The QCD phase diagram from Schwinger-Dyson Equations
Gutierrez, Enif; Ayala, Alejandro; Bashir, Adnan; Raya, Alfredo
2013-01-01
We study the phase diagram of quantum chromodynamics (QCD). For this purpose we employ the Schwinger-Dyson equations (SDEs) technique and construct a truncation of the infinite tower of equations by demanding a matching with the lattice results for the quark-anti-quark condensate at finite temperature (T), for zero quark chemical potential (mu), that is, the region where lattice calculations are expected to provide reliable results. We compute the evolution of the phase diagram away from T=0 for increasing values of the chemical potential by following the evolution of the heat capacity as a function of T and mu. The behavior of this thermodynamic variable clearly demonstrates the existence of a cross-over for mu less than a critical value. However, the heat capacity develops a singularity near mu approx 0.22 GeV marking the onslaught of a first order phase transition characterized by the existence of a critical point. The critical line continues until mu approx 0.53 GeV where Tc=0 and thus chiral symmetry is ...
Schwinger-Dyson Equation in Minkowski Space beyond the IE Approximation
Sasagawa, Shuji
2016-01-01
We investigate properties of mass functions for fermion in Quantum Electrodynamics calculated by Schwinger-Dyson equation in strong coupling region. Numerical results for the mass functions in which one-loop integration is performed in Minkowski space. Calculated results without the instantaneous exchange approximation are compared with those obtained in Euclidean space.
System of Schwinger-Dyson equations and asymptotic behavior in the Euclidean region
Energy Technology Data Exchange (ETDEWEB)
Rochev, V. E., E-mail: vladimir.rochev@ihep.ru [National Research Center Kurchatov Institute, Institute for High Energy Physics (Russian Federation)
2015-05-15
A system of Schwinger-Dyson equations for the model of scalar-field interaction is studied in a deep Euclidean region. It is shown that there exists a critical coupling constant that separates the weak-coupling region characterized by the asymptotically free behavior and the strong-coupling region, where the asymptotic behavior of field propagators becomes ultralocal.
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
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Gurau, Razvan, E-mail: rgurau@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo (Canada)
2012-12-01
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.
Kohyama, Hiroaki
2015-01-01
We study the regularization dependence on the quenched Schwinger-Dyson equations in general gauge by applying the two types of regularizations, the four and three dimensional momentum cutoffs. The obtained results indicate that the solutions are not drastically affected by the choice of two different cutoff prescriptions. We then think that both the regularizations can nicely be adopted in the analyses for the Schwinger-Dyson equations.
Gauge covariance of the fermion Schwinger-Dyson equation in QED
Jia, Shaoyang
2016-01-01
Any practical application of the Schwinger-Dyson equations to the study of $n$-point Green's functions of a field theory requires truncations, the best known being finite order perturbation theory. Strong coupling studies require a different approach. In the case of QED, gauge covariance is a powerful constraint. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the Landau-Khalatnikov-Fradkin transformations are linear operations on the spectral densities. Here we formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger-Dyson equation for the fermion 2-point function.
Strongly-Coupled Unquenched QED4 Propagators Using Schwinger-Dyson Equations
Kizilersu, Ayse; Williams, Anthony G
2013-01-01
We study unquenched QED in four dimensions using renormalised Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kizilersu-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime and is free of kinematic singularities. We find that the KP vertex performs very well as expected specially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in the nonperturbative case with the renormalised inverse photon propagator having zero crossing.
Real-Time Thermal Schwinger-Dyson Equation for Quark Self-energy in Landau Gauge
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A(p2)p - B(p2), we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A(p2) = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.
The IR sector of QCD: lattice versus Schwinger-Dyson equations
Binosi, Daniele
2010-01-01
Important information about the infrared dynamics of QCD is encoded in the behavior of its (of-shell) Green's functions, most notably the gluon and the ghost propagators. Due to recent improvements in the quality of lattice data and the truncation schemes employed for the Schwinger-Dyson equations we have now reached a point where the interplay between these two non-perturbative tools can be most fruitful. In this talk several of the above points will be reviewed, with particular emphasis on the implications for the ghost sector, the non-perturbative effective charge of QCD, and the Kugo-Ojima function.
The IR sector of QCD: lattice versus Schwinger-Dyson equations
Binosi, Daniele
2010-12-01
Important information about the infrared dynamics of QCD is encoded in the behavior of its (of-shell) Green's functions, most notably the gluon and the ghost propagators. Due to recent improvements in the quality of lattice data and the truncation schemes employed for the Schwinger-Dyson equations we have now reached a point where the interplay between these two non-perturbative tools can be most fruitful. In this talk several of the above points will be reviewed, with particular emphasis on the implications for the ghost sector, the non-perturbative effective charge of QCD, and the Kugo-Ojima function.
Institute of Scientific and Technical Information of China (English)
ZHANG Ying; WANG Qing
2008-01-01
@@ Gauge covariance for Green's functions of a gauge theory through a fermion propagator in the presence of arbitrary external gauge field is proven and a formalism of gauge and Lorentz covariant Schwinger-Dyson equation for the fermion propagator with external gauge field is built up within ladder approximation.
Metropolis updates for Diagrammatic Monte-Carlo algorithms from Schwinger-Dyson equations
Buividovich, P V
2016-01-01
We describe a general recipe for constructing Metropolis updates for Diagrammatic Monte-Carlo (DiagMC) algorithms, based on the Schwinger-Dyson equations in quantum field theory. This approach bypasses explicit duality transformations, enumeration or classification of diagrams and can be used for lattice quantum field theories with unknown or complicated dual representations (such as non-Abelian lattice gauge theories). DiagMC algorithms constructed in this way can still be plagued by the sign problem, which is, however, completely different from the sign problem in conventional Monte-Carlo simulations and has its origin in cancellations between diagrams with positive and negative weights. To test the presented approach, we apply DiagMC to calculate the first 7 orders of 1/N expansion in the quartic matrix model and find good agreement with analytic results, with the exception of the close vicinity of the critical coupling where the critical slowing down sets in.
How to solve the Schwinger-Dyson equations once and for all gauges
Energy Technology Data Exchange (ETDEWEB)
Bashir, A [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacan 58040 (Mexico); Raya, A [Facultad de Ciencias, Universidad de Colima. Bernal DIaz del Castillo hashmark 340, Col. Villa San Sebastian, Colima, Colima 28045 (Mexico)
2006-05-15
Study of the Schwinger-Dyson equation (SDE) for the fermion propagator to obtain dynamically generated chirally asymmetric solution in any covariant gauge is a complicated numerical exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the SDE for every value of the gauge parameter. Starting from the Landau gauge where the computational complications are still manageable, we apply the Landau-Khalatnikov-Fradkin transformation (LKFT) on the dynamically generated solution and find approximate analytical results for arbitrary value of the covariant gauge parameter. We also compare our results with exact numerical solutions.
The impact of the ghost-gluon vertex on the ghost Schwinger-Dyson equations
Aguilar, A C
2014-01-01
We derive an approximate dynamical equation for the form-factor of the ghost-gluon vertex that contributes to the Schwinger-Dyson equation of the ghost dressing function in the Landau gauge. In particular, we consider the "one-loop dressed" approximation of the corresponding equation governing the evolution of the ghost-gluon vertex, using fully dressed propagators and tree-level vertices in the relevant diagrams. Within this approximation, we then compute the aforementioned form factor for two special kinematic configurations, namely the soft gluon limit, in which the momentum carried by the gluon leg is zero, and the soft ghost limit, where the momentum of the anti-ghost leg vanishes. The results obtained display a considerable departure from the tree-level value, and are in rather good agreement with available lattice data. We next solve numerically the coupled system formed by the equation of the ghost dressing function and that of the the vertex form factor, in the soft ghost limit. Our results demonstra...
Schwinger-Dyson equation for quarks in a QCD inspired model
Shilin, V I; Pervushin, V N
2016-01-01
We discuss formulation of QCD in Minkowski-spacetime and effect of an operator product expansion by means of normal ordering of fields in the QCD Lagrangian. The formulation of QCD in the Minkowski-spacetime allows us to solve a constraint equation and decompose the gauge field propagator in the sum of an instantaneous part, which forms a bound state, and a retarded part, which contains the relativistic corrections. In Quantum Field Theory, if we not start with Lagrangian as normal ordering function of all operator fields, one can make normal ordering by means of the operator product expansion, then the gluon condensate appear. This gives us a natural way of obtaining a dimensional parameter in QCD, which is missing in the QCD Lagrangian. We derive a Schwinger-Dyson equation for a quark, which is studied both numerically and analytically. The critical value of the strong coupling constant $\\alpha_s = 4/{\\pi}$, above which a nontrivial solution appears and a spontaneous chiral symmetry breaking occurs, is foun...
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
Buividovich, P V
2010-01-01
We study stochastic methods for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of so-called nonlinear random processes. The set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansion of the theory. We describe stochastic algorithms for summation of planar diagrams in matrix-valued scalar field theory and in the Weingarten model of random planar surfaces on the lattice. For compact field variables, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into the self-consistent redefinition of expansion parameters. Stochastic solution of the self-consistency conditions can be implemented as a random process with memory. We illustrate this idea on the example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice gauge theories is discussed.
Energy Technology Data Exchange (ETDEWEB)
Baker, M.
1979-01-01
It was shown using the Schwinger-Dyson equations and the Slavnov-Taylor identities of Yang-Mills theory that no inconsistency arises if the gluon propagator behaves like (1/p/sup 2/)/sup 2/ for small p/sup 2/. To see whether the theory actually contains such singular long range behavior, a nonperturbative closed set of equations was formulated by neglecting the transverse parts of GAMMA and GAMMA/sub 4/ in the Schwinger-Dyson equations. This simplification preserves all the symmetries of the theory and allows the possibility for a singular low-momentum behavior of the gluon propagator. The justification for neglecting GAMMA/sup (T)/ and GAMMA/sub 4//sup (T)/ is not evident but it is expected that the present study of the resulting equations will elucidate this simplification, which leads to a closed set of equations.
Schwinger-Dyson functional in Chern-Simons theory
Guadagnini, Enore
2016-01-01
In perturbative SU(N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that the renormalized Schwinger-Dyson functional is related with the generating functional of the correlation functions of the gauge connections by some kind of duality transformation.
Schwinger-Dyson functional in Chern-Simons theory
Guadagnini, E.
2016-11-01
In perturbative SU (N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that the renormalized Schwinger-Dyson functional is related with the generating functional of the correlation functions of the gauge connections by some kind of duality transformation.
Institute of Scientific and Technical Information of China (English)
XIE Chuan-Mei; LI Heng-Mei; WAN Shao-Long
2009-01-01
The wave functions and electromagnetic form factor of charged scalar mesons are studied with a modified vector-vector flat-bottom potential model under the framework of the Schwinger-Dyeon and Bethe-Salpeter equations.The obtained results agree well with other theories.
Quark scalar, axial and tensor charges in the Schwinger-Dyson formalism
Energy Technology Data Exchange (ETDEWEB)
Yamanaka, Nodoka [2-1 Hirosawa, Wako, 351-0198 Saitama (Japan)
2016-01-22
The quark scalar, axial and tensor charges of nucleon are calculated in the Schwinger-Dyson formalism. We first calculate these charges in the rainbow-ladder truncation using the IR cut quark-gluon vertex, and show that the result is in agreement with the known data. We then perform the same calculation with the phenomenological IR singular quark-gluon vertex. In this case, the Schwinger-Dyson equation does not converge. We show that this result suggests the requirement of additional corrections to the rainbow-ladder truncation, due to the interaction between quark and gluons in the deep IR region.
Krishnaswami, G.S.
2008-01-01
We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G( ), are quadratic equations
Energy Technology Data Exchange (ETDEWEB)
Krishnaswami, Govind S [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Postbus 80.195, 3508 TD, Utrecht (Netherlands)], E-mail: govind.krishnaswami@durham.ac.uk
2008-04-11
We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G({xi}), are quadratic equations S{sup i}G=G{xi}{sup i}G in concatenation of correlations. The Schwinger-Dyson operator S{sup i} is built from the left annihilation operator, which does not satisfy the Leibnitz rule with respect to concatenation. So the loop equations are not differential equations. We show that left annihilation is a derivation of the graded shuffle product of gluon and ghost correlations. The shuffle product is the point-wise product of Wilson loops, expressed in terms of correlations. So in the limit where concatenation is approximated by shuffle products, the loop equations become differential equations. Remarkably, the Schwinger-Dyson operator as a whole is also a derivation of the graded shuffle product. This allows us to turn the loop equations into linear equations for the shuffle reciprocal, which might serve as a starting point for an approximation scheme.
Institute of Scientific and Technical Information of China (English)
WANG ZhiGang; WAN ShaoLong; WANG KeLin
2001-01-01
The kaon electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson equation in rainbow approximation and Bethe-Salpeter equation in ladder approximation with the modified fiat-bottom potential,which is the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All our numerical results give good fit to experimental values and other theoretical results.``
Krishnaswami, Govind S
2008-01-01
For a class of large-N multi-matrix models, we identify a group G that plays the same role as the group of loops on space-time does for Yang-Mills theory. G is the spectrum of a commutative shuffle-deconcatenation Hopf algebra that we associate to correlations. G is the exponential of the free Lie algebra. The generating series of correlations is a function on G and satisfies quadratic equations in convolution. These factorized Schwinger-Dyson or loop equations involve a collection of Schwinger-Dyson operators, which are shown to be right-invariant vector fields on G, one for each linearly independent primitive of the Hopf algebra. A large class of formal matrix models satisfying these properties are identified, including as special cases, the zero momentum limits of the Gaussian, Chern-Simons and Yang-Mills field theories. Moreover, the Schwinger-Dyson operators of the continuum Yang-Mills action are shown to be right-invariant derivations of the shuffle-deconcatenation Hopf algebra generated by sources labe...
Imai, Shotaro
2014-01-01
In terms of the structure of exotic hadrons and heavy hadronic states, diquarks have been considered as important effective degrees of freedom. The diquark is composed of two quarks with gluonic interaction, and it still strongly interacts with gluons because of its non-zero color charge. We investigate the gluonic dressing effect for a scalar diquark using the Schwinger-Dyson formalism in the Landau gauge. The scalar diquark is treated as an extended fundamental field like a meson in effective hadron models. The Schwinger-Dyson equation for the scalar diquark diagrammatically has an additional 4-point interaction term, in comparison with the single quark case. Here, we introduce an effective size of the diquark inside a hadron, since it is a bound-state-like object of two quarks. The effective size and the bare mass of the diquark are free parameters in this scalar theory. The diquark effective size $R$ can be taken to be smaller than a hadron, $R\\sim 1$ fm, and larger than a constituent quark, $R\\sim 0.3$ f...
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
The tanh-coth method combined with the Riccati equation for solving non-linear equation
Energy Technology Data Exchange (ETDEWEB)
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
Non-linear equation: energy conservation and impact parameter dependence
Kormilitzin, Andrey
2010-01-01
In this paper we address two questions: how energy conservation affects the solution to the non-linear equation, and how impact parameter dependence influences the inclusive production. Answering the first question we solve the modified BK equation which takes into account energy conservation. In spite of the fact that we used the simplified kernel, we believe that the main result of the paper: the small ($\\leq 40%$) suppression of the inclusive productiondue to energy conservation, reflects a general feature. This result leads us to believe that the small value of the nuclear modification factor is of a non-perturbative nature. In the solution a new scale appears $Q_{fr} = Q_s \\exp(-1/(2 \\bas))$ and the production of dipoles with the size larger than $2/Q_{fr}$ is suppressed. Therefore, we can expect that the typical temperature for hadron production is about $Q_{fr}$ ($ T \\approx Q_{fr}$). The simplified equation allows us to obtain a solution to Balitsky-Kovchegov equation taking into account the impact pa...
Estimation of saturation and coherence effects in the KGBJS equation - a non-linear CCFM equation
Deak, Michal
2012-01-01
We solve the modified non-linear extension of the CCFM equation - KGBJS equation - numerically for certain initial conditions and compare the resulting gluon Green functions with those obtained from solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.
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...
A Master Equation for Multi-Dimensional Non-Linear Field Theories
Park, Q H
1992-01-01
A master equation ( $n$ dimensional non--Abelian current conservation law with mutually commuting current components ) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik
2004-01-01
The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... 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...
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
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.
Institute of Scientific and Technical Information of China (English)
陈化; 罗壮初
2002-01-01
In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct × Cnx. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct × Cnx.
A scalar hyperbolic equation with GR-type non-linearity
Khokhlov, A M
2003-01-01
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate balance between linear and non-linear terms. We formulate two classes of second-order accurate central-difference schemes, CFLN and MOL, for numerical integration of this equation. Solutions produced by the schemes converge to exact solutions at any fixed time $t$ when numerical resolution is increased. However, in certain cases integration becomes asymptotically unstable when $t$ is increased and resolution is kept fixed. This behavior is caused by subtle changes in the balance between linear and non-linear terms when the equation is discretized. Changes in the balance occur without violating second-order accuracy of discretization. We thus demonstrate that a second-order accuracy, althoug necessary for convergence at finite $t$, does not guarantee a correct asymptotic behavior...
Application of homotopy-perturbation to non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cveticanin, L. [Faculty of Technical Sciences, 21000 Novi Sad, Trg D. Obradovica 6 (Serbia)], E-mail: cveticanin@uns.ns.ac.yu
2009-04-15
In this paper He's homotopy perturbation method has been adopted for solving non-linear partial differential equations. An approximate solution of the differential equation which describes the longitudinal vibration of a beam is obtained. The solution is compared with that found using the variational iteration method introduced by He. The difference between the two solutions is negligible.
Two-body bound states & the Bethe-Salpeter equation
Energy Technology Data Exchange (ETDEWEB)
Pichowsky, M. [Argonne National Lab., IL (United States); Kennedy, M. [Univ. of New Hampshire, Durham, NH (United States). Physics Dept.; Strickland, M. [Duke Univ., Durham, NC (United States)
1995-01-18
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated.
Non-local investigation of bifurcations of solutions of non-linear elliptic equations
Energy Technology Data Exchange (ETDEWEB)
Il' yasov, Ya Sh
2002-12-31
We justify the projective fibration procedure for functionals defined on Banach spaces. Using this procedure and a dynamical approach to the study with respect to parameters, we prove that there are branches of positive solutions of non-linear elliptic equations with indefinite non-linearities. We investigate the asymptotic behaviour of these branches at bifurcation points. In the general case of equations with p-Laplacian we prove that there are upper bounds of branches of positive solutions with respect to the parameter.
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.
Institute of Scientific and Technical Information of China (English)
Pascale KULISA; Cédric DANO
2006-01-01
Three linear two-equation turbulence models k- ε, k- ω and k- 1 and a non-linear k- l model are used for aerodynamic and thermal turbine flow prediction. The pressure profile in the wake and the heat transfer coefficient on the blade are compared with experimental data. Good agreement is obtained with the linear k- l model. No significant modifications are observed with the non-linear model. The balance of transport equation terms in the blade wake is also presented. Linear and non-linear k- l models are evaluated to predict the threedimensional vortices characterising the turbine flows. The simulations show that the passage vortex is the main origin of the losses.
Series solutions of non-linear Riccati differential equations with fractional order
Energy Technology Data Exchange (ETDEWEB)
Cang Jie; Tan Yue; Xu Hang [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China); Liao Shijun [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: sjliao@sjtu.edu.cn
2009-04-15
In this paper, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h. Besides, it is proved that well-known Adomian's decomposition method is a special case of the homotopy analysis method when h = -1. This work illustrates the validity and great potential of the homotopy analysis method for the non-linear differential equations with fractional order. The basic ideas of this approach can be widely employed to solve other strongly non-linear problems in fractional calculus.
Asymptotic theory for weakly non-linear wave equations in semi-infinite domains
Directory of Open Access Journals (Sweden)
Chirakkal V. Easwaran
2004-01-01
Full Text Available We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Lipschitz Operators and the Solvability of Non-linear Operator Equations
Institute of Scientific and Technical Information of China (English)
Huai Xin CAO; Zong Ben XU
2004-01-01
Let U and V be Banach spaces, L and N be non-linear operators from U into V. L is some basic properties of Lipschitz operators and then discuss the unique solvability, exact solvability,approximate solvability of the operator equations Lx = y and Lx + Nx = y. Under some conditions we prove the equivalence of these solvabilities. We also give an estimation for the relative-errors of the solutions of these two systems and an application of our method to a non-linear control system.
A solution to the non-linear equations of D=10 super Yang-Mills theory
Mafra, Carlos R
2015-01-01
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.
A method for solving systems of non-linear differential equations with moving singularities
Gousheh, S S; Ghafoori-Tabrizi, K
2003-01-01
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution.
Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions
Linander, Hampus; Nilsson, Bengt E. W.
2016-07-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F = 0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.
Canonical structure of evolution equations with non-linear dispersive terms
Indian Academy of Sciences (India)
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
A Bohmian approach to the perturbations of non-linear Klein--Gordon equation
Indian Academy of Sciences (India)
FARAMARZ RAHMANI; MEHDI GOLSHANI; MOHSEN SARBISHEI
2016-08-01
In the framework of Bohmian quantum mechanics, the Klein--Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave $\\phi(x)$ in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein--Gordon equation? We examine this approach for $\\phi_{4}(x)$ and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.
A computerized implementation of a non-linear equation to predict barrier shielding requirements.
Chamberlain, A C; Strydom, W J
1997-04-01
A non-linear equation to predict barrier shielding thickness from the work function of x- and gamma-ray generators is presented. This equation is incorporated into a model that takes into account primary, scatter, and leakage radiation components to determine the amount of shielding necessary. The case of multiple wall materials is also considered. The equation accurately models the radiation attenuation curves given in NCRP 49 for concrete and lead, thus eliminating the necessity to use graphical or tabular methods to calculate shielding thickness, which can be inaccurate.
Superdiffusions and positive solutions of non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Dynkin, E B [Cornell University, New York (United States)
2004-02-28
By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.
High order explicit symplectic integrators for the Discrete Non Linear Schr\\"odinger equation
Boreux, Jehan; Hubaux, Charles
2010-01-01
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes, that result to be explicit methods and thus very fast. The performances of the integrators are discussed, studied as functions of the integration time step and compared with some non symplectic methods.
On the non-linearity of the master equation describing spin-selective radical-ion-pair reactions
Kominis, I. K.
2010-01-01
We elaborate on the physical meaning of the non-linear master equation that was recently derived to account for spin-selective radical-ion-pair reactions. Based on quite general arguments, we show that such a non-linear master equation is indeed to be expected.
The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
Linander, Hampus
2016-01-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using $F=0$ to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this n...
Variational principle and a perturbative solution of non-linear string equations in curved space
Roshchupkin, S N
1999-01-01
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H
Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras
Zinn-Justin, P
1998-01-01
A set of coupled non-linear integral equations is derived for a class of models connected with the quantum group $U_q(\\hat g)$ ($q=e^{i\\gamma}$ and $g$ simply laced Lie algebra), which are solvable using the Bethe Ansatz; these equations describe arbitrary excited states of a system with finite spatial length $L$. They generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring model to affine Toda field theory with imaginary coupling constant. As an application, the central charge and all the conformal weights of the UV conformal field theory are extracted in a straightforward manner. The quantum group truncation for rational values of $\\gamma/\\pi$ is discussed in detail; in the UV limit we recover through this procedure the RCFTs with extended $W(g)$ conformal symmetry.
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.
Zia, Haider
2017-06-01
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.
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...
KPP reaction-diffusion equations with a non-linear loss inside a cylinder
Giletti, Thomas
2010-01-01
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
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.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Performance prediction of gas turbines by solving a system of non-linear equations
Energy Technology Data Exchange (ETDEWEB)
Kaikko, J.
1998-09-01
This study presents a novel method for implementing the performance prediction of gas turbines from the component models. It is based on solving the non-linear set of equations that corresponds to the process equations, and the mass and energy balances for the engine. General models have been presented for determining the steady state operation of single components. Single and multiple shad arrangements have been examined with consideration also being given to heat regeneration and intercooling. Emphasis has been placed upon axial gas turbines of an industrial scale. Applying the models requires no information of the structural dimensions of the gas turbines. On comparison with the commonly applied component matching procedures, this method incorporates several advantages. The application of the models for providing results is facilitated as less attention needs to be paid to calculation sequences and routines. Solving the set of equations is based on zeroing co-ordinate functions that are directly derived from the modelling equations. Therefore, controlling the accuracy of the results is easy. This method gives more freedom for the selection of the modelling parameters since, unlike for the matching procedures, exchanging these criteria does not itself affect the algorithms. Implicit relationships between the variables are of no significance, thus increasing the freedom for the modelling equations as well. The mathematical models developed in this thesis will provide facilities to optimise the operation of any major gas turbine configuration with respect to the desired process parameters. The computational methods used in this study may also be adapted to any other modelling problems arising in industry. (orig.) 36 refs.
Mártin, Daniel A; 10.1103/PhysRevE.80.056601
2012-01-01
We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative refraction index material with third order effective electric and magnetic non-linearities. Two coupled non-linear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.
A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-05-15
In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.
Particular solutions of the equation for the quark propagator in the infra-red region of QCD
Energy Technology Data Exchange (ETDEWEB)
Arbuzov, B.A.; Davydychev, A.I.; Kurennoy, S.S.
1987-01-01
A number of particular solutions of the Schwinger-Dyson equation for the quark propagator in the infra-red region of QCD is obtained taking account of the gauge identities. The solutions are of a nonperturbative character, some of them break the chiral invariance. The obtained solutions are analysed with the help of the effective potential method.
Directory of Open Access Journals (Sweden)
Kim Gaik Tay
2010-04-01
Full Text Available In the present work, by considering the artery as a prestressed thin-walled elastic tube with a symmetrical stenosis and the blood as an incompressible viscous fluid, we have studied the amplitude modulation of nonlinear waves in such a composite medium through the use of the reductive perturbation method [23]. The governing evolutions can be reduced to the dissipative non-linear Schrodinger (NLS equation with variable coefficient. The progressive wave solution to the above non-linear evolution equation is then sought.
Imbert, Cyril
2009-01-01
The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic i...
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.
DIFFERENCE METHODS FOR A NON-LINEAR ELLIPTIC SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS,
DIFFERENCE EQUATIONS, ITERATIONS), (*ITERATIONS, DIFFERENCE EQUATIONS), (* PARTIAL DIFFERENTIAL EQUATIONS , BOUNDARY VALUE PROBLEMS), EQUATIONS, FUNCTIONS(MATHEMATICS), SEQUENCES(MATHEMATICS), NONLINEAR DIFFERENTIAL EQUATIONS
Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles
Shakra, Farah Abou
2012-01-01
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.
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.
Anderson, Johan; Johansson, Jonas
2016-12-01
An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to \\exp ≤ft(-cw23/2\\right) , where w 2 is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.
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....
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Energy Technology Data Exchange (ETDEWEB)
Aminov, G. [ITEP, Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation); Mironov, A. [ITEP, Moscow (Russian Federation); Lebedev Physics Institute, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation)
2016-08-15
Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N = 3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter. (orig.)
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Aminov, G; Morozov, A
2016-01-01
Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta-functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N=3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.
Classical Field-Theoretical approach to the non-linear q-Klein-Gordon Equation
Plastino, A
2016-01-01
In the wake of efforts made in [EPL {\\bf 97}, 41001 (2012)], we extend them here by developing a classical field theory (FT)to the q-Klein-Gordon equation advanced in [Phys. Rev. Lett. {\\bf 106}, 140601 (2011)]. This makes it possible to generate a hipotetical conjecture regarding black matter. We also develop the classical field theory for a q-Schrodinger equation, different from the one in [EPL {\\bf 97}, 41001 (2012)], that was deduced in [Phys. Lett. A {\\bf 379}, 2690 (2015)] from the hypergeometric differential equation. Our two classical theories reduce to the usual quantum FT for $q\\rightarrow 1$.
Khachatryan, Kh A.
2015-04-01
We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate non-linear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
Chapline, George
2015-01-01
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations fo...
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Perturbative treatment of the non-linear q-Schr\\"odinger and q-Klein-Gordon equations
Zamora, D J; Plastino, A; Ferri, G L
2016-01-01
Interesting nonlinear generalization of both Schr\\"odinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\\bf 106}, 140601 (2011)]. There is much current activity going on in this area. The non-linearity is governed by a real parameter $q$. It is a fact that the ensuing non linear q-Schr\\"odinger and q-Klein-Gordon equations are natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for $q-$values close to unity [Nucl. Phys. A {\\bf 955}, 16 (2016), Nucl. Phys. A {\\bf 948}, 19 (2016)]. It is also well known that q-exponential behavior is found in quite different settings. An explanation for such phenomenon was given in [Physica A {\\bf 388}, 601 (2009)] with reference to empirical scenarios in which data are collected via set-ups that effect a normalization plus data's pre-processing. Precisely, the ensuing normalized output was there shown to be q-exponentially distributed if the input dat...
Madsen, Niels K; Godtliebsen, Ian H; Christiansen, Ove
2017-04-07
Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
Progress in solutions of the non-linear Boussinesq groundwater equation (Invited)
Dias, N. L.; Chor, T. L.; de Zarate, A. R.
2013-12-01
An existing truncated series solution, previously obtained from inversion techniques from the solution for the Blasius boundary-layer equation, is obtained directly for the Boussinesq equation in terms of a recurrence relation. The series is found to have a finite radius of convergence, which also explains why previous approximations to the solution of the Boussinesq equation had to resort to a combination of series/Padé expressions for small values of the independent variable and asymptotic approximations for large ones. The radius of convergence is obtained numerically to a high accuracy by means of path integration techniques that are able to identify the complex-plane singularities which determine that radius. New variable transformations are proposed for numerical integration of the equation that avoid singularities at the origin, and further asymptotic approximations, which remain necessary due to the finite radius of convergence, are also obtained. The approach can be extended to non-homogeneous boundary conditions at the origin, which is important in realistic scenarios where an aquifer discharges into a channel of finite-depth. Further recurrence relations are found for series solutions of the non-homogeneous case, as well as their radii of convergence and corresponding asymptotic approximations. Results obtained by joining ten terms of the series solution and the asymptotic approximation obtained by Heaslet and Alksne (1961).
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Explosive Solutions of Elliptic Equations with Absorption and Non-Linear Gradient Term
Indian Academy of Sciences (India)
Marius Ghergu; Constantin Niculescu; Vicenţiu Rădulescu
2002-08-01
Let be a non-decreasing $C^1$-function such that $f > 0$ on $(0, ∞), f(0) = 0, \\int_1^∞ 1/\\sqrt{F(t)}dt < ∞$ and $F(t)/f^{2/a}(t)→ 0$ as $t →∞$, where $F(t) = \\int_0^t f(s)ds$ and $a \\in (0,2]$. We prove the existence of positive large solutions to the equation $ u + q(x)|\
A General Method for Solving Systems of Non-Linear Equations
Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)
1995-01-01
The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.
Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities
Directory of Open Access Journals (Sweden)
Ana M. Martín-Caraballo
2015-08-01
Full Text Available but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position method and the tangent (or Newton-Raphson method, this last as example of fixed-point methods.
Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
Akant, L; Akant, Levent; Krishnaswami, Govind S.
2007-01-01
This work concerns single-trace correlations of Euclidean multi-matrix models. In the large-N limit we show that Schwinger-Dyson equations imply loop equations and non-anomalous Ward identities. Loop equations are associated to generic infinitesimal changes of matrix variables (vector fields). Ward identities correspond to vector fields preserving measure and action. The former are analogous to Makeenko-Migdal equations and the latter to Slavnov-Taylor identities. Loop equations correspond to leading large-N Schwinger-Dyson equations. Ward identities correspond to 1/N^2 suppressed Schwinger-Dyson equations. But they become leading equations since loop equations for non-anomalous vector fields are vacuous. We show that symmetries at infinite N persist at finite N, preventing mixing with multi-trace correlations. For one matrix, there are no non-anomalous infinitesimal symmetries. For two or more matrices, measure preserving vector fields form an infinite dimensional graded Lie algebra, and action preserving on...
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...... the computational performance, it is applied to the analysis of a compliant foil bearing modelled using the simple elastic foundation model. The model is derived and perturbed using complex notation. Top foil sagging effect is added to the bump foil compliance in terms of a close-form periodic function. For a foil...... bearing utilized in an industrial turbo compressor, the influence of boundary conditions and sagging on the pressure profile, shaft equilibrium position and dynamic coefficients is numerically simulated. The proposed scheme is faster, leading to the conclusion that it is suitable, not only for steady...
Stahl, A.; Landreman, M.; Embréus, O.; Fülöp, T.
2017-03-01
Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modeling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Stahl, A; Embréus, O; Fülöp, T
2016-01-01
Energetic electrons are of interest in many types of plasmas, however previous modelling of their properties have been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modelling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Directory of Open Access Journals (Sweden)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Energy Technology Data Exchange (ETDEWEB)
Fike, Jeffrey A.
2013-08-01
The construction of stable reduced order models using Galerkin projection for the Euler or Navier-Stokes equations requires a suitable choice for the inner product. The standard L2 inner product is expected to produce unstable ROMs. For the non-linear Navier-Stokes equations this means the use of an energy inner product. In this report, Galerkin projection for the non-linear Navier-Stokes equations using the L2 inner product is implemented as a first step toward constructing stable ROMs for this set of physics.
Energy Technology Data Exchange (ETDEWEB)
Jan Hesthaven
2012-02-06
Final report for DOE Contract DE-FG02-98ER25346 entitled Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Principal Investigator Jan S. Hesthaven Division of Applied Mathematics Brown University, Box F Providence, RI 02912 Jan.Hesthaven@Brown.edu February 6, 2012 Note: This grant was originally awarded to Professor David Gottlieb and the majority of the work envisioned reflects his original ideas. However, when Prof Gottlieb passed away in December 2008, Professor Hesthaven took over as PI to ensure proper mentoring of students and postdoctoral researchers already involved in the project. This unusual circumstance has naturally impacted the project and its timeline. However, as the report reflects, the planned work has been accomplished and some activities beyond the original scope have been pursued with success. Project overview and main results The effort in this project focuses on the development of high order accurate computational methods for the solution of hyperbolic equations with application to problems with strong shocks. While the methods are general, emphasis is on applications to gas dynamics with strong shocks.
Non-Linear Integral Equation and excited-states scaling functions in the sine-Gordon model
Destri, C
1997-01-01
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six vertex model.
The Numerical Approximation of Functional Differential Equations
Venturi, Daniele
2016-01-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equations), quantum field theory (Schwinger-Dyson equations) and statistical physics (equations for generating functionals and effective action methods). However, no effective numerical method has yet been developed to compute their solution. The purpose of this manuscript is to fill this gap, and provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
Fukuda, Hiroki; Suwa, Hideaki; Nakano, Atsushi; Sakamoto, Mari; Imazu, Miki; Hasegawa, Takuya; Takahama, Hiroyuki; Amaki, Makoto; Kanzaki, Hideaki; Anzai, Toshihisa; Mochizuki, Naoki; Ishii, Akira; Asanuma, Hiroshi; Asakura, Masanori; Washio, Takashi; Kitakaze, Masafumi
2016-11-01
Brain natriuretic peptide (BNP) is the most effective predictor of outcomes in chronic heart failure (CHF). This study sought to determine the qualitative relationship between the BNP levels at discharge and on the day of cardiovascular events in CHF patients. We devised a mathematical probabilistic model between the BNP levels at discharge (y) and on the day (t) of cardiovascular events after discharge for 113 CHF patients (Protocol I). We then prospectively evaluated this model on another set of 60 CHF patients who were readmitted (Protocol II). P(t|y) was the probability of cardiovascular events occurring after >t, the probability on t was given as p(t|y) = -dP(t|y)/dt, and p(t|y) = pP(t|y) = αyβP(t|y), along with p = αyβ (α and β were constant); the solution was p(t|y) = αyβ exp(-αyβt). We fitted this equation to the data set of Protocol I using the maximum likelihood principle, and we obtained the model p(t|y) = 0.000485y0.24788 exp(-0.000485y0.24788t). The cardiovascular event-free rate was computed as P(t) = 1/60Σi=1,…,60 exp(-0.000485yi0.24788t), based on this model and the BNP levels yi in a data set of Protocol II. We confirmed no difference between this model-based result and the actual event-free rate. In conclusion, the BNP levels showed a non-linear relationship with the day of occurrence of cardiovascular events in CHF patients.
Ender, I A; Flegontova, E Yu; Gerasimenko, A B
2016-01-01
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.;
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the non-linear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local non-linear analysis. The various methods of analysis combine to provide significant...
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
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
Directory of Open Access Journals (Sweden)
Kesavan.E
2013-04-01
Full Text Available This paper suggests an idea to design an adaptive PID controller for Non-linear liquid tank System and is implemented in PLC. Online estimation of linear parameters (Time constant and Gain brings an exact model of the process to take perfect control action. Based on these estimated values, the controller parameters will be well tuned by internal model control. Internal model control is an unremarkably used technique and provides well tuned controller in order to have a good controlling process. PLC with its ability to have both continues control for PID Control and digital control for fault diagnosis which ascertains faults in the system and provides alerts about the status of the entire process.
Energy Technology Data Exchange (ETDEWEB)
Zhu Shundong [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)], E-mail: zhusd1965@sina.com
2008-09-15
The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by the generalizing Riccati equation mapping method and picking up its new solutions. In order to test the validity of this approach, the (2 + 1)-dimensional Boiti-Leon-Pempinelle equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.
Energy Technology Data Exchange (ETDEWEB)
Merton, S. R.; Smedley-Stevenson, R. P. [Computational Physics Group, AWE Aldermaston, Reading, Berkshire RG7 4PR (United Kingdom); Pain, C. C. [Dept. of Earth Science and Engineering, Imperial College London, London SW7 2AZ (United Kingdom)
2012-07-01
This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
The vector Maxwell equations of nonlinear optics coupled to a single Lorentz oscillator and with instantaneous Kerr nonlinearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...... to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether's theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including...
Directory of Open Access Journals (Sweden)
Briti Sundar Sil
2016-01-01
Full Text Available Flood routing is of utmost importance to water resources engineers and hydrologist. Muskingum model is one of the popular methods for river flood routing which often require a huge computational work. To solve the routing parameters, most of the established methods require knowledge about different computer programmes and sophisticated models. So, it is beneficial to have a tool which is comfortable to users having more knowledge about everyday decision making problems rather than the development of computational models as the programmes. The use of micro-soft excel and its relevant tool like solver by the practicing engineers for normal modeling tasks has become common over the last few decades. In excel environment, tools are based on graphical user interface which are very comfortable for the users for handling database, modeling, data analysis and programming. GANetXL is an add-in for Microsoft Excel, a leading commercial spreadsheet application for Windows and MAC operating systems. GANetXL is a program that uses a Genetic Algorithm to solve a wide range of single and multi-objective problems. In this study, non-linear Muskingum routing parameters are solved using GANetXL. Statistical Model performances are compared with the earlier results and found satisfactory.
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Panda, Nishant; Dawson, Clint; Zhang, Yao; Kennedy, Andrew B.; Westerink, Joannes J.; Donahue, Aaron S.
2014-09-01
A local discontinuous Galerkin method for Boussinesq-Green-Naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal. Currently Green-Naghdi equations have many variants. In this paper a numerical method in one dimension is presented for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations for both the analytical problem and the numerical method. Verification is done against a linearized standing wave problem in flat bathymetry and h, p (denoted by K in this paper) error rates are plotted. Validation plots show good agreement of the numerical results with the experimental ones.
Post, U.; Kunz, J.; Mosel, U.
1987-01-01
We present a new method for the solution of the coupled differential equations which have to be solved in various field-theory models. For the solution of the eigenvalue problem a modified version of the imaginary time-step method is applied. Using this new scheme we prevent the solution from running into the negative-energy sea. For the boson fields we carry out a time integration with an additional damping term which forces the field to converge against the static solution. Some results are given for the Walecka model and the Friedberg-Lee model.
Carlen, Eric A.; Fröhlich, Jürg; Lebowitz, Joel
2016-02-01
We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrödinger equation with a focusing nonlinearity of order p transitions" and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein-Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to ∞. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and "chemical potential" determined by the stochastic noise term.
Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.; Chupakhin, A. P.
2016-06-01
This article considers method of describing the behaviour of hemodynamic parameters near vascular pathologies. We study the influence of arterial aneurysms and arteriovenous malformations on the vascular system. The proposed method involves using generalized model of Van der Pol-Duffing to find out the characteristic behaviour of blood flow parameters. These parameters are blood velocity and pressure in the vessel. The velocity and pressure are obtained during the neurosurgery measurements. It is noted that substituting velocity on the right side of the equation gives good pressure approximation. Thus, the model reproduces clinical data well enough. In regard to the right side of the equation, it means external impact on the system. The harmonic functions with various frequencies and amplitudes are substituted on the right side of the equation to investigate its properties. Besides, variation of the right side parameters provides additional information about pressure. Non-linear analogue of Nyquist diagrams is used to find out how the properties of solution depend on the parameter values. We have analysed 60 cases with aneurysms and 14 cases with arteriovenous malformations. It is shown that the diagrams are divided into classes. Also, the classes are replaced by another one in the definite order with increasing of the right side amplitude.
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....
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...... on the governing equations and methods of implementing....
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...
Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt
2012-12-01
Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.
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.......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...
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Oscillatons formed by non linear gravity
Obregón, O; Schunck, F E; Obregon, Octavio; Schunck, Franz E.
2004-01-01
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.
Açıkyıldız, Metin; Gürses, Ahmet; Güneş, Kübra; Yalvaç, Duygu
2015-11-01
The present study was designed to compare the linear and non-linear methods used to check the compliance of the experimental data corresponding to the isotherm models (Langmuir, Freundlich, and Redlich-Peterson) and kinetics equations (pseudo-first order and pseudo-second order). In this context, adsorption experiments were carried out to remove an anionic dye, Remazol Brillant Yellow 3GL (RBY), from its aqueous solutions using a commercial activated carbon as a sorbent. The effects of contact time, initial RBY concentration, and temperature onto adsorbed amount were investigated. The amount of dye adsorbed increased with increased adsorption time and the adsorption equilibrium was attained after 240 min. The amount of dye adsorbed enhanced with increased temperature, suggesting that the adsorption process is endothermic. The experimental data was analyzed using the Langmuir, Freundlich, and Redlich-Peterson isotherm equations in order to predict adsorption isotherm. It was determined that the isotherm data were fitted to the Langmuir and Redlich-Peterson isotherms. The adsorption process was also found to follow a pseudo second-order kinetic model. According to the kinetic and isotherm data, it was found that the determination coefficients obtained from linear method were higher than those obtained from non-linear method.
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].
Institute of Scientific and Technical Information of China (English)
Shu-hua Zhang; Tao Lin; Yan-ping Lin; Ming Rao
2001-01-01
In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Pastor, J
2004-07-01
We have determined the equation of state of nuclear matter according to relativistic non-linear models. In particular, we are interested in regions of high density and/or high temperature, in which the thermodynamic functions have very different behaviours depending on which model one uses. The high-density behaviour is, for example, a fundamental ingredient for the determination of the maximum mass of neutron stars. As an application, we have studied the process of two-pion annihilation into e{sup +}e{sup -} pairs in dense and hot matter. Accordingly, we have determined the way in which the non-linear terms modify the meson propagators occurring in this process. Our results have been compared with those obtained for the meson propagators in free space. We have found models that give an enhancement of the dilepton production rate in the low invariant mass region. Such an enhancement is in good agreement with the invariant mass dependence of the data obtained in heavy ions collisions at CERN/SPS energies. (author)
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
Ahlkrona, Josefin; Kirchner, Nina; Zwinger, Thomas
2015-01-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains under long time-intervals. The method couples the exact, full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem where the number of degrees of freedom is comparable to a real world application, ISCAL performs almost an order of magnitude faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
Ahlkrona, Josefin; Lötstedt, Per; Kirchner, Nina; Zwinger, Thomas
2016-03-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
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.
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
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...
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
Non-linear dynamics of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
by the rotation of the aerodynamic load and the curvature, as well as inertial induced non-linearities caused by the support point motion. The non-linear partial differential equations of motion in the moving frame of reference have been discretized, using the fixed base eigenmodes as a functional basis......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...
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...
Institute of Scientific and Technical Information of China (English)
M·T·穆斯塔法; K·玛苏德
2009-01-01
应用Lie对称法,当弹性能具有三阶非调和修正项时,分析纵向变形的非线性弹性波动方程.通过不同对称下的恒等条件,寻找对称代数,并将它简化为二阶常微分方程.对该简化的常微分方程作进一步分析后,获得若干个显式的精确解.分析Apostol的研究成果(Apostol B F.on a non-linear wave equation in elasticity.Phys Lett A,2003,318(6):545-552)发现,非调和修正项通常导致解在有限时间内具有时间相关奇异性.除了得到时间相关奇异性的解外,还得到无法显示时间相关奇异性的解.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
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...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
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...
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Institute of Scientific and Technical Information of China (English)
张洪生; 洪广文; 丁平兴; 曹振轶
2001-01-01
In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.
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...
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
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.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
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....
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....
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...
Non-linearity parameter / of binary liquid mixtures at elevated pressures
Indian Academy of Sciences (India)
J D Pandey; J Chhabra; R Dey; V Sanguri; R Verma
2000-09-01
When sound waves of high amplitude propagate, several non-linear effects occur. 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 mixtures using Tong and Dong equation at high pressures and = 303.15 K. Thermodynamic method has also been used to calculate the non-linearity parameter after making certain approximations.
Travelling and standing envelope solitons in discrete non-linear cyclic structures
Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph
2016-12-01
Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
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 for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Likelihood inference for discretely observed non-linear diffusions
1998-01-01
This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the lat...
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
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.
Non-Linear Relativity in Position Space
Kimberly, D; Medeiros-Neto, J F; Kimberly, Dagny; Magueijo, João; Medeiros, João
2003-01-01
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
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......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...... 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....
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
Non-linear irreversible thermodynamics of single-molecule experiments
Santamaria-Holek, I; Hidalgo-Soria, M; Perez-Madrid, A
2015-01-01
Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between di?erent con?gurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Institute of Scientific and Technical Information of China (English)
郝世峰; 楼茂园; 杨诗芳; 李超; 孔照林; 裘薇
2015-01-01
To solve atmospheric primitive equations, the finite difference approach would result in numerous problems, com-pared to the differential equations. Taking the semi-Lagrange model as an example, there exist two diﬃcult prob-lems——the particle trajectory computation and the solutions of the Helmholtz equations. In this study, based on the substitution of atmosphere pressure, the atmospheric primitive equations are linearized within an integral time step, which are broadly seen as ordinary differential equations and can be derived as semi-analytical solutions (SASs). The variables of SASs are continuous functions of time and discretized in a special direction, so the gradient and divergence terms are solved by the difference method. Since the numerical solution of the SASs can be calculated via a highly pre-cise numerical computational method of exponential matrix——the precise integration method, the numerical solution of SASs at any time in the future can be obtained via step-by-step integration procedure. For the SAS methodology, the pressure, as well as the wind vector and displacement, can be obtained without solving the Helmholtz formulations. Compared to the extrapolated method, the SAS is more reasonable as the displacements of the particle are solved via time integration. In order to test the validity of the algorithms, the SAS model is constructed and the same experi-ment of a non-linear density current as reported by Straka in 1993 is implemented, which contains non-linear dynamics, transient features and fine-scale structures of the fluid flow. The results of the experiment with 50 m spatial resolution show that the SAS model can capture the characters of generation and development process of the Kelvin-Helmholtz shear instability vortex; the structures of the perturbation potential temperature field are very close to the benchmark solutions given by Straka, as well as the structures of the simulated atmosphere pressure and wind field. To further
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
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 betwee...... 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.......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...
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
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 m
Meson masses in large Nf QCD from Bethe-Salpeter equation
Harada, M; Yamawaki, K; Harada, Masayasu; Kurachi, Masafumi; Yamawaki, Koichi
2003-01-01
We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. Quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for the consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.
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.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
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
. The accuracy of the nonlinear ASA is compared to the non-linear simulation program – Abersim, which is a numerical solution to the Burgers equation based on the OSM. Simulations are performed for a linear array transducer with 64 active elements, focus at 40 mm, and excitation by a 2-cycle sine wave......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...
Generalized Ghost Dark Energy with Non-Linear Interaction
Ebrahimi, E; Mehrabi, A; Movahed, S M S
2016-01-01
In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...
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.
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.
Fliess, Michel; Join, Cédric; Sira-Ramirez, Hebertt
2008-01-01
International audience; Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line ...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Fliess, Michel; Sira-Ramirez, Hebertt
2007-01-01
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Non Linear Behaviour in Learning Processes
Manfredi, Paolo; Manfredi, Vicenzo Rosario
2003-01-01
This article is mainly based on R. E. Kahn's contribution to the book Non Linear Dynamics in Human Behavior. As stressed by Bronowski, both in art and in science, a person becomes creative by finding "a new unity" that is a link between things which were not thought alike before. Indeed the creative mind is a mind that looks for unexpected likeness finding a more profound unity, a pattern behind chaotic phenomena. In the context of scientific discovery, it can also be argued that creativi...
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Limits on Non-Linear Electrodynamics
Fouché, M; Rizzo, C
2016-01-01
In this paper we set a framework in which experiments whose goal is to test QED predictions can be used in a more general way to test non-linear electrodynamics (NLED) which contains low-energy QED as a special case. We review some of these experiments and we establish limits on the different free parameters by generalizing QED predictions in the framework of NLED. We finally discuss the implications of these limits on bound systems and isolated charged particles for which QED has been widely and successfully tested.
A Non-linear Stochastic Model for an Office Building with Air Infiltration
DEFF Research Database (Denmark)
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model param...... heat load reduction during peak load hours, control of indoor air temperature and for generating forecasts of power consumption from space heating....
Ground State Mass Spectrum for Scalar Diquarks with Bethe-Salpeter Equation
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang; WAN Shao-Long; YANG Wei-Min
2007-01-01
In this article,we study the structures of the pseudoscalar mesons π,K and the scalar diquarks Ua,Da,Sa in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential.The u,d,s quarks have small current masses,and the renormalization is very large,the mass poles in the timelike region are absent which implements confinement naturally.The Bethe-Salpeter wavefunctions of the pseudoscalar mesons π,K,and the scalar diquarks Ua,Da,Sa have the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale about q2 = 1 GeV2,which happens to be the energy scale for the chiral symmetry breaking,the strong interactions in the infrared region result in bound (or quasi-bound) states.The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values,and the ground state masses of the scalar diquarks Ua,Da,Sa are consistent with the existing theoretical calculations.We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.
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
Non-Linear Dynamics of Saturn’s Rings
Esposito, Larry W.
2015-11-01
Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects
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.
Optimal non-linear health insurance.
Blomqvist, A
1997-06-01
Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Risks of non-linear climate change
Energy Technology Data Exchange (ETDEWEB)
Van Ham, J.; Van Beers, R.J.; Builtjes, P.J.H.; Koennen, G.P.; Oerlemans, J.; Roemer, M.G.M. [TNO-SCMO, Delft (Netherlands)
1995-12-31
Climate forcing as a result of increased concentrations of greenhouse gases has been primarily addressed as a problem of a possibly warmer climate. So far, such change has been obscured in observations, possibly as a result of natural climate variability and masking by aerosols. Consequently, projections of the effect of climate forcing have to be based on modelling, more specifically by applying Global Circulation Models GCMs. These GCMs do not cover all possible feedbacks; neither do they address all specific possible effects of climate forcing. The investigation reviews possible non-linear climate change which does not fall within the coverage of present GCMs. The review includes the potential relevance of changes in biogeochemical cycles, aerosol and cloud feedback, albedo instability, ice-flow instability, changes in the thermohaline circulation and changes resulting from stratospheric cooling. It is noted that these changes may have different time horizons. Three from the investigated issues provide indications for a possible non-linear change. On the decadal scale stratospheric cooling, which is the result of the enhanced greenhouse effect, in combination with a depleted ozone layer, could provide a positive feedback to further ozone depletion, in particular in the Arctic. Decreasing albedo on the Greenland ice sheet may enhance the runoff from this ice sheet significantly in case of warming on a timescale of a few centuries. Changes in ocean circulation in the North Atlantic could seasonally more than compensate a global warming of 3C in North-West Europe on a timescale of centuries to a millennium. 263 refs.
Multifrequency parametric resonance in a non-linear wave equation
Energy Technology Data Exchange (ETDEWEB)
Kolesov, Andrei Yu [Yaroslavl Demidov State University (Russian Federation); Rozov, Nikolai Kh [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
2002-12-31
We consider the boundary-value problem u{sub tt}+{epsilon}u{sub t}+(1+{epsilon}{sigma}{sub k=1}{sup m}{alpha}{sub k}cos 2{phi}{sub k})u = a{sup 2}u{sub xx}-u{sup 2}u{sub t}, u|{sub x=0}=u|{sub x={pi}}=0, where 0<{epsilon}<<1, a>0, {phi}{sub k}={sigma}{sub k}t+c{sub k}, k=1,...,m. We show that a suitable choice of a positive integer m and real parameters {alpha}{sub k}, {sigma}{sub k}, k=1,...,m, enables us to make this problem have any prescribed number of exponentially stable time-quasiperiodic solutions bifurcating from zero.
Recent topics in non-linear partial differential equations 4
Mimura, M
1989-01-01
This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
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
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Charged relativistic fluids and non-linear electrodynamics
Dereli, T.; Tucker, R. W.
2010-01-01
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.
Non-linear states of a positive or negative refraction index material in a cavity with feedback
Mártin, D. A.; Hoyuelos, M.
2010-06-01
We study a system composed by a cavity with plane mirrors containing a positive or negative refraction index material with third order effective electric and magnetic non-linearities. The aim of the work is to present a general picture of possible non-linear states in terms of the relevant parameters of the system. The parameters are the ones that appear in a reduced description that has the form of the Lugiato-Lefever equation. This equation is obtained from two coupled non-linear Schrödinger equations for the electric and magnetic field amplitudes.
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Nicolae–Doru Stănescu
2010-01-01
In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of...
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Directory of Open Access Journals (Sweden)
Nicolae–Doru Stănescu
2010-01-01
Full Text Available In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of the motion. Finally a numerical application is presented.
New holographic dark energy model with non-linear interaction
Oliveros, A
2014-01-01
In this paper the cosmological evolution of a holographic dark energy model with a non-linear interaction between the dark energy and dark matter components in a FRW type flat universe is analysed. In this context, the deceleration parameter $q$ and the equation state $w_{\\Lambda}$ are obtained. We found that, as the square of the speed of sound remains positive, the model is stable under perturbations since early times; it also shows that the evolution of the matter and dark energy densities are of the same order for a long period of time, avoiding the so--called coincidence problem. We have also made the correspondence of the model with the dark energy densities and pressures for the quintessence and tachyon fields. From this correspondence we have reconstructed the potential of scalar fields and their dynamics.
Non-linear Kalman filters for calibration in radio interferometry
Tasse, Cyril
2014-01-01
We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly cheap algorithm that we believe to be robust, especially in low signal-to-noise regime. Potentially the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visib...
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We consider a $d$-dimensional random field $u = \\{u(t,x)\\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \\in \\{1,2,3\\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
Non-linear Oscillations of Compact Stars and Gravitational Waves
Passamonti, A
2006-01-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative or...
Black Hole Hair Removal: Non-linear Analysis
Jatkar, Dileep P; Srivastava, Yogesh K
2009-01-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, -- degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Black hole hair removal: non-linear analysis
Jatkar, Dileep P.; Sen, Ashoke; Srivastava, Yogesh K.
2010-02-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, — degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Non-Linear Electrohydrodynamics in Microfluidic Devices
Directory of Open Access Journals (Sweden)
Jun Zeng
2011-03-01
Full Text Available Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications.
Monte Carlo Computation of Spectral Density Function in Real-Time Scalar Field Theory
Abbasi, Navid
2014-01-01
Non-perturbative study of "real-time" field theories is difficult due to the sign problem. We use Bold Schwinger-Dyson (SD) equations to study the real-time $\\phi^4$ theory in $d=4$ beyond the perturbative regime. Combining SD equations in a particular way, we derive a non-linear integral equation for the two-point function. Then we introduce a new method by which one can analytically perform the momentum part of loop integrals in this equation. The price we must pay for such simplification is to numerically solve a non-linear integral equation for the spectral density function. Using Bold diagrammatic Monte Carlo method we find non-perturbative spectral function of theory and compare it with the one obtained from perturbation theory. At the end we utilize our Monte Carlo result to find the full vertex function as the basis for the computation of real-time scattering amplitudes.
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...
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 model for compression tests on articular cartilage.
Grillo, Alfio; Guaily, Amr; Giverso, Chiara; Federico, Salvatore
2015-07-01
Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
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...
A variational model for fully non-linear water waves of Boussinesq type
Klopman, Gert; Dingemans, Maarten W.; Groesen, van Brenny; Grue, J.
2005-01-01
Using a variational principle and a parabolic approximation to the vertical structure of the velocity potential, the equations of motion for surface gravity waves over mildly sloping bathymetry are derived. No approximations are made concerning the non-linearity of the waves. The resulting model equ
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Response of Non-Linear Systems to Renewal Impulses by Path Integration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Iwankiewicz, R.
The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... additional discrete-valued state variables for which the stochastic equations are also formulated....
Non-Linear Unit Root Properties of Crude Oil Production
Svetlana Maslyuk; Russell Smyth
2007-01-01
While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as permanent stochastic disturbances. The objective of this paper is to test for non-linearities and un...
Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
Kol, Barak
2009-01-01
We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling Post-Newtonian gravitating binary. We use the effective field theory approach with the non-relativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a non-linear classical field theory coupled to point-like sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain non-linear world-line vertices, and we classify all the possible topologies of irreducible ...
Non-linear Constitutive Model for the Oligocarbonate Polyurethane Material
Institute of Scientific and Technical Information of China (English)
Marek Pawlikowski
2014-01-01
The polyurethane,which was the subject of the constitutive research presented in the paper,was based on oligocarbonate diols Desmophen C2100 produced by Bayer@.The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses.The polyurethane was assumed to be non-linearly viscohyperelastic,isotropic and incompressible.The constitutive equation was derived from the postulated strain energy function.The elastic and rheological constants were identified on the basis of experimental tests,i.e.relaxation tests and monotonic uniaxial tests at two different strain rates,i.e.λ =0.1 min-1 and λ =1.0 min-1.The stiffness tensor was derived and introduced to Abaqus@finite element (FE) software in order to numerically validate the constitutive model.The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material.
Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation
Rana, S.; Mehmood, R.; Narayana, PV S.; Akbar, N. S.
2016-12-01
The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10-5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.
A Non-linear Stochastic Model for an Office Building with Air Infiltration
DEFF Research Database (Denmark)
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...... parameters are estimated using a maximum likelihood technique. Based on the maximum likelihood value, the different models are statistically compared to each other using Wilk's likelihood ratio test. The model showing the best performance is finally verified in both the time domain and the frequency domain...
Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
Directory of Open Access Journals (Sweden)
Andrea Quadri
2014-04-01
Full Text Available We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE encoding the invariance of the SU(2 Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI amplitudes (both on-shell and off-shell can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed.
Graphical and Analytical Analysis of the Non-Linear PLL
de Boer, Bjorn; Radovanovic, S.; Annema, Anne J.; Nauta, Bram
The fixed width control pulses from the Bang-Bang Phase Detector in non-linear PLLs allow for operation at higher data rates than the linear PLL. The high non-linearity of the Bang- Bang Phase Detector gives rise to unwanted effects, such as limit-cycles, not yet fully described. This paper
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-degrees-of-freedom...
Non-linear Frequency Scaling Algorithm for FMCW SAR Data
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran
Non Linear Gauge Fixing for FeynArts
Gajdosik, Thomas
2007-01-01
We review the non-linear gauge-fixing for the Standard Model, proposed by F. Boudjema and E. Chopin, and present our implementation of this non-linear gauge-fixing to the Standard Model and to the minimal supersymmetric Standard Model in FeynArts.
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....
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....
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
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 important differences in their evolution.
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.
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Non-linear dielectric monitoring of biological suspensions
Energy Technology Data Exchange (ETDEWEB)
Treo, E F; Felice, C J [Departamento de BioingenierIa, Universidad Nacional de Tucuman and Consejo Nacional de Investigaciones Cientificas y Tecnicas. CC327, CP4000, San Miguel de Tucuman (Argentina)
2007-11-15
Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response.
Directory of Open Access Journals (Sweden)
A. D. Pataraya
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.
A conformal approach for the analysis of the non-linear stability of radiation cosmologies
Energy Technology Data Exchange (ETDEWEB)
Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Department of Mathematics, University of Leicester, University Road, LE1 8RH (United Kingdom); Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)
2013-01-15
The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.
Non-linear vorticity upsurge in Burgers flow
Lam, F
2016-01-01
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers, are chosen for our computations. Most of the solutions are carried out well into the fully turbulent regime over finely-resolved scales in space and in time. It is found that an abrupt spatio-temporal concentration in shear constitutes an essential part during the flow evolution. The vorticity surge has been instigated by the non-linearity complying with instantaneous enstrophy production while ad hoc disturbances play no role in the process. In particular, the present method predicts the precipitous vorticity re-distribution and accumulation, predominantly over localised regions of minute dimension. The growth rate depends on viscosity and is a strong function of initial data. Nevertheless, the long-time energy decay is history-independent and is inversely proportional to ti...
Galiev, Sh. U.
2003-08-01
A non-linear theory of transresonant wave phenomena based on consideration of perturbed wave equations is presented. In particular, the waves in a surface layer of a porous compressible viscoelastoplastic material are considered. For such layers the 3-D equations of deformable media are reduced to 1-D or 2-D perturbed wave equations. A set of approximate, closed-form, general solutions of these equations are presented, which take into account non-linear, dissipative, dispersive, topographic and boundary effects. Then resonant, site and liquefaction effects are analysed. Resonance is considered as a global parameter. Transresonant evolution of the equations is studied. Within the resonant band, utt~a20∇2u and the perturbed wave equations transform into non-linear diffusion equations, either to a basic highly non-linear ordinary differential equation or to the basic algebraic equation for travelling waves. Resonances can destroy predictability and wave reversibility. Surface topography (valleys, islands, etc.) is considered as a series of earthquake-induced resonators. A non-linear transresonant evolution of smooth seismic waves into shock-, jet- and mushroom-like waves and vortices is studied. The amplitude of the resonant waves may be of the order of the square or cube root of the exciting amplitude. Therefore, seismic waves with a moderate amplitude can be amplified very strongly in natural resonators, whereas strong seismic waves can be attenuated. Reports of the 1835 February 20 Chilean earthquake given by Charles Darwin are qualitatively examined using the non-linear theory. The theory qualitatively describes the `shivering' of islands and ridges, volcano spouts and generation of tsunami-like waves and supports Darwin's opinion that these events were part of a single phenomenon. Same-day earthquake/eruption events and catastrophic amplification of seismic waves near the edge of sediment layers are discussed. At the same time the theory can account for recent
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
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 ... 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...... Benjamin–Ono (BO) and Benjamin–Bona–Mahony (BBM) water wave equations....
Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.
Wigren, Torbjörn
2015-01-01
The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.
Frequency and Phase Noise in Non-Linear Microwave Oscillator Circuits
Tannous, C.
2003-01-01
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of stochastic differential equations representing the circuit. Our theoretical evaluations can be used in order to make detailed comparisons with the experimental measurements of phase noise spectra in selected oscillating circuits.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above.
Lyubimova, T; Zubova, N; Shevtsova, V
2017-03-01
The paper deals with the investigation of the onset and non-linear regimes of convection of liquid binary mixtures with negative Soret effect heated from above. The linear stability of a convectionless state in a horizontal layer is studied by the numerical solution of the linearized problem on the temporal evolution of small perturbations of the unsteady base state. Non-linear regimes of convection are investigated by the numerical solution of the non-linear unsteady equations for a horizontally elongated rectangular cavity. The calculations are performed for water-ethanol and water-isopropanol liquid mixtures and for colloidal suspensions. The dependences of the instability onset time and wave number of the most dangerous perturbations on the solutal Rayleigh number (gravity level) obtained by a linear stability analysis and non-linear calculations are found to be in a very good agreement. A favorable comparison with the existing experimental and numerical data is presented.
Towards a non-linear theory for induced seismicity in shales
Salusti, Ettore; Droghei, Riccardo
2014-05-01
We here analyze the pore transmission of fluid pressure pand solute density ρ in porous rocks, within the framework of the Biot theory of poroelasticity extended to include physico-chemical interactions. In more details we here analyze the effect of a strong external stress on the non-linear evolution of p and ρ in a porous rock. We here focus on the consequent deformation of the rock pores, relative to a non-linear Hooke equation among strain, linear/quadratic pressure and osmosis in 1-D. We in particular analyze cases with a large pressure, but minor than the 'rupture point'. All this gives relations similar to those discussed by Shapiro et al. (2013), which assume a pressure dependent permeability. Thus we analyze the external stress necessary to originate quick non-linear transients of combined fluid pressure and solute density in a porous matrix, which perturb in a mild (i.e. a linear diffusive phenomenon) or a more dramatic non-linear way (Burgers solitons) the rock structure. All this gives a novel, more realistic insight about the rock evolution, fracturing and micro-earthquakes under a large external stress.
Fluid flow of incompressible viscous fluid through a non-linear elastic tube
Energy Technology Data Exchange (ETDEWEB)
Lazopoulos, A.; Tsangaris, S. [National Technical University of Athens, Fluids Section, School of Mechanical Engineering, Zografou, Athens (Greece)
2008-11-15
The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung's (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain-energy density function. The fluid is described through a Navier-Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response. (orig.)
Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system
Kahraman, A.; Singh, R.
1991-04-01
Frequency response characteristics of a non-linear geared rotor-bearing system with time-varying mesh stiffness k h( overlinet) are examined in this paper. First, the single-degree-of-freedom spur gear pair model with backlash is extended to include sinusoidal or periodic mesh stiffness k h( overlinet) . Second, a three-degree-of-freedom model with k h( overlinet) and clearance non-lineariries associated with gear backlash and rolling element bearings, as excited by the static transmission error overlinee( overlinet) under a mean torque load, is developed. The governing equations are solved using digital simulation technique and only the primary resonances are studied. Resonances of the corresponding linear time-varying system associated with parametric and external excitations are identified using the method of multiple scales and digital simulation. Interactions between the mesh stiffness variation and clearance non-linearities have been investigated; a strong interaction between time-varying mesh stiffness k h( overlinet) and gear backlash is found, whereas the coupling between k h( overlinet) and bearing non-linearities is weak. Finally, our time-varying non-linear formulations yield reasonably good predictions when compared with the benchmark experimental results available in the literature.
Non-linear structural dynamics characterization using a scanning laser vibrometer
Pai, P. F.; Lee, S.-Y.
2003-07-01
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal velocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second, third, and fourth natural frequencies are examined in detail. Influences of the fixture mass, gravity, mass centers of mode shapes, and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances, energy transfer from high-frequency modes to the first mode, and amplitude- and phase-modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics
Institute of Scientific and Technical Information of China (English)
NI Guangjian; ZHANG Junhong; CHENG Xiaoming
2009-01-01
Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.
Massive Neutrinos and the Non-linear Matter Power Spectrum
Bird, Simeon; Haehnelt, Martin G
2011-01-01
We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation (Smith et al. 2003) to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k \\sim 1hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced n...
Kumar, K Vasanth; Sivanesan, S
2005-08-31
Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.
A study of non-linearity in rainfall-runoff response using 120 UK catchments
Mathias, Simon A.; McIntyre, Neil; Oughton, Rachel H.
2016-09-01
This study presents a catchment characteristic sensitivity analysis concerning the non-linearity of rainfall-runoff response in 120 UK catchments. Two approaches were adopted. The first approach involved, for each catchment, regression of a power-law to flow rate gradient data for recession events only. This approach was referred to as the recession analysis (RA). The second approach involved calibrating a rainfall-runoff model to the full data set (both recession and non-recession events). The rainfall-runoff model was developed by combining a power-law streamflow routing function with a one parameter probability distributed model (PDM) for soil moisture accounting. This approach was referred to as the rainfall-runoff model (RM). Step-wise linear regression was used to derive regionalization equations for the three parameters. An advantage of the RM approach is that it utilizes much more of the observed data. Results from the RM approach suggest that catchments with high base-flow and low annual precipitation tend to exhibit greater non-linearity in rainfall-runoff response. In contrast, the results from the RA approach suggest that non-linearity is linked to low evaporative demand. The difference in results is attributed to the aggregation of storm-flow and base-flow into a single system giving rise to a seemingly more non-linear response when applying the RM approach to catchments that exhibit a strongly dual storm-flow base-flow response. The study also highlights the value and limitations in a regionlization context of aggregating storm-flow and base-flow pathways into a single non-linear routing function.
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
Controlling ultrafast currents by the non-linear photogalvanic effect
Wachter, Georg; Lemell, Christoph; Tong, Xiao-Min; Yabana, Kazuhiro; Burgdörfer, Joachim
2015-01-01
We theoretically investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femto-second optical laser pulses. Ab-initio simulations based on time-dependent density functional theory predict ultrafast DC currents that can be viewed as a non-linear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the transition from non-linear polarization currents to the tunneling excitation regime. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. We find the ultrafast current control by the non-linear photogalvanic effect to be remarkably robust and insensitive to laser-pulse shape and carrier-envelope phase.
An algorithm for earthwork allocation considering non-linear factors
Institute of Scientific and Technical Information of China (English)
WANG Ren-chao; LIU Jin-fei
2008-01-01
For solving the optimization model of earthwork allocation considering non-linear factors, a hybrid al-gorithm combined with the ant algorithm (AA) and particle swarm optimization (PSO) is proposed in this pa-per. Then the proposed method and the LP method are used respectively in solving a linear allocation model of a high rockfill dam project. Results obtained by these two methods are compared each other. It can be conclu-ded that the solution got by the proposed method is extremely approximate to the analytic solution of LP method. The superiority of the proposed method over the LP method in solving a non-linear allocation model is illustrated by a non-linear case. Moreover, further researches on improvement of the algorithm and the allocation model are addressed.
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 Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Rudin, Sergey; Rupper, Greg
2012-02-01
The non-linear electron plasma response to electromagnetic signal applied to a gated graphene conduction channel can be used to make a graphene based Dyakonov-Shur terahertz detector. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. With less damping and higher mobility, the graphene conduction channels may provide higher quality plasma response than possible with semiconductor channels. Our analysis of plasma oscillations in a graphene channel is based on the hydrodynamic equations which we derive from the Boltzmann equation accounting for both electrons and holes, and including the effects of viscosity and finite mobility.
On the theory of ternary melt crystallization with a non-linear phase diagram
Toropova, L. V.; Dubovoi, G. Yu; Alexandrov, D. V.
2017-04-01
The present study is concerned with a theoretical analysis of unidirectional solidification process of ternary melts in the presence of a phase transition (mushy) layer. A new analytical solution of heat and mass transfer equations describing the steady-state crystallization scenario is found with allowance for a non-linear liquidus equation. The model under consideration takes into account the presence of two phase transition layers, namely, the primary and cotectic mushy regions. We demonstrate that the phase diagram nonlinearity leads to substantial changes of analytical solutions.
Non-linear growth and condensation in multiplex networks
Nicosia, Vincenzo; Latora, Vito; Barthelemy, Marc
2013-01-01
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which a single node connects to nearly all other nodes of a layer.
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available 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.
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...
Non-linear effects in bunch compressor of TARLA
Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin
2016-03-01
Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.
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.
Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory
Markovich, Tomer; Podgornik, Rudi
2016-01-01
We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.
GPU linear and non-linear Poisson–Boltzmann solver module for DelPhi
Colmenares, José; Ortiz, Jesús; Rocchia, Walter
2014-01-01
Summary: In this work, we present a CUDA-based GPU implementation of a Poisson–Boltzmann equation solver, in both the linear and non-linear versions, using double precision. A finite difference scheme is adopted and made suitable for the GPU architecture. The resulting code was interfaced with the electrostatics software for biomolecules DelPhi, which is widely used in the computational biology community. The algorithm has been implemented using CUDA and tested over a few representative cases of biological interest. Details of the implementation and performance test results are illustrated. A speedup of ∼10 times was achieved both in the linear and non-linear cases. Availability and implementation: The module is open-source and available at http://www.electrostaticszone.eu/index.php/downloads. Contact: walter.rocchia@iit.it Supplementary information: Supplementary data are available at Bioinformatics online PMID:24292939
Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data
Kukreja, Sunil L.
2008-01-01
Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
An efficient implementation of massive neutrinos in non-linear structure formation simulations
Ali-Haïmoud, Yacine
2012-01-01
Massive neutrinos make up a fraction of the dark matter, but due to their large thermal velocities, cluster significantly less than cold dark matter (CDM) on small scales. An accurate theoretical modelling of their effect during the non-linear regime of structure formation is required in order to properly analyse current and upcoming high-precision large-scale structure data, and constrain the neutrino mass. Taking advantage of the fact that massive neutrinos remain linearly clustered up to late times, this paper treats the linear growth of neutrino overdensities in a non-linear CDM background. The evolution of the CDM component is obtained via N-body computations. The smooth neutrino component is evaluated from that background by solving the Boltzmann equation linearised with respect to the neutrino overdensity. CDM and neutrinos are simultaneously evolved in time, consistently accounting for their mutual gravitational influence. This method avoids the issue of shot-noise inherent to particle-based neutrino ...
The SPH approach to the process of container filling based on non-linear constitutive models
Institute of Scientific and Technical Information of China (English)
Tao Jiang; Jie Ouyang; Lin Zhang; Jin-Lian Ren
2012-01-01
In this work,the transient free surface of container filling with non-linear constitutive equation's fluids is numerically investigated by the smoothed particle hydrodynamics (SPH) method.Specifically,the filling process of a square container is considered for non-linear polymer fluids based on the Cross model.The validity of the presented SPH is first verified by solving the Newtonian fluid and OldroydB fluid jet.Various phenomena in the filling process are shown,including the jet buckling,jet thinning,splashing or spluttering,steady filling.Moreover,a new phenomenon of vortex whirling is more evidently observed for the Cross model fluid compared with the Newtonian fluid case.
Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
Lee, Seungjin; Schlotterer, Oliver
2015-01-01
Recent progress on scattering amplitudes in super Yang--Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang--Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. In this work we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern--Carrasco--Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
Energy Technology Data Exchange (ETDEWEB)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.
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...
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...
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...
Range non-linearities correction in FMCW SAR
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
The limiting factor to the use of Frequency Modulated Continuous Wave (FMCW) technology with Synthetic Aperture Radar (SAR) techniques to produce lightweight, cost effective, low power consuming imaging sensors with high resolution, is the well known presence of non-linearities in the transmitted si
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...
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 is gra...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
Development and Control of a Non Linear Magnetic Levitation System
Directory of Open Access Journals (Sweden)
A Sanjeevi Gandhi
2013-06-01
Full Text Available Nowadays, studies to develop and control non linear systems is of great significance. Magnetic Levitation System has gained considerable interests due to its great practical importance in different engineering fields In this paper an electromagnetic levitation system was developed and mathematical model for the system was derived. The developed system was controlled manually.
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
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...
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 d
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
Burg, van der Eeke; Leeuw, de Jan
1988-01-01
In this paper we discuss the estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS). Starting points are the delta method equations, but the jack-knife and bootstrap are used to provide finite differen
Non-linear effects on solute transfer between flowing water and a sediment bed.
Higashino, Makoto; Stefan, Heinz G
2011-11-15
A previously developed model of periodic pore water flow in space and time, and associated solute transport in a stream bed of fine sand is extended to coarse sand and fine gravel. The pore water flow immediately below the sediment/water interface becomes intermittently a non-Darcy flow. The periodic pressure and velocity fluctuations considered are induced by near-bed coherent turbulent motions in the stream flow; they penetrate from the sediment/water interface into the sediment pore system and are described by a wave number (χ) and a period (T) that are given as functions of the shear velocity (U(∗)) between the flowing water and the sediment bed. The stream bed has a flat surface without bed forms. The flow field in the sediment pore system is described by the continuity equation and a resistance law that includes both viscous (Darcy) and non-linear (inertial) effects. Simulation results show that non-linear (inertial) effects near the sediment/water interface increase flow resistance and reduce mean flow velocities. Compared to pure Darcy flow, non-linear (inertial) effects reduce solute exchange rates between overlying water and the sediment bed but only by a moderate amount (less than 50%). Turbulent coherent flow structures in the stream flow enhance solute transfer in the pore system of a stream bed compared to pure molecular diffusion, but by much less than standing surface waves or bed forms.
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
Chmielewski, P; Murawski, K; Musielak, Z E
2014-01-01
We present simulation results of the impulsively generated linear and non-linear Alfven waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic equations to find the temporal signatures of the small and large-amplitude Alfven waves in the model atmosphere of open and expanding magnetic field configuration with a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfven waves at different heights of the model atmosphere, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfven waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfven waves show that they can contribute only to the plasma dynamics and heating of t...
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
Chmielewski, P.; Srivastava, A. K.; Murawski, K.; Musielak, Z. E.
2014-01-01
We present simulation results of the impulsively generated linear and non-linear Alfvén waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic equations to find the temporal signatures of the small and large-amplitude Alfvén waves in the model atmosphere of open and expanding magnetic field configuration with a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfvén waves at different heights of the model atmosphere, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfvén waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfvén waves shows that they can contribute only to the plasma dynamics and heating of the funnel-like magnetic flux-tubes associated with the polar coronal holes.
Non-linear aeroelastic prediction for aircraft applications
de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.
2007-05-01
Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
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.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M B; Machado, P A N; Saa, S
2016-01-01
The minimal $SO(5)/SO(4)$ sigma 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 $\\sigma$ mass allows 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 compl...
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-01
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
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...... and results are compared to test data. A novel test arrangement utilizing a water filled cushion to create the uniform pressure load on curved panel specimen is used to obtain the experimental data. The panel is modeled with three different commercial finite element codes. Two implicit and one explicit code...... are used with various element types, modeling approaches and material models. The results show that the theoretical and experimental methods generally show fair agreement in panel non-linear behavior before collapse. It is also shown that special attention to detail has to be taken, because the predicted...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
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 at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
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.
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...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Measuring the Non-Linear Effects of Monetary Policy
Christian Matthes; Regis Barnichon
2015-01-01
This paper proposes a method to identify the non-linear effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to monetary policy and find that the effect of a monetary intervention depends strongly on (i) the sign of the intervention, (ii) the size of the intervention, and (iii) the state of the business cycle at the time of the intervention. A contractionary policy has a strong adverse effect on output, much stronger t...
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Adaptive spectral identification techniques in presence of undetected non linearities
Cella, G; Guidi, G M
2002-01-01
The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and stationary noise. We study the possibility of improving the detection efficiency with a class of adaptive spectral identification techniques, analyzing their effect in presence of non stationarities and undetected non linearities in the noise
Non-linear dark matter collapse under diffusion
Velten, Hermano E S
2014-01-01
Diffusion is one of the physical processes allowed for describing the large scale dark matter dynamics. At the same time, it can be seen as a possible mechanism behind the interacting cosmologies. We study the non-linear spherical "top-hat" collapse of dark matter which undergoes velocity diffusion into a solvent dark energy field. We show constraints on the maximum magnitude allowed for the dark matter diffusion. Our results reinforce previous analysis concerning the linear perturbation theory.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Non-linear Higgs portal to Dark Matter
Bajo, Rocío del Rey
2016-01-01
The Higgs portal to scalar Dark Matter is considered in the context of non-linearly realised electroweak symmetry breaking. We determine the interactions of gauge bosons and the physical Higgs particle $h$ to a scalar singlet Dark Matter candidate $S$ in an effective description. The main phenomenological differences with respect to the standard scenario can be seen in the Dark Matter relic abundance, in direct/indirect searches and in signals at colliders.
Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan
2017-01-01
This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Non-linear polaronic conduction in magnetite nanowires
Energy Technology Data Exchange (ETDEWEB)
Singh, Pooja, E-mail: pooja7503@gmail.com [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rout, P.K., E-mail: pkrout.phy@gmail.com [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Husale, Sudhir; Gupta, Anurag [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Singh, Manju [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rakshit, R.K. [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Dogra, Anjana, E-mail: anjanad@nplindia.org [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India)
2016-12-01
We report the temperature dependent current (I) – voltage (V) characteristics of Fe{sub 3}O{sub 4} nanowires with varying width (w) of 132, 358, and 709 nm. While the widest nanowire (w=709 nm) shows ohmic I (V) curves for all temperatures, those for w=132 and 358 nm show nonlinearity, which can be expressed by a combination of linear (V) and cubic (V{sup 3}) terms. The behaviour of conductance (linear bias component of current) and non-linearity in these nanowires is related to small polaron hopping related conduction. Moreover, we observed an anomalously large hopping lengths, which may be related to the size of percolation cluster and/or antiphase domain. Our study presents first experimental evidence for such non-linear polaronic conduction in magnetite nanowires. - Highlights: • Temperature dependent I–V measurements of FIB fabricated magnetite nanowires. • Small polaron based conduction in non-linear I–V curves. • Anomalously large hopping lengths due to percolation effect and/or antiphase domains.
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.
Fitting and forecasting non-linear coupled dark energy
Casas, Santiago; Baldi, Marco; Pettorino, Valeria; Vollmer, Adrian
2015-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range $z=0-1.6$ and wave modes below $k=10 \\text{h/Mpc}$. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and w...
Testing non-linear vacuum electrodynamics with Michelson interferometry
Schellstede, Gerold O; Lämmerzahl, Claus
2015-01-01
We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Pleba\\'nski class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental set-ups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and...
On the theory of a non-linear neutral scalar field with spontaneously broken symmetry
Poluektov, Yu M
2015-01-01
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main approximation of the relativistic self-consistent field model, in which the influence of vacuum fluctuations is taken into account in constructing the one-particle states. The solutions of the self-consistent equations determine possible states, which also include the states with broken symmetries. Different states of the field are matched to particles, whose masses are determined by both parameters of the Lagrangian and vacuum fluctuations.
Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics
Lam, F
2013-01-01
A vorticity theory for incompressible fluid flows in the absence of solid boundaries is proposed. Some apriori bounds are established. They are used in an interpolation theory to show the well-posedness of the vorticity Cauchy problem. A non-linear integral equation for vorticity is derived and its solution is expressed in an expansion. Interpretations of flow evolutions starting from given initial data are given and elaborated. The kinetic theory for Maxwellian molecules with cut-off is revisited in order to link microscopic properties to flow characters on the continuum.
Beta-functions of non-linear $\\sigma$-models for disordered and interacting electron systems
Dell'Anna, Luca
2016-01-01
We provide and study complete sets of one-loop renormalization group equations, calculated at all orders in the interaction parameters, of several Finkel'stein non-linear $\\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors.
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. ...... and are systematically compared with the experimental results given by Watanabe et al. (1989, J. Soc. Naval Architects Japan, 166) and O’Dea et al. (1992, Proc. 19th Symp. on Naval Hydrodynamics). The agreement between the present predictions and the experiments is very encouraging....
The global non-linear stability of the Kerr-de Sitter family of black holes
Hintz, Peter
2016-01-01
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extending the linear and non-linear analysis on black hole spacetimes described in a sequence of earlier papers by the authors: We develop a general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations. In particular, the iteration scheme used to solve Einstein's equations automatically finds the parameters of the Kerr-de Sitter black hole that the solution is asymptotic to, the exponentially decaying tail of the solution, and the gauge in which we are able to find the solution; the gauge here is a wave map/DeTurck type gauge, modified by source terms which are treated as unknowns, lying in a suitable finite-dimensional space.
A finite element perspective on non-linear FFT-based micromechanical simulations
Zeman, Jan; Vondřejc, Jaroslav; Peerlings, Ron H J; Geers, Marc G D
2016-01-01
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the Fast Fourier Transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to non-linear problems conceptually difficult. This paper aims to establish a link between FE- and FFT-based methods, in order to develop a solver applicable to general history- and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of non-linear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus nee...
Energy Technology Data Exchange (ETDEWEB)
Meili, G.; Dubroca, G.; Pasquier, M.; Thepenier, J.
1982-06-01
The paper discusses a method for the mechanical testing of casebonded composite modified double base charges (CMDB) subjected to thermal cycling. The method proposed to determine stresses and safety margins takes into account the non-linear viscoelastic behaviour and the compressibility of the propellant. The non-linear behaviour is derived from tensile testing. The equations of equilibrium are solved numerically by deviding the grain web into many layers. The nonlinearities mainly concern the modulus; a multiaxial criterion and the time-temperature shift factors are used. At each time-step and for each layer the temperature, the reduced time, the non-linear factor, the Poisson's ratio and the damage according to the concept of Farris are calculated. Different charges (star, wagon wheel, finocyl) were subjected to various types of thermal cycles. The comparison between prediction and experimentation is acceptable even for complex histories in strain and temperature.
Higher order effects in non-linear evolution from a veto in rapidities
Chachamis, G.; Lublinsky, M.; Sabio Vera, A.
2005-02-01
Higher order corrections to the Balitsky-Kovchegov equation have been estimated by introducing a rapidity veto which forbids subsequent emissions to be very close in rapidity and is known to mimic higher order corrections to the linear BFKL equation. The rapidity veto constraint has been first introduced using analytical arguments obtaining a power growth with energy, Q(Y)˜e, of the saturation scale of λ˜0.45. Then a numerical analysis for the non-linear Balitsky-Kovchegov equation has been carried out for phenomenological rapidities: when a veto of about two units of rapidity is introduced for a fixed value of the coupling constant of α=0.2 the saturation scale λ decreases from ˜0.6 to ˜0.3, and when running coupling effects are taken into account it decreases from ˜0.4 to ˜0.3.
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
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
Energy Technology Data Exchange (ETDEWEB)
Frostig, Yeoshua; Sheinman, Izhak [Technion-Israel Inst. of Technology, Faculty of Civil and Environmental Engineering, Haifa (Israel); Thomsen, Ole Thybo [Aalborg Univ., Inst. of Mechanical Engineering, Aalborg (Denmark)
2005-03-01
The paper presents a general geometrically non-linear high-order theory of sandwich panels that takes into account the high-order geometrical non-linearities in the core as well as in the face sheets and is based on a variational approach. The formulation, which yields a set of rather complicated governing equations, has been simplified in two different approaches and has been compared with FEA results for verification. The first formulation uses the kinematic relations of large displacements with moderate rotations for the face sheets, non-linear kinematic relations for the core and it assumes that the distribution of the vertical normal stresses through the depth of the core are linear. The second approach uses the general formulation to the non-linear high-order theory of sandwich panels (HSAPT) that considers geometrical non-linearities in the face sheets and only linear high-order effects in the core. The numerical results of the two formulations are presented for a three point bending loading scheme, which is associated with a limit point behavior. The results of the two formulations are compared in terms of displacements, bending moments and shear stresses and transverse (vertical) normal stresses at the face-core interfaces on one hand, and load versus these structural quantities on the other hand. The results have compared well with FEA results obtained using the commercial codes ADINA and ANSYS. (Author)
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.
Global non-linear effect of temperature on economic production
Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward
2015-11-01
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 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....
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 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
Hans Hinterreiter’s non-linear transformations
DEFF Research Database (Denmark)
Makovicky, Emil
poster illustrates four different cases of this process, starting always with a plane-group pattern and showing both the application of non-linear transformations and coloured symmetry. In his more complex patterns, two of which are shown on the poster, Hinterreiter created domains of affinely...... of plane-group patterns onto curvilinear nets of different kinds, mostly combined with a skilful application of principles of dichroic or polychromatic symmetry. Unlike Escher, Hinterreiter strove to achieve the aesthetic ideal of a pure abstract form [2] with its inherent symmetries. His unique, two...
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).
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 optical titanyl arsenates: Crystal growth and properties
Nordborg, Jenni Eva Louise
Crystals are appreciated not only for their appearance, but also for their unique physical properties which are utilized by the photonic industry in appliances that we come across every day. An important part of enabling the technical use of optical devices is the manufacture of crystals. This dissertation deals with a specific group of materials called the potassium titanyl phosphate (KIP) family, known for their non-linear optical and ferroelectric properties. The isomorphs vary in their linear optical and dielectric properties, which can be tuned to optimize device performance by forming solid solutions of the different materials. Titanyl arsenates have a wide range of near-infrared transmission which makes them useful for tunable infrared lasers. The isomorphs examined in the present work were primarily RbTiOASO4 (RTA) and CsTiOAsO4 (CTA) together with the mixtures RbxCs 1-xTiOAsO4 (RCTA). Large-scale crystals were grown by top seeding solution growth utilizing a three-zone furnace with excellent temperature control. Sufficiently slow cooling and constant upward lifting produced crystals with large volumes useable for technical applications. Optical quality RTA crystals up to 10 x 12 x 20 mm were grown. The greater difficulty in obtaining good crystals of CTA led to the use of mixed RCTA materials. The mixing of rubidium and cesium in RCTA is more favorable to crystal growth than the single components in pure RTA and CTA. Mixed crystals are rubidium-enriched and contain only 20-30% of the cesium concentration in the flux. The cesium atoms show a preference for the larger cation site. The network structure is very little affected by the cation substitution; consequently, the non-linear optical properties of the Rb-rich isomorphic mixtures of RTA and CTA can be expected to remain intact. Crystallographic methods utilizing conventional X-ray tubes, synchrotron radiation and neutron diffraction have been employed to investigate the properties of the atomic
Non-linear Calibration Leads to Improved Correspondence between Uncertainties
DEFF Research Database (Denmark)
Andersen, Jens Enevold Thaulov
2007-01-01
an investigation of an uncomplicated expression of the non-linear working curve that is well suited to an assessment of predicted uncertainties. At small concentrations, the working curve reduces to a straight line that corresponds to the conventional calibration line. If no interferences were disturbing...... limit theorem, an excellent correspondence was obtained between predicted uncertainties and measured uncertainties. In order to validate the method, experiments were applied of flame atomic absorption spectrometry (FAAS) for the analysis of Co and Pt, and experiments of electrothermal atomic absorption...
Non-linear dynamics in pulse combustor: A review
Indian Academy of Sciences (India)
Sirshendu Mondal; Achintya Kukhopadhyay; Swarnendu Sen
2015-03-01
The state of the art of non-linear dynamics applied to pulse combustor theoretically and experimentally is reviewed. Pulse combustors are a class of air-breathing engines in which pulsations in combustion are utilized to improve the performance. As no analytical solution can be obtained for most of the nonlinear systems, the whole set of solutions can be investigated with the help of dynamical system theory. Many studies have been carried out on pulse combustors whose dynamics include limit cycle behaviour, Hopf bifurcation and period-doubling bifurcation. The dynamic signature has also been used for early prediction of extinction.
A non-linear UAV altitude PSO-PD control
Orlando, Calogero
2015-12-01
In this work, a nonlinear model based approach is presented for the altitude stabilization of a hexarotor unmanned aerial vehicle (UAV). The mathematical model and control of the hexacopter airframe is presented. To stabilize the system along the vertical direction, a Proportional Derivative (PD) control is taken into account. A particle swarm optimization (PSO) approach is used in this paper to select the optimal parameters of the control algorithm taking into account different objective functions. Simulation sets are performed to carry out the results for the non-linear system to show how the PSO tuned PD controller leads to zero the error of the position along Z earth direction.
Simulation of non-linear coaxial line using ferrite beads
Energy Technology Data Exchange (ETDEWEB)
Furuya, S.; Matsumoto, H.; Tachi, K.; Takano, S.; Irisawa, J. [Nagaoka Univ. of Technology, Niigata (Japan)
2002-06-01
A ferrite sharpener is a non-linear coaxial line using ferrite beads, which produces high-voltage, high-dV/dt pulses. We have been examining the characteristics of ferrite sharpeners experimentally, varying various parameters. Also we have made the simulation of the ferrite sharpener and compared the predictions with the experimental results in detail to analyze the characteristics of the sharpener. In this report, calculating the magnetization M of the ferrite bead, we divide the bead into n sections radially instead of adopting M at the average radius in the previous report. (author)
Hierarchical Non-linear Image Registration Integrating Deformable Segmentation
Institute of Scientific and Technical Information of China (English)
RAN Xin; QI Fei-hu
2005-01-01
A hierarchical non-linear method for image registration was presented, which integrates image segmentation and registration under a variational framework. An improved deformable model is used to simultaneously segment and register feature from multiple images. The objects in the image pair are segmented by evolving a single contour and meanwhile the parameters of affine registration transformation are found out. After that, a contour-constrained elastic registration is applied to register the images correctly. The experimental results indicate that the proposed approach is effective to segment and register medical images.
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).
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...
Non linear analyses of speech and prosody in Asperger's syndrome
DEFF Research Database (Denmark)
Fusaroli, Riccardo; Bang, Dan; Weed, Ethan
and explain this oddness of speech pattern. In this project, we quantify how the speech patterns of people with Asperger’s Syndrome (AS) differ from that of matched controls. To do so, we employed both traditional measures (pitch range and standard deviation, pause duration, and so on) and 2) non......-linear techniques measuring the structure (regularity and complexity) of verbal, prosodic and fluency behaviour. Our aims were (1) to achieve a more fine-grained understanding of the speech patterns in AS than has previously been achieved using traditional, linear measures of prosody and fluency, and (2) to employ...
Weak non-linear surface charging effects in electrolytic films
Dean, D. S.; Horgan, R. R.
2002-01-01
A simple model of soap films with nonionic surfactants stabilized by added electrolyte is studied. The model exhibits charge regularization due to the incorporation of a physical mechanism responsible for the formation of a surface charge. We use a Gaussian field theory in the film but the full non-linear surface terms which are then treated at a one-loop level by calculating the mean-field Poisson-Boltzmann solution and then the fluctuations about this solution. We carefully analyze the reno...
Solving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton Method
Directory of Open Access Journals (Sweden)
Zanariah A. Majid
2011-01-01
Full Text Available Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs. This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newtons method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems.
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 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 imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
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...
Polycarbonate-Based Blends for Optical Non-linear Applications
Stanculescu, F.; Stanculescu, A.
2016-02-01
This paper presents some investigations on the optical and morphological properties of the polymer (matrix):monomer (inclusion) composite materials obtained from blends of bisphenol A polycarbonate and amidic monomers. For the preparation of the composite films, we have selected monomers characterised by a maleamic acid structure and synthesised them starting from maleic anhydride and aniline derivatives with -COOH, -NO2, -N(C2H5)2 functional groups attached to the benzene ring. The composite films have been deposited by spin coating using a mixture of two solutions, one containing the matrix and the other the inclusion, both components of the composite system being dissolved in the same solvent. The optical transmission and photoluminescence properties of the composite films have been investigated in correlation with the morphology of the films. The scanning electron microscopy and atomic force microscopy have revealed a non-uniform morphology characterised by the development of two distinct phases. We have also investigated the generation of some optical non-linear (ONL) phenomena in these composite systems. The composite films containing as inclusions monomers characterised by the presence of one -COOH or two -NO2 substituent groups to the aromatic nucleus have shown the most intense second-harmonic generation (SHG). The second-order optical non-linear coefficients have been evaluated for these films, and the effect of the laser power on the ONL behaviour of these materials has also been emphasised.
Non Linear Analysis of MPPT for Power Quality Improvement
Directory of Open Access Journals (Sweden)
S. Sankar
2015-08-01
Full Text Available In this study the conventional inverter interfacing renewable energy sources with the grid, without any additional hardware cost. Here, the main idea is the maximum utilization of inverter rating which is most of the time underutilized due to intermittent nature of RES. Based on the non-linear characteristics of PV, these thesis designs a VSS controller to realize the maximum power output of PV arrays. The output power from renewable energy sources fluctuates because of weather variations. This study proposes an effective power quality control strategy of renewable energy sources connected to power system using Photovoltaic (PV array. If the main controller used is a PR controller, any dc offset in a control loop will propagate through the system and the inverter terminal voltage will have a nonzero average value. In this strategy both load and inverter current sensing is required to compensate the load current harmonics. The non-linear load current harmonics may result in voltage harmonics and can create a serious PQ problem in the power system network.
A non-linear model of information seeking behaviour
Directory of Open Access Journals (Sweden)
Allen E. Foster
2005-01-01
Full Text Available The results of a qualitative, naturalistic, study of information seeking behaviour are reported in this paper. The study applied the methods recommended by Lincoln and Guba for maximising credibility, transferability, dependability, and confirmability in data collection and analysis. Sampling combined purposive and snowball methods, and led to a final sample of 45 inter-disciplinary researchers from the University of Sheffield. In-depth semi-structured interviews were used to elicit detailed examples of information seeking. Coding of interview transcripts took place in multiple iterations over time and used Atlas-ti software to support the process. The results of the study are represented in a non-linear Model of Information Seeking Behaviour. The model describes three core processes (Opening, Orientation, and Consolidation and three levels of contextual interaction (Internal Context, External Context, and Cognitive Approach, each composed of several individual activities and attributes. The interactivity and shifts described by the model show information seeking to be non-linear, dynamic, holistic, and flowing. The paper concludes by describing the whole model of behaviours as analogous to an artist's palette, in which activities remain available throughout information seeking. A summary of key implications of the model and directions for further research are included.
The Linear-Non-Linear Frontier for the Goldstone Higgs
Energy Technology Data Exchange (ETDEWEB)
Gavela, M. B. [Madrid, IFT; Kanshin, K. [Padua U.; Machado, P. A.N. [Madrid, IFT; Saa, S. [Madrid, IFT
2016-10-25
The minimal $SO(5)/SO(4)$ sigma 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 $\\sigma$ mass allows 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.
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 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...
Polycarbonate-Based Blends for Optical Non-linear Applications.
Stanculescu, F; Stanculescu, A
2016-12-01
This paper presents some investigations on the optical and morphological properties of the polymer (matrix):monomer (inclusion) composite materials obtained from blends of bisphenol A polycarbonate and amidic monomers. For the preparation of the composite films, we have selected monomers characterised by a maleamic acid structure and synthesised them starting from maleic anhydride and aniline derivatives with -COOH, -NO2, -N(C2H5)2 functional groups attached to the benzene ring. The composite films have been deposited by spin coating using a mixture of two solutions, one containing the matrix and the other the inclusion, both components of the composite system being dissolved in the same solvent. The optical transmission and photoluminescence properties of the composite films have been investigated in correlation with the morphology of the films. The scanning electron microscopy and atomic force microscopy have revealed a non-uniform morphology characterised by the development of two distinct phases. We have also investigated the generation of some optical non-linear (ONL) phenomena in these composite systems. The composite films containing as inclusions monomers characterised by the presence of one -COOH or two -NO2 substituent groups to the aromatic nucleus have shown the most intense second-harmonic generation (SHG). The second-order optical non-linear coefficients have been evaluated for these films, and the effect of the laser power on the ONL behaviour of these materials has also been emphasised.
An Adaptive Non-Linear Map and Its Application
Institute of Scientific and Technical Information of China (English)
YAN Xuefeng
2006-01-01
A novel adaptive non-linear mapping (ANLM),integrating an adaptive mapping error (AME) with a chaosgenetic algorithm (CGA) including chaotic variable, was proposed to overcome the deficiencies of non-linear mapping (NLM). The value of AME weight factor is determined according to the relative deviation square of distance between the two mapping points and the corresponding original objects distance. The larger the relative deviation square between two distances is, the larger the value of the corresponding weight factor is. Due to chaotic mapping operator, the evolutional process of CGA makes the individuals of subgenerations distributed ergodically in the defined space and circumvents the premature of the individuals of subgenerations. The comparison results demonstrated that the whole performance of CGA is better than that of traditional genetic algorithm. Furthermore, a typical example of mapping eight-dimensional olive oil samples onto two-dimensional plane was employed to verify the effectiveness of ANLM. The results showed that the topology-preserving map obtained by ANLM can well represent the classification of original objects and is much better than that obtained by NLM.
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.
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 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 imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Left-Right Non-Linear Dynamical Higgs
Shu, Jing; Yepes, Juan
2016-12-01
All the possible CP-conserving non-linear operators up to the p4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)L × SU(2)R × U(1)B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators. J. Y. also acknowledges KITPC financial support during the completion of this work
Non-linear plasma wake growth of electron holes
Hutchinson, I. H.; Haakonsen, C. B.; Zhou, C.
2015-03-01
An object's wake in a plasma with small Debye length that drifts across the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind 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 size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations.
Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Botelho, Luiz Carlos Lobato
2010-01-01
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Energy Technology Data Exchange (ETDEWEB)
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
Directory of Open Access Journals (Sweden)
S.Jothimani
2014-08-01
Full Text Available This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various flow parameters in the form of dimensionless quantities on the flow field are discussed and presented graphically.
Non-linear dimensionality reduction of signaling networks
Directory of Open Access Journals (Sweden)
Ivakhno Sergii
2007-06-01
Full Text Available Abstract Background Systems wide modeling and analysis of signaling networks is essential for understanding complex cellular behaviors, such as the biphasic responses to different combinations of cytokines and growth factors. For example, tumor necrosis factor (TNF can act as a proapoptotic or prosurvival factor depending on its concentration, the current state of signaling network and the presence of other cytokines. To understand combinatorial regulation in such systems, new computational approaches are required that can take into account non-linear interactions in signaling networks and provide tools for clustering, visualization and predictive modeling. Results Here we extended and applied an unsupervised non-linear dimensionality reduction approach, Isomap, to find clusters of similar treatment conditions in two cell signaling networks: (I apoptosis signaling network in human epithelial cancer cells treated with different combinations of TNF, epidermal growth factor (EGF and insulin and (II combination of signal transduction pathways stimulated by 21 different ligands based on AfCS double ligand screen data. For the analysis of the apoptosis signaling network we used the Cytokine compendium dataset where activity and concentration of 19 intracellular signaling molecules were measured to characterise apoptotic response to TNF, EGF and insulin. By projecting the original 19-dimensional space of intracellular signals into a low-dimensional space, Isomap was able to reconstruct clusters corresponding to different cytokine treatments that were identified with graph-based clustering. In comparison, Principal Component Analysis (PCA and Partial Least Squares – Discriminant analysis (PLS-DA were unable to find biologically meaningful clusters. We also showed that by using Isomap components for supervised classification with k-nearest neighbor (k-NN and quadratic discriminant analysis (QDA, apoptosis intensity can be predicted for different
Ferrite core non-linearity in coils for magnetic neurostimulation.
RamRakhyani, Anil Kumar; Lazzi, Gianluca
2014-10-01
The need to correctly predict the voltage across terminals of mm-sized coils, with ferrite core, to be employed for magnetic stimulation of the peripheral neural system is the motivation for this work. In such applications, which rely on a capacitive discharge on the coil to realise a transient voltage curve of duration and strength suitable for neural stimulation, the correct modelling of the non-linearity of the ferrite core is critical. A demonstration of how a finite-difference model of the considered coils, which include a model of the current-controlled inductance in the coil, can be used to correctly predict the time-domain voltage waveforms across the terminals of a test coil is presented. Five coils of different dimensions, loaded with ferrite cores, have been fabricated and tested: the measured magnitude and width of the induced pulse are within 10% of simulated values.
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, non-linear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but these might not be faithful tr...
Hans Hinterreiter’s non-linear transformations
DEFF Research Database (Denmark)
Makovicky, Emil
Hans Hinterreiter (1902-1989) was a Swiss painter, belonging to the Constructivist movement, who spent most of his life in Ibiza, Spain. Since 1930 he occupied himself with the laws of form and colour. Parallel to Escher, he discovered laws of coloured symmetry before crystallographers started...... poster illustrates four different cases of this process, starting always with a plane-group pattern and showing both the application of non-linear transformations and coloured symmetry. In his more complex patterns, two of which are shown on the poster, Hinterreiter created domains of affinely......-step approach that combines plane group patterns with the principles of coloured symmetry and nonlinear transformations, his understanding of crystallographic and non-crystallographic symmetry and a meticulous application of these principles even to the most complex patterns produced a legacy close to the heart...
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
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Overall mass-transfer coefficients in non-linear chromatography
DEFF Research Database (Denmark)
Mollerup, Jørgen; Hansen, Ernst
1998-01-01
In case of mass transfer where concentration differences in both phases must be taken into account, one may define an over-all mass-transfer coefficient basd on the apparent over-all concentration difference. If the equilibrium relationship is linear, i.e. in cases where a Henry´s law relationship...... can be applied, the over-all mass-transfer coefficient will be concentration independent. However, in mass-transfer operations, a linear equilibrium relationship is in most cases not a valid approximation wherefore the over-all mass-transfer coefficient becomes strongly concentration dependent...... as shown in this paper. In this case one has to discard the use of over-all mass-transfer coefficients and calculate the rate of mass transfer from the two film theory using the appropriate non-linear relationship to calculate the equilibrium ratio at the interface between the two films....
Non-linear rheology in a model biological tissue
Matoz-Fernandez, D A; Barrat, Jean-Louis; Bertin, Eric; Martens, Kirsten
2016-01-01
Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.
Realising traceable electrostatic forces despite non-linear balance motion
Stirling, Julian; Shaw, Gordon A.
2017-05-01
Direct realisation of force, traceable to fundamental constants via electromagnetic balances, is a key goal of the proposed redefinition of the international system of units (SI). This will allow small force metrology to be performed using an electrostatic force balance (EFB) rather than subdivision of larger forces. Such a balance uses the electrostatic force across a capacitor to balance an external force. In this paper we model the capacitance of a concentric cylinder EFB design as a function of the displacement of its free electrode, accounting for the arcuate motion produced by parallelogram linkages commonly used in EFB mechanisms. From this model we suggest new fitting procedures to reduce uncertainties arising from non-linear motion as well as methods to identify misalignment of the mechanism. Experimental studies on both a test capacitor and the NIST EFB validate the model.
The mathematics of non-linear metrics for nested networks
Wu, Rui-Jie; Shi, Gui-Yuan; Zhang, Yi-Cheng; Mariani, Manuel Sebastian
2016-10-01
Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.
Biometric Authentication System using Non-Linear Chaos
Directory of Open Access Journals (Sweden)
Dr.N.Krishnan
2010-08-01
Full Text Available A major concern nowadays for any Biometric Credential Management System is its potential vulnerability to protect its information sources; i.e. protecting a genuine user’s template from both internal and external threats. These days’ biometric authentication systems face various risks. One of the most serious threats is the ulnerability of the template's database. An attacker with access to a reference template could try to impersonate a legitimate user by reconstructing the biometric sample and by creating a physical spoof.Susceptibility of the database can have a disastrous impact on the whole authentication system. The potential disclosure of digitally stored biometric data raises serious concerns about privacy and data protection. Therefore, we propose a method which would integrate conventional cryptography techniques with biometrics. In this work, we present a biometric crypto system which encrypts the biometric template and the encryption is done by generating pseudo random numbers, based on non-linear dynamics.
Responding to non-linear internationalisation of public policy
DEFF Research Database (Denmark)
Daugbjerg, Carsten
2016-01-01
The transfer of regulatory authority to international organisations can initiate domestic policy reform. The internationalisation process can be a one-off transfer of authority to international institutions or an ongoing process. In the latter situation, the level of internationalisation may...... be gradually increased by expanding the regulatory scope of the regime or by deepening it. However, internationalisation processes may also involve stalemate or even reversal. How do domestic policy makers respond to such non-linear internationalisation? To answer this question, this paper analyzes...... the relationship between developments in the GATT and WTO farm trade negotiations and the reform trajectory of the EU's Common Agricultural Policy (CAP) from the early 1990s to 2013. Until 2008, the EU gradually changed the support instruments of the CAP to limit their trade distorting impact. After the Doha Round...
Computational models of signalling networks for non-linear control.
Fuente, Luis A; Lones, Michael A; Turner, Alexander P; Stepney, Susan; Caves, Leo S; Tyrrell, Andy M
2013-05-01
Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.
Linear and non-linear bias: predictions vs. measurements
Hoffmann, Kai; Gaztanaga, Enrique
2016-01-01
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. Accociating galaxies with dark matter haloes in the MICE Grand Challenge N-body simulation we directly measure the bias parameters by comparing the smoothed density fluctuations of halos and matter in the same region at different positions as a function of smoothing scale. Alternatively we measure the bias parameters by matching the probablility 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 articles using the same data. We find an overall variation of the linear bias measurements and predictions of $\\sim 5 \\%$ with respect to results from two-point corr...
Non linear prompt neutron kinetics in multigroup diffusion theory
Energy Technology Data Exchange (ETDEWEB)
Ghatak, Ajoy Kumar
1963-06-15
It is shown that in the usual point kinetics formulation of the Fuch's model the assumption that the basic quantity is the ratio of prompt negative temperature coefficient to prompt neutron lifetime is correct in the limit that the higher mode effects can be neglected. The criticality calculation needed to calculate this coefficient is defined. The effect on the Fuch's model when the heat capacity and temperature coefficient vary linearly with temperature and delayed neutrons are taken into account is considered. The higher mode contributions in the presence of temperature feed-back effects are estimated. A method for calculating the space-dependent effects in non-linear kinetics is outlined. An analysis of the transient behavior of the TREAT reactor is also given. (C.E.S.)
An empirical evaluation of non-linear trading rules.
Directory of Open Access Journals (Sweden)
Sosvilla-Rivero, Simón
2003-01-01
Full Text Available In this paper we investigate the profitability of non-linear trading rules based on nearest neighbour (NN predictors. Applying this investment strategy to the New York Stock Exchange, our results suggest that, taking into account transaction costs, the NN-based trading rule is superior to both a riskadjusted buy-and-hold strategy and a linear ARIMA-based strategy in terms of returns for all of the years studied (1997-2002. Regarding other profitability measures, the NN-based trading rule yields higher Sharpe ratios than the ARIMA-based strategy for all of the years in the sample except for 2001. As for 2001, in 36 out of the 101 cases considered, the ARIMA-based strategy gives higher Sharpe ratios than those from the NN-trading rule, in 18 cases the opposite is true, and in the remaining 36 cases both strategies yield the same ratios.
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.
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 Linear Lorentz Transformation and Doubly Special Relativity
Atehortua, A N; Mira, J M; Vanegas, N
2012-01-01
We generate non-linear representations of the Lorentz Group by unitary transformation over the Lorentz generators. To do that we use deformed scale transformations by introducing momentum-depending parameters. The momentum operator transformation is found to be equivalent to a particle momentum transformation. The configuration space transformation is found to depend on the old momentum operator and we show that this transformation generates models with two scales, one for the velocity ($c$) and another one for the energy. A Lagrangian formalism is proposed for these models and an effective metric for the deformed Minkowski space is found. We show that the Smolin model is one in a family of doubly special relativity. Finally we construct an ansatz for the quantization of such theories.
Non-linear scalable TFETI domain decomposition based contact algorithm
Dobiáš, J.; Pták, S.; Dostál, Z.; Vondrák, V.; Kozubek, T.
2010-06-01
The paper is concerned with the application of our original variant of the Finite Element Tearing and Interconnecting (FETI) domain decomposition method, called the Total FETI (TFETI), to solve solid mechanics problems exhibiting geometric, material, and contact non-linearities. The TFETI enforces the prescribed displacements by the Lagrange multipliers, so that all the subdomains are 'floating', the kernels of their stiffness matrices are known a priori, and the projector to the natural coarse grid is more effective. The basic theory and relationships of both FETI and TFETI are briefly reviewed and a new version of solution algorithm is presented. It is shown that application of TFETI methodology to the contact problems converts the original problem to the strictly convex quadratic programming problem with bound and equality constraints, so that the effective, in a sense optimal algorithms is to be applied. Numerical experiments show that the method exhibits both numerical and parallel scalabilities.
Considering Complexity: Toward A Strategy for Non-linear Analysis
Directory of Open Access Journals (Sweden)
Ken Hatt
2009-01-01
Full Text Available This paper explores complexity and a strategy for non-linear analysis with a consistent ontological, epistemological and methodological orientation. Complexity is defined and approaches in the natural sciences, ecosystems research, discursive studies and the social sciences are reviewed. In social science, theoretical efforts associated with problems of social order (Luhmann, critical sociology (Byrne and post-structuralism (Cilliers as well as representative studies are examined. The review concludes that there is need for an approach that will address morphogenesis and facilitate analysis of multilateral mutual causal relations. The remainder of the paper approaches these matters by outlining Archer’s approach to morphogenesis, Maruyama’s morphogenetic casual-loop model of epistemology and illustrating Maruyama’s method for analysis which employs both positive and negative feedback loops. The result is a strategy based on morphogenetic causal loop models that can be used to analyze structuring and the connections through which structures may be reproduced or transformed.
Institute of Scientific and Technical Information of China (English)
WANG Zhongmin; GAO Jingbo; LI Huixia; LIU Hongzhao
2008-01-01
The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
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
Non-linear dynamics of a spur gear pair
Kahraman, A.; Singh, R.
1990-10-01
Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.
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
Modeling Non-Linear Material Properties in Composite Materials
2016-06-28
will be used to calculate the thermal strains. In equation [6], α is the coefficient of thermal expansion tensor . To determine the effects of the...governing equation for the microscale, where I is the identity tensor and Hk(y) is a Y-periodic tensor on the micro- scale relating T1 to the macro...9c] is the governing equation for the global scale. In this equation, � represents the effective thermal conductivity tensor , � is the
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.
Development of a non-linear mathematical model for Stirling engines
Serrate, O. A. G.; Parise, J. A. R.
The development of a simulation model for Stirling engines is discussed. The model follows the control-volume method, in which the engine is divided into five volumes of control: the hot expansion and cold compression spaces, the heater and cooler, and the regenerator. The engine thermodynamic cycle is divided into a number of time-steps, and a system of nonlinear ordinary differential equations, which describe the energy balances over the gas control volumes, as well as in the regenerator material, is solved numerically. The model features some recent advances in the analysis of Stirling engines. Pressure drop equations for the gas flow passages are considered. These equations are solved simultaneously with the rest of the model. The power dependence of the pressure drop on the gas mass flow rate introduces non-linearities in the system of equations. These equations will provide the rate of variation with time of the dependent variables (pressure, temperature, velocity, and mass) at each control volume. Techniques to enhance convergence have been employed. Predicted results for a typical engine are compared with experimental data.
Keesman, K.J.
2006-01-01
In this short paper for the panel discussion on ¿Experience and challenges in identification of non-linear systems¿ some major issues with respect to identification of non-linear biochemical and environmental systems are presented.
KIM, DONG-HYUN; LEE, IN
2000-07-01
A two-degree-of-freedom airfoil with a freeplay non-linearity in the pitch and plunge directions has been analyzed in the transonic and low-supersonic flow region, where aerodynamic non-linearities also exist. The primary purpose of this study is to show aeroelastic characteristics due to freeplay structural non-linearity in the transonic and low-supersonic regions. The unsteady aerodynamic forces on the airfoil were evaluated using two-dimensional unsteady Euler code, and the resulting aeroelastic equations are numerically integrated to obtain the aeroelastic time responses of the airfoil motions and to investigate the dynamic instability. The present model has been considered as a simple aeroelastic model, which is equivalent to the folding fin of an advanced generic missile. From the results of the present study, characteristics of important vibration responses and aeroelastic instabilities can be observed in the transonic and supersonic regions, especially considering the effect of structural non-linearity in the pitch and plunge directions. The regions of limit-cycle oscillation are shown at much lower velocities, especially in the supersonic flow region, than the divergent flutter velocities of the linear structure model. It is also shown that even small freeplay angles can lead to severe dynamic instabilities and dangerous fatigue conditions for the flight vehicle wings and control fins.
Adaptive set-point tracking of the Lorenz chaotic system using non-linear feedback
Energy Technology Data Exchange (ETDEWEB)
Haghighatdar, F. [Department of Electronic Engineering, University of Isfahan, Hezar-Jerib St., Postal code: 8174673441, Isfahan (Iran, Islamic Republic of)], E-mail: fr_haghighat@yahoo.com; Ataei, M. [Department of Electronic Engineering, University of Isfahan, Hezar-Jerib St., Postal code: 8174673441, Isfahan (Iran, Islamic Republic of)], E-mail: mataei1971@yahoo.com
2009-05-30
In this paper, an adaptive control method for set-point tracking of the Lorenz chaotic system by using non-linear feedback is proposed. The design procedure of the proposed controller is accomplished in two steps. At the first step, using Lyapunov's direct method, a non-linear state feedback is selected so that without any need to apply identification techniques, in despite of the uncertain parameters existence in the system state equations, the asymptotic stability of the general Lorenz system is guaranteed in a stochastic point of the manifold containing general system equilibrium points. At the second step, a linear state feedback with adaptive gain is added to the prior controller to eliminate the tracking error. In order to guarantee the system asymptotic stability at desired set-point, the indirect Lyapunov's method is used. Finally, to show the effectiveness of the proposed methodology, the simulation results of different experiments including system parameters changes and set-point variation are provided.
Strong Glacial Cooling In The Middle Tropical Troposphere Due To Non-linear Effects
Lorenz, S. J.; Lohmann, G.
Numerical experiments with an atmospheric general circulation model for glacial and interglacial climates have been performed. Our model experiments reveal that slightly cooler tropical sea surface temperatures (SST) relative to the ones previously recon- structed by the CLIMAP project (1981) are sufficient to exhibit a strong glacial cool- ing reconstructed by tropical snow lines. The increased cooling in our experiments can be attributed to two non-linear effects: Firstly, there is an increased environmental lapse rate in the free atmosphere. Slightly cooler glacial SSTs provide for less abso- lute moisture content and the Clausius-Clapeyron equation of moisture is accountable for an increased lapse rate. In our LGM simulation we find an additional two degrees cooling in the tropical middle troposphere. Secondly, the surface air temperature near tropical glaciers is further cooled by a longer duration of snow cover. Our model result provides a consistent view of the last glacial maximum climate with much colder tem- peratures than today in the tropical mountains in concordance with moderate lowering of tropical SSTs. We propose that these non-linearities in the climate system are also important when detecting global warming from tropical snow lines.
Study of Linear and Non-Linear Optical Parameters of Zinc Selenide Thin Film
Directory of Open Access Journals (Sweden)
H. N. Desai
2015-06-01
Full Text Available Thin film of Zinc Selenide (ZnSe was deposited onto transparent glass substrate by thermal evaporation technique. ZnSe thin film was characterized by UV-Visible spectrophotometer within the wavelength range of 310 nm-1080 nm. The Linear optical parameters (linear optical absorption, extinction coefficient, refractive index and complex dielectric constant of ZnSe thin film were analyzed from absorption spectra. The optical band gap and Urbach energy were obtained by Tauc’s equation. The volume and surface energy loss function of ZnSe thin film were obtained by complex dielectric constant. The Dispersion parameters (dispersion energy, oscillation energy, moment of optical dispersion spectra, static dielectric constant and static refractive index were calculated using theoretical Wemple-DiDomenico model. The oscillation strength, oscillator wavelength, high frequency dielectric constant and high frequency refractive index were calculated by single Sellmeier oscillator model. Also, Lattice dielectric constant, N/m* and plasma resonance frequency were obtained. The electronic polarizibility of ZnSe thin film was estimated by Clausius-Mossotti local field polarizibility. The nonlinear optical parameters (non-linear susceptibility and non-linear refractive index were estimated.
A non-linear stochastic model for an office building with air infiltration
Directory of Open Access Journals (Sweden)
Anders Thavlov
2015-06-01
Full Text Available This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model parameters are estimated using a maximum-likelihood technique. Based on the maximum-likelihood value, the different models are statistically compared to each other using Wilk's likelihood ratio test. The model showing the best performance is finally verified in both the time domain and the frequency domain using the auto-correlation function and cumulated periodogram. The proposed model which includes air-infiltration shows a significant improvement compared to previously proposed linear models. The model has subsequently been used in applications for provision of power system services, e.g. by providing heat load reduction during peak load hours, control of indoor air temperature and for generating forecasts of power consumption from space heating.
An effective description of dark matter and dark energy in the mildly non-linear regime
Lewandowski, Matthew; Senatore, Leonardo
2016-01-01
In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the information resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark en...
Non-linear simulations of combustion instabilities with a quasi-1D Navier-Stokes code
Haugen, Nils Erland L; Sannan, Sigurd
2010-01-01
As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities with high accuracy. The inherent non-linearities in combustion instabilities can be of crucial importance, and we here propose an approach in which the one-dimensional Navier-Stokes and scalar transport equations are solved for geometries of variable cross-section. The focus is on attached flames, and for this purpose a new phenomenological model for the unsteady heat release from a flame front is introduced. In the attached flame method (AFM) the heat release occurs over the full length of the flame. The non-linear code with the use of the AFM approach is validated against results from an experimental study of thermoacoustic instabilities in oxy-fuel flames by Ditaranto and Hals [Combustion and Flame, 146, 493-512 (2006)]. The numerical simulations are in accordance with the...
On the formation of shocks of electromagnetic plane waves in non-linear crystals
Christodoulou, Demetrios
2015-01-01
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global $C^2$-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density...
On the formation of shocks of electromagnetic plane waves in non-linear crystals
Christodoulou, Demetrios; Perez, Daniel Raoul
2016-08-01
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global C2-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density, assuming no dispersion.
A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure
Albertazzi, A.; Viotti, M. R.; Veiga, C. L. N.; Fantin, A. V.
2016-08-01
Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.
Yadav, Manish; Singh, Nitin Kumar
2017-08-01
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.
State-variable analysis of non-linear circuits with a desk computer
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Discriminating Non-Linearity from Linearity: Its Cognitive Foundations in Five-Year-Olds
Ebersbach, Mirjam; Van Dooren, Wim; Goudriaan, Margje N.; Verschaffel, Lieven
2010-01-01
People often have difficulties in understanding situations that involve non-linear processes. Also, the topic of non-linear functions is introduced relatively late in the curriculum. Previous research has nevertheless shown that already children aged 6 years and older are able to discriminate non-linear from linear processes. Within the present…
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Norman, M. R.
2013-12-01
Differential Transforms (DTs), a core component of so-called "automatic" or "algorithmic" differentiation, offer significant flexibility and efficiency to any numerical method. The i-th and j-th DT, U(i,j), of a function, u(x,y), is simply U(i,j)=1/(i!j!)*∂(i+j)u/∂xi∂yj. Being a term in the Taylor series of u(x,y) makes the reverse transform trivial. This relation also computes initial DTs from known spatial derivatives. What is novel about DTs is how they simplify a complex PDE system, transforming most arithmetic, trigonometric, and other operators into simple recurrence relations in derivative space. This allows one to simply and quickly compute analytical derivatives of highly complex and non-linear functions. Consider a pseudo-conservation law system, u(x)t+f(u,x)x=s(u,x), for instance. The fluxes and source terms could be (and often are) highly complex, non-linear functions of the state vector and independent variables. Regardless of the spatial discretization (variational / finite-element, weak / finite-volume, or strong / finite-difference), one nearly always must resort to tensored quadrature to evaluate face fluxes and body source terms, and this treatment is expensive. However, if one uses DTs to analytically compute spatial derivatives of the flux and source terms, given spatial derivatives of u, then the fluxes and source terms are directly expanded as polynomials, allowing for significantly cheaper, quadrature-free integration, sampling, and differentiation with a single dot product. Besides being simpler, this also allows flexibility for Galerkin methods in particular to analytically and cheaply compute body integrals, which are often approximated inexactly with quadrature. Computing Nth-order DTs in D dimensions is of O(D2*N) complexity, and whether for transport or non-linear compressible Euler equations, they are cheaper to compute and integrate analytically than quadrature. Further, because time-dependent PDE systems relate spatial
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
Non-linear controls on the persistence of La Nina
Di Nezio, P. N.; Deser, C.
2013-12-01
Non-linear controls on the persistence of La Nina Pedro DiNezio and Clara Deser Up to half of the observed La Nina events last for two years or more. Most El Nino events, in contrast, last no longer than one year. The physical processes causing this asymmetry in the duration of warm and cold ENSO events is unknown. The persistence of La Nina, not only exacerbates the climate impacts, especially in regions prone to drought, but also is highly unpredictable. In this talk we will explore the nonlinear processes that generate the persistence of La Nina in observations and in CCSM4 - a coupled climate model that simulates this feature realistically. First, we develop a non-linear delayed-oscillator model (nonlinDO) based on CCSM4's heat budget. All positive and negative feedbacks of nonlinDO capture the nonlinear and seasonal dependence exhibited by CCSM4. The nonlinear behavior is due to: 1) weaker atmospheric damping of cold events with respect to warm events, 2) stronger wind response for large warm events, and 3) weaker coupling between thermocline and sea-surface temperature anomalies when the thermocline deepens. We force the simple model with white Gaussian noise resulting in seasonal modulation of variance and skewness, and a spectral peak, that are in agreement with CCSM4. Sensitivity experiments with nonlinDO show that the thermocline nonlinearity (3) is the sole process controlling the duration of La Nina events. Linear ENSO theory indicates that La Nina events drive a delayed thermocline deepening that leads to their demise. However, the thermocline nonlinearity (3) renders this response ineffective as La Nina events become stronger. This diminishing of the delayed-thermocline feedback prevents the equatorial Pacific from returning to neutral or warm conditions and cold conditions persist for a second year. Observations show evidence for this thermocline nonlinearity suggesting that this process could be at work in the real world. Last, we show evidence that
Filtering Non-Linear Transfer Functions on Surfaces.
Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice
2014-07-01
Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few
Non-linear hydrodynamics of axion dark matter: relative velocity effects and "quantum forces"
Marsh, David J E
2015-01-01
The non-linear hydrodynamic equations for axion/scalar field dark matter (DM) in the non-relativistic Madelung-Shcr\\"{o}dinger form are derived in a simple manner, including the effects of universal expansion and Hubble drag. The hydrodynamic equations are used to investigate the relative velocity between axion DM and baryons, and the moving-background perturbation theory (MBPT) derived. Axions massive enough to be all of the DM do not affect the coherence length of the relative velocity, but the MBPT equations are modified by the inclusion of the axion effective sound speed. These MBPT equations are necessary for accurately modelling the effects of axion DM on the formation of the first cosmic structures, and suggest that the 21cm power spectrum could improve constraints on axion mass by up to four orders of magnitude with respect to the current best constraints. A further application of these results uses the "quantum force" analogy to model scalar field gradient energy in a smoothed-particle hydrodynamics ...
Non-linear rotation-free shell finite-element models for aortic heart valves.
Gilmanov, Anvar; Stolarski, Henryk; Sotiropoulos, Fotis
2017-01-04
Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves. Copyright © 2016. Published by Elsevier Ltd.
Non-linear signal detection improvement by radiation damping in single-pulse NMR spectra.
Schlagnitweit, Judith; Morgan, Steven W; Nausner, Martin; Müller, Norbert; Desvaux, Hervé
2012-02-01
When NMR lines overlap and at least one of them is affected by radiation damping, the resonance line shapes of all lines are no longer Lorentzian. We report the appearance of narrow signal distortions, which resemble hole-burnt spectra. This new experimental phenomenon facilitates the detection of tiny signals hidden below the main resonance. Theoretical analysis based on modified Maxwell-Bloch equations shows that the presence of strong transverse magnetization creates a feedback through the coil, which influences the magnetization of all spins with overlapping resonance lines. In the time domain this leads to cross-precession terms between magnetization densities, which ultimately cause non-linear behavior. Numerical simulations corroborate this interpretation.
Non-linear variability in microquasars in relation with the winds from their accretion disks
Janiuk, Agnieszka; Sukova, Petra; Capitanio, Fiamma; Bianchi, Stefano; Kowalski, Wojtek
2016-01-01
The microquasar IGR J17091, which is the recently discovered analogue of the well known source GRS 1915+105, exhibits quasi-periodic outbursts, with a period of 5-70 seconds, and regular amplitudes, referred to as "heartbeat state". We argue that these states are plausibly explained by accretion disk instability, driven by the dominant radiation pressure. Using our GLobal Accretion DIsk Simulation hydrodynamical code, we model these outbursts quantitatively. We also find a correlation between the presence of massive outflows launched from the accretion disk and the stabilization of its oscillations. We verify the theoretical predictions with the available timing and spectral observations. Furthermore, we postulate that the underlying non-linear differential equations that govern the evolution of an accretion disk are responsible for the variability pattern of several other microquasars, including XTE J1550-564, GX 339-4, and GRO J1655-40. This is based on the signatures of deterministic chaos in the observed ...
Non-linear diffusion of cosmic rays escaping from supernova remnants I: the effect of neutrals
Nava, Lara; Marcowith, Alexandre; Morlino, Giovanni; Ptuskin, Vladimir S
2016-01-01
Supernova remnants are believed to be the main sources of galactic Cosmic Rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disk volume, where most supernovae explode, and are characterised by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that stream...
Comparing non-linear mathematical models to describe growth of different animals
Directory of Open Access Journals (Sweden)
Jhony Tiago Teleken
2017-02-01
Full Text Available The main objective of this study was to compare the goodness of fit of five non-linear growth models, i.e. Brody, Gompertz, Logistic, Richards and von Bertalanffy in different animals. It also aimed to evaluate the influence of the shape parameter on the growth curve. To accomplish this task, published growth data of 14 different groups of animals were used and four goodness of fit statistics were adopted: coefficient of determination (R2, root mean square error (RMSE, Akaike information criterion (AIC and Bayesian information criterion (BIC. In general, the Richards growth equation provided better fits to experimental data than the other models. However, for some animals, different models exhibited better performance. It was obtained a possible interpretation for the shape parameter, in such a way that can provide useful insights to predict animal growth behavior.
Non-planar and Non-linear Second Sound Waves in He Ⅱ
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; KIMURA Seiji; MURAKAMI Masahide; WANG Ru-zhu
2000-01-01
Non-planar and non-linear second sound wave are experimentally investigated in an open He Ⅱ bath. It is found that second sound wave characterized by a negative tail part in an open He Ⅱ bath is different from that propagating through a channel, and the shape of the negative tail part of second sound wave varies at different location in an open He Ⅱ bath. Theoretical consideration is also carried out based on two-fluid model and vortex evolution equation. It is found that experimental and theoretical results agree rather well with each other. Second sound wave may develop into the thermal shock wave provided that the heat flux is large.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
-numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...... of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......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...
The Non-linear Saturation of the Goldreich-Schubert-Fricke Instability
Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey
2015-11-01
The Goldreich-Schubert-Fricke (GSF) instability is an important process in stellar interiors and possibly in exoplanetary atmospheres. While the linear phase of the instability has been explored for nearly fifty years, its non-linear saturation has not been explored in detail. The GSF is a double-diffusive instability in which Rayleigh unstable perturbations are robbed of buoyant stability by thermal diffusion. Here, we will present results from a suite of direct numerical simulations using the Spiegel-Veronis Boussinesq equations in the Dedalus framework. These DNS are designed to explore the behavior of the GSF over a range of Prandtl numbers. In stellar interiors, Pr ~=10-6 , but we are limited by computational resources to much higher values, so instead we will discuss the Pr scaling of transport and mixing. We will also discuss the impact of the Boussinesq approximation in the case where large aspect ration perturbations exceed a scale height.
Superfast non-linear diffusion: Capillary transport in particulate porous media
Lukyanov, A V; Baines, M J; Theofanous, T G
2013-01-01
The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving bounda...
A SIMPLE FINITE ELEMENT FOR NON-LINEAR ANALYSIS OF COMPOSITE PLATES
Directory of Open Access Journals (Sweden)
V.B. Tungikar
2011-06-01
Full Text Available Finite Element Analysis for geometrically nonlinear behaviour of laminated composite plates is presented andcompared with the reported investigations. However structural non-linearity is encountered in certain cases andneeds attention. A higher order displacement field that accounts for transverse shear effects under geometricnonlinear condition is employed in the formulation of a four node, rectangular, element with thirteen degrees offreedom per node. First order Zigzag terms have been included in displacement field for improvement in theresponse. Von Karman strain approach is considered in the present analysis. Incremental Pica iterative scheme isused to solve resulting nonlinear equilibrium equations. The formulation demonstrates its excellence in theperformance for predicting response at various lay ups and plies conditions.
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...
Analyses of non-linear systems and their application to biology: a review.
Sato, S
1994-01-01
In this review article, Wiener's analyses of non-linear systems and other topics on non-linear noise and non-stationary signals are introduced. Firstly, application and limitation of linear aspects on a biological system and a background of introduction of the Wiener's theory to non-linear analysis are briefly mentioned. The practical applications, however, were not so successful for several reasons. We shall see how these problems are solved under collaboration between biologists and engineers who have a knowledge of the subject and utilizing computational facility. Several aspects of the methodology involving non-linear systems, non-linear noise and non-stationary signals are also reviewed.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time
NLHB : A Non-Linear Hopper Blum Protocol
Madhavan, Mukundan; Sankarasubramaniam, Yogesh; Viswanathan, Kapali
2010-01-01
In this paper, we propose a light-weight provably-secure authentication protocol called the NLHB protocol, which is a variant of the HB protocol. The HB protocol uses the complexity of decoding linear codes for security against passive attacks. In contrast, security for the NLHB protocol is proved by reducing passive attacks to the problem of decoding a class of non-linear codes\\footnote that are provably hard. We demonstrate that the existing passive attacks on the HB protocol family, which have contributed to considerable reduction in its effective key-size, are ineffective against the NLHB protocol. From the evidence, we conclude that smaller-key sizes are sufficient for the NLHB protocol to achieve the same level of passive attack security as the HB Protocol. Further, for this choice of parameters, we provide an implementation instance for the NLHB protocol for which the Prover/Verifier complexity is lower than the HB protocol, enabling authentication on very low-cost devices like RFID tags. Finally, in t...
Organic non-linear optics and opto-electronics
Maldonado, J. L.; Ramos-Ortíz, G.; Rodríguez, M.; Meneses-Nava, M. A.; Barbosa-García, O.; Santillán, R.; Farfán, N.
2010-12-01
π-conjugated organic molecules and polymers are of great importance in physics, chemistry, material science and engineering. It is expected that, in the near future, organic materials will find widespread use in many technological applications. In the case of organic opto-electronic systems, the list of devices includes light emitting diodes (OLEDs), photovoltaic cells (OPVs), field-effect transistors (OFET), photorefractive materials for light manipulation, among others. These materials are also used for photonic applications: all-optical switching, modulators, optical correlators, plastic waveguides, all polymeric integrated circuits, solid-state lasers, and for biophotonic applications as in the case of the development of organic labels for multiphoton microscopy and photodynamic therapy. The advances in the developing of organic compounds with better mechanical, electrical, and optical (linear and non-linear) characteristics are of a great importance for this field. Here, we present the research on this area carried out at the Centro de Investigaciones en Óp-tica (CIO), in collaboration with Chemistry Departments of different institutions. This work focuses on the optical characterization of materials through several techniques such as TOF, FWM, TBC, THG Maker Fringes, HRS, Z-scan, and TPEF. Additionally, some applications, such as dynamic holography by using photorefractive polymers, and OPVs cells will be discussed.
Non-linear Dynamics of Speech in Schizophrenia
DEFF Research Database (Denmark)
Fusaroli, Riccardo; Simonsen, Arndis; Weed, Ethan
Background The speech of patients with schizophrenia is often described as monotonous, flat and without emotion. Distinctive speech patterns are qualitatively assessed in the diagnostic process and deeply impact the quality of everyday social interactions. In this project, we investigate and mode...... to the symptoms. Automated analysis of voice dynamics reveals potential for the assessment and monitoring of the disorder. Future work includes further validation of the approach, as well as more detailed investigation of the relation between speech patterns and other symptoms.......Background The speech of patients with schizophrenia is often described as monotonous, flat and without emotion. Distinctive speech patterns are qualitatively assessed in the diagnostic process and deeply impact the quality of everyday social interactions. In this project, we investigate and model...... 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...
Non linear inversion of gravity gradients and the GGI gradiometer
Talwani, Manik
2011-12-01
All gradiometers currently operating for exploration in the field are based on Lockheed Martin's GGI gradiometer. The working of this gradiometer is described and a method for robust non linear inversion of gravity gradients is presented. The inversion method involves obtaining the gradient response of a trial body consisting of vertical rectangular prisms. The inversion adjusts the depth to the tops or bases of the prisms. In the trial model all the prisms are not required to have the same area of cross section or the same density (which can also be allowed to vary with depth). The depth to the tops and bottoms of each prism can also be different. This response is compared with the observed values of gradient and through an iterative procedure, the difference is minimized in a least square sense to arrive at a best fitting model by varying the position of the tops or bottoms of the prisms. Each gradient can be individually inverted or one or more gradients can be jointly inverted. The method is extended to invert gravity values individually or jointly with gradient values. The use of Differential Curvature, a quantity which is directly obtained by current gradiometers in use and which is an invariant under a rotation in the horizontal plane, is emphasized. Synthetic examples as well as a field example of inversion are given.
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.
The weakly non-linear density-velocity relation
Chodorowski, Michal J.; Lokas, Ewa L.
1997-05-01
We rigorously derive up to third order in perturbation theory the weakly non-linear relation between the cosmic density and velocity fields. The density field is described by the mass density contrast, delta. The velocity field is described by the variable theta proportional to the velocity divergence, theta=-f (Omega)^-1H ^-1_0∇. v, where f (Omega)~=Omega^0.6, Omega is the cosmological density parameter and H_0 is the Hubble constant. Our calculations show that mean delta given theta is a third-order polynomial in theta, --_theta=a _1theta+a_2(theta ^2-sigma^2_theta)+ a_3theta^3. This result constitutes an extension of the formula --_theta=theta+a _2(theta^2-sigma^2 _theta) found by Bernardeau which involved second-order perturbative solutions. Third-order perturbative corrections introduce the cubic term. They also, however, cause the coefficient a_1 to depart from unity, in contrast with the linear theory prediction. We compute the values of the coefficients a_p for scale-free power spectra, as well as for standard cold dark matter (CDM), for Gaussian smoothing. The coefficients obey a hierarchy a_3Ganon et al. The results provide a method for breaking the Omega-bias degeneracy in comparisons of cosmic density and velocity fields such as IRAS-potent.
Non-linear BFKL dynamics: color screening vs. gluon fusion
Fiore, R; Zoller, V R
2012-01-01
A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken $x$ is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is $R_c\\simeq 0.2-0.3$ fermi. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter $\\sim R_c^2/8B$, with the diffraction cone slope $B$ standing for the characteristic size of the interaction region. It should slowly $\\propto 1/\\ln Q^2$ decrease at large $Q^2$. Smallness of the ratio $R_c^2/8B$ makes the non-linear effects rather weak even at lowest Bjorken $x$ available at HERA. We re...
Non-linear modulation of short wavelength compressional Alfven eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Bortolon, A. [University of California, Irvine, California 92697 (United States); Crocker, N. A. [University of California, Los Angeles, California 90095 (United States); Levinton, F. M.; Yuh, H. [Nova Photonics, Princeton, New Jersey 08543 (United States)
2013-04-15
Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Non-linear controllers in ship tracking control system
Institute of Scientific and Technical Information of China (English)
LESZEK M
2005-01-01
The cascade systems which stabilize the transverse deviation of the ship in relation to the set path is presented. The ship's path is determined as a broken line with specified coordinates of way points. Three controllers are used in the system. The main primary controller is the trajectory controller. The set value of heading for the course control system or angular velocity for the turning control system is generated. The course control system is used on the straight line of the set trajectory while the turning controller is used during a change of the set trajectory segment. The characteristics of the non-linear controllers are selected in such a way that the properties of the control system with the rate of turn controller are modelled by the first-order inertia, while the system with the course keeping controller is modelled by a second-order linear term. The presented control system is tested in computer simulation. Some results of simulation tests are presented and discussed.
Non-linear evolution of the cosmic neutrino background
Villaescusa-Navarro, Francisco; Peña-Garay, Carlos; Viel, Matteo
2012-01-01
We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations. Our set of simulations explore the properties of neutrinos in a reference $\\Lambda$CDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass $10^{11}-10^{15}$ $h^{-1}$M$_{\\odot}$, 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. 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 ...
Non-linear optical microscopy sheds light on cardiovascular disease.
Directory of Open Access Journals (Sweden)
Valentina Caorsi
Full Text Available Many cardiac diseases have been associated with increased fibrosis and changes in the organization of fibrillar collagen. The degree of fibrosis is routinely analyzed with invasive histological and immunohistochemical methods, giving a limited and qualitative understanding of the tissue's morphological adaptation to disease. Our aim is to quantitatively evaluate the increase in fibrosis by three-dimensional imaging of the collagen network in the myocardium using the non-linear optical microscopy techniques Two-Photon Excitation microscopy (TPE and Second Harmonic signal Generation (SHG. No sample staining is needed because numerous endogenous fluorophores are excited by a two-photon mechanism and highly non-centrosymmetric structures such as collagen generate strong second harmonic signals. We propose for the first time a 3D quantitative analysis to carefully evaluate the increased fibrosis in tissue from a rat model of heart failure post myocardial infarction. We show how to measure changes in fibrosis from the backward SHG (B(SHG alone, as only backward-propagating SHG is accessible for true in vivo applications. A 5-fold increase in collagen I fibrosis is detected in the remote surviving myocardium measured 20 weeks after infarction. The spatial distribution is also shown to change markedly, providing insight into the morphology of disease progression.
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.
Non-linear Least Squares Fitting in IDL with MPFIT
Markwardt, Craig B
2009-01-01
MPFIT is a port to IDL of the non-linear least squares fitting program MINPACK-1. MPFIT inherits the robustness of the original FORTRAN version of MINPACK-1, but is optimized for performance and convenience in IDL. In addition to the main fitting engine, MPFIT, several specialized functions are provided to fit 1-D curves and 2-D images; 1-D and 2-D peaks; and interactive fitting from the IDL command line. Several constraints can be applied to model parameters, including fixed constraints, simple bounding constraints, and "tying" the value to another parameter. Several data weighting methods are allowed, and the parameter covariance matrix is computed. Extensive diagnostic capabilities are available during the fit, via a call-back subroutine, and after the fit is complete. Several different forms of documentation are provided, including a tutorial, reference pages, and frequently asked questions. The package has been translated to C and Python as well. The full IDL and C packages can be found at http://purl.co...
Non Linear Force Free Field Modeling for a Pseudostreamer
Karna, Nishu; Savcheva, Antonia; Gibson, Sarah; Tassev, Svetlin V.
2017-08-01
In this study we present a magnetic configuration of a pseudostreamer observed on April 18, 2015 on southern west limb embedding a filament cavity. We constructed Non Linear Force Free Field (NLFFF) model using the flux rope insertion method. The NLFFF model produces the three-dimensional coronal magnetic field constrained by observed coronal structures and photospheric magnetogram. SDO/HMI magnetogram was used as an input for the model. The high spatial and temporal resolution of the SDO/AIA allows us to select best-fit models that match the observations. The MLSO/CoMP observations provide full-Sun observations of the magnetic field in the corona. The primary observables of CoMP are the four Stokes parameters (I, Q, U, V). In addition, we perform a topology analysis of the models in order to determine the location of quasi-separatrix layers (QSLs). QSLs are used as a proxy to determine where the strong electric current sheets can develop in the corona and also provide important information about the connectivity in complicated magnetic field configuration. We present the major properties of the 3D QSL and FLEDGE maps and the evolution of 3D coronal structures during the magnetofrictional process. We produce FORWARD-modeled observables from our NLFFF models and compare to a toy MHD FORWARD model and the observations.
Non-linear calibration models for near infrared spectroscopy.
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-02-27
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.
Are oil markets chaotic? A non-linear dynamic analysis
Energy Technology Data Exchange (ETDEWEB)
Panas, E.; Ninni, V. [Athens University of Economics and Business, Athens (Greece)
2000-10-01
The analysis of products' price behaviour continues to be an important empirical issue. This study contributes to the current literature on price dynamics of products by examining for the presence of chaos and non-linear dynamics in daily oil products for the Rotterdam and Mediterranean petroleum markets. Previous studies using only one invariant, such as the correlation dimension may not effectively determine the chaotic structure of the underlying time series. To obtain better information on the time series structure, a framework is developed, where both invariant and non-invariant quantities were also examined. In this paper various invariants for detecting a chaotic time series were analysed along with the associated Brock's theorem and Eckman-Ruelle condition, to return series for the prices of oil products. An additional non-invariant quantity, the BDS statistic, was also examined. The correlation dimension, entropies and Lyapunov exponents show strong evidence of chaos in a number of oil products considered. 30 refs.
Non-Linear Optical Microscopy Sheds Light on Cardiovascular Disease
Caorsi, Valentina; Toepfer, Christopher; Sikkel, Markus B.; Lyon, Alexander R.; MacLeod, Ken; Ferenczi, Mike A.
2013-01-01
Many cardiac diseases have been associated with increased fibrosis and changes in the organization of fibrillar collagen. The degree of fibrosis is routinely analyzed with invasive histological and immunohistochemical methods, giving a limited and qualitative understanding of the tissue's morphological adaptation to disease. Our aim is to quantitatively evaluate the increase in fibrosis by three-dimensional imaging of the collagen network in the myocardium using the non-linear optical microscopy techniques Two-Photon Excitation microscopy (TPE) and Second Harmonic signal Generation (SHG). No sample staining is needed because numerous endogenous fluorophores are excited by a two-photon mechanism and highly non-centrosymmetric structures such as collagen generate strong second harmonic signals. We propose for the first time a 3D quantitative analysis to carefully evaluate the increased fibrosis in tissue from a rat model of heart failure post myocardial infarction. We show how to measure changes in fibrosis from the backward SHG (BSHG) alone, as only backward-propagating SHG is accessible for true in vivo applications. A 5-fold increase in collagen I fibrosis is detected in the remote surviving myocardium measured 20 weeks after infarction. The spatial distribution is also shown to change markedly, providing insight into the morphology of disease progression. PMID:23409139
Addressing the unemployment-mortality conundrum: non-linearity is the answer.
Bonamore, Giorgio; Carmignani, Fabrizio; Colombo, Emilio
2015-02-01
The effect of unemployment on mortality is the object of a lively literature. However, this literature is characterized by sharply conflicting results. We revisit this issue and suggest that the relationship might be non-linear. We use data for 265 territorial units (regions) within 23 European countries over the period 2000-2012 to estimate a multivariate regression of mortality. The estimating equation allows for a quadratic relationship between unemployment and mortality. We control for various other determinants of mortality at regional and national level and we include region-specific and time-specific fixed effects. The model is also extended to account for the dynamic adjustment of mortality and possible lagged effects of unemployment. We find that the relationship between mortality and unemployment is U shaped. In the benchmark regression, when the unemployment rate is low, at 3%, an increase by one percentage point decreases average mortality by 0.7%. As unemployment increases, the effect decays: when the unemployment rate is 8% (sample average) a further increase by one percentage point decreases average mortality by 0.4%. The effect changes sign, turning from negative to positive, when unemployment is around 17%. When the unemployment rate is 25%, a further increase by one percentage point raises average mortality by 0.4%. Results hold for different causes of death and across different specifications of the estimating equation. We argue that the non-linearity arises because the level of unemployment affects the psychological and behavioural response of individuals to worsening economic conditions. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
A bijection for tri-cellular maps
DEFF Research Database (Denmark)
Han, Hillary Siwei; Reidys, Christian
2013-01-01
the Schwinger-Dyson equation \\cite{Schwinger}. In this paper we present a bijective proof of the corresponding coefficient equation. Our result is a bijection that transforms a unicellular map of genus $g$ into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge...
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
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.
Interactive Classroom Graphics--Simulating Non-Linear Arrhenius Plots.
Ben-Zion, M.; Hoz, S.
1980-01-01
Describes two simulation programs using an interactive graphic display terminal that were developed for a course in physical organic chemistry. Demonstrates the energetic conditions that give rise to deviations from linearity in the Arrhenius equation. (CS)
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Institute of Scientific and Technical Information of China (English)
王廷春; 郭柏灵
2011-01-01
Two compact difference schemes for one-dimensional cubic nonlinear Schrodinger equation are proposed. Both of the schemes are proved to conserve the discrete mass and energy. Unconditional convergence in maximum norm of the difference solutions with forth order in space and second order in time is also proved by utilizing the discrete energy method and two techniques. For computing the nonlinear algebraical system generated by the nonlinear compact scheme, an iterative algorithm is constructed and proved to be convergent. As a byproduct of the iterative algorithm, a linearized compact difference scheme with high accuracy is obtained. Numerical examples are given to support the theoretical analysis, and two Richardson extrapolations are introduced to achieve higher order numerical accuracy.%本文对一维非线性Schr(o)dinger方程给出两个紧致差分格式,运用能量方法和两个新的分析技巧证明格式关于离散质量和离散能量守恒,而且在最大模意义下无条件收敛.对非线性紧格式构造了一个新的迭代算法,证明了算法的收敛性,并在此基础上给出一个新的线性化紧格式.数值算例验证了理论分析的正确性,并通过外推进一步提高了数值解的精度.
A non-Linear transport model for determining shale rock characteristics
Ali, Iftikhar; Malik, Nadeem
2016-04-01
Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007
A kinetic formulation of piezoresistance in N-type silicon: Application to non-linear effects
Charbonnieras, A. R.; Tellier, C. R.
1999-07-01
This paper is devoted to the theoretical study of the influence of the temperature and of the doping on the piezoresistance of N-type silicon. In the first step the fractional change in the resistivity caused by stresses is calculated in the framework of a multivalley model using a kinetic transport formulation based on the Boltzmann transport equation. In the second step shifts in the minima of the conduction band and the resulting shift of the Fermi level are expressed in terms of deformation potentials and of stresses. General expressions for the fundamental linear, π_{11} and π_{12}, and non-linear, π_{111}, π_{112}, π_{122} and π_{123}, piezoresistance coefficients are then derived. Plots of the non-linear piezoresistance coefficients against the reduced shift of the Fermi level or against temperature allow us to characterize the influence of doping and temperature. Finally some attempts are made to estimate the non-linearity for heavily doped semiconductor gauges. Cette publication est consacrée à l'étude théorique de l'influence de la température et du dopage sur la piezorésistivité du silicium type N. Dans une première étape nous adoptons le modèle de vallées et nous utilisons une formulation cinétique du transport électronique faisant appel à l'équation de transport de Boltzmann pour calculer la variation de la résistivité du semiconducteur sous contrainte. Dans la deuxième étape nous exprimons les déplacements des minima de la bande de conduction et du niveau de Fermi en termes de potentiels de déformation et de contraintes. Nous proposons ensuite des expressions générales pour les coefficients piezorésistifs fondamentaux linéaires, π_{11} et π_{12}, et non-linéaires, π_{111}, π_{112}, π_{122} et π_{123}. Des représentations graphiques des variations des coefficients non-linéaires permettent de caractériser l'influence du dopage et de la température. Enfin nous fournissons une première pré-estimation des effets
Adaptive discontinuous Galerkin methods for non-linear reactive flows
Uzunca, Murat
2016-01-01
The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.
A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption
Directory of Open Access Journals (Sweden)
George K
2005-07-01
the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. The dual-sorption model is an initial/boundary value problem which consists of (1 one non-linear, two-dimensional, second-order parabolic equation, (2 boundary conditions, (3 one initial condition. Note that, the number of boundary conditions are, six and four, respectively, if the permeation process under consideration is, during the application of the vehicle and during the removal of the vehicle. Adopting the approach of method of lines, the initial/boundary value problem is transformed into an initial-value problem, which consists of (1 a system of non-linear ordinary differential equations, (2 one initial condition. The system of non-linear ordinary differential equations contains time-dependent non-homogeneous terms, if the permeation process under consideration is, during the application of the vehicle. To solve this initial-value problem, an eight-stage sequential algorithm which is second-order accurate, and requires only tri-diagonal solvers, is developed. Results Simulation of the numerical methods described is carried out with various values of the parameter C. The illustrations are given in the form of figures. The concentration profiles are viewed as parabolas along the mesh lines parallel to x-axis or y-axis. The flow rates in different subregions of the skin-region are studied. The shapes of the concentration profiles are examined before and after the steady-state concentration is reached. The concentration reaches steady-state when the flux reaches the steady state. The plots of flux versus time and cumulative amount of drug eliminated into the receptor cell versus time are given. Conclusion Based on the various values of the parameter, C, conclusions are drawn about (1 flow rate of the drug in different regions of the skin, (2 shape of the concentration profiles, (3 the time required to reach the steady
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 u...
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.
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.
Ripamonti, Francesco; Orsini, Lorenzo; Resta, Ferruccio
2015-04-01
Non-linear behavior is present in many mechanical system operating conditions. In these cases, a common engineering practice is to linearize the equation of motion around a particular operating point, and to design a linear controller. The main disadvantage is that the stability properties and validity of the controller are local. In order to improve the controller performance, non-linear control techniques represent a very attractive solution for many smart structures. The aim of this paper is to compare non-linear model-based and non-model-based control techniques. In particular the model-based sliding-mode-control (SMC) technique is considered because of its easy implementation and the strong robustness of the controller even under heavy model uncertainties. Among the non-model-based control techniques, the fuzzy control (FC), allowing designing the controller according to if-then rules, has been considered. It defines the controller without a system reference model, offering many advantages such as an intrinsic robustness. These techniques have been tested on the pendulum nonlinear system.
Hossein-Zadeh, Navid Ghavi
2016-08-01
The aim of this study was to compare seven non-linear mathematical models (Brody, Wood, Dhanoa, Sikka, Nelder, Rook and Dijkstra) to examine their efficiency in describing the lactation curves for milk fat to protein ratio (FPR) in Iranian buffaloes. Data were 43 818 test-day records for FPR from the first three lactations of Iranian buffaloes which were collected on 523 dairy herds in the period from 1996 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly FPR records of buffaloes using the non-linear mixed model procedure (PROC NLMIXED) in SAS and the parameters were estimated. The models were tested for goodness of fit using Akaike's information criterion (AIC), Bayesian information criterion (BIC) and log maximum likelihood (-2 Log L). The Nelder and Sikka mixed models provided the best fit of lactation curve for FPR in the first and second lactations of Iranian buffaloes, respectively. However, Wood, Dhanoa and Sikka mixed models provided the best fit of lactation curve for FPR in the third parity buffaloes. Evaluation of first, second and third lactation features showed that all models, except for Dijkstra model in the third lactation, under-predicted test time at which daily FPR was minimum. On the other hand, minimum FPR was over-predicted by all equations. Evaluation of the different models used in this study indicated that non-linear mixed models were sufficient for fitting test-day FPR records of Iranian buffaloes.
Salamatin, A.
2016-11-01
Numerical algorithm is developed for modelling non-linear mass transfer process in supercritical fluid extraction (SFE). The ground raw material is considered as polydisperse, characterized by discrete number of effective particle fractions. Two continuous interacting counterparts separated by permeable membrane are distinguished in plant material build-up. The apoplast plays role of transport channels during extraction, and symplast contains extractable oil. The complete SFE model is non-linear as a result of non-linearity of oil dissolution kinetics. The computational scheme is based on the finite-volume approximation method and Thomas elimination procedure. The resulting system of algebraic equations is solved iteratively. Special attention is paid to polydisperse substrates, when particle scale characteristics of all fractions interact with each other through pore phase concentration on the vessel scale. Stability of the developed algorithm is demonstrated in numerical tests. Special iterative procedure guarantees a monotonic decrease of oil content in individual particles of substrate. It is also shown that in the limit of the so-called shrinking core approach the number of mesh nodes on a particle scale should be increased.
Energy Technology Data Exchange (ETDEWEB)
Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn [Department of Mechanics, Tianjin University, 300072, Tianjin (China); Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin (China); Zhang, W. D., E-mail: zhangwenditju@126.com; Xu, J., E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, 300072, Tianjin (China)
2014-03-15
The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.
Non-linear stochastic optimal control of acceleration parametrically excited systems
Wang, Yong; Jin, Xiaoling; Huang, Zhilong
2016-02-01
Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.
Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger
2017-01-01
Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods. PMID:28166542
A New Problem and the Possible Solution in the Technicoloured Preon Model
Matumoto, K.
1989-02-01
A version of technicoloured preon model, giving the appropriate order of fermion mass despite the large mass scale of the preonic dynamics of the order of the axion decay constant, is presented, where the dynamics is described by the chiral symmetry breaking solution of the ladder Schwinger-Dyson-Nambu-Jona-Lasinio-hybrid equation.
Raya, Alfredo
2009-01-01
Dynamical chiral symmetry breaking and confinement are two crucial features of Quantum Chromodynamics responsible for the nature of the hadron spectrum. These phenomena, presumably coincidental, can account for 98% of the mass of our visible universe. In this set of lectures, I shall present an introductory review of them in the light of the Schwinger-Dyson equations.
From continuum QCD to hadron observables
Directory of Open Access Journals (Sweden)
Binosi Daniele
2016-01-01
Full Text Available We show that the form of the renormalization group invariant quark-gluon interaction predicted by a refined nonperturbative analysis of the QCD gauge sector is in quantitative agreement with the one required for describing a wide range of hadron observables using sophisticated truncation schemes of the Schwinger-Dyson equations relevant in the matter sector.
Dynamical Symmetry Breaking in RN Quantum Gravity
Directory of Open Access Journals (Sweden)
A. T. Kotvytskiy
2011-01-01
Full Text Available We show that in the RN gravitation model, there is no dynamical symmetry breaking effect in the formalism of the Schwinger-Dyson equation (in flat background space-time. A general formula for the second variation of the gravitational action is obtained from the quantum corrections hμν (in arbitrary background metrics.
An analysis of the intermediate field theory of $T^4$ tensor model
Nguyen, Viet Anh; Eynard, Bertrand
2014-01-01
In this paper we analyze the multi-matrix model arising from the intermediate field representation of the tensor model with all quartic melonic interactions. We derive the saddle point equation and the Schwinger-Dyson constraints. We then use them to describe the leading and next-to-leading eigenvalues distribution of the matrices.
Leading CFT constraints on multi-critical models in d > 2
DEFF Research Database (Denmark)
Codello, Alessandro; Safari, Mahmoud; Vacca, Gian Paolo
2017-01-01
We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial ϕm below their upper critical dimensions dc=2mm−2, and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension...
Elizondo, D.; Cappelaere, B.; Faure, Ch.
2002-04-01
Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.
Non-linear hydraulic properties of woodchips necessary to design denitrification beds
Ghane, Ehsan; Feyereisen, Gary W.; Rosen, Carl J.
2016-11-01
Denitrification beds are being used to reduce the transport of water-soluble nitrate via subsurface drainage systems to surface water. Only recently has the non-linearity of water flow through woodchips been ascertained. To successfully design and model denitrification beds with optimum nitrate removal, a better understanding of flow in denitrification beds is needed. The main objectives of this study were to characterize the hydraulic properties of old degraded woodchips and provide a better understanding of the factors affecting flow. To achieve this goal, we conducted constant-head column experiments using old woodchips that were excavated from a four-year old denitrification bed near Willmar, Minnesota, USA. For Izbash's equation, the non-Darcy exponent (n) ranged from 0.76 to 0.87 that indicates post-linear regime, and the permeability coefficient (M10) at 10°C ranged from 0.9 to 2.6 cm s-1. For Forchheimer's equation, the intrinsic permeability of 5.6 × 10-5 cm2 and ω constant of 0.40 (at drainable porosity of 0.41) closely resembled the in-situ properties found in a previous study. Forchheimer's equation was better than that of Izbash's for describing water flow through old woodchips, and the coefficients of the former provided stronger correlations with drainable porosity. The strong correlation between intrinsic permeability and drainable porosity showed that woodchip compaction is an important factor affecting water flow through woodchips. Furthermore, we demonstrated the importance of temperature effects on woodchip hydraulics. In conclusion, the hydraulic properties of old woodchips should be characterized using a non-Darcy equation to help design efficient systems with optimum nitrate removal.
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.
Non-linear QCD dynamics and exclusive production
Machado, M V T; Meneses, A R
2010-01-01
In this contribution we analyse the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky-Kovchegov equation including running coupling corrections. Comparisons to DESY-HERA data on exclusive processes and predictions to the Large Hadron Electron Collider, LHeC, are presented.
Strubbe, David A.; Andrade, Xavier; Rubio, Angel; Louie, Steven G.
2010-03-01
Chloroform is often used as a solvent when measuring non-linear optical properties of organic molecules. We assess the influence of the solution environment on the molecular properties by calculating directly the non-linear susceptibilities of liquid chloroform at optical frequencies. We use the Sternheimer equation in time-dependent density-functional theory [J. Chem. Phys. 126, 184106 (2007)], on snapshots from ab initio molecular dynamics. We compare the results to those in the gas and solid phases, and to experimental values. We also calculate ab initio local-field factors, used to analyze electric-field-induced second-harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS) experiments.
Katsouleas, Thomas; Sahai, Aakash
2015-11-01
The excitation of a non-linear ion-wake by a train of non-linear electron wake of an electron and a positron beam is modeled and its use for positron acceleration is explored. The ion-wake is shown to be a driven non-linear ion-acoustic wave in the form of a cylindrical ion-soliton similar to the solution of the cKdV equation. The phases of the oscillating radial electric fields of the slowly-propagating electron wake are asymmetric in time and excite time-averaged inertial ion motion radially. The radial field of the electron compression region sucks-in the ions and the field of space-charge region of the wake expels them, driving a cylindrical ion-soliton structure with on-axis and bubble-edge density-spikes. Once formed, the channel-edge density-spike is driven radially outwards by the thermal pressure of the thermalized wake energy. Its channel-like structure due to the flat-residue left behind by the propagating ion-soliton, is independent of the energy-source driving the non-linear electron wake. We explore the use of the partially-filled channel formed by the cylindrical ion-soliton for a novel regime of positron acceleration. PIC simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration (arXiv:1504.03735). Work supported by the US Department of Energy under DE-SC0010012 and the National Science Foundation under NSF-PHY-0936278.
Pulse-driven non-linear Alfvén waves and their role in the spectral line broadening
Chmielewski, P.; Srivastava, A. K.; Murawski, K.; Musielak, Z. E.
2013-01-01
We study the impulsively generated non-linear Alfvén waves in the solar atmosphere and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfvén waves in the solar atmosphere model of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfvén waves at different heights of the model atmosphere and estimate its contribution to the unresolved non-thermal motions caused by the waves. We find that the pulse-driven non-linear Alfvén waves with the amplitude Av = 50 km s- 1 are the most likely candidates for the non-thermal broadening of Si viii λ1445.75 Å line profiles in the polar coronal hole as reported by Banerjee et al. We also demonstrate that the Alfvén waves driven by comparatively smaller velocity pulse with amplitude Av = 25 km s- 1 may contribute to the spectral line width of the same line at various heights in coronal hole broadening. We conclude that the non-linear Alfvén waves excited impulsively in the lower solar atmosphere may be responsible for the observed spectral line broadening in polar coronal holes. This is an important result as it allows us to conclude that such large amplitude and pulse-driven Alfvén waves may indeed exist in solar coronal holes. The existence of these waves may impart the required momentum to accelerate the solar wind.
Directory of Open Access Journals (Sweden)
Hongbo Liu
2015-11-01
Full Text Available The electrocaloric (EC effect has been paid great attentions recently for applications on cooling or electricity generation. However, the directly commercial measurement equipment for the effect is still unavailable. Here we report a novel method to predict EC effect by non-linear behaviors of dielectric permittivity under temperature and electric fields. According to the method, the analytical equations of EC temperature change ΔT are directly given for normal ferroelectrics and relaxor. The calculations have been performed on several materials and it is shown that the method is suitable for both inorganic and organic ferroelectrics, and relaxor.
Non linear evolution: revisiting the solution in the saturation region
Contreras, Carlos; Meneses, Rodrigo
2014-01-01
In this paper we revisit the problem of the solution to Balitsky-Kovchegov equation deeply in the saturation domain. We find that solution has the form of Levin-Tuchin solution but it depends on variable $\\bar{z} = \\ln(r^2 Q^2_s) + \\mbox{Const}$ and the value of $\\mbox{Const}$ is calculated in this paper. We propose the solution for full BFKL kernel at large $z$ in the entire kinematic region that satisfies the McLerram-Venugopalan initial condition
Nordtvedt, Kenneth
2015-01-01
A method for constructing metric gravity's N-body Lagrangian is developed which uses iterative, liner algebraic euqations which enforce invariance properties of gravity --- exterior effacement, interior effacement, and the time dilation and Lorentz contraction of matter under boosts. The method is demonstrated by obtaining the full 1/c^4 order Lagrangian, and a combination of exterior and interior effacement enforcement permits construction of the full Schwarzschild temporal and spatial metric potentials.
Non-linear analysis of vibrations of irregular plates
Lobitz, D. W.; Nayfeh, A. H.; Mook, D. T.
1977-01-01
A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Nonlinear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, these modes and the resultants are used to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.
Non-linearly weighted fuzzy correlation for color-image retrieval
Institute of Scientific and Technical Information of China (English)
Guoguang Mu(母国光); Hongchen Zhai(翟宏琛); Siyuan Zhang(张思远)
2003-01-01
An algorithm with non-linear weight factors in the summation process for fuzzy correlation of color his-tograms is presented, in which non-linear weights are assigned to some characteristic colors of interest.Experimental results show that this can improve the retrieval of color images with partial aberrations orwith local color characters.
Measurements of dynamical response of non-linear systems. How hard can it be?
DEFF Research Database (Denmark)
Darula, Radoslav
2015-01-01
Measurements of a dynamical response of linear system are widely used in praxis, they are standardized and well known. On the other hand, for the non-linear systems the principle of superposition can’t be applied and also the non-linear systems can excite the harmonics or undergo jump phenomena...
Robust Non-Linear Control of a 400 kW Wind Turbine
DEFF Research Database (Denmark)
Tøffner-Clausen, S.; Andersen, Palle; Knudsen, Torben
1996-01-01
The purpose of this paper is to describe a robust non-linear control design for a variable pitch constant speed 400 kW horisontal axis wind turbine.......The purpose of this paper is to describe a robust non-linear control design for a variable pitch constant speed 400 kW horisontal axis wind turbine....
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.
A COMPUTER PROGRAMME FOR THE NON-LINEAR ANALYSIS OF COMPLETE STRUCTURES
Directory of Open Access Journals (Sweden)
Turgay ÇOŞGUN
2003-02-01
Full Text Available The progress made on the analysis of the structures by using non-linear theory and the significant findings on both theorical and empirical works, enable better understanding of the behaviours of structures under external loads. Determination of the failure load and designing the structures accordingly requires developments of analysis methods, which take both the non-linear behaviour of structural elements and the non-linear effects of geometric changes into consideration. Therefore, in this study, a FORTRAN code, which analyses structures and calculates the failure loads by considering the non-linear behaviour of materials under increasing loads (due to the non-linear relationship of stress-strain and moment-curvature and second-order theory of structural systems is developed.
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...
Water environmental planning considering the influence of non-linear characteristics
Institute of Scientific and Technical Information of China (English)
ZENG Guang-ming; QIN Xiao-sheng; WANG Wei; HUANG Guo-he; LI Jian-bing; B. Statzner
2003-01-01
In practical water environmental planning, the influence of the non-linear characteristics on the benefit of environmental investment was seldom taken into consideration. This paper demonstrates that there exist a lot of non-linear behaviors in water environment by emphatically analyzing the influence of the non-linear characteristics of the economic scale, the meandering river and the model on water environmental planning, which will make a certain impact on the water environmental planning that sometimes cannot be neglected. This paper also preliminarily explores how to integrate the non-linear characteristics into water environmental planning. The results showed that compared with traditional methods, water environmental planning considering non-linear characteristics has its prevalence and it is necessary to develop the relevant planning theories and methods.
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
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...... 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...... 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...
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.
Phantom expansion with non-linear Schr\\"{o}dinger-type formulation of scalar field cosmology
Phetnora, Theerakarn; Gumjudpai, Burin
2008-01-01
We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schr\\"{o}dinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of Schr\\"{o}dinger quantities as similar to those in time-independent quantum mechanics. We assume the expansion to be superfast, i.e. phantom expansion. We report all Schr\\"{o}dinger-analogous quantities to scalar field cosmology. Effective equation of state coefficient is analyzed and illustrated. We show that in a non-flat universe, there is no fixed $w_{\\rm eff}$ value for the phantom divide. In a non-flat universe, even $w_{\\rm eff} > -1$, the expansion can be phantom. Moreover, in open universe, phantom expansion can happen even with $w_{\\rm eff} > 0$. We also report scalar field exact solutions within frameworks of the Friedmann formulation and the NLS formulation in non-flat universe cases.
Non-linear station motions in the DGFI realization of the ITRF2014
Seitz, Manuela; Bloßfeld, Mathis; Angermann, Detlef; Schmid, Ralf
2016-04-01
The DGFI Terrestrial Reference Frame DTRF2014 is the most recent realization of the International Terrestrial Reference System computed by DGFI-TUM. It comprises 3-dimensional station coordinates and velocities which are estimated in a common adjustment together with Earth orientation parameters (EOP). The input data for the DTRF2014 are observations of the four fundamental space geodetic techniques (GNSS, VLBI, SLR and DORIS) from 1979 until 2015 as well as terrestrial difference vectors (local ties) between the technique-specific reference points. In previous ITRS realizations, the motions of the crust-fixed reference points were approximated through linear velocities. Un-modeled and/or residual non-linear station motions were neglected and, therefore, deteriorated station coordinates, velocities as well as commonly adjusted EOP. For the DTRF2014, geophysical non-tidal loading corrections provided by the IERS Global Geophysical Fluids Center (IERS-GGFC) which account for atmospheric and hydrological effects were considered. In this study, we present the strategy to apply non-tidal loading corrections at the normal equation level of the Gauss-Markov model. We compare DTRF2014 solutions with and without non-tidal loading corrections and investigate their impact on TRF parameters (station coordinates, velocities, geodetic datum) and EOP. Furthermore, a validation of different DTRF2014 solutions with independent ITRS realizations computed by other institutions is shown.
Non-linear mixed models in the analysis of mediated longitudinal data with binary outcomes.
Blood, Emily A; Cheng, Debbie M
2012-01-24
Structural equation models (SEMs) provide a general framework for analyzing mediated longitudinal data. However when interest is in the total effect (i.e. direct plus indirect) of a predictor on the binary outcome, alternative statistical techniques such as non-linear mixed models (NLMM) may be preferable, particularly if specific causal pathways are not hypothesized or specialized SEM software is not readily available. The purpose of this paper is to evaluate the performance of the NLMM in a setting where the SEM is presumed optimal. We performed a simulation study to assess the performance of NLMMs relative to SEMs with respect to bias, coverage probability, and power in the analysis of mediated binary longitudinal outcomes. Both logistic and probit models were evaluated. Models were also applied to data from a longitudinal study assessing the impact of alcohol consumption on HIV disease progression. For the logistic model, the NLMM adequately estimated the total effect of a repeated predictor on the repeated binary outcome and were similar to the SEM across a variety of scenarios evaluating sample size, effect size, and distributions of direct vs. indirect effects. For the probit model, the NLMM adequately estimated the total effect of the repeated predictor, however, the probit SEM overestimated effects. Both logistic and probit NLMMs performed well relative to corresponding SEMs with respect to bias, coverage probability and power. In addition, in the probit setting, the NLMM may produce better estimates of the total effect than the probit SEM, which appeared to overestimate effects.
Aboveground biomass and carbon stocks modelling using non-linear regression model
Ain Mohd Zaki, Nurul; Abd Latif, Zulkiflee; Nazip Suratman, Mohd; Zainee Zainal, Mohd
2016-06-01
Aboveground biomass (AGB) is an important source of uncertainty in the carbon estimation for the tropical forest due to the variation biodiversity of species and the complex structure of tropical rain forest. Nevertheless, the tropical rainforest holds the most extensive forest in the world with the vast diversity of tree with layered canopies. With the usage of optical sensor integrate with empirical models is a common way to assess the AGB. Using the regression, the linkage between remote sensing and a biophysical parameter of the forest may be made. Therefore, this paper exemplifies the accuracy of non-linear regression equation of quadratic function to estimate the AGB and carbon stocks for the tropical lowland Dipterocarp forest of Ayer Hitam forest reserve, Selangor. The main aim of this investigation is to obtain the relationship between biophysical parameter field plots with the remotely-sensed data using nonlinear regression model. The result showed that there is a good relationship between crown projection area (CPA) and carbon stocks (CS) with Pearson Correlation (p < 0.01), the coefficient of correlation (r) is 0.671. The study concluded that the integration of Worldview-3 imagery with the canopy height model (CHM) raster based LiDAR were useful in order to quantify the AGB and carbon stocks for a larger sample area of the lowland Dipterocarp forest.