the problem to one- or two-dimensional systems via asymptotic analysis. The resulting equations may be readily solved numerically and in many cases admit exact analytic solutions. The systematic asymptotic breakdown presented is used to elucidate the relative importance of furnace temperature profile, convection, surface radiation and conduction in each portion of the furnace and the role of each in controlling the glass temperature. The models derived predict many of the qualitative features observed in real industrial processes, such as the glass temperature profile within the furnace and the sharp transition in fibre thickness. The models thus offer a desirable route to quick scenario testing, providing valuable practical information about the dependencies of the solution on the parameters and the dominant heat-transport mechanism. © 2013 Springer Science+Business Media Dordrecht.
Asymptotic solutions for flow in microchannels with ridged walls and arbitrary meniscus protrusion
Kirk, Toby
2017-11-01
Flow over structured surfaces exhibiting apparent slip, such as parallel ridges, have received much attention experimentally and numerically, but analytical and asymptotic solutions that account for the microstructure have so far been limited to unbounded geometries such as shear-driven flows. Analysis for channel flows has been limited to (close to) flat interfaces spanning the grooves between ridges, but in applications the interfaces (menisci) can highly protrude and have a significant impact on the apparent slip. In this presentation, we consider pressure-driven flow through a microchannel with longitudinal ridges patterning one or both walls. With no restriction on the meniscus protrusion, we develop explicit formulae for the slip length using a formal matched asymptotic expansion. Assuming the ratio of channel height to ridge period is large, the periodicity is confined to an inner layer close to the ridges, and the expansion is found to all algebraic orders. As a result, the error is exponentially small and, under a further ``diluteness'' assumption, the explicit formulae are compared to finite element solutions. They are found to have a very wide range of validity in channel height (even when the menisci can touch the opposing wall) and so are useful for practitioners.
Li, Can; Deng, Wei-Hua
2014-07-01
Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.
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J. Kalas
2012-01-01
Full Text Available The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for $t$ approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
Rani, Neelam; Vijayan, N; Maurya, K K; Haranath, D; Saini, Parveen; Rathi, Brijesh; Wahab, M A; Bhagavanarayana, G
2012-11-01
Nonlinear optical single crystals are getting attention because of its enormous applications in the area of fiber optic communication and optical signal processing. In this article, we are reporting the single crystal growth of l-lysine monohydrochloride by slow evaporation solution growth technique, by using double distilled water as the solvent. We found that the grown single crystal is bulk in size and fairly transparent. But after a period of time, due to its hygroscopic nature, the transparency is completely vanished and became opaque. Then we have attempted to coat the poly methyl methacrylate (PMMA) polymer on the surface of l-lysine monohydrochloride (l-LMHCL) single crystal by dip coating method. This polymer coating is giving resistance to hygroscopic nature and also acting as thin protective covering layer without affecting the other properties. Then we have systematically studied the different properties of bare, polymer coated and hygroscopic l-LMCHL single crystals. Its crystalline perfection was examined by high resolution X-ray diffractometer and found major differences in crystalline quality. Its structural and optical behavior was assessed by powder X-ray diffraction, UV-vis and luminescence analyses. Copyright © 2012 Elsevier B.V. All rights reserved.
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Bologna, Mauro, E-mail: mauroh69@libero.i [Instituto de Alta Investigacion, Universidad de Tarapaca-Casilla 7-D Arica (Chile)
2010-09-17
This paper addresses the problem of finding an asymptotic solution for first- and second-order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of the paper is to go beyond the Tauberian theorem in the case of integral-differential equations which are widely used by the scientific community. The results are applied to the convolute form of the Lindblad equation setting generic conditions on the kernel in such a way as to generate a positive definite density matrix, and show that the structure of the eigenvalues of the correspondent Liouvillian operator plays a crucial role in determining the positivity of the density matrix.
Bochicchio, Marco
2016-05-01
Employing a new class of string theories we construct a family of S -matrix amplitudes that factorize over linear Regge trajectories, and that are good candidates to be asymptotically free, i.e. to lead to asymptotically-free correlation functions working out the LS Z formulae the other way around. In particular, we propose a candidate for a string solution of QCD with NF massless quarks in the large-N 't Hooft limit, for the glueball and meson spectrum, and for certain S-matrix amplitudes in the collinear limit. The solution extends to massive quarks of equal mass.
Asymptotically flat scalar, Dirac and Proca stars: Discrete vs. continuous families of solutions
Herdeiro, Carlos A. R.; Pombo, Alexandre M.; Radu, Eugen
2017-10-01
The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field - geons - was conjectured more than half a century ago. If one insists on exact stationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar) boson stars. Similar geons have subsequently been found in Einstein-Dirac theory and, more recently, in Einstein-Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin 0 , 1 / 2 and 1, emphasizing the mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermionic cases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case.
Asymptotically flat scalar, Dirac and Proca stars: Discrete vs. continuous families of solutions
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Carlos A.R. Herdeiro
2017-10-01
Full Text Available The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field – geons – was conjectured more than half a century ago. If one insists on exact stationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar boson stars. Similar geons have subsequently been found in Einstein–Dirac theory and, more recently, in Einstein–Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin 0,1/2 and 1, emphasizing the mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermionic cases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case.
Mohanty, R. K.; Singh, Swarn
2007-11-01
We propose a new two-level implicit difference method of O(k2+kh2+h4) for the solution of singularly perturbed non-linear parabolic differential equation [epsilon](uxx+uyy)=f(x,y,t,u,ux,uy,ut), 00 subject to appropriate initial and Dirichlet boundary conditions, where k>0 and h>0 are grid sizes in time and space directions, respectively, and [epsilon]>0 is a small parameter. We also develop new methods of O(kh2+h4) for the estimates of ([partial differential]u/[partial differential]x) and ([partial differential]u/[partial differential]y). In all cases, we use 9-spatial grid points and a single computational cell. The proposed methods are directly applicable to singular problems. We do not require any special scheme to solve singular problems. We also discuss alternating direction implicit (ADI) method for solving diffusion equation in polar cylindrical coordinates. This method permits multiple use of the one-dimensional tri-diagonal algorithm with a considerable saving in computing time, and produces a very efficient solver. It is shown that the ADI method is unconditionally stable. Numerical experiments are conducted to test the high accuracy of the proposed methods and compared with the exact solutions.
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Javed Ali
2012-01-01
Full Text Available We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM. The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM, variational iteration (VIM, homotopy perturbation (HPM, and variational iteration decomposition method (VIDM. The results show that the proposed method is more effective and reliable.
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Bezyaev Vladimir Ivanovich
2014-09-01
Full Text Available The authors present an efficient algorithm different from the previously known to construct the asymptotics of solutions of nonautonomous systems of ordinary differential equations with meromorphic matrix. Schrödinger equation, Dirac system, Lippman-Schwinger equation and other equations of quantum mechanics with spherically symmetric and meromorphic potentials may be reduced to such systems. The Schrödinger equation and the Dirac system describe the stationary states of an electron in a Coulomb field with a fixed point charge in the description of the relativistic and nonrelativistic hydrogen atom. The Lippman-Schwinger equation of scattering theory describes the results of collision and interaction of quantum-mechanical particles in mathematical language after these particles have already diverged a long way from one another and ceased to interact. The observed algorithm supplements the known results and allows you to approach the analysis of the problems of this type with a fairly simple and at the same time, a universal point of view.
An asymptotic solution of the Schroedinger equation for the elliptic wire in the magnetic field
Energy Technology Data Exchange (ETDEWEB)
Bejenari, I; Kantser, V [Institute of Electronic Engineering and Industrial Technologies, Academiei str., 3/3, MD2028 Chisinau (Moldova, Republic of)], E-mail: bejenari@iieti.asm.md
2008-10-03
An asymptotic solution of the Schroedinger equation with non-separable variables is obtained for a particle confined to an infinite elliptic cylinder potential well under an applied uniform longitudinal magnetic field. Using the standard-problem method, dimension-quantized eigenvalues have been calculated when the magnetic length is large enough in comparison with the half of the distance between the boundary ellipse focuses. In semi-classical approximation, the confined electron (hole) states are divided into the boundary states (BS), ring states (RS), hyperbolic caustic states (HCS) and harmonic oscillator states (HOS). For large angular momentum quantum numbers and small radial quantum numbers, the BS and RS are grouped into the 'whispering gallery' mode. They associate with particles moving along the wire cross section boundary. The motion is limited from the wire core by the elliptic caustic. Consisting of the HCS and HOS, the 'jumping ball' modes correspond to the states of particle moving along a wire diameter when the angular momentum quantum number is much less than the radial quantum number. In this case, the motion is restricted by the hyperbolic caustics and two boundary ellipse arcs. For excited hole states in a Bi wire, the energy spectrum and space probability distribution are analyzed.
Bulatov, Vitaly V
2012-01-01
The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density and the shape of the floor are modeled with specific functions. In a general case when the characteristics of stratified media and the boundary conditions are arbitrary, the dynamics of internal waves can be only approximated with numerical methods. However, numerical solutions do not describe the wave field qualitatively. At the same time, the need for a qualitative analysis of the far field of internal waves arises in studies applying remote sensing methods in space-based radar applications. In this case, the dynamics of internal waves can be described using asymptotic models. In this paper, we derive asymptotic solutions to the problem of characterizing the far field of internal gravity waves propagating in a stratified medium with a smoothly varying floor.
Asymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cells
Richardson, Giles
2012-11-15
Organic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley-Read-Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents-i.e., at reverse bias or moderate forward bias-the structure of the solution is independent of the total current. For large currents-i.e., at strong forward bias-the current varies linearly with the voltage and is primarily controlled by drift of charges in the organic layers. There is then a narrow range of currents where the behavior undergoes a transition between the two regimes. The magnitude of the parameter that quantifies the interfacial recombination rate is critical in determining where the transition occurs. The extension of the theory to organic solar cells generating current under illumination is discussed as is the analogous current-voltage curves derived where the photo current is small. Finally, by comparing the analytic results to real experimental data, we show how the model parameters can be extracted from the shape of current-voltage curves measured in the dark. © 2012 Society for Industrial and Applied Mathematics.
Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates.
Constantin, A; Johnson, R S
2017-04-01
Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Non-linear WKB analysis of the string equation
Energy Technology Data Exchange (ETDEWEB)
Fucito, F. (Dipartimento di Fisica, Univ. di Roma II Tor Vergata and INFN, Sezione di Roma Tor Vergata, Via Carnevale, 00173 Roma (Italy)); Gamba, A. (Milan Univ. (Italy). Ist. di Matematica); Martellini, M. (INFN, Sezione Di Roma I, Piazzale Aldo Moro 5, Roma (Italy)); Ragnisco, O. (Dipartimento di Fisica, Univ. di Roma I La Sapienza and INFN, Sezione di Roma I, Piazzale Aldo Moro 5, Roma (Italy))
1992-07-10
The authors apply non-linear WKB analysis to the study of the string equation. Even though the solutions obtained with this method are not exact, they approximate extremely well the true solutions, as we explicitly show using numerical simulations. Physical solutions are seen to be separatrices corresponding to degenerate Riemann surfaces. We obtain an analytic approximation in excellent agreement with the numerical solution found by Parisi et al. for the k = 3 case.
Maksimova, N.V.; Akhmetov, R. G.
2013-01-01
The work deals with a boundary value problem for a quasilinear partial elliptical equation. The equation describes a stationary process of convective diffusion near a cylinder and takes into account the value of a chemical reaction for large Peclet numbers and for large constant of chemical reaction. The quantity the rate constant of the chemical reaction and Peclet number is assumed to have a constant value. The leading term of the asymptotics of the solution is constructed in the boundary l...
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Directory of Open Access Journals (Sweden)
Yaojun Ye
2010-01-01
Full Text Available The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt+Au+a|ut|p−1ut=b|u|q−1u in a bounded domain is studied, where A=(−Δm, m≥1 is a nature number, and a,b>0 and p,q>1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method.
Maci, S.; Neto, A.
2004-01-01
This second part of a two-paper sequence deals with the uniform asymptotic description of the Green's function of an infinite slot printed between two different homogeneous dielectric media. Starting from the magnetic current derived in Part I, the dyadic green's function is first formulated in
Asymptotic solution on the dynamic buckling of a column stressed by ...
African Journals Online (AJOL)
This paper analysis the dynamic stability of a dynamically oscillatory system with slowly varying time dependent parameters. It utilizes the concept of multiple times scaling in an asymptotic evaluation of the dynamic buckling load of the imperfect elastic structure under investigation. Unlike most similar investigations to date ...
Directory of Open Access Journals (Sweden)
Liaqat Ali
2016-09-01
Full Text Available In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4 and Optimal Homotopy Asymptotic Method (OHAM-1. The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.
Russell, John
2000-11-01
A modified Orr-Sommerfeld equation that applies to the asymptotic suction boundary layer was reported by Bussmann & Münz in a wartime report dated 1942 and by Hughes & Reid in J.F.M. ( 23, 1965, p715). Fundamental systems of exact solutions of the Orr-Sommerfeld equation for this mean velocity distribution were reported by D. Grohne in an unpublished typescript dated 1950. Exact solutions of the equation of Bussmann, Münz, Hughes, & Reid were reported by P. Baldwin in Mathematika ( 17, 1970, p206). Grohne and Baldwin noticed that these exact solutions may be expressed either as Barnes integrals or as convolution integrals. In a later paper (Phil. Trans. Roy. Soc. A, 399, 1985, p321), Baldwin applied the convolution integrals in the contruction of large-Reynolds number asymptotic approximations that hold uniformly. The present talk discusses the subtleties that arise in the construction of such convolution integrals, including several not reported by Grohne or Baldwin. The aim is to recover the full set of seven solutions (one well balanced, three balanced, and three dominant-recessive) postulated by W.H. Reid in various works on the uniformly valid solutions.
The Importance of Non-Linearity on Turbulent Fluxes
DEFF Research Database (Denmark)
Rokni, Masoud
2007-01-01
Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...
Wu, Junde; Zhou, Fujun
2017-05-01
In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that nutrient concentration on the boundary is less than external supply due to a Gibbs-Thomson relation and the problem has two radial stationary solutions, which differs from widely studied tumor spheroid model with surface tension effect. We first establish local well-posedness by using a functional approach based on Fourier multiplier method and analytic semigroup theory. Then we investigate stability of each radial stationary solution. By employing a generalized principle of linearized stability, we prove that the radial stationary solution with a smaller radius is always unstable, and there exists a positive threshold value γ* of cell-to-cell adhesiveness γ, such that the radial stationary solution with a larger radius is asymptotically stable for γ >γ*, and unstable for 0 < γ <γ*.
On global asymptotic stability of solutions of a system of ordinary differential equations
Filimonov, M. Yu.
2017-12-01
To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system.
Non-linear DSGE Models and The Central Difference Kalman Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper introduces a Quasi Maximum Likelihood (QML) approach based on the Cen- tral Difference Kalman Filter (CDKF) to estimate non-linear DSGE models with potentially non-Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models...
Sameh Turki
2012-01-01
This paper deals with the existence and the asymptotic behavior of positive continuous solutions of the nonlinear elliptic system \\(\\Delta u=p(x)u^{\\alpha}v^r\\), \\(\\Delta v = q(x)u^s v^{\\beta}\\), in the half space \\(\\mathbb{R}^n_+ :=\\{x=(x_1,..., x_n)\\in \\mathbb{R}^n : x_n \\gt 0\\}\\), \\(n \\geq 2\\), where \\(\\alpha, \\beta \\gt 1\\) and \\(r, s \\geq 0\\). The functions \\(p\\) and \\(q\\) are required to satisfy some appropriate conditions related to the Kato class \\(K^{\\infty}(\\mathbb{R}^n_+)\\). Our app...
Sekerzh-Zen'kovich, S. Ya.
2017-10-01
Statement of the hydrodynamic problem in the framework of the potential tsunami model with "simple" source whose solution is chosen as the reference one. Generalized Cauchy problem for the Boussinesq equation and its reduction to the classical one. Analytical solution of the Cauchy problem for the Boussinesq equation. An explanation of the incorrectness of the formulation of the problem. Derivation of an approximate equation for the correct setting of the Cauchy problem. The known reference solution of the problem. An analytical solution of the correct problem and the derivation of its asymptotic representation in the "far zone." Comparison of the graphs of the temporal history of wave height calculated by the formulas of the asymptotic and reference solutions. Estimation of the accuracy of the asymptotic solution by a three-level scale. Discussion. A remark concerning the referees.
Directory of Open Access Journals (Sweden)
Edgardo Alvarez
2016-10-01
Full Text Available We study weighted pseudo almost automorphic solutions for the nonlinear fractional difference equation $$ \\Delta^{\\alpha}u(n=Au(n+1+f(n, u(n,\\quad n\\in \\mathbb{Z}, $$ for $0<\\alpha \\leq 1$, where A is the generator of an $\\alpha$-resolvent sequence $\\{S_{\\alpha}(n\\}_{n\\in\\mathbb{N}_0}$ in $\\mathcal{B}(X$. We prove the existence and uniqueness of a weighted pseudo almost automorphic solution assuming that f(.,. is weighted almost automorphic in the first variable and satisfies a Lipschitz (local and global type condition in the second variable. An analogous result is also proved for $\\mathcal{S}$-asymptotically $\\omega$-periodic solutions.
Aguareles, M.
2014-06-01
In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Long-term cavity closure in non-linear rocks
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel Walter
2017-08-01
The time dependent closure of pressurized cavities in viscous rocks due to far-field loads is a problem encountered in many applications like drilling, cavity abandonment and porosity closure. The non-linear nature of the flow of rocks prevents the use of simple solutions for hole closure and calls for the development of appropriate expressions reproducing all the dependencies observed in nature. An approximate solution is presented for the closure velocity of a pressurized cylindrical cavity in a non-linear viscous medium subjected to a combined pressure and shear stress load in the far field. The embedding medium is treated as homogeneous, isotropic, and incompressible and follows a Carreau viscosity model. We derive analytical solutions for the end-member cases of the pressure and shear loads. The exact analytical solution for pressure loads shows that the closure velocity vR is given by the implicit expression {Δ p}/{2{μ _0D_{II}^*}} = - 1/2B( {v_R^2}/{RD_{II^* + v_R^2}};1/2, - 1/{2n}} ), where Δp is the pressure load, R is the hole radius, B is the incomplete beta function, and μ0, D_{II}^*, n are, respectively, the threshold viscosity, transition rate and stress exponent of the Carreau model. The closure velocity is dominated by the linear mechanism under pressure loads smaller than 1.8{μ _0}D_{II}^* and by the non-linear one under large pressure loads. In the non-linear regime, pressure variations support an increasing part of the load with increasing degree of non-linearity. The decay of the stress perturbation in the non-linear zone varies as r- 2/n where r is the radial distance to the hole. A solution for the maximum closure velocity at the cavity rim vRmax under far-field shear is given: v_{R\\max} = ( {1 + {\\overline {M_s}}^{-1/2})R\\overline D_{II}, where \\overline M_s = (1 +{\\overline{D_{II}}^2} \\big nD_{II}^*^2} ) \\big ( 1 + {\\overline {D_{II}}^2} \\big D{_{II}^*}^2 ) and \\overline D_{II} is the second invariant of the far
Non-linear Post Processing Image Enhancement
Hunt, Shawn; Lopez, Alex; Torres, Angel
1997-01-01
A non-linear filter for image post processing based on the feedforward Neural Network topology is presented. This study was undertaken to investigate the usefulness of "smart" filters in image post processing. The filter has shown to be useful in recovering high frequencies, such as those lost during the JPEG compression-decompression process. The filtered images have a higher signal to noise ratio, and a higher perceived image quality. Simulation studies comparing the proposed filter with the optimum mean square non-linear filter, showing examples of the high frequency recovery, and the statistical properties of the filter are given,
Directory of Open Access Journals (Sweden)
Hiroshi Matsuzawa
2006-01-01
Full Text Available In this article, we consider the semilinear elliptic problem $$ -varepsilon^{2}Delta u=h(|x|^2(u-a(|x|(1-u^2 $$ in $B_1(0$ with the Neumann boundary condition. The function $a$ is a $C^1$ function satisfying $|a(x|< 1$ for $xin [0,1]$ and $a'(0=0$. In particular we consider the case $a(r=0$ on some interval $Isubset [0,1]$. The function $h$ is a positive $C^1$ function satisfying $h'(0=0$. We investigate an asymptotic profile of the global minimizer corresponding to the energy functional as $varepsilono 0$. We use the variational procedure used in [4] with a few modifications prompted by the presence of the function $h$.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
2013-01-01
This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.
Non-linear reduced order models for steady aerodynamics
DEFF Research Database (Denmark)
Zimmermann, Ralf; Goertz, Stefan
2010-01-01
transformation for obtaining problem-adapted global basis modes is introduced. Model order reduction is achieved by parameter space sampling, reduced solution space representation via global POD and restriction of a CFD flow solver to the reduced POD subspace. Solving the governing equations of fluid dynamics...... is replaced by solving a non-linear least-squares optimization problem. Methods for obtaining feasible starting solutions for the optimization procedure are discussed. The method is demonstrated by computing reduced-order solutions to the compressible Euler equations for the NACA 0012 airfoil based on two...
Controller Reconfiguration for non-linear systems
Kanev, S.K.; Verhaegen, M.H.G.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting
Pharmaceutical applications of non-linear imaging
Strachan, Clare J.; Windbergs, Maike; Offerhaus, Herman L.
2011-01-01
Non-linear optics encompasses a range of optical phenomena, including two- and three-photon fluorescence, second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), third harmonic generation (THG), coherent anti-Stokes Raman scattering (CARS), and
Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations
Directory of Open Access Journals (Sweden)
P. Polacik
2000-01-01
Full Text Available Time-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have the same period as the equation, but, possibly, there might be others with larger minimal periods (these are called subharmonic solutions. The problem of existence of stable subharmonic solutions is therefore of fundamental importance in the study of the behavior of solutions. We address this problem for two classes of reaction diffusion equations under Neumann boundary conditions. Namely, we consider spatially inhomogeneous equations, which can have stable subharmonic solutions on any domain, and spatially homogeneous equations, which can have such solutions on some (necessarily non-convex domains.
Non-linear dendrites can tune neurons
Directory of Open Access Journals (Sweden)
Romain Daniel Cazé
2014-03-01
Full Text Available A signature of visual, auditory, and motor cortices is the presence of neurons tuned to distinct features of the environment. While neuronal tuning can be observed in most brain areas, its origin remains enigmatic, and new calcium imaging data complicate this problem. Dendritic calcium signals, in a L2/3 neuron from the mouse visual cortex, display a wide range of tunings that could be different from the neuronal tuning (Jia et al 2010. To elucidate this observation we use multi-compartmental models of increasing complexity, from a binary to a realistic biophysical model of L2/3 neuron. These models possess non-linear dendritic subunits inside which the result of multiple excitatory inputs is smaller than their arithmetic sum. While dendritic non-linear subunits are ad-hoc in the binary model, non-linearities in the realistic model come from the passive saturation of synaptic currents. Because of these non-linearities our neuron models are scatter sensitive: the somatic membrane voltage is higher when presynaptic inputs target different dendrites than when they target a single dendrite. This spatial bias in synaptic integration is, in our models, the origin of neuronal tuning. Indeed, assemblies of presynaptic inputs encode the stimulus property through an increase in correlation or activity, and only the assembly that encodes the preferred stimulus targets different dendrites. Assemblies coding for the non-preferred stimuli target single dendrites, explaining the wide range of observed tunings and the possible difference between dendritic and somatic tuning. We thus propose, in accordance with the latest experimental observations, that non-linear integration in dendrites can generate neuronal tuning independently of the coding regime.
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n
Directory of Open Access Journals (Sweden)
Meng-Rong Li
2013-11-01
Full Text Available In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1
Energy Technology Data Exchange (ETDEWEB)
Traytak, Sergey D., E-mail: sergtray@mail.ru [Centre de Biophysique Moléculaire, CNRS-UPR4301, Rue C. Sadron, 45071 Orléans (France); Le STUDIUM (Loire Valley Institute for Advanced Studies), 3D av. de la Recherche Scientifique, 45071 Orléans (France); Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow (Russian Federation)
2014-06-14
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.
Non-Linear Forced Vibrations of AN Inhomogeneous Layer
COSKUN, I.; ENGIN, H.; ERGÜVEN, M. E.
1999-11-01
The non-linear vibrations of an inhomogeneous soil layer which is subjected to a harmonic motion along its bottom are investigated in this study. The Ramberg-Osgood model is transformed to a suitable form to obtain an analytical solution and it is assumed that the shear modulus of the layer varies with depth. The governing equation is a non-linear partial differential equation. Because of weak non-linearity, the displacement and forcing frequency are expanded into perturbation series by using the Lindstedt-Poincaré technique, and it is assumed that the response has the same periodicity as the forcing. Then, the zeroeth and the first order linear equations of motion and boundary conditions are obtained. Different types of solutions are obtained for the zeroeth order equation depending on the inhomogeneity parameter α. The orthogonality condition of Millman-Keller [1] is used to extract secular terms which are important in the resonance region. Then, the variation of the amplitude at the top versus the forcing frequency Ω is investigated for some values of inhomogeneity and perturbation parameters.
Energy Technology Data Exchange (ETDEWEB)
Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece); School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Hadjinicolaou, Maria [School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Karahalios, George T. [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece)
2016-08-15
The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses
Non-linear Static Analysis of Offshore Steep Wave Riser
Directory of Open Access Journals (Sweden)
Qiao Hongdong
2016-01-01
Full Text Available A new solution combining finite difference method and shooting method is developed to analyze the behavior of steep wave riser suffering from current loading. Based on the large deformation beam theory and mechanics equilibrium principle, a set of non-linear ordinary differential equations describing the motion of the steep wave riser are obtained. Then, finite difference method and shooting method are adopted and combined to solve the ordinary differential equations with zero moment boundary conditions at both the seabed end and surface end of the steep wave riser. The resulting non-linear finite difference formulations can be solved effectively by Newton-Raphson method. To improve iterative efficiency, shooting method is also employed to obtain the initial value for Newton-Raphson method. Results are compared with that of FEM by OrcaFlex, to verify the accuracy and reliability of the numerical method.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
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Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Chaos and non-linear phenomena in renal vascular control
DEFF Research Database (Denmark)
Yip, K P; Holstein-Rathlou, N H
1996-01-01
condition for the interaction is that the nephrons derive their blood supply from the same cortical radial artery. Development of hypertension is associated with a shift from periodic oscillations of tubular pressure to random-like fluctuations. Numerical analyses indicate that these fluctuations...... a variety of non-linear phenomena. In halothane-anesthetized, normotensive rats the TGF system oscillates regularly at 2-3 cycles/min because of the non-linearities and the time delays within the feedback system. Oscillations are present in single nephron blood flow, tubular pressure and flow......, and in the tubular solute concentrations. Nephrons deriving their afferent arteriole from the same cortical radial artery are entrained, and consequently oscillate at the same frequency. Experimental studies have shown that the synchronization is due to an interaction of the TGF between nephrons. A necessary...
Directory of Open Access Journals (Sweden)
Zhoujin Cui
2007-01-01
Full Text Available This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of blow-up is uniform in all compact subsets of the domain, the blow-up rate of |u(t|∞ is precisely determined.
Asymptotic behaviour of solutions to a system of Schrödinger equations
Czech Academy of Sciences Publication Activity Database
Carvajal, X.; Gamboa, P.; Nečasová, Šárka; Nguyen, H. H.; Vero, O.
2017-01-01
Roč. 2017, č. 171 (2017), s. 1-23 ISSN 1072-6691 R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : coupled Schrodinger system * energy conservation * global solution * growth of solutions Subject RIV: BA - General Mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2017/171/abstr.html
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Non-linear evanescent-field imaging
Energy Technology Data Exchange (ETDEWEB)
Oheim, Martin [Laboratory of Neurophysiology and New Microscopies, CNRS FRE 2500, INSERM U 603, Ecole Superieure de Physique et Chimie Industrielles (ESPCI), 10 rue Vauquelin, F-75005 Paris (France); Schapper, Florian [Freie Universitaet Berlin, Institut fuer Experimentalphysik, Arbeitsgruppe Wolf, Arnimallee 14, D-14195 Berlin (Germany)
2005-05-21
Total internal reflection fluorescence (TIRF), a general term that embraces any spectroscopic or microscopic technique based on the evanescent field created by TIR of light, is further establishing itself as an important tool for studying near-surface phenomena. Impingement of a femtosecond-pulsed infrared beam on a reflecting interface creates the conditions for 'macroscopic' evanescent-field two-photon fluorescence excitation. The two-photon fluorescence excitation volume is confined by both the non-linearity of the multi-photon process and the spatial inhomogeneity of the evanescent field. The absence of scattered excitation resulting in a low background and the possibility of simultaneous multi-colour fluorescence excitation should make non-linear evanescent-field excitation particularly attractive for quantitative single-molecule observation and ultra-sensitive screening assays. In this topical review, we survey the requirements, present the current results and explore the potential of this novel non-linear microscopy. (topical review)
Thermal stability analysis of nonlinearly charged asymptotic AdS black hole solutions
Dehghani, M.; Hamidi, S. F.
2017-08-01
In this paper, the four-dimensional nonlinearly charged black hole solutions have been considered in the presence of the power Maxwell invariant electrodynamics. Two new classes of anti-de Sitter (AdS) black hole solutions have been introduced according to different amounts of the parameters in the nonlinear theory of electrodynamics. The conserved and thermodynamical quantities of either of the black hole classes have been calculated from geometrical and thermodynamical approaches, separately. It has been shown that the first law of black hole thermodynamics is satisfied for either of the AdS black hole solutions we just obtained. Through the canonical and grand canonical ensemble methods, the black hole thermal stability or phase transitions have been analyzed by considering the heat capacities with the fixed black hole charge and fixed electric potential, respectively. It has been found that the new AdS black holes are stable if some simple conditions are satisfied.
Gilliam, Ashley E.; Wunsch, Jared; Lerman, Abraham
2017-09-01
Systems of simultaneous or parallel chemical reactions of the type A → B → C → Other products are often treated as first order or pseudo-first order. For a system of simultaneous first and second order reactions — dB/dt = kABA - kBCB2 and dC/dt = kBCB2 - kCC, where A, B, and C are concentrations, t is time, and the reaction rate parameters kAB and kC in yr-1 are 1st-order and kBC in cm3 molecule-1 yr-1 is 2nd-order — no explicit solution is available, as far as we are aware. This paper presents explicit and asymptotic solutions of simultaneous 1st- and 2nd order Riccati equations and applies them to a simplified sequence of gas reactions in the atmosphere of Titan, the largest satellite of Saturn: CH4 methane (1st order, k12) → CH3 methyl (2nd order, k23) → C2H6 ethane (1st order, k3) → Other products. The Titan's atmosphere contains methane (CH4) at the present-day partial pressure of 0.1 bar, out of a total atmospheric pressure made up by nitrogen (N2) of 1.5 bar, comparable to Earth's. Methyl CH3 and ethane C2H6 are minor components. On Titan, methyl (CH3) is an intermediate product from methane to ethane, the latter raining out as liquid on Titan's surface. The main points of this paper are: (1) the asymptotic solutions that approximate near-steady state of Titan's atmosphere about 4.5 billion years after its accretion; (2) the computed present-day concentrations of the three gases in Titan's scale atmosphere (i.e., scale atmosphere is a model of an isothermal well mixed reservoir); and (3) the agreement between Titan's reported and computed atmospheric concentrations of CH4, CH3, and C2H6. The reaction rate parameters of the species are constants representative of their mean values during the satellite's cooling history. The present-day concentrations of methyl (CH3) and ethane (C2H6) are several orders of magnitude lower than the concentration of methane (CH4). Since Titan's accretion about 4.5 billion years B.P., steady-state concentrations
Said-Houari, Belkacem
2012-03-01
In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.
Spin waves cause non-linear friction
Magiera, M. P.; Brendel, L.; Wolf, D. E.; Nowak, U.
2011-07-01
Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.
Non-linear Models for Longitudinal Data
Serroyen, Jan; Molenberghs, Geert; Verbeke, Geert; Davidian, Marie
2009-01-01
While marginal models, random-effects models, and conditional models are routinely considered to be the three main modeling families for continuous and discrete repeated measures with linear and generalized linear mean structures, respectively, it is less common to consider non-linear models, let alone frame them within the above taxonomy. In the latter situation, indeed, when considered at all, the focus is often exclusively on random-effects models. In this paper, we consider all three families, exemplify their great flexibility and relative ease of use, and apply them to a simple but illustrative set of data on tree circumference growth of orange trees. PMID:20160890
Positive solutions with specific asymptotic behavior for a polyharmonic problem on R^{n}
Directory of Open Access Journals (Sweden)
Abdelwaheb Dhifli
2015-01-01
Full Text Available This paper is concerned with positive solutions of the semilinear polyharmonic equation \\((-\\Delta^{m} u = a(x{u}^{\\alpha}\\ on \\(\\mathbb{R}^{n}\\, where \\(m\\ and \\(n\\ are positive integers with \\(n\\gt 2m\\, \\(\\alpha\\in (-1,1\\. The coefficient \\(a\\ is assumed to satisfy \\[a(x\\approx{(1+|x|}^{-\\lambda}L(1+|x|\\quad \\text{for}\\quad x\\in \\mathbb{R}^{n},\\] where \\(\\lambda\\in [2m,\\infty\\ and \\(L\\in C^{1}([1,\\infty\\ is positive with \\(\\frac{tL'(t}{L(t}\\longrightarrow 0\\ as \\(t\\longrightarrow \\infty\\; if \\(\\lambda=2m\\, one also assumes that \\(\\int_{1}^{\\infty}t^{-1}L(tdt\\lt \\infty\\. We prove the existence of a positive solution \\(u\\ such that \\[u(x\\approx{(1+|x|}^{-\\widetilde{\\lambda}}\\widetilde{L}(1+|x| \\quad\\text{for}\\quad x\\in \\mathbb{R}^{n},\\] with \\(\\widetilde{\\lambda}:=\\min(n-2m,\\frac{\\lambda-2m}{1-\\alpha}\\ and a function \\(\\widetilde{L}\\, given explicitly in terms of \\(L\\ and satisfying the same condition at infinity. (Given positive functions \\(f\\ and \\(g\\ on \\(\\mathbb{R}^{n}\\, \\(f\\approx g\\ means that \\(c^{-1}g\\leq f\\leq cg\\ for some constant \\(c\\gt 1\\.
Non-linear feedback neural networks VLSI implementations and applications
Ansari, Mohd Samar
2014-01-01
This book aims to present a viable alternative to the Hopfield Neural Network (HNN) model for analog computation. It is well known that the standard HNN suffers from problems of convergence to local minima, and requirement of a large number of neurons and synaptic weights. Therefore, improved solutions are needed. The non-linear synapse neural network (NoSyNN) is one such possibility and is discussed in detail in this book. This book also discusses the applications in computationally intensive tasks like graph coloring, ranking, and linear as well as quadratic programming. The material in the book is useful to students, researchers and academician working in the area of analog computation.
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Non linear effects in piezoelectric materials
Directory of Open Access Journals (Sweden)
Gonnard, P.
2002-02-01
Full Text Available The static and dynamic non-linear behaviours of a soft and a hard zirconate titanate composition are investigated in this paper as a function of electrical and mechanical fields. The calculated Rayleigh coefficients show that they are similar for the permittivity ε ^{T}_{33} and the piezoelectric constant and nul for the voltage constant d_{33} and the compliance at zero D (D = dielectric displacement. A non-linear electromechanical equivalent circuit is built up with components proportional to D. Finally an extended model to non-Rayleigh type behaviours is proposed.
Los comportamientos no lineales estáticos y dinámicos de composiciones blandas y duras de titanato circonato de plomo se investigan en este trabajo en función de campos eléctricos y mecánicos. Los coeficientes de Rayleigh calculados son similares para la permitividad ε^{T}_{33} y la constantes piezoléctrica d_{33} y nulos para la constante g_{33} y la complianza a D cero (D=desplazamiento dieléctrico. Se construye un circuito electromecánico no lineal equivalente con componentes proporcionales a D. Finalmente se propone un modelo extendido a comportamientos de tipo no-Rayleigh.
Pharmaceutical applications of non-linear imaging.
Strachan, Clare J; Windbergs, Maike; Offerhaus, Herman L
2011-09-30
Non-linear optics encompasses a range of optical phenomena, including two- and three-photon fluorescence, second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), third harmonic generation (THG), coherent anti-Stokes Raman scattering (CARS), and stimulated Raman scattering (SRS). The combined advantages of using these phenomena for imaging complex pharmaceutical systems include chemical and structural specificities, high optical spatial and temporal resolutions, no requirement for labels, and the ability to image in an aqueous environment. These features make such imaging well suited for a wide range of pharmaceutical and biopharmaceutical investigations, including material and dosage form characterisation, dosage form digestion and drug release, and drug and nanoparticle distribution in tissues and within live cells. In this review, non-linear optical phenomena used in imaging will be introduced, together with their advantages and disadvantages in the pharmaceutical context. Research on pharmaceutical and biopharmaceutical applications is discussed, and potential future applications of the technology are considered. Copyright © 2010 Elsevier B.V. All rights reserved.
Non-linear Abelian gauge model
Chauca, J.; Doria, R.; Soares, W.
2012-10-01
Based on the principle that nature acts together one proposes the presence of N-potential fields rotating under a same group. It introduces a new performance for the gauge approach. It yields a set of N-fields where each one is associated to a proper polynomial gauge transformation. As consequence, a non-linear abelian gauge model is obtained. It derives an abelian Lagrangian that beyond the usual case contains a longitudinal kinetic sector plus massive and interactive terms. This work establishes their gauge invariant conditions and writes the so-called Global Maxwell's equations and associated Global Lorentz force. Beyond Faraday lines, it yields physical lines of force in terms of potential fields.
Directory of Open Access Journals (Sweden)
Hai Zhang
2017-01-01
Full Text Available This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.
Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates
Johnson, R. S.
2017-01-01
Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered. PMID:28484341
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Energy Technology Data Exchange (ETDEWEB)
Dranishnikov, A N [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2000-12-31
In this paper we study the similarity between local topology and its global analogue, so-called asymptotic topology. In the asymptotic case, the notions of dimension, cohomological dimension, and absolute extensor are introduced and some basic facts about them are proved. The Higson corona functor establishing a connection between macro- and micro-topology is considered. A relationship between problems of general asymptotic topology and the Novikov conjecture on higher signatures is discussed. Some new results concerning the Novikov conjecture and other related conjectures are presented.
Canonical structure of evolution equations with non-linear ...
Indian Academy of Sciences (India)
In the recent past, Rosenau and Hyman [2] introduced a family of non-linear partial differential equations with non-linear dispersive terms. For brevity, we refer to these equations as fully non-linear evolution (FNE) equa- tions. It was hoped that these might be useful to study formation of patterns in liquids. The solitary wave ...
Quasi-integrability in the modified defocusing non-linear Schrödinger model and dark solitons
Energy Technology Data Exchange (ETDEWEB)
Blas, H. [Instituto de Física, Universidade Federal de Mato Grosso,Av. Fernando Correa, 2367, Bairro Boa Esperança, Cep 78060-900, Cuiabá, MT (Brazil); Zambrano, M. [Instituto de Ciências Matemáticas e de Computação, ICMC/USP, Universidade de São Paulo,Caixa Postal 668, CEP 13560-970, São Carlos-SP (Brazil)
2016-03-02
The concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schrödinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of deformations of the sine-Gordon, Bullough-Dodd and focusing NLS models, holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potential V=ηI{sup 2}−(ϵ/6)I{sup 3} and the saturable type potential satisfying V{sup ′}[I]=2ηI−((ϵI{sup q})/(1+I{sup q})), q∈/sf Z/kern -.4em Z{sub +}, with a deformation parameter ϵ∈/rm I/kern -.18em R and I=|ψ|{sup 2}. The issue of the renormalization of the charges and anomalies, and their (quasi)conservation laws are properly addressed. The saturable NLS supports elastic scattering of two soliton solutions for a wide range of values of {η,ϵ,q}. Our results may find potential applications in several areas of non-linear science, such as the Bose-Einstein condensation.
Application of non-linear discretetime feedback regulators with assignable closed-loop dynamics
Directory of Open Access Journals (Sweden)
Dubljević Stevan
2003-01-01
Full Text Available In the present work the application of a new approach is demonstrated to a discrete-time state feedback regulator synthesis with feedback linearization and pole-placement for non-linear discrete-time systems. Under the simultaneous implementation of a non-linear coordinate transformation and a non-linear state feedback law computed through the solution of a system of non-linear functional equations, both the feedback linearization and pole-placement design objectives were accomplished. The non-linear state feedback regulator synthesis method was applied to a continuous stirred tank reactor (CSTR under non-isothermal operating conditions that exhibits steady-state multiplicity. The control objective was to regulate the reactor at the middle unstable steady state by manipulating the rate of input heat in the reactor. Simulation studies were performed to evaluate the performance of the proposed non-linear state feedback regulator, as it was shown a non-linear state feedback regulator clearly outperformed a standard linear one, especially in the presence of adverse disturbance under which linear regulation at the unstable steady state was not feasible.
Modified Alternating Step Generators with Non-Linear Scrambler
Directory of Open Access Journals (Sweden)
Wicik Robert
2014-03-01
Full Text Available Pseudorandom generators, which produce keystreams for stream ciphers by the exclusiveor sum of outputs of alternately clocked linear feedback shift registers, are vulnerable to cryptanalysis. In order to increase their resistance to attacks, we introduce a non-linear scrambler at the output of these generators. Non-linear feedback shift register plays the role of the scrambler. In addition, we propose Modified Alternating Step Generator with a non-linear scrambler (MASG1S built with non-linear feedback shift register and regularly or irregularly clocked linear feedback shift registers with non-linear filtering functions
Sharp Asymptotics for Einstein-{λ}-Dust Flows
Friedrich, Helmut
2017-03-01
We consider the Einstein-dust equations with positive cosmological constant {λ} on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold {S}. It is shown that the set of standard Cauchy data for the Einstein-{λ}-dust equations on {S} contains an open (in terms of suitable Sobolev norms) subset of data which develop into solutions that admit at future time-like infinity a space-like conformal boundary J^+ that is C^{∞} if the data are of class C^{∞} and of correspondingly lower smoothness otherwise. The class of solutions considered here comprises non-linear perturbations of FLRW solutions as very special cases. It can conveniently be characterized in terms of asymptotic end data induced on J^+. These data must only satisfy a linear differential equation. If the energy density is everywhere positive they can be constructed without solving differential equations at all.
Peters, C. (Principal Investigator)
1980-01-01
A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.
Energy Technology Data Exchange (ETDEWEB)
Griesbaum, R.; Ehrhard, P.; Mueller, U.
1994-05-01
Based on the approximate solution for the liminar far wake of an isothermal cylinder, we derive a model for the far wake of a weakly-heated cylinder. Forced flow is upward against gravity, while the problem is considered to be two-dimensional and steady. A scaled version of boundary layer equations in conjunction with Boussinesq`s approximation are the basis for an asymptotic expansion using the small parameter {epsilon}=1/{radical}Re. Two leading orders of this expansion are discussed. In a first order we find the well-known flow field associated with the linearized far wake of a cylinder in conjunction with a gaussian temperature profile resulting from heat input. There are, however, no buoyancy forces present in the momentum equation of this approximation. The second order accounts for nonlinearities of momentum and heat transport and includes buoyant effects. The typical properties of this heated far wake, as e.g. kinematic or thermal boundary layer thickness and velocity or temperature amplitudes are discussed in their functional dependancy on the parameters. The parameters considered are the Reynolds-number, the Pradtl-number, the Grashof-number, as well as geometry. (orig.) [Deutsch] Ausgehend von der Naeherungsloesung fuer den laminaren, isothermen Zylindernachlauf wird der laminare Nachlauf hinter einem schwach beheizten Zylinder modelliert. Der Zylinder wird entgegen der Richtung des Schwerevektors angestroemt. Das Problem wird zweidimensional und stationaer betrachtet. Unter Verwendung der Boussinesq-Approximation bilden die skalierten Grenzschichtgleichungen die Basis zur Beschreibung dieser Stroemung. Die gesuchten asymptotischen Loesungen werden nach dem Parameter {epsilon}=1/{radical}Re entwickelt. Die ersten beiden Ordnungen dieser Entwicklung werden betrachtet. Die Loesung der ersten Ordnung liefert das bekannte Stromfeld des linearisierten Zylindernachlaufs. Darueber hinaus ist das Temperaturprofil durch die eingebrachte Waerme gekennzeichnet. Die
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Linear stability analysis and homoclinic orbit for a generalized non-linear heat transfer
Directory of Open Access Journals (Sweden)
Liu Jun
2012-01-01
Full Text Available This paper studies the linear stability and dynamic structure for a generalized non-linear heat equation, and obtains novel analytic solutions such as homoclinc orbit and breather solitary solutions for the first time based on Hirota method.
Passive non-linear microrheology for determining extensional viscosity
Hsiao, Kai-Wen; Dinic, Jelena; Ren, Yi; Sharma, Vivek; Schroeder, Charles M.
2017-12-01
Extensional viscosity is a key property of complex fluids that greatly influences the non-equilibrium behavior and processing of polymer solutions, melts, and colloidal suspensions. In this work, we use microfluidics to determine steady extensional viscosity for polymer solutions by directly observing particle migration in planar extensional flow. Tracer particles are suspended in semi-dilute solutions of DNA and polyethylene oxide, and a Stokes trap is used to confine single particles in extensional flows of polymer solutions in a cross-slot device. Particles are observed to migrate in the direction transverse to flow due to normal stresses, and particle migration is tracked and quantified using a piezo-nanopositioning stage during the microfluidic flow experiment. Particle migration trajectories are then analyzed using a second-order fluid model that accurately predicts that migration arises due to normal stress differences. Using this analytical framework, extensional viscosities can be determined from particle migration experiments, and the results are in reasonable agreement with bulk rheological measurements of extensional viscosity based on a dripping-onto-substrate method. Overall, this work demonstrates that non-equilibrium properties of complex fluids can be determined by passive yet non-linear microrheology.
Non-linear corrections to inflationary power spectrum
Energy Technology Data Exchange (ETDEWEB)
Gong, Jinn-Ouk [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2333 CA Leiden (Netherlands); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Hwang, Jai-chan, E-mail: jinn-ouk.gong@cern.ch, E-mail: hr@kasi.re.kr, E-mail: jchan@knu.ac.kr [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of)
2011-04-01
We study non-linear contributions to the power spectrum of the curvature perturbation on super-horizon scales, produced during slow-roll inflation driven by a canonical single scalar field. We find that on large scales the linear power spectrum dominates and leading non-linear corrections remain negligible, indicating that we can safely rely on linear perturbation theory to study inflationary power spectrum. We also briefly comment on the infrared and ultraviolet behaviour of the non-linear corrections.
Non-linear behavior of fiber composite laminates
Hashin, Z.; Bagchi, D.; Rosen, B. W.
1974-01-01
The non-linear behavior of fiber composite laminates which results from lamina non-linear characteristics was examined. The analysis uses a Ramberg-Osgood representation of the lamina transverse and shear stress strain curves in conjunction with deformation theory to describe the resultant laminate non-linear behavior. A laminate having an arbitrary number of oriented layers and subjected to a general state of membrane stress was treated. Parametric results and comparison with experimental data and prior theoretical results are presented.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Non-linear analytical solutions for laterally loaded sandwich plates
DEFF Research Database (Denmark)
Riber, Hans Jørgen
1997-01-01
This work focuses on the response of orthotropic sandwich composite plates with large deflections due to high lateral loads. The results have special application to the design of ship structures. A geometrical nonlinear theory is outlined, on the basis of the classical sandwich plate theory...
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated...... problems as indicated in the following cases....
Oracle Inequalities for Convex Loss Functions with Non-Linear Targets
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions......This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...... is linear this inequality also provides an upper bound of the estimation error of the estimated parameter vector. These are new results and they generalize the econometrics and statistics literature. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically...
Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Jørgen Arendt
2013-01-01
A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly...... increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated...... with a center frequency of 5 MHz. The speed is increased approximately by a factor of 140 and the calculation time is 12 min with a standard PC, when simulating the second harmonic pulse at the focal point. For the second harmonic point spread function the full width error is 1.5% at 6 dB and 6.4% at 12 d...
Non Linear Assessment of Musical Consonance
Trulla, Lluis Lligoña; Guiliani, Alessandro; Zimatore, Giovanna; Colosimo, Alfredo; Zbilut, Joseph P.
2005-12-01
The position of intervals and the degree of musical consonance can be objectively explained by temporal series formed by mixing two pure sounds covering an octave. This result is achieved by means of Recurrence Quantification Analysis (RQA) without considering neither overtones nor physiological hypotheses. The obtained prediction of a consonance can be considered a novel solution to Galileo's conjecture on the nature of consonance. It constitutes an objective link between musical performance and listeners' hearing activity..
On the design of approximate non-linear parametric controllers
Savaresi, Sergio M.; Nijmeijer, Henk; Guardabassi, Guido O.
2000-01-01
This paper focuses on the design of non-linear parametric controllers, around a nominal input/output trajectory of a discrete-time non-linear system. The main result provided herein is a relationship between the tracking performance of the closed-loop control system in the neighbourhood of a nominal
Non-linear stochastic response of a shallow cable
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2004-01-01
The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two...
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report ...
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Modeling Non-Linear Material Properties in Composite Materials
2016-06-28
Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions
Linearity and Non-linearity of Photorefractive effect in Materials ...
African Journals Online (AJOL)
In this paper we have studied the Linearity and Non-linearity of Photorefractive effect in materials using the band transport model. For low light beam intensities the change in the refractive index is proportional to the electric field for linear optics while for non- linear optics the change in refractive index is directly proportional ...
THE USE OF DIFFERENTIAL TRANSFORMATIONS FOR SOLVING NON-LINEAR BOUNDARY VALUE PROBLEMS
Directory of Open Access Journals (Sweden)
Viacheslav Gusynin
2016-12-01
Full Text Available Purpose: The aim of our study is comparison of method applications based on differential transformations for solving boundary value problems which are described by non-linear ordinary differential equations. Methods: This article reviews two approaches based on differential transformations for solving non-linear boundary value problems: the modified differential transform method and the system-analogue simulation method. Results: In this paper, we present results of the numerical solution of non-linear boundary value problem by methods based on differential transformations for demonstration the effectiveness and applicability of techniques. The relative error for given solutions, obtained with using first 6 discretes of differential spectra is presented. Discussion: Comparison of numerical solutions obtained by modified differential transform method and system-analogue simulation method with exact solution shows that both methods have good agreement with exact solution of non-linear boundary value problem for small intervals. However, application of system-analogue simulation method is preferential for big intervals, on which the boundary value problem is solved.
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei
2018-01-01
Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233
Painlevйe analysis and integrability of two-coupled non-linear ...
Indian Academy of Sciences (India)
For non-linear systems integrating the equations of motion completely, obtaining analytical solutions and finding acceptable constants of motions seem to be rare. From a qualitative point of view, integrability can be considered as a mathemat- ical property that can be successfully used to obtain more predictive power and.
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...
Rimbert, Nicolas; Séro-Guillaume, Olivier
2004-05-01
In this paper, it will be shown that “totally skewed to the left” log-stable distributions are suitable asymptotic solutions to a fragmentation equation. This result generalizes Kolmogorov’s work on log-normal distribution for the drops’ size number distribution of particles under pulverization. Indeed, Kolmogorov’s discrete process is extended to a continuous time Markov process for the volume distribution instead of the number distribution. New hypotheses are then introduced which lead to log-stable distributions as asymptotic solutions of the fragmentation equation. Log-stable laws are then used to fit experimental probability distribution function (pdf) of Simmons and Hanratty measuring drop sizes in a horizontal annular gas-liquid flow at high Weber number [Int. J. Multiphase Flow 27, 861 (2001)]. Log-stable pdf better fits to the experimental pdf than usual empirical spray pdf and especially, because of the heavy tail of the associated stable distribution, in the small drops part of the distribution.
Directory of Open Access Journals (Sweden)
Carlos A Bustamante Chaverra
2013-03-01
Full Text Available Un método sin malla es desarrollado para solucionar una versión genérica de la ecuación no lineal de convección-difusión-reacción en dominios bidimensionales. El método de Interpolación Local Hermítica (LHI es empleado para la discretización espacial, y diferentes estrategias son implementadas para solucionar el sistema de ecuaciones no lineales resultante, entre estas iteración de Picard, método de Newton-Raphson y el Método de Homotopía truncado (HAM. En el método LHI las Funciones de Base Radial (RBFs son empleadas para construir una función de interpolación. A diferencia del Método de Kansa, el LHI es aplicado localmente y los operadores diferenciales de las condiciones de frontera y la ecuación gobernante son utilizados para construir la función de interpolación, obteniéndose una matriz de colocación simétrica. El método de Newton-Rapshon se implementa con matriz Jacobiana analítica y numérica, y las derivadas de la ecuación gobernante con respecto al paramétro de homotopía son obtenidas analíticamente. El esquema numérico es veriﬁcado mediante la comparación de resultados con las soluciones analíticas de las ecuaciones de Burgers en una dimensión y Richards en dos dimensiones. Similares resultados son obtenidos para todos los solucionadores que se probaron, pero mejores ratas de convergencia son logradas con el método de Newton-Raphson en doble iteración.A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diﬀusion-reaction equation in two-dim-ensional domains. The Local Hermitian Interpolation (LHI method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM. The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs
DEFF Research Database (Denmark)
Garde, Henrik
2018-01-01
. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method......Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity...... properties of either the Neumann-to-Dirichlet map (non-linear) or its FrÃ©chet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain...
Energy Technology Data Exchange (ETDEWEB)
Russell, Steven J. [Los Alamos National Laboratory; Carlsten, Bruce E. [Los Alamos National Laboratory
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
Non-linear corrections to inflationary power spectrum
Gong, Jinn-Ouk; Hwang, Jai-chan
2011-01-01
We study non-linear contributions to the power spectrum of the curvature perturbation on super-horizon scales, produced during slow-roll inflation driven by a canonical single scalar field. We find that on large scales the linear power spectrum completely dominates and leading non-linear corrections remain totally negligible, indicating that we can safely rely on linear perturbation theory to study inflationary power spectrum. We also briefly comment on the infrared and ultraviolet behaviour of the non-linear corrections.
Non-linear dynamics of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced....... Important non-linear couplings between the fundamental blade mode and edgewise modes have been identified based on a resonance excitation of the wing, caused by a harmonically varying support point motion with the circular frequency omega. Assuming that the fundamental blade and edgewise eigenfrequencies...
Computer modeling of batteries from non-linear circuit elements
Waaben, S.; Federico, J.; Moskowitz, I.
1983-08-01
A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.
Non-linear electron photoemission from metals with ultrashort pulses
Energy Technology Data Exchange (ETDEWEB)
Ferrini, Gabriele; Banfi, Francesco; Giannetti, Claudio [Dipartimento di Matematica e Fisica, Universita Cattolica del Sacro Cuore, I-25121 Brescia (Italy); Parmigiani, Fulvio [Dipartimento di Fisica, Universita di Trieste and Sincrotrone Trieste, Strada Statale 14, I-34012 Basovizza, Trieste (Italy)], E-mail: fulvio.parmigiani@elettra.trieste.it
2009-03-21
In this review we describe the development of ultrafast non-linear photoemission spectroscopy on metals from the first historic observations in the sixties to state-of-the-art experiments. We present an account that is focused on electron spectroscopy experiments that use short laser pulses to investigate the non-equilibrium response of electrons in metals. Several examples of the application of non-linear spectroscopy to the investigation of many-body effects and highly non-equilibrium processes will be illustrated. Furthermore, we give a brief overview of the wide spectrum of experimental methods based on non-linear photoemission spectroscopy.
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method......In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...
Vinas, A. F.; Scudder, J. D.
1986-01-01
A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.
DEFF Research Database (Denmark)
Farrokhzad, F.; Mowlaee, P.; Barari, Amin
2011-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified......, and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation....
A non-linear least squares enhanced POD-4DVar algorithm for data assimilation
Directory of Open Access Journals (Sweden)
Xiangjun Tian
2015-01-01
Full Text Available This paper presents a novel non-linear least squares enhanced proper orthogonal decomposition (POD-based 4DVar algorithm (referred as NLS-4DVar for the non-linear ensemble-based 4DVar. In the algorithm, the Gauss–Newton iterative method is employed to handle the non-quadratic non-linearity of the 4DVar cost function while the overall structure of the algorithm still resembles the original POD-4DVar algorithm. It is proved that the original POD-4DVar algorithm is a special case of the proposed NLS-4DVar algorithm under the assumption of the linear relationship between the model perturbations (MPs and the simulated observation perturbations (OPs. Under the assumption it is also shown that the solution of POD-4DVar algorithm coincides with the solution of the proposed NLS-4DVar algorithm. On the contrary, if the linear relationship assumption is dropped, the solution of the POD-4DVar algorithm is only the first iteration of the proposed NLS-4DVar algorithm. As a result, our analysis provides an explanation for the degraded and inaccurate performance of the POD-4DVar algorithm when the underlying forecast model or (and the observation operator is strongly non-linear. The potential merits and advantages of the proposed NLS-4DVar are demonstrated by a group of Observing System Simulation Experiments with Advanced Research WRF (ARW using accumulated rainfall-observations.
Non-Linear Cosmological Redshift According to General Relativity
Rabounski, Dmitri
2012-03-01
A new method of calculation of the frequency of a photon is applied. It means solving the scalar geodesic equation (equation of energy) of the photon. In the space of Schwarzschild's mass-point metric, the well-known gravitational redshift has been obtained. No frequency shift has been found in the space of Gödel's metric, and in the space of Einstein's metric (a homogeneous distribution of ideal liquid and physical vacuum). The other obtained solutions manifest a cosmological effect: its magnitude increases with distance travelled by the photon. This is the parabolic cosmological blueshift found in the space of Schwarzschild's metric of a sphere of incompressible liquid, and in the space of a sphere filled with physical vacuum (de Sitter's metric). The exponential cosmological redshift has been found in the expanding space of Friedmann's metric (empty or filled with ideal liquid and physical vacuum). The redshift is non-linear when approaching the event horizon, where it reaches the ultimate hugh value z = e^π ,,= 22.14. This explains the observed accelerate expansion of the Universe. These results were obtained in the purely geometric way, without the use of the Doppler effect. The paper has been submitted to The Abraham Zelmanov Journal.
MATHEMATICAL MODELING IN NON-LINEAR AEROELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
V. I. Morozov
2014-01-01
Full Text Available The modern aircraft aeroelasticity problems solving are considered. Mathematical models of aeroelasticity joined by non-linear vortex methods of numerical aerodynamics are described for different objects.
The Effect of Non-Linear Structure on Cosmological Observables
Kaiser, Nick
2018-01-01
I shall review the various ways in which the emergence of non-linear structure in the universe may affect cosmological observables. I consider the distance-redshift relation, which has implications for the CMB and for cosmic flows, and attempt to clarify the meaning of some of the effects that have been found in non-linear perturbation theory. I will also critically examine some recent proposals for dynamical backreaction from structure affecting the expansion rate.
GDTM-Padé technique for the non-linear differential-difference equation
Directory of Open Access Journals (Sweden)
Lu Jun-Feng
2013-01-01
Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.
Non-linear dynamics in biological microtubules: solitons and dissipation-free energy transfer
Mavromatos, Nick E.
2017-08-01
I review some recent developments concerning soliton solutions in biological microtubules and their significance in transferring energy without dissipation. I discuss various types of soliton solutions, as well as ‘spikes’, of the associated non-linear Lagrange equations describing the dynamics of a ‘pseudo-spin non-linear σ-model’ that models the dynamics of a microtubule system with dipole-dipole interactions. These results will hopefully contribute to a better understanding of the functional properties of microtubules, including the motor protein dynamics and the information transfer processes. With regards to the latter we also speculate on the use of microtubules as ‘logical’ gates. Our considerations are classical, but the soliton solutions may have a microscopic quantum origin, which we briefly touch upon.
Asymptotically flat multiblack lenses
Tomizawa, Shinya; Okuda, Taika
2017-03-01
We present an asymptotically flat and stationary multiblack lens solution with biaxisymmetry of U (1 )×U (1 ) as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of L (n ,1 )=S3/Zn as well as a sphere S3. Moreover, we show that, in contrast to the higher-dimensional Majumdar-Papapetrou multiblack hole and multi-Breckenridge-Myers-Peet-Vafa (BMPV) black hole spacetime, the metric is smooth on each horizon even if the horizon topology is spherical.
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Ganapathysubramanian, Baskar; Zabaras, Nicholas
2008-06-01
Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Non-linear behaviour of large-area avalanche photodiodes
Fernandes, L M P; Monteiro, C M B; Santos, J M; Morgado, R E
2002-01-01
The characterisation of photodiodes used as photosensors requires a determination of the number of electron-hole pairs produced by scintillation light. One method involves comparing signals produced by X-ray absorptions occurring directly in the avalanche photodiode with the light signals. When the light is derived from light-emitting diodes in the 400-600 nm range, significant non-linear behaviour is reported. In the present work, we extend the study of the linear behaviour to large-area avalanche photodiodes, of Advanced Photonix, used as photosensors of the vacuum ultraviolet (VUV) scintillation light produced by argon (128 nm) and xenon (173 nm). We observed greater non-linearities in the avalanche photodiodes for the VUV scintillation light than reported previously for visible light, but considerably less than the non-linearities observed in other commercially available avalanche photodiodes.
Non-linear modal analysis of structural components subjected to unilateral constraints
Attar, M.; Karrech, A.; Regenauer-Lieb, K.
2017-02-01
In this paper, we present a detailed numerical study of the non-linear dynamics in structural components under unilateral contact constraints. Here, the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction, either compressive or tensile. Thus, the non-differentiability of the contact law at the discontinuity point is the only source of non-linearity. In our approach, the discrete lattice method (DLM) is used to treat the continuous system as a piecewise linear model. Thus, the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them. The application of the one-step integration scheme allows us to detect the occurrence of contact (i.e. the instants that the lattice nodes cross the discontinuity boundary) and consequently update the active constraints. We also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error. Subsequently, the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non-smooth modal analysis. In analogy with the smooth non-linear systems, the evolution of non-smooth periodic motions is presented in the frequency-stiffness plots. We apply our method to obtain non-linear normal modes (NNMs) for a number of representative problems, including a bar-obstacle system, a beam-substrate system and a granular chain with tensionless interactions. These numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy-independent non-linear modes across the range of contact stiffnesses. Moreover, the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of
Directory of Open Access Journals (Sweden)
Imed Bachar
2014-01-01
Full Text Available We are interested in the following fractional boundary value problem: Dαu(t+atuσ=0, t∈(0,∞, limt→0t2-αu(t=0, limt→∞t1-αu(t=0, where 1<α<2, σ∈(-1,1, Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞ satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.
Stochastic development regression on non-linear manifolds
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded......We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...
Implementation of neural network based non-linear predictive
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems including open loop unstable and non-minimum phase systems, but has also been proposed extended for the control of non......-linear systems. GPC is model-based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis on an efficient Quasi......-Newton optimization algorithm. The performance is demonstrated on a pneumatic servo system....
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Non Linear Analysis on Multi Lobe Journal Bearings
Udaya Bhaskar, S.; Manzoor Hussian, M.; Yousuf Ali, Md.
2017-08-01
Multi lobe journal bearings are used in machines which operate at high speeds and high loads. In this paper the multi lobe bearing are analyzed to determine the effect of surface roughness during non linear loading. A non-linear time transient analysis is performed using the fourth order Runge Kutta method. The finite difference method is used to predict the pressure distribution over the bearing surface. The effect of eccentric ratio is studied and the variation of attitude angle is discussed. The journal center trajectories were calculated and plotted.
Completely integrable models of non-linear optics
Maimistov, Andrei
2000-01-01
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency, and parametric interaction of three waves. At the present time there are a number of the theories based on completely integrable systems of equations, which are both generations of the original known models and new ones. The modifie...
Directory of Open Access Journals (Sweden)
A. D. Pataraya
1997-01-01
Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Dynamic stability of a vertically excited non-linear continuous system
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
2015-01-01
Roč. 155, July (2015), s. 106-114 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : non-linear systems * auto-parametric systems * semi-trivial solution * dynamic stability * system recovery * post-critical response Subject RIV: JM - Building Engineering Impact factor: 2.425, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045794915000024
Describing Growth Pattern of Bali Cows Using Non-linear Regression Models
Directory of Open Access Journals (Sweden)
Mohd. Hafiz A.W
2016-12-01
Full Text Available The objective of this study was to evaluate the best fit non-linear regression model to describe the growth pattern of Bali cows. Estimates of asymptotic mature weight, rate of maturing and constant of integration were derived from Brody, von Bertalanffy, Gompertz and Logistic models which were fitted to cross-sectional data of body weight taken from 74 Bali cows raised in MARDI Research Station Muadzam Shah Pahang. Coefficient of determination (R2 and residual mean squares (MSE were used to determine the best fit model in describing the growth pattern of Bali cows. Von Bertalanffy model was the best model among the four growth functions evaluated to determine the mature weight of Bali cattle as shown by the highest R2 and lowest MSE values (0.973 and 601.9, respectively, followed by Gompertz (0.972 and 621.2, respectively, Logistic (0.971 and 648.4, respectively and Brody (0.932 and 660.5, respectively models. The correlation between rate of maturing and mature weight was found to be negative in the range of -0.170 to -0.929 for all models, indicating that animals of heavier mature weight had lower rate of maturing. The use of non-linear model could summarize the weight-age relationship into several biologically interpreted parameters compared to the entire lifespan weight-age data points that are difficult and time consuming to interpret.
Rahali, Radouane
2013-03-01
In this paper, we investigate the decay property of a Timoshenko system in thermoelasticity of type III in the whole space where the heat conduction is given by the Green and Naghdi theory. Surprisingly, we show that the coupling of the Timoshenko system with the heat conduction of Green and Naghdi\\'s theory slows down the decay of the solution. In fact we show that the L-2-norm of the solution decays like (1 + t)(-1/8), while in the case of the coupling of the Timoshenko system with the Fourier or Cattaneo heat conduction, the decay rate is of the form (1 + t)(-1/4) [25]. We point out that the decay rate of (1 + t)(-1/8) has been obtained provided that the initial data are in L-1 (R) boolean AND H-s (R); (s >= 2). If the wave speeds of the fi rst two equations are di ff erent, then the decay rate of the solution is of regularity-loss type, that is in this case the previous decay rate can be obtained only under an additional regularity assumption on the initial data. In addition, by restricting the initial data to be in H-s (R) boolean AND L-1,L-gamma (R) with gamma is an element of [0; 1], we can derive faster decay estimates with the decay rate improvement by a factor of t(-gamma/4).
Design Wave Load Prediction by Non-Linear Strip Theories
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
1998-01-01
Some methods for predicting global stochastic wave load responses in ships are presented. The methods take into account the elastic behaviour of the ship and at least some of the non-linearities in the wave-induced loadings.Numerical rsults obtained for actual ships are reviewed with special...
Efficient algorithms for non-linear four-wave interactions
Van Vledder, G.P.
2012-01-01
This paper addresses the on-going activities in the development of efficient methods for computing the non-linear four-wave interactions in operational discrete third-generation wind-wave models. It is generally assumed that these interactions play an important role in the evolution of wind
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
Determination of Non-Linear Dynamic Aerodynamic Coefficients for Aircraft
1997-01-01
Representation - a Time Domain Perspective", AGARD CP-497, Nov. 1991. (10) Jenkins, J. E. and Haniff , E. S., "Non-Linear and Unsteady Aerodynamic Responses of a...8217 Delta Wing Oscillating in Roll", AIAA 94-3507. (12) Haniff , E., "Dynamic Nonlinear Airloads-Representation and Measurement", AGARD CP-386, May, 1985 (13
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such
Effect of Integral Non-Linearity on Energy Calibration of ...
African Journals Online (AJOL)
The integral non-linearity (INL) of four spectroscopy systems, two integrated (A1 and A2) and two classical (B1 and B2) systems was determined using pulses from a random pulse generator. The effect of INL on the system's energy calibration was also determined. The effect is minimal in the classical system at high ...
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
A non-linear viscoelastic model for the tympanic membrane.
Motallebzadeh, Hamid; Charlebois, Mathieu; Funnell, W Robert J
2013-12-01
The mechanical behavior of the tympanic membrane displays both non-linearity and viscoelasticity. Previous finite-element models of the tympanic membrane, however, have been either non-linear or viscoelastic but not both. In this study, these two features are combined in a non-linear viscoelastic model. The constitutive equation of this model is a convolution integral composed of a non-linear elastic part, represented by an Ogden hyperelastic model, and an exponential time-dependent part, represented by a Prony series. The model output is compared with the relaxation curves and hysteresis loops observed in previous measurements performed on strips of tympanic membrane. In addition, a frequency-domain analysis is performed based on the obtained material parameters, and the effect of strain rate is explored. The model presented here is suitable for modeling large deformations of the tympanic membrane for frequencies less than approximately 3 rad/s or about 0.6 Hz. These conditions correspond to the pressurization involved in tympanometry.
Non-linear Behavior of Curved Sandwich Panels
DEFF Research Database (Denmark)
Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.
2003-01-01
In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure load...
A cubic interpolation algorithm for solving non-linear equations ...
African Journals Online (AJOL)
A new Algorithm - based on cubic interpolation have been developed for solving non-linear algebraic equations. The Algorithm is derived from LaGrange's interpolation polynomial. The method discussed here is faster than the \\"Regular Falsi\\" which is based on linear interpolation. Since this new method does not involve ...
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter...
Semiclassical approximations in non-linear. sigma. omega. models
Energy Technology Data Exchange (ETDEWEB)
Centelles, M.; Vinas, X.; Barranco, M. (Dept. ECM, Univ. Barcelona (Spain)); Marcos, S. (Dept. de Fisica Moderna, Univ. de Cantabria, Santander (Spain)); Lombard, R.J. (Div. de Physique Theorique, Inst. de Physique Nucleaire, 91 - Orsay (France))
1992-02-24
Extended Thomas-Fermi calculations up to second order in {Dirac h} have been performed for relativistic non-linear {sigma}{omega} models and compared with the corresponding Hartree calculations. In several respects, the relativistic phenomenology quite resembles the one previously found in the non-relativistic context using Skyrme forces. (orig.).
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Non-linear optics for transducers: Principles and materials
Hoekstra, Hugo; Krijnen, Gijsbertus J.M.; Driessen, A.; Lambeck, Paul; Popma, T.J.A.
This paper concentrates on intensity-dependent refractive-index changes due to the third-order optical non-linearity. Materials exhibiting such effects are good candidates for applications in all-optical devices. The discussion will be on these materials, and characterization techniques and an
Non-Linear Interactive Stories in Computer Games
DEFF Research Database (Denmark)
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag...
Non-linear dynamics in pulse combustor: A review
Indian Academy of Sciences (India)
2015-02-19
Feb 19, 2015 ... Home; Journals; Pramana – Journal of Physics; Volume 84; Issue 3. Non-linear dynamics in ... Mechanical Engineering Department, Jadavpur University, Kolkata 700 032, India ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science
Nockowska-Rosiak, Magdalena
2016-01-01
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \\Delta \\left( r_{n} \\Delta \\left( x_{n}+q_{n}x_{n-\\tau}\\right)\\right)= a_{n}f(x_{n-\\sigma})+b_n%, \\ n\\geq n_0 $$ with respect to $(q_n)$. For $q_n\\to1$, $q_n\\in(0,1)$ the standard fixed point approach is not sufficed to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for $p\\ge 1$ a...
Qin, Yuming
2016-01-01
This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.
AdS3 to dS3 transition in the near horizon of asymptotically de Sitter solutions
Sadeghian, S.; Vahidinia, M. H.
2017-08-01
We consider two solutions of Einstein-Λ theory which admit the extremal vanishing horizon (EVH) limit, odd-dimensional multispinning Kerr black hole (in the presence of cosmological constant) and cosmological soliton. We show that the near horizon EVH geometry of Kerr has a three-dimensional maximally symmetric subspace whose curvature depends on rotational parameters and the cosmological constant. In the Kerr-dS case, this subspace interpolates between AdS3 , three-dimensional flat and dS3 by varying rotational parameters, while the near horizon of the EVH cosmological soliton always has a dS3 . The feature of the EVH cosmological soliton is that it is regular everywhere on the horizon. In the near EVH case, these three-dimensional parts turn into the corresponding locally maximally symmetric spacetimes with a horizon: Kerr-dS3 , flat space cosmology or BTZ black hole. We show that their thermodynamics match with the thermodynamics of the original near EVH black holes. We also briefly discuss the holographic two-dimensional CFT dual to the near horizon of EVH solutions.
Gravitational geons in asymptotically anti-de Sitter spacetimes
Martinon, Grégoire; Fodor, Gyula; Grandclément, Philippe; Forgács, Peter
2017-06-01
We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.
Effect of non-linear permeability in a spherically symmetric model of hydrocephalus.
Sobey, Ian; Wirth, Benedikt
2006-12-01
We examine a spherically symmetric model of the brain and apply non-linear permeability in a small strain poroelastic framework. Numerical solutions to the model show that non-linear effects tend to improve predictions of ventricle wall displacement and pressure increase in acute hydrocephalus in comparison with a constant permeability model. Our model is used to study different mechanisms for hydrocephalus: complete blockage of the aqueduct and normal pressure hydrocephalus (NPH), as well as offering observations on mechanical effects in idiopathic intracranial hypertension. In each situation it is possible to apply different parameter conditions to quantify mechanical effects that correspond to some observed symptoms. The results support and quantify ideas from Levine (2000, Ventricle size in pseudotumor cerebri and the theory of impaired CSF absorption. J. Neurol. Sci., 177, 85-94) on a poroelastic mechanism for some features of NPH and idiopathic intracranial hypertension.
Uniqueness of non-linear ground states for fractional Laplacians in R
DEFF Research Database (Denmark)
Frank, Rupert L.; Lenzmann, Enno
2013-01-01
We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 fractional Laplacian in one dimension. In particular, we answer affirmatively an open question...... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... + = (−Δ) s +1−(α+1)Q α is non-degenerate; i.e., its kernel satisfies ker L + = span{Q′}. This result about L + proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for non-linear dispersive PDEs with fractional Laplacians, such as the generalized...
Non-linear approach to the entrainment matrix of superfluid nucleon mixture at zero temperature
Leinson, Lev B.
2017-09-01
The superfluid drag effect, in hydrodynamics of pulsating neutron stars, is conventionally described with the aid of the entrainment matrix relating the mass currents with the velocities of superfluid flows in the system. Equations for the entrainment matrix of a superfluid mixture of neutrons and protons are derived with allowance for the strong dependence of the energy gaps on the velocities of superfluid flows. The calculations are carried out in the frame of the Fermi-liquid theory. The equations obtained are highly non-linear. Numerical solutions to the equations for some typical cases demonstrate that the components of the entrainment matrix possess a highly non-linear dependence on the velocities of the two superflows simultaneously. This effect, previously ignored, can greatly influence the dynamics of neutron stars.
Distribution pharmacokinetics of warfarin in the rat, a non-linear multicompartment model.
Kekki, M; Julkunen, R J; Wahlström, B
1977-03-01
Preliminary analysis and linear two-compartment solutions of warfarin plasma concentrations recorded in the rat after intravenous bolus injections of 1, 2, 8 and 40 mg/kg of sodium warfarin revealed marked non-linearities. The half-life of total warfarin concentration in the plasma from 1-12h remained unchanged with all the doses used, but that of free warfarin was shorter with 40 mg/kg, possibly as the result of an increase in the binding of the drug to plasma proteins as the high total warfarin concentration decreased. The apparent volume of distribution generally increased with increasing dose, and differed according to the method used for its calculation. Liver warfarin data could be solved with Langmuir type saturation kinetics, but the saturation phenomena were slight in the concentration range studied. A non-linear multicompartment model was constructed, the physiological spaces of which were plasma, interstitial fluid and tissue. The binding of free warfarin to plasma proteins, interstitial fluid proteins and tissue structures was assumed to occur instantaneously, with saturable binding to plasma and interstitial fluid proteins, and a constant binding to tissues. The fluxes between the free warfarin pools of plasma and interstitial fluid as well as elimination were assumed to be linear. Following parameters were simulated simultaneously, using an analog hybrid computer: two for the above-mentioned fluxes, four for zero time drug mass distribution between plasma and interstitial fluid, and one for tissue binding. According to the best fits, warfarin is preferentially distributed into plasma, interstitial fluid and highly perfused tissues. The solution suggests that non-linearities in the pharmacokinetics of warfarin, a highly plasma protein-bound drug, first occur in plasma and interstitial fluid. Therefore, it is believed that the quantitative non-linear multicompartment approach presented in this paper might be useful in studying the kinetic behaviour of
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...... fundamental and second harmonic elds. The focused piston transducer with a center frequency of 5 MHz is excited by a waveform generator emitting a 6-cycle sine wave. The hydrophone is mounted in the focal plane 118 mm from the transducer. The point spread functions at the focal depth from Field II...
On non-linear very large sea wave groups
Energy Technology Data Exchange (ETDEWEB)
Arena, F. [University ' Mediterranea' of Reggio Calabria (Italy). Department of Mechanics and Materials
2005-08-01
The paper deals with the non-linear effects for sea wave groups. Boccotti's quasi-determinism theory, which is exact to the first-order in a Stokes expansion, gives the mechanics of sea wave groups when either a very high crest (first formulation of the theory - 'New Wave'), or a large crest-to-trough wave height (second formulation of the theory) occurs. In this paper, quasi-determinism theory, in both formulations, is extended to the second-order, by obtaining the expressions of free surface displacement and velocity potential, as a function of wave spectrum. Finally it is shown that analytical predictions are in good agreement with both field data and data of Monte Carlo simulations of non-linear random waves. (author)
Isotopic effects on non-linearity, molecular radius and intermolecular ...
Indian Academy of Sciences (India)
Non-linearity parameter; molecular radius; free length; intermolecular inter- ... parameter (B/A) [3,4], molecular radius (rm) [5] and intermolecular free length (Lf) ... X. 2βT. ) and K = 1. 2. (. 1 +. S∗(1 + αT). αT. ) , where S∗ =1+ 4. 3. αT. Computation of molecular radius has been carried out by employing the relation r = A.
Applications of non-linear algebra to biology
Cartwright, Dustin Alexander
2010-01-01
We present two applications of non-linear algebra to biology. Our first application is to the analysis of gene expression data from Arabidoposis roots. In Chapter 2, we present a method forcomputing non-negative roots to certain systems of polynomials. This algorithm is based on a generalization of the Expectation-Maximization and Iterative Proportional Fitting from statistics. In Chapter 3, this method is applied to a model for gene expression coming from roots of the Arabidopsis plant. Vari...
Focusing SAR data acquired from non-linear sensor trajectories
Frey, O.; Magnard, C; RÜEGG, M.; Meier, E.
2008-01-01
Standard focusing of SAR data assumes a straight recording track of the sensor platform. Small non-linearities of airborne platform tracks are corrected for during a motion compensation step while keeping the assumption of a linear flight path. In the following, the processing of SAR data from nonlinear tracks is discussed as may originate from small aircraft or drones flying at low altitude. They fly not a straight track but one dependent on topography, influences of weather and wind, or ...
Non-linear graphene optics for terahertz applications
Mikhailov, S. A.
2008-01-01
The linear electrodynamic properties of graphene -- the frequency-dependent conductivity, the transmission spectra and collective excitations -- are briefly outlined. The non-linear frequency multiplication effects in graphene are studied, taking into account the influence of the self-consistent-field effects and of the magnetic field. The predicted phenomena can be used for creation of new devices for microwave and terahertz optics and electronics.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability qu...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas
Hnat, B.
2011-09-01
Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.
Isotopic effects on non-linearity, molecular radius and intermolecular ...
Indian Academy of Sciences (India)
Computation of non-linearity parameter (/), molecular radius (rm) and intermolecular free length (f) for H2O, C6H6, C6H12, CH3OH, C2H5OH and their deuterium-substituted compounds have been carried out at four different temperatures, viz., 293.15, 303.15, 313.15 and 323.15 K. The aim of the investigation is an ...
Non-linear Q-clouds around Kerr black holes
Directory of Open Access Journals (Sweden)
Carlos Herdeiro
2014-12-01
Full Text Available Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.
Non-linear Q-clouds around Kerr black holes
Energy Technology Data Exchange (ETDEWEB)
Herdeiro, Carlos; Radu, Eugen; Rúnarsson, Helgi, E-mail: helgi.runarsson@gmail.com
2014-12-12
Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.
Non-linear continuous time random walk models★
Stage, Helena; Fedotov, Sergei
2017-11-01
A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional equation either for the probability density function of the walker at a certain position and time, or the mean number of walkers. The question arises how one can extend this equation to the non-linear case, where the random walkers interact. The aim of this work is to take into account this interaction under a mean-field approximation where the statistical properties of the random walker depend on the mean number of walkers. The implementation of these non-linear effects within the CTRW integral equations or fractional equations poses difficulties, leading to the alternative methodology we present in this work. We are concerned with non-linear effects which may either inhibit anomalous effects or induce them where they otherwise would not arise. Inhibition of these effects corresponds to a decrease in the waiting times of the random walkers, be this due to overcrowding, competition between walkers or an inherent carrying capacity of the system. Conversely, induced anomalous effects present longer waiting times and are consistent with symbiotic, collaborative or social walkers, or indirect pinpointing of favourable regions by their attractiveness. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Fabrication and characterization of non-linear parabolic microporous membranes.
Rajasekaran, Pradeep Ramiah; Sharifi, Payam; Wolff, Justin; Kohli, Punit
2015-01-01
Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L - t(1/2). Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric "off-centered PMS" and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Non-linear absorption for concentrated solar energy transport
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, O. A; Del Rio, J.A; Huelsz, G [Centro de Investigacion de Energia, UNAM, Temixco, Morelos (Mexico)
2000-07-01
In order to determine the maximum solar energy that can be transported using SiO{sub 2} optical fibers, analysis of non-linear absorption is required. In this work, we model the interaction between solar radiation and the SiO{sub 2} optical fiber core to determine the dependence of the absorption of the radioactive intensity. Using Maxwell's equations we obtain the relation between the refractive index and the electric susceptibility up to second order in terms of the electric field intensity. This is not enough to obtain an explicit expression for the non-linear absorption. Thus, to obtain the non-linear optical response, we develop a microscopic model of an harmonic driven oscillators with damp ing, based on the Drude-Lorentz theory. We solve this model using experimental information for the SiO{sub 2} optical fiber, and we determine the frequency-dependence of the non-linear absorption and the non-linear extinction of SiO{sub 2} optical fibers. Our results estimate that the average value over the solar spectrum for the non-linear extinction coefficient for SiO{sub 2} is k{sub 2}=10{sup -}29m{sup 2}V{sup -}2. With this result we conclude that the non-linear part of the absorption coefficient of SiO{sub 2} optical fibers during the transport of concentrated solar energy achieved by a circular concentrator is negligible, and therefore the use of optical fibers for solar applications is an actual option. [Spanish] Con el objeto de determinar la maxima energia solar que puede transportarse usando fibras opticas de SiO{sub 2} se requiere el analisis de absorcion no linear. En este trabajo modelamos la interaccion entre la radiacion solar y el nucleo de la fibra optica de SiO{sub 2} para determinar la dependencia de la absorcion de la intensidad radioactiva. Mediante el uso de las ecuaciones de Maxwell obtenemos la relacion entre el indice de refraccion y la susceptibilidad electrica hasta el segundo orden en terminos de intensidad del campo electrico. Esto no es
Asymptotic vacua with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Non-linear direct effects of acid rain on leaf photosynthetic rate of terrestrial plants.
Dong, Dan; Du, Enzai; Sun, Zhengzhong; Zeng, Xuetong; de Vries, Wim
2017-12-01
Anthropogenic emissions of acid precursors have enhanced global occurrence of acid rain, especially in East Asia. Acid rain directly suppresses leaf function by eroding surface waxes and cuticle and leaching base cations from mesophyll cells, while the simultaneous foliar uptake of nitrates in rainwater may directly benefit leaf photosynthesis and plant growth, suggesting a non-linear direct effect of acid rain. By synthesizing data from literature on acid rain exposure experiments, we assessed the direct effects of acid rain on leaf photosynthesis across 49 terrestrial plants in China. Our results show a non-linear direct effect of acid rain on leaf photosynthetic rate, including a neutral to positive effect above pH 5.0 and a negative effect below that pH level. The acid rain sensitivity of leaf photosynthesis showed no significant difference between herbs and woody species below pH 5.0, but the impacts above that pH level were strongly different, resulting in a significant increase in leaf photosynthetic rate of woody species and an insignificant effect on herbs. Our analysis also indicates a positive effect of the molar ratio of nitric versus sulfuric acid in the acid solution on leaf photosynthetic rate. These findings imply that rainwater acidity and the composition of acids both affect the response of leaf photosynthesis and therefore result in a non-linear direct effect. Copyright © 2017 Elsevier Ltd. All rights reserved.
Non-linear waves in heterogeneous elastic rods via homogenization
Quezada de Luna, Manuel
2012-03-01
We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.
Towards a non-linear theory for fluid pressure and osmosis in shales
Droghei, Riccardo; Salusti, Ettore
2015-04-01
In exploiting deep hydrocarbon reservoirs, often injections of fluid and/or solute are used. To control and avoid troubles as fluid and gas unexpected diffusions, a reservoir characterization can be obtained also from observations of space and time evolution of micro-earthquake clouds resulting from such injections. This is important since several among the processes caused by fluid injections can modify the deep matrix. Information about the evolution of such micro-seismicity clouds therefore plays a realistic role in the reservoir analyses. To reach a better insight about such processes, and obtain a better system control, we here analyze the initial stress necessary to originate strong non linear transients of combined fluid pressure and solute density (osmosis) in a porous matrix. All this can indeed perturb in a mild (i.e. a linear diffusion) or dramatic non linear way the rock structure, till inducing rock deformations, micro-earthquakes or fractures. I more detail we here assume first a linear Hooke law relating strain, stress, solute density and fluid pressure, and analyze their effect in the porous rock dynamics. Then we analyze its generalization, i.e. the further non linear effect of a stronger external pressure, also in presence of a trend of pressure or solute in the whole region. We moreover characterize the zones where a sudden arrival of such a front can cause micro-earthquakes or fractures. All this allows to reach a novel, more realistic insight about the control of rock evolution in presence of strong pressure fronts. We thus obtain a more efficient reservoir control to avoid large geological perturbations. It is of interest that our results are very similar to those found by Shapiro et al.(2013) with a different approach.
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
Interacting localized solutions for the Zakharov-Kusnetsov equation
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio E-mail: solitone@yahoo.it
2004-09-01
Analytical investigation of the Zakharov-Kusnetsov equation shows the existence of approximate interacting localized solutions. Using the asymptotic perturbation method, based on Fourier expansion and spatio-temporal rescaling, it is found that the amplitude slow modulation of Fourier modes is described by a C-integrable (solvable via an appropriate change of variables) system of non-linear evolution equations. It is demonstrated the existence of localized solutions (dromions, lumps, ring solitons and breathers) as well as of multiple instanton solutions. The interaction between the localized solutions are completely elastic, because they pass through each other and preserve their shape, the only change being a phase shift.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Definition of a linear equivalent model for a non-linear system with impacts
Thenint, Thibaud; BALMES, Etienne; Corus, Mathieu
2012-01-01
International audience; Modal characteristics of non-linear system are typically studied through response to harmonic excitation and using various definitions of non-linear modes. However, few results are available for systems under broadband excitation. The end objective sought here is to generate a linear system, in some sense equivalent to the non-linear system, whose modal characteristics evolve with a level of non-linearity. The considered application is the contact non-linearity found b...
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Global non-linear effect of temperature on economic production.
Burke, Marshall; Hsiang, Solomon M; Miguel, Edward
2015-11-12
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...... in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy...
Structure/property relationships in non-linear optical materials
Energy Technology Data Exchange (ETDEWEB)
Cole, J.M. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)]|[Durham Univ. (United Kingdom); Howard, J.A.K. [Durham Univ. (United Kingdom); McIntyre, G.J. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory......Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Non-linear DSGE Models and The Optimized Particle Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper improves the accuracy and speed of particle filtering for non-linear DSGE models with potentially non-normal shocks. This is done by introducing a new proposal distribution which i) incorporates information from new observables and ii) has a small optimization step that minimizes...... the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and this filter is therefore much more efficient than the standard particle filter....
D-brane models with non-linear supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, I.; Benakli, K. E-mail: karim.benakli@cern.ch; Laugier, A
2002-06-03
We study a class of type I string models with supersymmetry broken on the world-volume of some D-branes and vanishing tree-level potential. Despite the non-supersymmetric spectrum, supersymmetry is non-linearly realized on these D-branes, while it is spontaneously broken in the bulk by Scherk-Schwarz boundary conditions. These models can easily accommodate 3-branes with interesting gauge groups and chiral fermions. We also study the effective field theory and in particular we compute the four-fermion couplings of the localized goldstino with the matter fermions on the brane.
Studies for an alternative LHC non-linear collimation system
Lari, L; Boccone, V; Cerutti, F; Versaci, R; Vlachoudis, V; Mereghetti, A; Faus-Golfe, A; Resta-Lopez, J
2012-01-01
A LHC non-linear betatron cleaning collimation system would allow larger gap for the mechanical jaws, reducing as a consequence the collimator-induced impedance, which may limit the LHC beam intensity. In this paper, the performance of the proposed system is analyzed in terms of beam losses distribution around the LHC ring and cleaning efficiency in stable physics condition at 7TeV for Beam1. Moreover, the energy deposition distribution on the machine elements is compared to the present LHC Betatron cleaning collimation system in the Point 7 Insertion Region (IR).
Stochastic development regression on non-linear manifolds
DEFF Research Database (Denmark)
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion proce...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....
Utilization of non-linear converters for audio amplification
DEFF Research Database (Denmark)
Iversen, Niels Elkjær; Birch, Thomas; Knott, Arnold
2012-01-01
Class D amplifiers fits the automotive demands quite well. The traditional buck-based amplifier has reduced both the cost and size of amplifiers. However the buck topology is not without its limitations. The maximum peak AC output voltage produced by the power stage is only equal the supply voltage....... The introduction of non-linear converters for audio amplification defeats this limitation. A Cuk converter, designed to deliver an AC peak output voltage twice the supply voltage, is presented in this paper. A 3V prototype has been developed to prove the concept. The prototype shows that it is possible to achieve...
A discrete homotopy perturbation method for non-linear Schrodinger equation
Directory of Open Access Journals (Sweden)
H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
The Asymptotic Approach to the Twin Paradox
National Research Council Canada - National Science Library
Spiridon Dumitru
2008-01-01
The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant...
The Asymptotic Approach to the Twin Paradox
National Research Council Canada - National Science Library
Dumitru S
2008-01-01
The argument of twins’ asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant...
Semiclassical Limit of the Non-linear Schroedinger-Poisson Equation With Subcritical Initial Data
2002-12-01
lim ∇xargψ. As noted earlier, this argument is self - consistent as long as the solution of the Euler- Poisson system (1.5)-(1.6) remains classical...00-2003 to 00-00-2003 4. TITLE AND SUBTITLE Semiclassical Limit of the Non-linear Schrodinger - Poisson Equation with Subcritical Initial Data 5a...classical limit of a self - consistent quantum-Vlasov equation in 3-D, Math. Models Methods Appl. Sci., 3 (1993), pp. 109–124. [SMM] C. Sparber, P. Markowich
Non-linear Plasma Wake Growth of Electron Holes
Hutchinson, I H; Zhou, C
2015-01-01
An object's wake in a plasma with small Debye length that drifts \\emph{across} the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind wake and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable...
The linear-non-linear frontier for the Goldstone Higgs
Energy Technology Data Exchange (ETDEWEB)
Gavela, M.B.; Saa, S. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Kanshin, K. [Universita di Padova, Dipartimento di Fisica e Astronomia ' G. Galilei' , Padua (Italy); INFN, Padova (Italy); Machado, P.A.N. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Fermi National Accelerator Laboratory, Theoretical Physics Department, Batavia, IL (United States)
2016-12-15
The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)
Primordial black holes in linear and non-linear regimes
Allahyari, Alireza; Abolhasani, Ali Akbar
2016-01-01
Using the concept of apparent horizon for dynamical black holes, we revisit the formation of primordial black holes (PBH) in the early universe for both linear and non-linear regimes. First, we develop the perturbation theory for spherically symmetric spacetimes to study the formation of spherical PBHs in linear regime and we fix two gauges. We also introduce a well defined gauge invariant quantity for the expansion. Using this quantity, we argue that PBHs do not form in the linear regime. Finally, we study the non-linear regime. We adopt the spherical collapse picture by taking a closed FRW model in the radiation dominated era to investigate PBH formation. Taking the initial condition of the spherical collapse from the linear theory of perturbations, we allow for both density and velocity perturbations. Our model gives a constraint on the velocity perturbation. This model also predicts that the apparent horizon of PBHs forms when $\\delta > 3$. Applying the sound horizon constraint, we have shown the threshol...
PV Degradation Curves: Non-Linearities and Failure Modes
Energy Technology Data Exchange (ETDEWEB)
Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill; Kurtz, Sarah R.
2016-09-03
Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually, in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.
Non-linear leak currents affect mammalian neuron physiology
Directory of Open Access Journals (Sweden)
Shiwei eHuang
2015-11-01
Full Text Available In their seminal works on squid giant axons, Hodgkin and Huxley approximated the membrane leak current as Ohmic, i.e. linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells.
Non-linear growth of the line-driving instability
Feldmeier, Achim; Thomas, Timon
2017-08-01
Winds from hot massive stars are driven by scattering of continuum radiation in bound-bound transitions. This radiative driving is subject to a strong instability, leading to shocks and X-ray emission. Time-dependent simulations of the instability encounter problems both for absorption and scattering lines, and it is necessary to introduce an artificially low opacity cut-off κm. The non-linear growth of the instability in the inner steeply accelerating wind is, so far, badly resolved. We present simulations with time-dependent Euler and Lagrange codes for pure line absorption at maximum growth rates of the instability in winds with a linear velocity law. This allows us to study the onset of non-linear growth in detail, and to follow unstable growth over orders of magnitude in velocity perturbations and length-scales. We find that distance-stretching in the accelerating wind causes unstable growth to proceed beyond the limit of a few thermal speeds that applies for short-scale perturbations. We increase the opacity cut-off to realistic values and find that the rarefied intershell gas is more strongly accelerated at larger κm, as is expected.
Adaptive ensemble Kalman filtering of non-linear systems
Directory of Open Access Journals (Sweden)
Tyrus Berry
2013-07-01
Full Text Available A necessary ingredient of an ensemble Kalman filter (EnKF is covariance inflation, used to control filter divergence and compensate for model error. There is an on-going search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra (1970, 1972 enabled adaptivity in the context of linear dynamics with white noise model errors by showing how to estimate the model error and observation covariances. We propose an adaptive scheme, based on lifting Mehra's idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases, results in a natural additive inflation that improves state estimation. It can be incorporated into non-linear filters such as the extended Kalman filter (EKF, the EnKF and their localised versions. We test the adaptive EnKF on a 40-dimensional Lorenz96 model and show the significant improvements in state estimation that are possible. We also discuss the extent to which such an adaptive filter can compensate for model error, and demonstrate the use of localisation to reduce ensemble sizes for large problems.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
Directory of Open Access Journals (Sweden)
Javier Zamora
2016-12-01
Full Text Available Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601. There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q − values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27. It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1 or with its NRT non-linear q-generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ∼ 1 instance via a perturbative analysis of the NRT equations.
Non-linear optical crystal vibration sensing device
Energy Technology Data Exchange (ETDEWEB)
Kalibjian, R.
1992-12-31
The report describes a non-linear optical crystal vibration sensing device including a photorefractive crystal and a laser. The laser produces a coherent light beam which is split by a beam splitter into a first laser beam and a second laser beam. After passing through the crystal the first laser beam is counter-propagated back upon itself by a retro-mirror, creating a third laser beam . The laser beams are modulated, due to the mixing effect within the crystal by vibration of the crystal. In the third laser beam modulation is stable and such modulation is converted by a photodetector into a usable electrical output, intensity modulated in accordance with vibration applied to the crystal.
Predictability of extremes in non-linear hierarchically organized systems
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
Non-linear optical crystal vibration sensing device
Kalibjian, R.
1994-08-09
A non-linear optical crystal vibration sensing device including a photorefractive crystal and a laser is disclosed. The laser produces a coherent light beam which is split by a beam splitter into a first laser beam and a second laser beam. After passing through the crystal the first laser beam is counter-propagated back upon itself by a retro-mirror, creating a third laser beam. The laser beams are modulated, due to the mixing effect within the crystal by vibration of the crystal. In the third laser beam, modulation is stable and such modulation is converted by a photodetector into a usable electrical output, intensity modulated in accordance with vibration applied to the crystal. 3 figs.
Discriminative Non-Linear Stationary Subspace Analysis for Video Classification.
Baktashmotlagh, Mahsa; Harandi, Mehrtash; Lovell, Brian C; Salzmann, Mathieu
2014-12-01
Low-dimensional representations are key to the success of many video classification algorithms. However, the commonly-used dimensionality reduction techniques fail to account for the fact that only part of the signal is shared across all the videos in one class. As a consequence, the resulting representations contain instance-specific information, which introduces noise in the classification process. In this paper, we introduce non-linear stationary subspace analysis: a method that overcomes this issue by explicitly separating the stationary parts of the video signal (i.e., the parts shared across all videos in one class), from its non-stationary parts (i.e., the parts specific to individual videos). Our method also encourages the new representation to be discriminative, thus accounting for the underlying classification problem. We demonstrate the effectiveness of our approach on dynamic texture recognition, scene classification and action recognition.
Image enhancement by non-linear extrapolation in frequency space
Anderson, Charles H. (Inventor); Greenspan, Hayit K. (Inventor)
1998-01-01
An input image is enhanced to include spatial frequency components having frequencies higher than those in an input image. To this end, an edge map is generated from the input image using a high band pass filtering technique. An enhancing map is subsequently generated from the edge map, with the enhanced map having spatial frequencies exceeding an initial maximum spatial frequency of the input image. The enhanced map is generated by applying a non-linear operator to the edge map in a manner which preserves the phase transitions of the edges of the input image. The enhanced map is added to the input image to achieve a resulting image having spatial frequencies greater than those in the input image. Simplicity of computations and ease of implementation allow for image sharpening after enlargement and for real-time applications such as videophones, advanced definition television, zooming, and restoration of old motion pictures.
Non-linear Dynamics of Speech in Schizophrenia
DEFF Research Database (Denmark)
Fusaroli, Riccardo; Simonsen, Arndis; Weed, Ethan
-effects inference. SANS and SAPS scores were predicted using a 10-fold cross-validated multiple linear regression. Both analyses were iterated 1000 to test for stability of results. Results: Voice dynamics allowed discrimination of patients with schizophrenia from healthy controls with a balanced accuracy of 85...... speech patterns of people with schizophrenia contrasting them with matched controls and in relation to positive and negative symptoms. We employ both traditional measures (pitch mean and range, pause number and duration, speech rate, etc.) and 2) non-linear techniques measuring the temporal structure...... (regularity and complexity) of speech. Our aims are (1) to achieve a more fine-grained understanding of the speech patterns in schizophrenia than has previously been achieved using traditional, linear measures of prosody and fluency, and (2) to employ the results in a supervised machine-learning process...
Non-linear PIC simulation in a penning trap
Energy Technology Data Exchange (ETDEWEB)
Delzanno, G. L. (Gian L.); Lapenta, G. M. (Giovanni M.); Finn, J. M. (John M.)
2001-01-01
We study the non-linear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column. A new cylindrical PIC code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as it is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a reference Eulerian fluid code. We compare the dynamics of three different models: a model with compression effects, the standard Euler model and a geophysical fluid dynamics model. The results of our investigation prove that Penning traps can really be used to simulate geophysical fluids.
Non-linear dispersive interaction in superconducting circuit QED
Yin, Yi; Wang, Haohua; Mariantoni, Matteo; Bialczak, Radoslaw C.; Lenander, Mike; Lucero, Eric; Neeley, Matthew; O'Connell, Aaron; Sank, Daniel; Wenner, Jim; Yamamoto, Tsuyoshi; Cleland, Andrew; Martinis, John
2011-03-01
In circuit quantum electrodynamics, the strong coupling between superconducting qubits and a coplanar waveguide resonator (CPW) has been utilized to study the light-atom interaction. When the qubit is detuned far away from the resonator in frequency, linear dispersive interaction has been used for the readout of qubit states by measuring the pulling frequency of the resonator. Alternatively, we investigate dispersive interaction in a broader regime by measuring the accumulated dynamic phase with Wigner tomography. In the quasi-adiabatic process of tuning the qubit frequency, the dynamic phase measurement can be pushed to the case of zero detuning with up to the five-photon Fock state in the CPW resonator. The exotic non-linear behaviors of the qubit on resonator cat state and coherent state have been revealed, strongly depending on the strength of dispersive interaction. Our experimental data are consistent with the numerical calculation using the Jaynes-Cumming model.
Robust C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems. The intention is that the routines should use the currently best algorithms available. All routines have standardized calls, and the user does not have...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Non-linearities in Theory-of-Mind Development
Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.
2017-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72–78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths. PMID:28101065
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Directory of Open Access Journals (Sweden)
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
Sigmoid curves, non-linear double-reciprocal plots and allosterism.
Bardsley, W G; Childs, R E
1975-08-01
1. The theory of plane curves was applied to the graphical methods used in enzyme kinetics and a mathematical analysis of the possible graph shapes is given. 2. The belief that allosterism can be inferred from steady-state data alone is subjected to criticism and the mathematical significance of sigmoid curves and non-linear double-reciprocal plots is explored. 3. It is suggested that the usual methods of interpreting steady-state kinetic data are often based on over-restrictive assumptions which prevent maximum utilization of the available data. 4. Methods for obtaining the degree of the rate equation from graph shapes obtained directly from initial-rate measurements and from replots of asymptotic behaviour as chi approach the level 0 and chi approach the level infinity are discussed. 5. Detailed proofs of the theorems given in the text have been deposited as Supplementary Publication SUP 50049 (10 pages) at the British Library (Lending Division), Boston Spa, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1975), 145, 5.
On resource-efficient algorithm for non-linear systems approximate reachability set construction
Parshikov, G. V.; Matviychuk, A. R.
2017-10-01
The research considers the numerical solution method of the reachability set construction problem for non-linear dynamical system in n-dimensional Euclidean space. The study deals with the dynamical system on the finite time interval, which is described by differential equation satisfying a set of defined conditions. The existing step-by-step pixel methods are based on the time interval sampling and applying the step-by-step reachability set constructing procedure to every time moment in partition. These methods allow us to solve the approximate reachability set constructing problem for the complex non-linear systems, which do not have analytical solutions. However, applying these methods causes a sharp increase of number of points used for reachability set constructing on the next step of time partition. This results in increase of calculation time as well as lack of computing device memory. To reduce the calculation time and satisfy the existing constraints of used device memory, we developed the set filtration algorithm based on some way of picking the points, which are used on the next step of reachability set constructing algorithm. Moreover, the computations are moved from CPU to the CUDA based on GPU, which allows us to run computations with the hundreds of parallel threads. In this research, we provide the description of the algorithm and give some information about its efficiency.
Directory of Open Access Journals (Sweden)
Spannenberg Jescica
2017-09-01
Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.
Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.
2017-09-01
Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
Retarded Electromagnetic Interaction and the Origin of Non-linear Phenomena in Optics
Xiaochun, Mei
2002-01-01
The non-linear relation between electric polarization and electric field strength is achieved through introducing the retarded electromagnetic interactions between classical charge particles. The result agrees with the phenomenological theory in current non-linear optics, means that the non-linear phenomena in optics come from the retarded electromagnetic interaction between charged particles. The result slao shows that that most of non-linear phenomenon in optics violate symmetry of time rev...
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....
A non-linear state space approach to model groundwater fluctuations
Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.
2006-01-01
A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual
Linear and non-linear simulation of joints contact surface using ...
African Journals Online (AJOL)
The joint modelling including non-linear effects needs accurate and precise study of their behaviors. When joints are under the dynamic loading, micro, macro- slip happens in contact surface which is non-linear reason of the joint contact surface. The non-linear effects of joint contact surface on total behavior of structure are ...
Non-linear evolution of the cosmic neutrino background
Energy Technology Data Exchange (ETDEWEB)
Villaescusa-Navarro, Francisco; Viel, Matteo [INAF/Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34143, Trieste (Italy); Bird, Simeon [Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540 (United States); Peña-Garay, Carlos, E-mail: villaescusa@oats.inaf.it, E-mail: spb@ias.edu, E-mail: penya@ific.uv.es, E-mail: viel@oats.inaf.it [Instituto de Física Corpuscular, CSIC-UVEG, E-46071, Paterna, Valencia (Spain)
2013-03-01
We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations which incorporate cold dark matter (CDM) and neutrinos as independent particle species. Our set of simulations explore the properties of neutrinos in a reference ΛCDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass 10{sup 11}−10{sup 15} h{sup −1}M{sub s}un, over a redshift range z = 0−2. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula, once the neutrino contribution to the total matter is removed. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes. The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided. The neutrino profile, unlike the cold dark matter one, is found to be cored with core size and central density that depend on the neutrino mass, redshift and mass of the halo, for halos of masses larger than ∼ 10{sup 13.5}h{sup −1}M{sub s}un. For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations. The results we obtain are numerically converged in terms of neutrino profiles at the 10% level for scales above ∼ 200 h{sup −1}kpc at z = 0, and are stable with
Robust MPC for a non-linear system - a neural network approach
Luzar, Marcel; Witczak, Marcin
2014-12-01
The aim of the paper is to design a robust actuator fault-tolerant control for a non-linear discrete-time system. Considered system is described by the Linear Parameter-Varying (LPV) model obtained with recurrent neural network. The proposed solution starts with a discretetime quasi-LPV system identification using artificial neural network. Subsequently, the robust controller is proposed, which does not take into account actuator saturation level and deals with the previously estimated faults. To check if the compensation problem is feasible, the robust invariant set is employed, which takes into account actuator saturation level. When the current state does not belong to the set, then a predictive control is performed in order to make such set larger. This makes it possible to increase the domain of attraction, which makes the proposed methodology an efficient solution for the fault-tolerant control. The last part of the paper presents an experimental results regarding wind turbines.
GROWTH ANALYSIS IN RABBIT USING GOMPERTZ NON-LINEAR MODEL
Directory of Open Access Journals (Sweden)
A. Setiaji
2014-10-01
Full Text Available An experiment was conducted to compare the growth curve of rabbit. Three breeds of rabbit,namely Indonesian Local Rabbit (IL, Flamish Giant (FG and Rex (R were used in the study.Individual body weights of each breed was measured from birth to 63 days of age with 3-days interval.Those periodical data were separated into different sex, be then it was averaged to analysis growthpattern. Growth curve parameters were estimated to fit growth data. There was no difference in bodyweight between sexs within breed. Indonesian local rabbit had the lowest body weight. The resultsshowed that growth curve paramaters among three breeds were significantly different (P<0.05 for bothsexes. FG had the highest value of asymptotic mature weight, followed by R and IL. In conclusion,Gompertz model was excellent fit for the growth data in rabbit with a high coefficient determination (R2= 0.999.
Non-linear signal processing in digital hearing aids.
Lunner, T; Hellgren, J; Arlinger, S; Elberling, C
1998-01-01
Three different non-linear digital signal processing algorithms were developed; LinEar, DynEar and RangeEar. All three provided individual frequency shaping via a seven-band low-power filterbank and compression in two channels. RangeEar and DynEar used wide dynamic range syllabic compression in the low-frequency (LF) channel, while LinEar used compression limiting. In the high-frequency (HF) channel, RangeEar used a slow-acting automatic volume control, while DynEar and LinEar used compression limiting. Wearable digital signal processing-based experimental instruments were used to evaluate the fitting algorithms under real world conditions with experienced hearing aid users. Evaluation included laboratory testing of speech recognition in noise and questionnaires on sound quality ratings. Results did not indicate one general good-for-all algorithm, but different algorithms resulting in preference and performance depending on the hearing loss configuration. Preference for any of the new algorithms could be predicted based on auditory dynamic range measurements. It was hypothesized that the different preferences were affected by different susceptibility to masking of HF sounds by amplified LF sounds.
A Design of a Hybrid Non-Linear Control Algorithm
Directory of Open Access Journals (Sweden)
Farinaz Behrooz
2017-11-01
Full Text Available One of the high energy consuming devices in the buildings is the air-conditioning system. Designing a proper controller to consider the thermal comfort and simultaneously control the energy usage of the device will impact on the system energy efficiency and its performance. The aim of this study was to design a Multiple-Input and Multiple-Output (MIMO, non-linear, and intelligent controller on direct expansion air-conditioning system The control algorithm uses the Fuzzy Cognitive Map method as a main controller and the Generalized Predictive Control method is used for assigning the initial weights of the main controller. The results of the proposed controller shows that the controller was successfully designed and works in set point tracking and under disturbance rejection tests. The obtained results of the Generalized Predictive Control-Fuzzy Cognitive Map controller are compared with the previous MIMO Linear Quadratic Gaussian control design on the same direct expansion air-conditioning system under the same conditions. The comparative results indicate energy savings would be achieved with the proposed controller with long-term usage. Energy efficiency and thermal comfort conditions are achieved by the proposed controller.
Non linear processes modulated by low doses of radiation exposure
Mariotti, Luca; Ottolenghi, Andrea; Alloni, Daniele; Babini, Gabriele; Morini, Jacopo; Baiocco, Giorgio
The perturbation induced by radiation impinging on biological targets can stimulate the activation of several different pathways, spanning from the DNA damage processing to intra/extra -cellular signalling. In the mechanistic investigation of radiobiological damage this complex “system” response (e.g. omics, signalling networks, micro-environmental modifications, etc.) has to be taken into account, shifting from a focus on the DNA molecule solely to a systemic/collective view. An additional complication comes from the finding that the individual response of each of the involved processes is often not linear as a function of the dose. In this context, a systems biology approach to investigate the effects of low dose irradiations on intra/extra-cellular signalling will be presented, where low doses of radiation act as a mild perturbation of a robustly interconnected network. Results obtained through a multi-level investigation of both DNA damage repair processes (e.g. gamma-H2AX response) and of the activation kinetics for intra/extra cellular signalling pathways (e.g. NFkB activation) show that the overall cell response is dominated by non-linear processes - such as negative feedbacks - leading to possible non equilibrium steady states and to a poor signal-to-noise ratio. Together with experimental data of radiation perturbed pathways, different modelling approaches will be also discussed.
Non-linear image scanning microscopy (Conference Presentation)
Gregor, Ingo; Ros, Robert; Enderlein, Jörg
2017-02-01
Nowadays, multiphoton microscopy can be considered as a routine method for the observation of living cells, organs, up to whole organisms. Second-harmonics generation (SHG) imaging has evolved to a powerful qualitative and label-free method for studying fibrillar structures, like collagen networks. However, examples of super-resolution non-linear microscopy are rare. So far, such approaches require complex setups and advanced synchronization of scanning elements limiting the image acquisition rates. We describe theory and realization of a super-resolution image scanning microscope [1, 2] using two-photon excited fluorescence as well as second-harmonic generation. It requires only minor modifications compared to a classical two-photon laser-scanning microscope and allows image acquisition at the high frame rates of a resonant galvo-scanner. We achieve excellent sensitivity and high frame-rate in combination with two-times improved lateral resolution. We applied this method to fixed cells, collagen hydrogels, as well as living fly embryos. Further, we proofed the excellent image quality of our setup for deep tissue imaging. 1. Müller C.B. and Enderlein J. (2010) Image scanning microscopy. Phys. Rev. Lett. 104(19), 198101. 2. Sheppard C.J.R. (1988) Super-resolution in confocal imaging. Optik (Stuttg) 80 53-54.
Searching for Non-linearities in Natural Language
Ribarov, Kiril; Smrz, Otakar
2003-08-01
Inspired by wide range of applicability of what is commonly referred to as chaos theories, we explore the nature of energy series of a signal of human speech in the light of nonlinear dynamics. Using the TISEAN software package, analyses on various recordings of the language energy series were carried out (single speaker — different speeches; single speech - different speakers; dialogues; talkshows). Also correlated to other tenths of experiments conveyed on different linguistic inputs as written and morphologically analyzed texts, the presented experiment outputs (up to our knowledge, similar experiments have not been performed yet) reveal the complex and tricky nature of the language and are in favor of certain linguistic hypotheses. However, without further research, they do not encourage us to make explicit claims about the language signal such as dimension estimations (although probably possible) or attractor reconstruction. Our main considerations include: (a) a look into the stochastic nature of the language aiming towards reduction of the currently very large number of parameters present in language models based on Hidden Markov Models on language n-grams; (b) visualization of the behavior of the language and revelation of what could possibly be behind the `noisy' stream of sounds/letters/word-classes observed in our experiments; and last but not least (c) presentation of a new type of signal to the community exploring natural non-linear phenomena.
Improved simple optimization (SOPT algorithm for unconstrained non-linear optimization problems
Directory of Open Access Journals (Sweden)
J. Thomas
2016-09-01
Full Text Available In the recent years, population based meta-heuristic are developed to solve non-linear optimization problems. These problems are difficult to solve using traditional methods. Simple optimization (SOPT algorithm is one of the simple and efficient meta-heuristic techniques to solve the non-linear optimization problems. In this paper, SOPT is compared with some of the well-known meta-heuristic techniques viz. Artificial Bee Colony algorithm (ABC, Particle Swarm Optimization (PSO, Genetic Algorithm (GA and Differential Evolutions (DE. For comparison, SOPT algorithm is coded in MATLAB and 25 standard test functions for unconstrained optimization having different characteristics are run for 30 times each. The results of experiments are compared with previously reported results of other algorithms. Promising and comparable results are obtained for most of the test problems. To improve the performance of SOPT, an improvement in the algorithm is proposed which helps it to come out of local optima when algorithm gets trapped in it. In almost all the test problems, improved SOPT is able to get the actual solution at least once in 30 runs.
Analyzing systemic risk using non-linear marginal expected shortfall and its minimum spanning tree
Song, Jae Wook; Ko, Bonggyun; Chang, Woojin
2018-02-01
The aim of this paper is to propose a new theoretical framework for analyzing the systemic risk using the marginal expected shortfall (MES) and its correlation-based minimum spanning tree (MST). At first, we develop two parametric models of MES with their closed-form solutions based on the Capital Asset Pricing Model. Our models are derived from the non-symmetric quadratic form, which allows them to consolidate the non-linear relationship between the stock and market returns. Secondly, we discover the evidences related to the utility of our models and the possible association in between the non-linear relationship and the emergence of severe systemic risk by considering the US financial system as a benchmark. In this context, the evolution of MES also can be regarded as a reasonable proxy of systemic risk. Lastly, we analyze the structural properties of the systemic risk using the MST based on the computed series of MES. The topology of MST conveys the presence of sectoral clustering and strong co-movements of systemic risk leaded by few hubs during the crisis. Specifically, we discover that the Depositories are the majority sector leading the connections during the Non-Crisis period, whereas the Broker-Dealers are majority during the Crisis period.
Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity
Rand, J. L.; Wakefield, D. S.
Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may
Non-linear Dynamics in $QED_{3}$ and Non-trivial Infrared Structure
Mavromatos, Nikolaos E
1999-01-01
In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated consistently. The non-linearity of the equations gives rise to highly non-trivial constraints among the mass and effective (`running') gauge coupling, which impose lower and upper bounds on the latter for dynamical mass generation to occur. Possible implications of this to the theory of high-temperature superconductivity are...
Non-linear Imaging using an Experimental Synthetic Aperture Real Time Ultrasound Scanner
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
This paper presents the first non-linear B-mode image of a wire phantom using pulse inversion attained via an experimental synthetic aperture real-time ultrasound scanner (SARUS). The purpose of this study is to implement and validate non-linear imaging on SARUS for the further development of new...... non-linear techniques. This study presents non-linear and linear B-mode images attained via SARUS and an existing ultrasound system as well as a Field II simulation. The non-linear image shows an improved spatial resolution and lower full width half max and -20 dB resolution values compared to linear...
Carlberg, Kevin
2010-10-28
A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.
Lecler, Sylvain; Haacke, Stefan; Lecong, Nhan; Crégut, Olivier; Rehspringer, Jean-Luc; Hirlimann, Charles
2007-04-16
The two-photon excited fluorescence from a dye solution is enhanced when a small amount of micro-meter sized silica beads are added. This observation is made in the simple scattering regime (inter-sphere distance four times larger than their radius) and is shown to depend on the concentration of the silica spheres. For a solution of rhodamine B, the enhancement can reach more than 30 %. As complementary experiments show that the fluorescence efficiency is unchanged, we argue that the non-linear absorption is enhanced due to focussing of the incident beam in the near-field of the spheres, a situation previously referred to as photonic (nano-)jets [3]. Our calculations indeed show that for the parameters of the spheres studied near-field focussing leads to an intensity concentration close to the sphere surface. We suggest that these photonic jets could be used to enhance other non-linear optical effects.
Dattoli, Giuseppe
2005-01-01
The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high intensity electron accelerators. A code devoted to the analysis of this type of problems should be fast and reliable: conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problem in accelerators. The extension of these method to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique, using exponential operators implemented numerically in C++. We show that the integration procedure is capable of reproducing the onset of an instability and effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, parametric studies a...
Non-linear pattern formation in bone growth and architecture.
Salmon, Phil
2014-01-01
The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here - chaotic non-linear pattern formation (NPF) - which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of "group intelligence" exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called "particle swarm optimization" (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating "socially" in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or "feedback" between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the emergent
Linear and non-linear bias: predictions versus measurements
Hoffmann, K.; Bel, J.; Gaztañaga, E.
2017-02-01
We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the Marenostrum Institut de Ciències de l'Espai (MICE) Grand Challenge N-body simulation, we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively, we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous papers using the same data. We find an overall variation of the linear bias measurements and predictions of ˜5 per cent with respect to results from two-point correlations for different halo samples with masses between ˜1012and1015 h-1 M⊙ at the redshifts z = 0.0 and 0.5. Variations between the second- and third-order bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher order clustering statistics.
Bifurcation for non linear ordinary differential equations with singular perturbation
Directory of Open Access Journals (Sweden)
Safia Acher Spitalier
2016-10-01
Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.
The Asymptotic Approach to the Twin Paradox
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Dumitru S.
2008-04-01
Full Text Available The argument of twins’ asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.
The Asymptotic Approach to the Twin Paradox
Directory of Open Access Journals (Sweden)
Dumitru S.
2008-04-01
Full Text Available The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.
Directory of Open Access Journals (Sweden)
Sorribas Albert
2011-08-01
Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.
Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert
2011-08-25
Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
Wavelet analysis of the slow non-linear dynamics of wave turbulence
Energy Technology Data Exchange (ETDEWEB)
Miquel, Benjamin; Mordant, Nicolas, E-mail: benjamin.miquel@lps.ens.fr [Laboratoire de Physique Statistique, Ecole Normale Superieure (France)
2011-12-22
In wave turbulence, the derivation of solutions in the frame of the Weak Turbulence Theory relies on the existence of a double time-scale separation: first, between the period of the waves and characteristic nonlinear time t{sub NL} corresponding to energy exchange among waves; and secondly, between t{sub NL} and the characteristic dissipation time t{sub d}. Due to the lack of space and time resolved measurement, this hypothesis have remained unverified so far. We study the turbulence of flexion waves in thin elastic plates. t{sub d} is measured using the decline stage of the turbulence whereas a wavelet analysis is performed to measure the characteristic non-linear time t{sub NL}.
Hybrid Model Representation of a TLP Including Flexible Topsides in Non-Linear Regular Waves
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Christof Wehmeyer
2014-08-01
Full Text Available The rising demand for renewable energy solutions is forcing the established industries to expand and continue evolving. For the wind energy sector, the vast resources in deep sea locations have encouraged research towards the installation of turbines in deeper waters. One of the most promising technologies able to solve this challenge is the floating wind turbine foundation. For the ultimate limit state, where higher order wave loads have a significant influence, a design tool that couples non-linear excitations with structural dynamics is required. To properly describe the behavior of such a structure, a numerical model is proposed and validated by physical test results. The model is applied to a case study of a tension leg platform with a flexible topside mimicking the tower and a lumped mass mimicking the rotor-nacelle assembly. The model is additionally compared to current commercial software, where the need for the coupled higher order dynamics proposed in this paper becomes evident.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
Non linear predictive control of a LEGO mobile robot
Merabti, H.; Bouchemal, B.; Belarbi, K.; Boucherma, D.; Amouri, A.
2014-10-01
Metaheuristics are general purpose heuristics which have shown a great potential for the solution of difficult optimization problems. In this work, we apply the meta heuristic, namely particle swarm optimization, PSO, for the solution of the optimization problem arising in NLMPC. This algorithm is easy to code and may be considered as alternatives for the more classical solution procedures. The PSO- NLMPC is applied to control a mobile robot for the tracking trajectory and obstacles avoidance. Experimental results show the strength of this approach.
Energy Technology Data Exchange (ETDEWEB)
Khan, Masood [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hashim, E-mail: hashim_alik@yahoo.com [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hussain, M. [Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad 44000 (Pakistan); Azam, M. [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan)
2016-08-15
This paper presents a study of the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Carreau fluid over a convectively heated surface. The analysis of heat transfer is further performed in the presence of non-linear thermal radiation. The appropriate transformations are employed to bring the governing equations into dimensionless form. The numerical solutions of the partially coupled non-linear ordinary differential equations are obtained by using the Runge-Kutta Fehlberg integration scheme. The influence of non-dimensional governing parameters on the velocity, temperature, local skin friction coefficient and local Nusselt number is studied and discussed with the help of graphs and tables. Results proved that there is significant decrease in the velocity and the corresponding momentum boundary layer thickness with the growth in the magnetic parameter. However, a quite the opposite is true for the temperature and the corresponding thermal boundary layer thickness. - Highlights: • We investigated the Magnetohydrodynamic flow of Carreau constitutive fluid model. • Impact of non-linear thermal radiation is further taken into account. • Runge-Kutta Fehlberg method is employed to obtain the numerical solutions. • Fluid velocity is higher in case of hydromagnetic flow in comparison with hydrodynamic flow. • The local Nusselt number is a decreasing function of the thermal radiation parameter.
Khan, Masood; Hashim; Hussain, M.; Azam, M.
2016-08-01
This paper presents a study of the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Carreau fluid over a convectively heated surface. The analysis of heat transfer is further performed in the presence of non-linear thermal radiation. The appropriate transformations are employed to bring the governing equations into dimensionless form. The numerical solutions of the partially coupled non-linear ordinary differential equations are obtained by using the Runge-Kutta Fehlberg integration scheme. The influence of non-dimensional governing parameters on the velocity, temperature, local skin friction coefficient and local Nusselt number is studied and discussed with the help of graphs and tables. Results proved that there is significant decrease in the velocity and the corresponding momentum boundary layer thickness with the growth in the magnetic parameter. However, a quite the opposite is true for the temperature and the corresponding thermal boundary layer thickness.
Asymptotic stability of a catalyst particle
DEFF Research Database (Denmark)
Wedel, Stig; Michelsen, Michael L.; Villadsen, John
1977-01-01
The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...
Influence of Non-Linearity on Selected Cryptographic Criteria of 8x8 S-Boxes
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Petr Tesař
2017-12-01
Full Text Available The article defines standard criteria used to characterize the cryptographic quality of the S box: regularity, non linearity, autocorrelation, avalanche and immunity against differential cryptanalysis. The values of autocorrelation, avalanche and immunity against differential cryptanalysis for regular 8x8 S-boxes with non-linearity 98 and regular 8x8 S-boxes with non linearity 104 are compared. It is statistically verified that higher non-linearity improves the values of these criteria in a cryptographically advantageous sense.
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...... convergence of the postbuckling coefficients. (C) 1998 John Wiley & Sons, Ltd....
Adding flexibility to the search for robust portfolios in non-linear water resource planning
Tomlinson, James; Harou, Julien
2017-04-01
To date robust optimisation of water supply systems has sought to find portfolios or strategies that are robust to a range of uncertainties or scenarios. The search for a single portfolio that is robust in all scenarios is necessarily suboptimal compared to portfolios optimised for a single scenario deterministic future. By contrast establishing a separate portfolio for each future scenario is unhelpful to the planner who must make a single decision today under deep uncertainty. In this work we show that a middle ground is possible by allowing a small number of different portfolios to be found that are each robust to a different subset of the global scenarios. We use evolutionary algorithms and a simple water resource system model to demonstrate this approach. The primary contribution is to demonstrate that flexibility can be added to the search for portfolios, in complex non-linear systems, at the expense of complete robustness across all future scenarios. In this context we define flexibility as the ability to design a portfolio in which some decisions are delayed, but those decisions that are not delayed are themselves shown to be robust to the future. We recognise that some decisions in our portfolio are more important than others. An adaptive portfolio is found by allowing no flexibility for these near-term "important" decisions, but maintaining flexibility in the remaining longer term decisions. In this sense we create an effective 2-stage decision process for a non-linear water resource supply system. We show how this reduces a measure of regret versus the inflexible robust solution for the same system.
Non-linear mapping for exploratory data analysis in functional genomics
Directory of Open Access Journals (Sweden)
Chesneau Alban
2005-01-01
Full Text Available Abstract Background Several supervised and unsupervised learning tools are available to classify functional genomics data. However, relatively less attention has been given to exploratory, visualisation-driven approaches. Such approaches should satisfy the following factors: Support for intuitive cluster visualisation, user-friendly and robust application, computational efficiency and generation of biologically meaningful outcomes. This research assesses a relaxation method for non-linear mapping that addresses these concerns. Its applications to gene expression and protein-protein interaction data analyses are investigated Results Publicly available expression data originating from leukaemia, round blue-cell tumours and Parkinson disease studies were analysed. The method distinguished relevant clusters and critical analysis areas. The system does not require assumptions about the inherent class structure of the data, its mapping process is controlled by only one parameter and the resulting transformations offer intuitive, meaningful visual displays. Comparisons with traditional mapping models are presented. As a way of promoting potential, alternative applications of the methodology presented, an example of exploratory data analysis of interactome networks is illustrated. Data from the C. elegans interactome were analysed. Results suggest that this method might represent an effective solution for detecting key network hubs and for clustering biologically meaningful groups of proteins. Conclusion A relaxation method for non-linear mapping provided the basis for visualisation-driven analyses using different types of data. This study indicates that such a system may represent a user-friendly and robust approach to exploratory data analysis. It may allow users to gain better insights into the underlying data structure, detect potential outliers and assess assumptions about the cluster composition of the data.
On the non-linear dynamics of a space platform based mobile flexible manipulator
Modi, V. J.; Mah, H. W.; Misra, A. K.
This paper aims at development of a rather versatile tool for studying the dynamics and control of an orbiting flexible manipulator. It is motivated by the Canadian contribution, in the form of the mobile servicing system (MSS), to the U.S. led Space Station program, scheduled to be operational by the turn of the century. To begin with, a relatively general dynamical formulation is developed for a large class of systems characterized by interconnected beam and/or rigid articulating members forming a chain-type geometry. As can be expected, the governing non-linear, non-autonomous and coupled equations of motion, extremely long even in matrix notation, are not amenable to any known closed form solution. Hence attention is focused towards development of an efficient numerical code, in a modular format, to help assess the relative importance of the various system parameters. Validity of the formulation and the computer code are assessed and their operational aspects demonstrated through a parametric response analysis. Emphasis throughout is on methodology and general approach leading to understanding of the multibody dynamics problem at the fundamental level. The versatility of the formulation and corresponding code permits dynamical analysis and non-linear control of a wide class of space- and ground-based manipulators. Results suggest that interaction between the Space Station and MSS can lead to undesirable librational and vibrational response for the station. The station response, in turn, may diminish performance of the highly flexible manipulator system. The versatility of the formulation is demonstrated in its application to several other configurations: scientific and communications satellites with flexible beam-type members as well as tethered systems.
Non-linear dynamic response of a wind turbine blade
Chopra, I.; Dugundji, J.
1979-01-01
The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.
Optimal asymptotic cloning machines
Chiribella, Giulio; Yang, Yuxiang
2014-06-01
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic cloners enjoy a universality property, consisting in the fact that scaling of their fidelity does not depend on the specific details of the input states, but only on the number of free parameters needed to specify them.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
Measurements of non-linear noise re-distribution in an SOA
DEFF Research Database (Denmark)
Öhman, Filip; Tromborg, Bjarne; Mørk, Jesper
2004-01-01
Measurements of the noise statistics after a semiconductor optical amplifier (SOA) demonstrate non-linear noise re-distribution with a strong power and bandwidth dependence.......Measurements of the noise statistics after a semiconductor optical amplifier (SOA) demonstrate non-linear noise re-distribution with a strong power and bandwidth dependence....
Hovardas, Tasos
2016-01-01
Although ecological systems at varying scales involve non-linear interactions, learners insist thinking in a linear fashion when they deal with ecological phenomena. The overall objective of the present contribution was to propose a hypothetical learning progression for developing non-linear reasoning in prey-predator systems and to provide…
Bosgra, S.; Vlaming, M.L.H.; Vaes, W.H.J.
2015-01-01
Non-linearities occur no more frequently between microdose and therapeutic dose studies than in therapeutic range ascending-dose studies. Most non-linearities are due to known saturable processes, and can be foreseen by integrating commonly available preclinical data. The guidance presented here may
Large number of small non-linear power consumers causing power quality problems
Timens, R.B.; Buesink, Frederik Johannes Karel; Cuk, V.; Cobben, J.F.G.; Kling, W.L.; Leferink, Frank Bernardus Johannes
2011-01-01
In modern buildings virtually all electric loads are non-linear. The applicable standards for consumption of electrical energy do not take into account the replacement of linear loads by non-linear loads. The exemptions made in those standards for low power devices, and the widespread use of such
Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities
van Rooij, A.C.L.M.
2017-01-01
Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik
2004-01-01
equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...
Rigatos, Gerasimos G
2016-06-01
It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.
Yadav, Manish; Singh, Nitin Kumar
2017-12-01
A comparison of the linear and non-linear regression method in selecting the optimum isotherm among three most commonly used adsorption isotherms (Langmuir, Freundlich, and Redlich-Peterson) was made to the experimental data of fluoride (F) sorption onto Bio-F at a solution temperature of 30 ± 1 °C. The coefficient of correlation (r2) was used to select the best theoretical isotherm among the investigated ones. A total of four Langmuir linear equations were discussed and out of which linear form of most popular Langmuir-1 and Langmuir-2 showed the higher coefficient of determination (0.976 and 0.989) as compared to other Langmuir linear equations. Freundlich and Redlich-Peterson isotherms showed a better fit to the experimental data in linear least-square method, while in non-linear method Redlich-Peterson isotherm equations showed the best fit to the tested data set. The present study showed that the non-linear method could be a better way to obtain the isotherm parameters and represent the most suitable isotherm. Redlich-Peterson isotherm was found to be the best representative (r2 = 0.999) for this sorption system. It is also observed that the values of β are not close to unity, which means the isotherms are approaching the Freundlich but not the Langmuir isotherm.
Single-photon non-linear optics with a quantum dot in a waveguide.
Javadi, A; Söllner, I; Arcari, M; Hansen, S Lindskov; Midolo, L; Mahmoodian, S; Kiršanskė, G; Pregnolato, T; Lee, E H; Song, J D; Stobbe, S; Lodahl, P
2015-10-23
Strong non-linear interactions between photons enable logic operations for both classical and quantum-information technology. Unfortunately, non-linear interactions are usually feeble and therefore all-optical logic gates tend to be inefficient. A quantum emitter deterministically coupled to a propagating mode fundamentally changes the situation, since each photon inevitably interacts with the emitter, and highly correlated many-photon states may be created. Here we show that a single quantum dot in a photonic-crystal waveguide can be used as a giant non-linearity sensitive at the single-photon level. The non-linear response is revealed from the intensity and quantum statistics of the scattered photons, and contains contributions from an entangled photon-photon bound state. The quantum non-linearity will find immediate applications for deterministic Bell-state measurements and single-photon transistors and paves the way to scalable waveguide-based photonic quantum-computing architectures.
Short- and long-term variations in non-linear dynamics of heart rate variability
DEFF Research Database (Denmark)
Kanters, J K; Højgaard, M V; Agner, E
1996-01-01
variability. METHODS: Twelve healthy subjects were investigated by 3-h ambulatory ECG recordings repeated on 3 separate days. Correlation dimension, non-linear predictability, mean heart rate, and heart rate variability in the time and frequency domains were measured and compared with the results from......OBJECTIVES: The purpose of the study was to investigate the short- and long-term variations in the non-linear dynamics of heart rate variability, and to determine the relationships between conventional time and frequency domain methods and the newer non-linear methods of characterizing heart rate...... corresponding surrogate time series. RESULTS: A small significant amount of non-linear dynamics exists in heart rate variability. Correlation dimensions and non-linear predictability are relatively specific parameters for each individual examined. The correlation dimension is inversely correlated to the heart...
Wilkie, S
2000-01-01
In recent years, novel non-linear organic materials have generated great interest in the development of all-optical non-linear devices. Such materials have been optically characterised, mainly for the purposes of second harmonic generation and electro-optic modulation, within the Chemistry department of Strathclyde University since the mid-1980's. This thesis documents the continued development and enhancement of this core research speciality in the growth, preparation and optical characterisation of two such novel organic non-linear materials, namely NMU and MBANP. A literature search that reviewed the linear and non-linear optical properties of a select number of novel organic non-linear materials was conducted. All too often sample crystal quality was not detailed and hence the quality of crystals upon which the material characterisation was based remained unknown. Surprisingly, the availability of reliable, accurate data was found to be scarce. The optical investigation of NMU represented the first ever e...
Non-linear effects in the post-Newtonian approximation of a spherically symmetric field
Energy Technology Data Exchange (ETDEWEB)
Gambi, J.M.; Zamorano, P. [Madrid Univ. Carlos 3, Madrid (Spain). Dept. de Matematicas; Romero, P.; Garcia del Pino, M.L. [Madrid Univ. Complutense, Madrid (Spain). Dept. de Astronomia y Geodesia
2000-02-01
Conditions for the compatibility of the exterior metric of a spherically symmetric object with the field equations for the empty space and equations of motion and of trajectories for test particles, written in polar Gaussian and Fermi coordinates, are obtained to show that, although their explicit exact solutions cannot be derived in these coordinates, the post-Newtonian limits of these solutions can, nevertheless, be obtained. With these limits, it is next shown that the cited post-Newtonian equations do not fit into the standard post-Newtonian approximation either. It is then shown that these coordinates can, nevertheless, be included in a more general formalism together with the usual post-Newtonian (standard, harmonic, Painleve and isotropic) coordinates so that their respective equations of motion may be compared to each other and, finally, it is demonstrated that the only non-linear term taken in the Christoffel symbols with these usual coordinates in the standard post-Newtonian equations of motion to explain some known perturbations is not needed when polar Gaussian or Fermi coordinates are used to explain also those perturbations. In fact, it is demonstrated that these are the only coordinates for which that term becomes zero.
Non-linear Schrödinger Dynamics of Matrix D-branes
Mavromatos, Nikolaos E; Mavromatos, Nick E.; Szabo, Richard J.
2001-01-01
We formulate an effective Schroedinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the worldsheet partition function of a deformed sigma-model describing the system, which includes the quantum recoil due to the exchange of string states between the individual D-particles. We arrive at an effective Fokker-Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three possible solutions of the associated non-linear Schroedinger equation depending on the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves. When the string coupling constant reaches a dynamically determined critical value, the system is described by minimal unc...
The Asymptotic Expansion Method via Symbolic Computation
Directory of Open Access Journals (Sweden)
Juan F. Navarro
2012-01-01
Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Lovrekovic, Iva
2017-11-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for nontrivial boundary conditions is five dimensional and it leads to global geon solution with nonvanishing charges.
Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
Cha, Ye Sle; Sakovich, Anna
2016-01-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
Asymptotic behavior of a system of linear fractional difference equations
Directory of Open Access Journals (Sweden)
Nurkanović M
2005-01-01
Full Text Available We investigate the global asymptotic behavior of solutions of the system of difference equations , , , where the parameters , , , and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. We obtain some asymptotic results for the positive equilibrium of this system.
Electrically charged black hole solutions in generalized gauge field theories
Diaz-Alonso, J.; Rubiera-Garcia, D.
2011-09-01
We summarize the main features of a class of anomalous (asymptotically flat, but non Schwarzschild-like) gravitational configurations in models of gravitating non-linear electrodynamics (G-NED) whose Lagrangian densities are defined as arbitrary functions of the two field invariants and constrained by several physical admissibility conditions. This class of models and their associated electrostatic spherically symmetric black hole (ESSBH) solutions are characterized by the behaviours of the Lagrangian densities around the vacuum and at the boundary of their domain of definition.
Electrically charged black hole solutions in generalized gauge field theories
Energy Technology Data Exchange (ETDEWEB)
Diaz-Alonso, J; Rubiera-Garcia, D, E-mail: joaquin.diaz@obspm.fr, E-mail: diego.rubiera-garcia@obspm.fr [LUTH, Observatoire de Paris, CNRS, Universite Paris Diderot. 5 Place Jules Janssen, 92190 Meudon (France); Departamento de Fisica, Universidad de Oviedo. Avda. Calvo Sotelo 18, 33007 Oviedo, Asturias (Spain)
2011-09-22
We summarize the main features of a class of anomalous (asymptotically flat, but non Schwarzschild-like) gravitational configurations in models of gravitating non-linear electrodynamics (G-NED) whose Lagrangian densities are defined as arbitrary functions of the two field invariants and constrained by several physical admissibility conditions. This class of models and their associated electrostatic spherically symmetric black hole (ESSBH) solutions are characterized by the behaviours of the Lagrangian densities around the vacuum and at the boundary of their domain of definition.
The non-linear evolution of magnetic flux ropes: 3. effects of dissipation
Directory of Open Access Journals (Sweden)
C. J. Farrugia
Full Text Available We study the evolution (expansion or oscillation of cylindrically symmetric magnetic flux ropes when the energy dissipation is due to a drag force proportional to the product of the plasma density and the radial speed of expansion. The problem is reduced to a single, second-order, ordinary differential equation for a damped, non-linear oscillator. Motivated by recent work on the interplanetary medium and the solar corona, we consider polytropes whose index, γ, may be less than unity. Numerical analysis shows that, in contrast to the small-amplitude case, large-amplitude oscillations are quasi-periodic with frequencies substantially higher than those of undamped oscillators. The asymptotic behaviour described by the momentum equation is determined by a balance between the drag force and the gradient of the gas pressure, leading to a velocity of expansion of the flux rope which may be expressed as (1/2γr/t, where r is the radial coordinate and t is the time. In the absence of a drag force, we found in earlier work that the evolution depends both on the polytropic index and on a dimensionless parameter, κ. Parameter κ was found to have a critical value above which oscillations are impossible, and below which they can exist only for energies less than a certain energy threshold. In the presence of a drag force, the concept of a critical κ remains valid, and when κ is above critical, the oscillatory mode disappears altogether. Furthermore, critical κ remains dependent only on γ and is, in particular, independent of the normalized drag coefficient, ν^{*}. Below critical κ, however, the energy required for the flux rope to escape to infinity depends not only on κ (as in the conservative force case but also on ν^{*}. This work indicates how under certain conditions a small change in the viscous drag coefficient or the initial energy may alter the evolution drastically. It is thus important
The non-linear evolution of magnetic flux ropes: 3. effects of dissipation
Directory of Open Access Journals (Sweden)
C. J. Farrugia
1997-02-01
Full Text Available We study the evolution (expansion or oscillation of cylindrically symmetric magnetic flux ropes when the energy dissipation is due to a drag force proportional to the product of the plasma density and the radial speed of expansion. The problem is reduced to a single, second-order, ordinary differential equation for a damped, non-linear oscillator. Motivated by recent work on the interplanetary medium and the solar corona, we consider polytropes whose index, γ, may be less than unity. Numerical analysis shows that, in contrast to the small-amplitude case, large-amplitude oscillations are quasi-periodic with frequencies substantially higher than those of undamped oscillators. The asymptotic behaviour described by the momentum equation is determined by a balance between the drag force and the gradient of the gas pressure, leading to a velocity of expansion of the flux rope which may be expressed as (1/2γr/t, where r is the radial coordinate and t is the time. In the absence of a drag force, we found in earlier work that the evolution depends both on the polytropic index and on a dimensionless parameter, κ. Parameter κ was found to have a critical value above which oscillations are impossible, and below which they can exist only for energies less than a certain energy threshold. In the presence of a drag force, the concept of a critical κ remains valid, and when κ is above critical, the oscillatory mode disappears altogether. Furthermore, critical κ remains dependent only on γ and is, in particular, independent of the normalized drag coefficient, ν*. Below critical κ, however, the energy required for the flux rope to escape to infinity depends not only on κ (as in the conservative force case but also on ν*. This work indicates how under certain conditions a small change in the viscous drag coefficient or the initial energy may alter the evolution drastically. It is thus important to determine ν* and κ from observations.
Study of the non-linear autocorrelations within the Gaussian regime
Kutner, R.; Świtała, F.
2003-06-01
defined by the spatial and temporal fractional dimensions of the walking state. To adapt the model to the description of empirical data (or discrete time series) which are collected with a discrete time-step we used in the continuous-time series produced by the model a discretization procedure. We observed that such a procedure generates, in general, long-range non-linear autocorrelations even in the Gaussian regime, which appear to be similar to those observed, e.g., in the financial time series [3 6], although single steps of the walker within continuous time are, by definition, uncorrelated. This suggests a surprising explanation alternative to the one proposed very recently ( cf. [7] and Refs. therein) although both approaches involve related variants of the well-known CTRW formalism applied yet in many different branches of knowledge [8 10].
Asymptotic analysis of radiation extinction of stretched premixed flames
Energy Technology Data Exchange (ETDEWEB)
Ju, Y.; Masuya, G. [Tohoku Univ., Sendai (Japan). Dept. of Aeronautics and Space Engineering; Liu, F. [National Research Council, Ottawa, Ontario (Canada). Inst. for Chemical Prpcess and Environmental Technology; Hattori, Yuji [Tohoku Univ., Sendai (Japan). Inst. of Fluid Science; Riechelmann, D. [Ishikawajima-Harima Heavy Industry, Tokyo (Japan). Research Inst.
2000-01-01
The flammability limit, radiation extinction of stretched premixed flame and effect of non-unity Lewis numbers are analyzed by the large-activated-energy asymptotic method. Particular attention is paid to the effect of Lewis number, the upstream and downstream radiation heat losses as well as the non-linearity of radiation. Explicit expressions for the flame temperature, extinction limit and flammability limit are obtained. The C-shaped extinction curve is reproduced. The dependence of radiation heat loss and the Lewis number effect on the stretch rate and flame separation distance is investigated. The effects of fuel Lewis number, oxidizer Lewis number, upstream radiation heat loss and the non-linearity of radiation on the C-shaped extinction curve are also examined. The results demonstrate a significant influence of these parameters on the radiation extinction and flammability limit and provide a good explanation to the experimental results and numerical simulations. (Author)
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
1994-01-01
It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.
Directory of Open Access Journals (Sweden)
Manna S.K.
2005-01-01
Full Text Available This paper develops an infinite time-horizon deterministic economic order quantity (EOQ inventory model with deterioration based on discounted cash flows (DCF approach where demand rate is assumed to be non-linear over time. The effects of inflation and time-value of money are also taken into account under a trade-credit policy of type "α/T1 net T". The results are illustrated with a numerical example. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.
Quadratic maps without asymptotic measure
Hofbauer, Franz; Keller, Gerhard
1990-02-01
An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences.
Non-Linear Rheological Properties and Neutron Scattering Investigation on Dilute Ring-Linear Blends
DEFF Research Database (Denmark)
Pyckhout-Hintzen, W.; Bras, A.R.; Wischnewski, A.
Linear and non-linear Rheology on dilute blends of polystyrene ring polymers in linear matrix is combined with Small Angle Neutron Scattering (SANS) investigations. In this way 2 different entanglement interactions become clear. After stretching the samples to different hencky strains up to 2...... with interpenetrating linear chains. At the same time the non-linear rheological and mechanical data fit to a non-affine slip-tube model as for moderately crosslinked networks and to interchain pressure models or a modified non-linear Doi-Edwards description for the observed strain hardening during the extensional...
Some experiences in the estimation of parameters in non-linear differential equations.
Barnes, J G.P.
1969-03-01
The author describes a procedure developed by himself and his colleagues for obtaining estimates of the parameters of rate equations, together with information about confidence regions for the estimates. The program has been used successfully for processing results from the chemical engineering industry, with highly non-linear model systems, particularly since temperature was a variable, and the "rate constants" were non-linear combinations of other constants. In biochemical situations, in which investigations are almost always at constant temperature, the non-linearity should not be so extreme, and the procedure may well be capable of dealing with more than 5 to 7 parameters for which it is recommended.
Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers
Directory of Open Access Journals (Sweden)
Andreas W. Schell
2016-12-01
Full Text Available Two-photon absorption is an important non-linear process employed for high resolution bio-imaging and non-linear optics. In this work, we realize two-photon excitation of a quantum emitter embedded in a two-dimensional (2D material. We examine defects in hexagonal boron nitride (hBN and show that the emitters exhibit similar spectral and quantum properties under one-photon and two-photon excitation. Furthermore, our findings are important to deploy two-dimensional hexagonal boron nitride for quantum non-linear photonic applications.
Rajeswaran, Jeevanantham; Blackstone, Eugene H
2017-02-01
In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.
ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2017-11-01
Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
Directory of Open Access Journals (Sweden)
M. Pattnaik
2013-08-01
Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
Nguyen, Van Minh
In this paper we present a new approach to the spectral theory of non-uniformly continuous functions and a new framework for the Loomis-Arendt-Batty-Vu theory. Our approach is direct and free of C-semigroups, so the obtained results, that extend previous ones, can be applied to large classes of evolution equations and their solutions.
Kim, Jongrae; Bates, Declan G; Postlethwaite, Ian; Heslop-Harrison, Pat; Cho, Kwang-Hyun
2008-05-15
Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. The software used in this article is available from http://sbie.kaist.ac.kr/software
Numerical Simulations of Asymptotically AdS Spacetimes
Bantilan, Hans
In this dissertation, we introduce a numerical scheme to construct asymptotically anti-de Sitter spacetimes with Lorentzian signature, focusing on cases that preserve five-dimensional axisymmetry. We study the field theories that are dual to these spacetimes by appealing to the AdS/CFT correspondence in the regime where the gravity dual is completely described by Einstein gravity. The numerical scheme is based on generalized harmonic evolution, and we begin by obtaining initial data defined on some Cauchy hypersurface. For the study described in this dissertation, we use a scalar field to source deviations from pure AdS5, and obtain data that correspond to highly deformed black holes. We evolve this initial data forward in time, and follow the subsequent ringdown. What is novel about this study is that the initial horizon geometry cannot be considered a small perturbation of the final static horizon, and hence we are probing an initial non-linear phase of the evolution of the bulk spacetime. On the boundary, we find that the dual CFT stress tensor behaves like that of a thermalized N = 4 SYM fluid. We find that the equation of state of this fluid is consistent with conformal invariance, and that its transport coefficients match those previously calculated for an N = 4 SYM fluid via holographic methods. Modulo a brief transient that is numerical in nature, this matching appears to hold from the initial time onwards. We transform these solutions computed in global AdS onto a Minkowski piece of the boundary, and examine the temperature of the corresponding fluid flows. Under this transformation, the spatial profile of temperature at the initial time resembles a Lorentz-flattened pancake centered at the origin of Minkowski space. By interpreting the direction along which the data is flattened as the beam-line direction, our initial data can be thought of as approximating a head-on heavy ion collision at its moment of impact.
Scheven, U. M.; Harris, R.; Johns, M. L.
2008-12-01
The experimental characterization of voidspaces in porous media generally includes measurements of volume averaged scalar properties such as porosity, dispersivity, or the hydrodynamic radius rh = V/S, where V and S are the volume and surface area of the pore space respectively. Displacement encoding NMR experiments have made significant contributions to this characterization. It is clear, however, that NMR derived dispersivities in packed beds—the one random porous system for which there exist canonical but incompatible theoretical predictions with few or no adjustable parameters—can be affected by the same experimental complications which have substantially contributed to the puzzling scatter in published dispersion results based on elution experiments. Notable among these are macroscopic flow heterogeneities near walls, and inhomogeneous flow injection. Using the first three cumulants we delineate a transition from a pre-asymptotic to a quasi-asymptotic dispersion regime and determine the true dispersivity of the random pack of spheres.
Directory of Open Access Journals (Sweden)
Ahmadi, K.
2013-01-01
Full Text Available The relationship between tree height and diameter is an important element in growth and yield models, in carbon budget and timber volume models, and in the description of stand dynamics. Six non-linear growth functions (i.e. Chapman-Richards, Schnute, Lundqvist/Korf, Weibull, Modified Logistic and Exponential were fitted to tree height-diameter data of oriental beech in the Hyrcanian mixed hardwood forests of Iran. The predictive performance of these models was in the first place assessed by means of different model evaluation criteria such as adjusted R squared (adjR2, root mean square error (RMSE, Akaike information criterion (AIC, mean difference (MD, mean absolute difference (MAD and mean square (MS error criteria. Although each of the six models accounted for approximately 75% of total variation in height, a large difference in asymptotic estimates was observed. Apart from this, the predictive performance of the models was also evaluated by means of cross-validation and by splitting the data into 5-cm diameter classes. Plotting the MD in relation to these diameter at breast height (DBH classes showed for all growth functions, except for the Modified Logistic function, similar mean prediction errors for small- and medium-sized trees. Large-sized trees, however, showed a higher mean prediction error. The Modified Logistic function showed the worst performance due to a large model bias. The Exponential and Lundqvist/Korf models were discarded due to their showing biologically illogical behavior and unreasonable estimates for the asymptotic coefficient, respectively. Considering all the above-mentioned criteria, the Chapman-Richards, Weibull, and Schnute functions provided the most satisfactory height predictions. However, we would recommend the Chapman-Richards function for further analysis because of its higher predictive performance.
Crystal growth of an organic non-linear optical material from the vapour phase
Hou, W
1999-01-01
Due to the potential applications of organic non-linear optical materials in the areas of optical processing and communication, the investigation of the crystal growth of new organic NLO materials has been an active field for the last 20 years. For such uses it is necessary to produce single crystals of high quality and perfection, free of strain and defects. When crystals are grown from the solution and the melt, solvent and the decomposition component in the melt can introduce impurities and imperfection to the as-grown crystals. For crystals grown from vapour phase, in the absence of the solvent, this cannot occur and the method promises to yield single crystals of higher quality. Despite this attraction, little attention has been paid to the vapour phase growth of organic NLO crystals. It was with this in mind that the following investigation was carried out. Using Methyl p-hydroxybenzoate (p-MHB), a potential organic NLO material, a comparison investigation was made of its crystal growth from both the va...
Gauge coupling of non-linear σ-model and a generalized Mazur identity
Carter, B.
An inversionsymmetric class of non-linear σ-models is constructed. The original pure model with field values in the coset space of a classical matrix group G with respect to an isotropy subgroup under the adjoint action is generalized to a minimally gauge coupled model in which the field is a section in a bundle with group G acting on the coset space as fibre with a nontrivial connection of (for example) Yang-Mills type. It is shown that the gauge coupled models admit a natural generalisation of the identities originally constructed by Mazur for the pure nonlinear σ-models whereby the divergence of a quantity whose surface integral vanishes when suitable boundary conditions are satisfied is shown to be equal to a functional of the difference between two sets of field variables that is positive definite in many relevant situation. In such cases, which occur when the base-space metric is positive definite (so that the system is of elliptic type) and the isotropy subgroup is compact, the identities lead directly to uniqueness theorems for the solutions.
Unified Einstein-Virasoro master equation in the general non-linear $\\sigma$ model
De Boer, J
1997-01-01
The Virasoro master equation (VME) describes the general affine-Virasoro construction T=L^{ab}J_aJ_b+iD^a \\dif J_a in the operator algebra of the WZW model, where L^{ab} is the inverse inertia tensor and D^a is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field L^{ab} to the background fields of the sigma model. For a particular solution L_G^{ab}, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model w...
Identification of a Non-Linear Landing Gear Model Using Nature-Inspired Optimization
Directory of Open Access Journals (Sweden)
Felipe A.C. Viana
2008-01-01
Full Text Available This work deals with the application of a nature-inspired optimization technique to solve an inverse problem represented by the identification of an aircraft landing gear model. The model is described in terms of the landing gear geometry, internal volumes and areas, shock absorber travel, tire type, and gas and oil characteristics of the shock absorber. The solution to this inverse problem can be obtained by using classical gradient-based optimization methods. However, this is a difficult task due to the existence of local minima in the design space and the requirement of an initial guess. These aspects have motivated the authors to explore a nature-inspired approach using a method known as LifeCycle Model. In the present formulation two nature-based methods, namely the Genetic Algorithms and the Particle Swarm Optimization were used. An optimization problem is formulated in which the objective function represents the difference between the measured characteristics of the system and its model counterpart. The polytropic coefficient of the gas and the damping parameter of the shock absorber are assumed as being unknown: they are considered as design variables. As an illustration, experimental drop test data, obtained under zero horizontal speed, were used in the non-linear landing gear model updating of a small aircraft.
Energy Technology Data Exchange (ETDEWEB)
Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex,Falmer Campus, Brighton, BN1 9QH (United Kingdom); Sannino, Francesco [CP-Origins & the Danish Institute for Advanced Study Danish IAS, University of Southern Denmark,Campusvej 55, DK-5230 Odense (Denmark)
2014-12-31
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed....
National Research Council Canada - National Science Library
Rahul Kumar Gupta; Qiongfeng Shi; Lokesh Dhakar; Tao Wang; Chun Huat Heng; Chengkuo Lee
2017-01-01
.... In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g-2.0 g...
Estimations of non-linearities in structural vibrations of string musical instruments
Ege, Kerem; Boutillon, Xavier
2012-01-01
Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies, we characterise weak non-linearities by a signal-model approach based on cascade of Hammerstein models. In this approach, in a chain of two non-linear systems, two measurements are sufficient to estimate the non-linear contribution of the second (sub-)system which cannot be directly linearly driven, as a function of the exciting frequency. The experiment consists in exciting the instrument acoustically. The linear and non-linear contributions to the response of (a) the loudspeaker coupled to the room, (b) the instrument can be separated. Some methodological issues will be discussed. Findings pertaining to several instruments - one piano, two guitars, one violin - will be presented.
Hybrid finite-volume-ROM approach to non-linear aerospace fluid-structure interaction modelling
CSIR Research Space (South Africa)
Mowat, AGB
2011-06-01
Full Text Available A fully-coupled partitioned fluid-structure interaction (FSI) scheme is developed for sub- and transonic aeroelastic structures undergoing non-linear displacements. The Euler equations, written in an Arbitrary Lagrangian Eulerian (ALE) coordinate...
Parametric Stability of Non-Linearly Elastic Composite Plates by Lyapunov Exponents
GILAT, R.; ABOUDI, J.
2000-08-01
The dynamic stability of non-linearly elastic composite plates subjected to periodic in-plane loading is investigated. Infinitely wide plates made of resin matrix composite are considered. The non-linearly elastic behavior of the resin matrix is modelled by the generalized Ramberg-Osgood representation. The effect of the matrix non-linearity on the overall response of the composite is predicted by the micromechanical method of cells. The dynamic stability analysis is performed by evaluating the largest Lyapunov exponent, the sign of which indicates whether the system is stable or not. It is shown that this approach forms a convenient tool for predicting parametric stability of non-linear composite structures.
A new approach of binary addition and subtraction by non-linear ...
Indian Academy of Sciences (India)
optical domain by exploitation of proper non-linear material-based switching technique. In this communication, the authors extend this technique for both adder and subtractor accommodating the spatial input encoding system.
Non-linearity parameter of binary liquid mixtures at elevated pressures
Indian Academy of Sciences (India)
. Ultrasonic studies in liquid mixtures provide valuable information about structure and interaction in such systems. The present investigation comprises of theoretical evaluation of the acoustic non-linearity parameter / of four binary liquid ...
Non-linear Synthesis of Complex Laser Waveforms at Remote Distances
Berti, Nicolas; Hermelin, Sylvain; Kasparian, Jérôme; Wolf, Jean-Pierre
2015-01-01
Strong deformation of ultrashort laser pulse shapes is unavoidable when delivering high intensities at remote distances due to non-linear effects taking place while propagating. Relying on the reversibility of laser filamentation, we propose to explicitly design laser pulse shapes so that propagation serves as a non-linear field synthesizer at a remote target location. Such an approach allows, for instance, coherent control of molecules at a remote distance, in the context of standoff detection of pathogens or explosives.
A magnetic betelgeuse? Numerical simulations of non-linear dynamo action
DEFF Research Database (Denmark)
Dorch, S. B. F.
2004-01-01
question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible...... and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action....
Analysis of the Non-Linearity of El Niño Southern Oscillation Teleconnections
Frauen, Claudia; Dommenget, Dietmar; Rezny, Michael; Wales, Scott
2014-05-01
The El Niño Southern Oscillation (ENSO) has significant variations and non-linearities in its pattern and strength. ENSO events are shifted along the equator, with some located in the central Pacific (CP) and others in the east Pacific (EP). To study how these variations are reflected in global ENSO teleconnections we analyze observations and idealized atmospheric general circulation model (AGCM) simulations. Clear non-linearities exist in observed teleconnections of sea level pressure (SLP) and precipitation. However, it is difficult to distinguish if these are caused by the different signs, strengths or spatial patterns of events (strong El Niño events mostly being EP events and strong La Niña events mostly being CP events) or by combinations of these. Therefore, sensitivity experiments are performed with an AGCM forced with idealized EP and CP ENSO sea surface temperature (SST) patterns with varying signs and strengths. It can be shown that in general the response is stronger for warm events than for cold events and the teleconnections shift following the SST anomaly patterns. EP events show stronger non-linearities than CP events. The non-linear responses to ENSO events can be explained as a combination of non-linear responses to a linear ENSO (fixed pattern but varying signs and strengths) and a linear response to a non-linear ENSO (varying patterns). Any observed event is a combination of these aspects. While in most tropical regions these add up leading to stronger non-linear responses than expected from the single components, in some regions they cancel each other resulting in little overall non-linearity. This leads to strong regional differences in ENSO teleconnections.
Measurements and simulations of non-linear noise re-distribution in an SOA
DEFF Research Database (Denmark)
Öhman, Filip; Tromborg, Bjarne; Mørk, Jesper
2004-01-01
Measurements and statistical simulations demonstrate that a semiconductor optical amplifier (SOA) induces non-linear noise re-distribution with a strong power and bandwidth dependence. © 2004 Optical Society of America......Measurements and statistical simulations demonstrate that a semiconductor optical amplifier (SOA) induces non-linear noise re-distribution with a strong power and bandwidth dependence. © 2004 Optical Society of America...
Bifurcation Analysis of a Non-linear On-Board Rotor-Bearing System
Dakel, M. Zaki; Baguet, Sébastien; Dufour, Régis
2014-01-01
International audience; The non-linear dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings and subject to rigid base excitations is investigated in this work. The proposed finite element rotor model takes into account the geometric asymmetry of shaft and/or rigid disk and considers six types of base deterministic motions (rotations and translations) and non-linear fluid film forces obtained from the Reynoldsequation. The equations of motion contain time-varying para...
Caillon, J C
2002-01-01
The longitudinal response functions for quasielastic electron scattering on sup 1 sup 2 C, sup 4 sup 0 Ca and sup 5 sup 6 Fe have been calculated in relativistic non-linear models taking into account RPA correlations. For these calculations, a covariant, consistent, calculation of the nuclear matter linear response has been performed. The effect of the non-linear terms on the longitudinal response has been discussed.
Aeroelastic characteristics of slender wing/bodies with freeplay non-linearities
Garcia-Fogeda Nuñez, Pablo; Arevalo Lozano, Felix
2011-01-01
This article presents a time domain approach to the flutter analysis of a missile-type wing/body configuration with concentrated structural non-linearities. The missile wing is considered fully movable and its rotation angle contains the structural freeplay-type non-linearity. Although a general formulation for flexible configurations is developed, only two rigid degrees of freedom are taken into account for the results: pitching of the whole wing/body configuration and wing rotation angle ar...
DEFF Research Database (Denmark)
Arlunno, Valeria; Zhang, Xu; Larsen, Knud J.
2011-01-01
We experimentally demonstrate that digital non-linear equalization allows for using independent tunable DFB lasers spaced at 12.5 GHz for ultradense WDM PM-QPSK flexible capacity channels for metro core networking.......We experimentally demonstrate that digital non-linear equalization allows for using independent tunable DFB lasers spaced at 12.5 GHz for ultradense WDM PM-QPSK flexible capacity channels for metro core networking....
Directory of Open Access Journals (Sweden)
Francisco Paulo Lépore Neto
2006-01-01
Full Text Available When the surfaces of two elastic bodies present relative motions under certain amount of contact pressure the mechanical system can be unstable. Experiments conducted on elastic bodies in contact shown that the dynamic system is self-excited by the non-linear behavior of the friction forces. The main objective of this paper is to estimate the friction force using the vibrations signals, measured on a reciprocating wear testing machine, by the proposed non-linear signal analysis formulation. In the proposed formulation the system global output is the sum of two outputs produced by a linear path associated in parallel with a non-linear path. This last path is a non-linear model that represents the friction force. Since the linear path can be identified by traditional signal analysis, the non-linear function can be evaluated by the global input/output relationships. Validation tests are conducted in a tribological system composed by a sphere in contact with and a prismatic body, which has an imposed harmonic motion. The global output force is simultaneously measured by a piezoelectric and by a piezoresistive load cells. The sphere and prismatic body vibrations are measured by a laser Doppler vibrometer and by an accelerometer respectively. All signals are digitalized at the same time base and the data is transferred to a microcomputer. The non-linear signal analysis technique uses this data to identify the friction force.
Correction of non-linear thickness effects in HAADF STEM electron tomography
Energy Technology Data Exchange (ETDEWEB)
Van den Broek, W., E-mail: wouter.vandenbroek@uni-ulm.de [Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp (Belgium); Rosenauer, A. [Institut fuer Festkoerperphysik (IFP), Universitaet Bremen, Otto-Hahn-Allee 1, 28359 Bremen (Germany); Goris, B.; Martinez, G.T.; Bals, S.; Van Aert, S.; Van Dyck, D. [Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp (Belgium)
2012-05-15
In materials science, high angle annular dark field scanning transmission electron microscopy is often used for tomography at the nanometer scale. In this work, it is shown that a thickness dependent, non-linear damping of the recorded intensities occurs. This results in an underestimated intensity in the interior of reconstructions of homogeneous particles, which is known as the cupping artifact. In this paper, this non-linear effect is demonstrated in experimental images taken under common conditions and is reproduced with a numerical simulation. Furthermore, an analytical derivation shows that these non-linearities can be inverted if the imaging is done quantitatively, thus preventing cupping in the reconstruction. -- Highlights: Black-Right-Pointing-Pointer In HAADF STEM, a thickness dependent, non-linear damping of the projected intensities occurs. Black-Right-Pointing-Pointer In tomography, this leads to underestimated intensities in the interior of homogeneous particles, the cupping artifact. Black-Right-Pointing-Pointer The non-linear damping is demonstrated in experimental images and reproduced with numerical simulations. Black-Right-Pointing-Pointer The non-linear damping can be undone if the imaging is done quantitatively. Black-Right-Pointing-Pointer Experimental proof is provided showing that cupping can be prevented.
Asymptotics of perturbed soliton for Davey-Stewartson; 2, equation
Gadylshin, R R
1998-01-01
It is shown that, under a small perturbation of lump (soliton) for Davey-Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.
Non-linear partial differential equations an algebraic view of generalized solutions
Rosinger, Elemer E
1990-01-01
A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen
Relativistic lagrangian non-linear field theories supporting non-topological soliton solutions
Rubiera García, Diego
2008-01-01
En el contexto de la teoría de campos el interés en soluciones extendidas describiendo campos asociados a partículas puntuales data de los años 30, con los intentos de Born e Infeld para construir una electrodinámica no-lineal cuyas soluciones electrostáticas a simetría esférica eliminaran la divergencia de la autoenergía del electrón en Electrodinámica Clásica.En esta tesis realizamos un amplio estudio de una extensa clase de teorías relativistas de campos que contienen soluciones de tipo so...
Physical-Chemical and non-linear rheological properties of aqueous solutions of agave fructans
Directory of Open Access Journals (Sweden)
Jamné A. Ponce S.
2008-01-01
Full Text Available Los fructanos son carbohidratos de reserva formados por unidades fructofuranosil con enlaces tipo B principalmente, que se encuentran presentes en diversas variedades de plantas. Los fructanos empleados en el presente estudio, fueron obtenidos mediante una extracción acuosa a partir de piñas maduras de Agave tequilana Weber var. azul. Se sabe que las moléculas de fructanos derivados del agave, poseen una configuración ramificada a diferencia de la configuración lineal presente en la inulina comercial (derivada de la Cichorium intybus, lo que les podría otorgar diferentes propiedades y aplicaciones tecnológicas. La composición de los fructanos de agave obtenidos en éste estudio, mostró una mezcla con diferentes tamaños y pesos moleculares promedio de 3,182 Da así como un grado de polimerización promedio de 18. Las soluciones acuosas de fructanos de agave fueron preparadas (de 5-90% p/p y sometidas a una serie de pruebas como pH y densidad a 30, 40, 50 y 60 °C; adicionalmente, la conductividad y el tamaño de partícula (QLS por sus siglas en inglés fueron analizadas a temperatura ambiente. Los resultados de las pruebas mencionadas anteriormente sugieren que, los fructanos derivados del agave pueden formar agregados a concentraciones superiores al 28% p/p. Por otro lado, las mediciones reológicas no lineales de las soluciones acuosas de fructanos de agave se llevaron a cabo a 30, 40, 50 y 60 °C (previa estabilización de la muestra a la temperatura de medición mostrando que presentan comportamientos Newtonianos excepto aquellas a 80 y 90 % p/p, donde comportamientos de adelgazamiento y espesamiento al corte fueron observados. Finalmente, los resultados reológicos aportan valiosa información sobre la formación de agregados en las soluciones acuosas de fructanos de agave en el intervalo de concentraciones de 30 a 70 % p/p, por medio de mediciones de velocidad de corte en estado estacionario efectuadas a 30, 40, 50 y 60°C.
Influence of non-linear flow on the pumping tests in karstified and fractured aquifers
Farkas-Karay, Gyöngyi; Birk, Steffen; Vasvári, Vilmos; Hajnal, Géza; Mayaud, Cyril
2017-04-01
When evaluating pumping test data in karstified or fractured aquifers remarkable deviations from the theoretically estimated curves can be observed. The assumptions of the commonly used evaluation methods (Theis, Cooper-Jacob, Papadopulus-Cooper) usually do not fit to properties in hard rock aquifers, where often non-linear, heterogeneous and non-isotropic conditions can appear. The analysis of the effect of these conditions helps to better evaluate the pumping test data and to avoid the mistakes caused by the use of traditional methods. In this study the influence of non-linear flow was analysed based on field data and computer-generated time series. Using Non-Linear Flow Process for MODFLOW (Mayaud, C., Walker, P., Hergarten, S. and Birk, S., 2015, Nonlinear Flow Process: A New Package to Compute Nonlinear Flow in MODFLOW. Groundwater, 53: 645-650) allowed the simulation of non-linear flow in aquifers based on the Forchheimer equation. The analysis showed that the detection of non-linear flow can be subserved by separate evaluation of drawdown and recovery time series or by using additional observation wells. Recovery data and data from observation wells far enough from the pumped well are not disturbed by nonlinearity; the comparison with drawdown data of observation wells and the pumped well therefore can show whether or not non-linear flow appears. In particular, proper results of aquifer parameters can be obtained from recovery data. If only drawdown data from the pumped well are available it is helpful to replace the losses caused by non-linear flow by non-linear well losses (see also Mathias, S. A., and L. C. Todman, 2010, Step-drawdown tests and the Forchheimer equation, Water Resour. Res., 46, W07514). The applicability of the Jacob's step-drawdown-test evaluation in Forchheimer-flow cases is demonstrated by comparison with the numerical non-linear flow model. Inaccurate parameter estimates resulting from neglecting non-linear flow demonstrate the
Kravchenko, Vladislav V.; Torba, Sergii M.
2017-01-01
A representation for a solution $u(\\omega,x)$ of the equation $-u"+q(x)u=\\omega^2 u$, satisfying the initial conditions $u(\\omega,0)=1$, $u'(\\omega,0)=i\\omega$ is derived in the form \\[ u(\\omega,x)=e^{i\\omega x}\\left( 1+\\frac{u_1(x)}{\\omega}+ \\frac{u_2(x)}{\\omega^2}\\right) +\\frac{e^{-i\\omega x}u_3(x)}{\\omega^2}-\\frac{1}{\\omega^2}\\sum_{n=0}^{\\infty} i^{n}\\alpha_n(x)j_n(\\omega x), \\] where $u_m(x)$, $m=1,2,3$ are given in a closed form, $j_n$ stands for a spherical Bessel function of order $n$ ...
van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; The LHD Experiment Group
2017-12-01
A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.
Asymptotic structures of cardinals
Directory of Open Access Journals (Sweden)
Oleksandr Petrenko
2014-07-01
Full Text Available A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Tackling non-linearities with the effective field theory of dark energy and modified gravity
Frusciante, Noemi; Papadomanolakis, Georgios
2017-12-01
We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.
Parsa, V; Parker, P; Scott, R
1998-03-01
Somatosensory evoked potentials (SEPs) are a sub-class of evoked potentials (EPs) that are very useful in diagnosing various neuromuscular disorders and in spinal cord and peripheral-nerve monitoring. Most often, the measurements of these signals are contaminated by stimulus-evoked artefact. Conventional stimulus-artifact (SA) reduction schemes are primarily hardware-based and rely on some form of input blanking during the SA phase. This procedure can result in partial SEP loss if the tail of the SA interferes with the SEP. Adaptive filters offer an attractive solution to this problem by iteratively reducing the SA waveform while leaving the SEP intact. Owing to the inherent non-linearities in the SA generation system, non-linear adaptive filters (NAFs) are most suitable. SA reduction using NAFs based on truncated second-order Volterra expansion series is investigated. The focus is on the performance of two main adaptation algorithms, the least mean square (LMS) and recursive least squares (RLS) algorithms, in the context of non-linear adaptive filtering. A comparison between the convergence and performance characteristics of these two algorithms is made by processing both simulated and experimental SA data. It is found that, in high artefact-to-noise ratio (ANR) SA cancellation, owing to the large eigenvalue spreads, the RLS-based NAF is more efficient than the LMS-based NAF. However, in low-ANR scenarios, the RLS- and LMS-based NAFs exhibit similar convergence properties, and the computational simplicity of the LMS-based NAFs makes them the preferred option.
Simultaneous 160 Gb/s Add-Drop Multiplexing in a Non-Linear Optical Loop Mirror
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Oxenløwe, Leif Katsuo; Galili, Michael
2006-01-01
We report on a demonstration of error-free simultaneous add-drop multiplexing of 160 Gb/s data in a non-linear optical loop mirror composed of 100 m highly non-linear fibre......We report on a demonstration of error-free simultaneous add-drop multiplexing of 160 Gb/s data in a non-linear optical loop mirror composed of 100 m highly non-linear fibre...
Pothanna, N.; Aparna, P.; Gorla, R. S. R.
2017-12-01
In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.
Directory of Open Access Journals (Sweden)
Gustavo C. Buscaglia
2001-01-01
Full Text Available A new numerical approach is proposed to alleviate the computational cost of solving non-linear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost.
Pillai, Goonaseelan Colin; Mentré, France; Steimer, Jean-Louis
2005-04-01
Few scientific contributions have made significant impact unless there was a champion who had the vision to see the potential for its use in seemingly disparate areas-and who then drove active implementation. In this paper, we present a historical summary of the development of non-linear mixed effects (NLME) modeling up to the more recent extensions of this statistical methodology. The paper places strong emphasis on the pivotal role played by Lewis B. Sheiner (1940-2004), who used this statistical methodology to elucidate solutions to real problems identified in clinical practice and in medical research and on how he drove implementation of the proposed solutions. A succinct overview of the evolution of the NLME modeling methodology is presented as well as ideas on how its expansion helped to provide guidance for a more scientific view of (model-based) drug development that reduces empiricism in favor of critical quantitative thinking and decision making.
Directory of Open Access Journals (Sweden)
Pothanna N.
2017-12-01
Full Text Available In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.
Non-linear actions of physiological agents: Finite disarrangements elicit fitness benefits.
Sedlic, Filip; Kovac, Zdenko
2017-10-01
Finite disarrangements of important (vital) physiological agents and nutrients can induce plethora of beneficial effects, exceeding mere attenuation of the specific stress. Such response to disrupted homeostasis appears to be universally conserved among species. The underlying mechanism of improved fitness and longevity, when physiological agents act outside their normal range is similar to hormesis, a phenomenon whereby toxins elicit beneficial effects at low doses. Due to similarity with such non-linear response to toxins described with J-shaped curve, we have coined a new term "mirror J-shaped curves" for non-linear response to finite disarrangement of physiological agents. Examples from the clinical trials and basic research are provided, along with the unifying mechanisms that tie classical non-linear response to toxins with the non-linear response to physiological agents (glucose, oxygen, osmolarity, thermal energy, calcium, body mass, calorie intake and exercise). Reactive oxygen species and cytosolic calcium seem to be common triggers of signaling pathways that result in these beneficial effects. Awareness of such phenomena and exploring underlying mechanisms can help physicians in their everyday practice. It can also benefit researchers when designing studies and interpreting growing number of scientific data showing non-linear responses to physiological agents. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.
Non-linear actions of physiological agents: Finite disarrangements elicit fitness benefits
Directory of Open Access Journals (Sweden)
Filip Sedlic
2017-10-01
Full Text Available Finite disarrangements of important (vital physiological agents and nutrients can induce plethora of beneficial effects, exceeding mere attenuation of the specific stress. Such response to disrupted homeostasis appears to be universally conserved among species. The underlying mechanism of improved fitness and longevity, when physiological agents act outside their normal range is similar to hormesis, a phenomenon whereby toxins elicit beneficial effects at low doses. Due to similarity with such non-linear response to toxins described with J-shaped curve, we have coined a new term “mirror J-shaped curves” for non-linear response to finite disarrangement of physiological agents. Examples from the clinical trials and basic research are provided, along with the unifying mechanisms that tie classical non-linear response to toxins with the non-linear response to physiological agents (glucose, oxygen, osmolarity, thermal energy, calcium, body mass, calorie intake and exercise. Reactive oxygen species and cytosolic calcium seem to be common triggers of signaling pathways that result in these beneficial effects. Awareness of such phenomena and exploring underlying mechanisms can help physicians in their everyday practice. It can also benefit researchers when designing studies and interpreting growing number of scientific data showing non-linear responses to physiological agents.
Non-Linearly Interacting Ghost Dark Energy in Brans-Dicke Cosmology
Ebrahimi, E
2016-01-01
In this paper we extend the form of interaction term into the non-linear regime in the ghost dark energy model. A general form of non-linear interaction term is presented and cosmic dynamic equations are obtained. Next, the model is detailed for two special choice of the non-linear interaction term. According to this the universe transits at suitable time ($z\\sim 0.8$) from deceleration to acceleration phase which alleviate the coincidence problem. Squared sound speed analysis revealed that for one class of non-linear interaction term $v_s^2$ can gets positive. This point is an impact of the non-linear interaction term and we never find such behavior in non interacting and linearly interacting ghost dark energy models. Also statefinder parameters are introduced for this model and we found that for one class the model meets the $\\Lambda CDM$ while in the second choice although the model approaches the $\\Lambda CDM$ but never touch that.
Alkhalifah, Tariq Ali
2012-09-25
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
Analysis of non-linear response of the human body to vertical whole-body vibration.
Tarabini, Marco; Solbiati, Stefano; Moschioni, Giovanni; Saggin, Bortolino; Scaccabarozzi, Diego
2014-01-01
The human response to vibration is typically studied using linear estimators of the frequency response function, although different literature works evidenced the presence of non-linear effects in whole-body vibration response. This paper analyses the apparent mass of standing subjects using the conditioned response techniques in order to understand the causes of the non-linear behaviour. The conditioned apparent masses were derived considering models of increasing complexity. The multiple coherence function was used as a figure of merit for the comparison between the linear and the non-linear models. The apparent mass of eight male subjects was studied in six configurations (combinations of three vibration magnitudes and two postures). The contribution of the non-linear terms was negligible and was endorsed to the change of modal parameters during the test. Since the effect of the inter-subject variability was larger than that due to the increase in vibration magnitude, the biodynamic response should be more meaningfully modelled using a linear estimator with uncertainty rather than looking for a non-linear modelling.
The effect of non-linear human visual system components on linear model observers
Zhang, Yani; Pham, Binh T.; Eckstein, Miguel P.
2004-05-01
Linear model observers have been used successfully to predict human performance in clinically relevant visual tasks for a variety of backgrounds. On the other hand, there has been another family of models used to predict human visual detection of signals superimposed on one of two identical backgrounds (masks). These masking models usually include a number of non-linear components in the channels that reflect properties of the firing of cells in the primary visual cortex (V1). The relationship between these two traditions of models has not been extensively investigated in the context of detection in noise. In this paper, we evaluated the effect of including some of these non-linear components into a linear channelized Hotelling observer (CHO), and the associated practical implications for medical image quality evaluation. In particular, we evaluate whether the rank order evaluation of two compression algorithms (JPEG vs. JPEG 2000) is changed by inclusion of the non-linear components. The results show: a) First that the simpler linear CHO model observer outperforms CHO model with the nonlinear components investigated. b) The rank order of model observer performance for the compression algorithms did not vary when the non-linear components were included. For the present task, the results suggest that the addition of the physiologically based channel non-linearities to a channelized Hotelling might add complexity to the model observers without great impact on medical image quality evaluation.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Asymptotic Behavior of Certain Integrodifferential Equations
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Said Grace
2016-01-01
Full Text Available This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: atx′t′=e(t+∫ct(t-sα-1k(t,sf(s,x(sds, c>1, 0<α<1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.
Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.
2017-05-01
Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 , in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential V=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.
Research of Non-linear 2.5D Fluid-structure Interaction Model of Gravity Dam
Li, Yiran; Xu, Menghua; Sun, Hao
2017-10-01
Aseismic safety of dam involves people’s lives and properties, even has a great impact on national economic development. The key to this project is to have a fairly complete fluid-structure interaction (FSI) theory and a calculation method with a good accuracy. Therefore, focused on the FSI dynamic problem of gravity dam under seismic action, this paper presented the non-linear 2.5D dynamic theoretical model of concrete gravity dam established by segmenting fluid model and numerical solution method, compared the numerical simulation result under preliminary gravity action with 3D model. The study showed that the 2.5D dynamic calculation model could well reflect the seismic dynamic FSI behavior and effect of concrete gravity dam in the respects of displacement and stress and benefited the large-scale non-linear 3D aseismic calculation of gravity dam because of the effective reduction of 3D FSI numerical calculation time, which improved the calculation efficiency.
DSP-based Mitigation of RF Front-end Non-linearity in Cognitive Wideband Receivers
Grimm, Michael; Sharma, Rajesh K.; Hein, Matthias A.; Thomä, Reiner S.
2012-09-01
Software defined radios are increasingly used in modern communication systems, especially in cognitive radio. Since this technology has been commercially available, more and more practical deployments are emerging and its challenges and realistic limitations are being revealed. One of the main problems is the RF performance of the front-end over a wide bandwidth. This paper presents an analysis and mitigation of RF impairments in wideband front-ends for software defined radios, focussing on non-linear distortions in the receiver. We discuss the effects of non-linear distortions upon spectrum sensing in cognitive radio and analyse the performance of a typical wideband software-defined receiver. Digital signal processing techniques are used to alleviate non-linear distortions in the baseband signal. A feed-forward mitigation algorithm with an adaptive filter is implemented and applied to real measurement data. The results obtained show that distortions can be suppressed significantly and thus increasing the reliability of spectrum sensing.
Anti-D3 branes and moduli in non-linear supergravity
Garcia del Moral, Maria P.; Parameswaran, Susha; Quiroz, Norma; Zavala, Ivonne
2017-10-01
Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and α' corrections.
Non-linear simulations of ELMs in ASDEX Upgrade including diamagnetic drift effects
Energy Technology Data Exchange (ETDEWEB)
Lessig, Alexander; Hoelzl, Matthias; Krebs, Isabel; Franck, Emmanuel; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstrasse 2, 85748 Garching (Germany); Orain, Francois; Morales, Jorge; Becoulet, Marina [CEA-IRFM, Cadarache, 13108 Saint-Paul-Lez-Durance (France); Huysmans, Guido [ITER Organization, 13067 Saint-Paul-Lez-Durance (France)
2015-05-01
Large edge localized modes (ELMs) are a severe concern for ITER due to high transient heat loads on divertor targets and wall structures. Using the non-linear MHD code JOREK, we have performed ELM simulations for ASDEX Upgrade (AUG) including diamagnetic drift effects. The influence of diamagnetic terms onto the evolution of the toroidal mode spectrum for different AUG equilibria and the non-linear interaction of the toroidal harmonics are investigated. In particular, we confirm the diamagnetic stabilization of high mode numbers and present new features of a previously introduced quadratic mode coupling model for the early non-linear evolution of the mode structure. Preliminary comparisons of full ELM crashes with experimental observations are shown aiming at code validation and the understanding of different ELM types. Work is ongoing to include toroidal and neoclassical poloidal rotation in our simulations.
Angular spectrum approach for fast simulation of pulsed non-linear ultrasound fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
The paper presents an Angular Spectrum Approach (ASA) for simulating pulsed non-linear ultrasound fields. The source of the ASA is generated by Field II, which can simulate array transducers of any arbitrary geometry and focusing. The non-linear ultrasound simulation program - Abersim, is used...... as the reference. A linear array transducer with 64 active elements is simulated by both Field II and Abersim. The excitation is a 2-cycle sine wave with a frequency of 5 MHz. The second harmonic field in the time domain is simulated using ASA. Pulse inversion is used in the Abersim simulation to remove...... the fundamental and keep the second harmonic field, since Abersim simulates non-linear fields with all harmonic components. ASA and Abersim are compared for the pulsed fundamental and second harmonic fields in the time domain at depths of 30 mm, 40 mm (focal depth) and 60 mm. Full widths at -6 dB (FWHM) are f0...
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical......Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Applications of Kalman filters based on non-linear functions to numerical weather predictions
Directory of Open Access Journals (Sweden)
G. Galanis
2006-10-01
Full Text Available This paper investigates the use of non-linear functions in classical Kalman filter algorithms on the improvement of regional weather forecasts. The main aim is the implementation of non linear polynomial mappings in a usual linear Kalman filter in order to simulate better non linear problems in numerical weather prediction. In addition, the optimal order of the polynomials applied for such a filter is identified. This work is based on observations and corresponding numerical weather predictions of two meteorological parameters characterized by essential differences in their evolution in time, namely, air temperature and wind speed. It is shown that in both cases, a polynomial of low order is adequate for eliminating any systematic error, while higher order functions lead to instabilities in the filtered results having, at the same time, trivial contribution to the sensitivity of the filter. It is further demonstrated that the filter is independent of the time period and the geographic location of application.
Single Image Super-Resolution by Non-Linear Sparse Representation and Support Vector Regression
Directory of Open Access Journals (Sweden)
Yungang Zhang
2017-02-01
Full Text Available Sparse representations are widely used tools in image super-resolution (SR tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR. Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained.
Classical non-Gaussianity from non-linear evolution of curvature perturbations
Gong, Jinn-Ouk; Noh, Hyerim
2011-01-01
We study the non-linear evolution of the curvature perturbations during matter dominated era. We show that regardless of the origin of the primordial perturbation, the Bardeen potential receives sizable contributions from the classical non-linear evolution effects, and quantify them exactly. We divide these effects into two groups, being dominant on super- and sub-horizon scales. The former gives rise to squeezed peak of the bispectrum and contributes, in terms of the local non-linear parameter, -3/2 < f_{NL} < -2/5, depending on the configuration of momenta. The latter is highly scale dependent with equilateral shape, and can serve as a potential probe of general relativity.
A New Method for Generating High Non-linearity S-Boxes
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P. Tesar
2010-04-01
Full Text Available Substitution boxes are important parts in many block and stream ciphers. The emergence of a range of crypto-attacks has led to the development of criteria for repelling such attacks. The non-linearity criterion provides some protection against well- known attacks, such as linear cryptanalysis and differential cryptanalysis. The open problem is constructed by generating methods which will be rapid and will generate S-boxes with the highest possible non-linearity. This paper deals with a new rapid method for generating regular 8x8 S-boxes with non-linearity up to a value of 104. The new method combines the special genetic algorithm with total tree searching.
Aeroelastic Analysis of a Flexible Airfoil with a Freeplay Non-Linearity
Kim, S.-H.; Lee, I.
1996-06-01
A two-dimensional flexible airfoil with a freeplay non-linearity in pitch has been analyzed in the subsonic flow range. Structurally, the airfoil is modelled as finite beam elements and two spring elements in pitch and plunge. A doublet lattice method is used for the two-dimensional unsteady aerodynamics to include the camber deflection effect. The fictitious mass modal approach is adopted in order to use the consistent modal co-ordinates for the structures with non-linearity. Non-linear aeroelastic analyses for both the frequency domain and time domain are performed for rigid and flexible airfoil models to investigate the flexibility effect. Results are shown for models of different pitch-to-plunge frequency ratio. Responses involving limit cycle oscillation and chaotic motion are observed and they are highly influenced by the pitch-to-plunge frequency ratio.
The non-linear power spectrum of the Lyman alpha forest
Energy Technology Data Exchange (ETDEWEB)
Arinyo-i-Prats, Andreu [Institut de Ciències del Cosmos, Universitat de Barcelona, IEEC-UB, Barcelona 08028, Catalonia (Spain); Miralda-Escudé, Jordi [Institució Catalana de Recerca i Estudis Avançats, Barcelona, Catalonia (Spain); Viel, Matteo [INAF, Astronomical Observatory of Trieste, 34131 Trieste (Italy); Cen, Renyue, E-mail: andreuaprats@gmail.com, E-mail: miralda@icc.ub.edu, E-mail: viel@oats.inaf.it, E-mail: cen@astro.princeton.edu [Princeton University Observatory, Princeton, NJ 08544 (United States)
2015-12-01
The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate the comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.
Non-linear classification of heart rate parameters as a biomarker for epileptogenesis.
Kheiri, Farshad; Bragin, Anatol; Engel, Jerome; Almajano, Joel; Winden, Eamon
2012-06-01
To characterize a biomarker for epileptogenesis based on cardiac interbeat interval characteristics. Electrocardiograph (ECG) and electroencephalogram (EEG) signals were recorded from freely moving rats (n = 23) before status epilepticus (SE) induced by i.p. pilocarpine (PILO) injection as baseline, and on days 1, 3 and 7 after SE. We assessed several features from cardiac interbeat intervals, including linear, non-linear and frequency parameters of interbeat intervals, and power spectra of interpolated intervals during epileptogenesis. After thresholding, the altered values were applied to a non-linear classifier. The non-linear classifier divided animals into two groups; with and without epilepsy, based on all collected data. We found that none of the single altered parameters in cardiac activity emerged as a sole biomarker for epileptogenesis. However, the non-linear classifier distinguished animals that later developed from those and did not develop epilepsy. The non-linear classification was performed on preliminary findings from 23 animals; six did not develop epilepsy and the rest did. The average positive predictive value (precision rate) was 78%. This was calculated based on the average sensitivity and specificity, which were 80.6% and 35.2% respectively, for the 100 classification passes. We also showed that these numbers would have increased as the number of subjects increased. Changes to the brain caused by status epilepticus that lead to epileptogenesis have systemic effects, and alter cardiac activity. A non-linear classifier performed on several extracted features of cardiac interbeat intervals may be useful as a biomarker to identify animals with low and high probability of developing epilepsy after status epilepticus. Published by Elsevier B.V.
Calcium intake and bone mineral density as an example of non-linearity and threshold analysis.
Breitling, L P
2015-04-01
Non-linearity is a likely phenomenon in bone metabolism, but is often ignored in pertinent epidemiological studies. Using NHANES III data on calcium intake and bone mineral density, the most important non-linear methods are introduced and discussed. The results should motivate researchers to consider non-linearity in this field more frequently. Many relationships in bone metabolism and homeostasis are likely to follow non-linear patterns. Detailed dose-response analyses allowing for non-linear associations nonetheless remain scarce in this field. A detailed analysis of NHANES III data on dietary calcium intake and bone mineral density was used to demonstrate the application and some of the challenges of the most important dose-response methods, including LOESS, categorical analysis, fractional polynomials, restricted cubic splines, and segmented regression. The spline estimate suggested increasing bone mineral density up to a calcium intake of about 1 g/day and a plateau thereafter. In segmented regression, the break-point marking the beginning of the plateau was placed at an intake of 0.58 (95 % confidence interval, 0.33 to 0.82) g/day. Sensitivity analyses suggested a less curved dose-response in women. Knowing about the possibilities and limitations of non-linear dose-response approaches should encourage researchers to consider these methods more frequently in studies on bone health and disease. The example analysis suggested bone mineral density to reach a plateau slightly below current calcium intake recommendations, with fairly pronounced differences of the dose-response shape by sex and menopausal status.
Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps
Directory of Open Access Journals (Sweden)
Deep Parikh
2015-08-01
Full Text Available This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current motors used in quad-copter UAV (Unmanned Aerial Vehicles. The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM. Traditionally, quad-copter BLDC motor speed control uses simple linear motor-control map defined by the motor-constant specification. However, practical BLDC motors show non-linear characteristic, particularly when operated across wide operating speed-range as is commonly required in quad-copter UAV flight operations. In this paper, our investigations to compare performance of linear versus non-linear motor-control maps are presented. The investigations cover simulation-based and experimental study of BLDC motor speed control systems for quad-copter vehicle available. First the non-linear map relating rotor RPM to motor voltage for quad-copter BLDC motor is obtained experimentally using an optical speed encoder. The performance of the linear versus non-linear motor-control-maps for the speed control are studied. The investigations also cover study of time-responses for various standard test input-signals e.g. step, ramp and pulse inputs, applied as the reference speed-commands. Also, simple 2-degree of freedom test-bed is developed in our laboratory to help test the open-loop and closed-loop experimental investigations. The non-linear motor-control map is found to perform better in BLDC motor speed tracking control performance and thereby helping achieve better quad-copter roll-angle attitude control.
An axisymmetrical non-linear finite element model for induction heating in injection molding tools
DEFF Research Database (Denmark)
Guerrier, Patrick; Nielsen, Kaspar Kirstein; Menotti, Stefano
2016-01-01
To analyze the heating and cooling phase of an induction heated injection molding tool accurately, the temperature dependent magnetic properties, namely the non-linear B-H curves, need to be accounted for in an induction heating simulation. Hence, a finite element model has been developed...... in to the injection molding tool. The model shows very good agreement with the experimental temperature measurements. It is also shown that the non-linearity can be used without the temperature dependency in some cases, and a proposed method is presented of how to estimate an effective linear permeability to use...
Estimation of non-linear site response in a deep Alpine valley
Roten, D.; Fäh, D.; Bonilla, L. F.; Alvarez-Rubio, S.; Weber, T. M.; Laue, J.
2009-09-01
We simulate non-linear behaviour of soils during strong ground motion in the Rhône valley in southern Switzerland. Previous studies of the site response using weak ground motion, ambient noise and linear 3-D FD simulations suggest that the 2-D structure of the basin will lead to amplification factors of up to 12 in the frequency band between 0.5 and 10 Hz. To estimate the importance of non-linear soil behaviour during strong ground motion in the Rhône valley we simulate the response of a superficial soft layer with a fully non-linear 1-D finite difference code. The non-linear wave propagator is based on an effective stress constitutive soil model capable of predicting pore pressure evolution due to shear. We determine the required dilatancy parameters from laboratory analysis of soil samples using cyclic triaxial tests. In order to include the effect of the strong 2-D structure in our non-linear analysis synthetic seismograms are convolved with the transfer function of the basin and then propagated through a 1-D non-linear layer. We find that reduced amplification due to soil non-linearity can be expected at rock accelerations above 0.5 ms-2, and that de-amplification occurs at ground motion levels of approximately 2 ms-2. Nevertheless, the spectral accelerations simulated for the valley centre are still exceeding the design spectra at about 0.5 Hz for magnitudes above 6.0, which reflects the strong amplification of ground motion by the deep 2-D resonance of the basin. For frequencies above 1 Hz the design spectra are generally in agreement with the strongest simulated accelerations. We evaluate the occurrence of soil failure using the 5 per cent strain criterion as a function of hypocentral distance and magnitude. Results confirm observations of liquefaction reported after the 1855 Mw 6.4 earthquake of Visp, and they suggest that soil liquefaction may occur at distances beyond those predicted by empirical relations in the valley. Near the basin edge, however
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representation. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation....... Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representaton. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation....... Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...
Non-linear cancer classification using a modified radial basis function classification algorithm.
Wang, Hong-Qiang; Huang, De-Shuang
2005-10-01
This paper proposes a modified radial basis function classification algorithm for non-linear cancer classification. In the algorithm, a modified simulated annealing method is developed and combined with the linear least square and gradient paradigms to optimize the structure of the radial basis function (RBF) classifier. The proposed algorithm can be adopted to perform non-linear cancer classification based on gene expression profiles and applied to two microarray data sets involving various human tumor classes: (1) Normal versus colon tumor; (2) acute myeloid leukemia (AML) versus acute lymphoblastic leukemia (ALL). Finally, accuracy and stability for the proposed algorithm are further demonstrated by comparing with the other cancer classification algorithms.
Non-linear molecular pattern classification using molecular beacons with multiple targets.
Lee, In-Hee; Lee, Seung Hwan; Park, Tai Hyun; Zhang, Byoung-Tak
2013-12-01
In vitro pattern classification has been highlighted as an important future application of DNA computing. Previous work has demonstrated the feasibility of linear classifiers using DNA-based molecular computing. However, complex tasks require non-linear classification capability. Here we design a molecular beacon that can interact with multiple targets and experimentally shows that its fluorescent signals form a complex radial-basis function, enabling it to be used as a building block for non-linear molecular classification in vitro. The proposed method was successfully applied to solving artificial and real-world classification problems: XOR and microRNA expression patterns. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Baxt, W G
1994-03-15
Background is presented to suggest that a great many biologic processes are chaotic. It is well known that chaotic processes can be accurately characterized by non-linear technologies. Evidence is presented that an artificial neural network, which is a known method for the application of non-linear statistics, is able to perform more accurately in identifying patients with and without myocardial infarction than either physicians or other computer paradigms. It is suggested that the improved performance may be due to the network's better ability to characterize what is a chaotic process imbedded in the problem of the clinical diagnosis of this entity.
Non-Linearities, Large Forecasters And Evidential Reasoning Under Rational Expectations
Ali al-Nowaihi; Sanjit Dhami
2005-01-01
Rational expectations is typically taken to mean that, conditional on the information set and the relevant economic theory, the expectation formed by an economic agent should be equal to its mathematical expectation. This is correct only when actual inflation is “linear” in the aggregate inflationary expectation or if it is non-linear then forecasters are “small” and use “causal reasoning”. We show that if actual in- flation is non-linear in expected inflation and (1) there are “large” foreca...
Few-photon Non-linearities in Nanophotonic Devices for Quantum Information Technology
DEFF Research Database (Denmark)
Nysteen, Anders
In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices...... by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between...