Nonlinear simulation of electromagnetic current diffusive interchange mode turbulence

International Nuclear Information System (INIS)

Yagi, M.; Itoh, S.I.; Fukuyama, A.

1998-01-01

The anomalous transport in toroidal plasmas has been investigated extensively. It is pointed out that the nonlinear instability is important in driving the microturbulence[1], i.e., the self-sustained plasma turbulence. This concept is explained as follows; when the electron motion along the magnetic field line is resisted by the background turbulence, it gives rise to the effective resistivity and enhances the level of the turbulence. The nonlinear simulation of the electrostatic current diffusive interchange mode (CDIM) in the two dimensional sheared slab geometry has been performed as an example. The occurrence of the nonlinear instability and the self-sustainment of the plasma turbulence were confirmed by this simulation[2]. On the other hand, the electromagnetic turbulence is sustained in the high pressure limit. The possibility of the self-organization with more variety has been pointed out[3]. It is important to study the electromagnetic turbulence based on the nonlinear simulation. In this paper, the model equation for the electrostatic CDIM turbulence[2] is extended for both electrostatic and electromagnetic turbulence. (1) Not only E x B convective nonlinearity but also the electromagnetic nonlinearity which is related to the parallel flow are incorporated into the model equation. (2) The electron and ion pressure evolution equations are solved separately, making it possible to distinguish the electron and ion thermal diffusivities. The two dimensional nonlinear simulation of the electromagnetic CDIM is performed based on the extended fluid model. This paper is organized as follows. The model equation is explained in section II. The result of simulation is shown in section III. The conclusion and discussion are given in section IV. (author)

Nonlinear diffuse scattering of the random-phased wave

International Nuclear Information System (INIS)

Kato, Yoshiaki; Arinaga, Shinji; Mima, Kunioki.

1983-01-01

First experimental observation of the nonlinear diffuse scattering is reported. This new effect was observed in the propagation of the random-phased wave through a nonlinear dielectric medium. This effect is ascribed to the diffusion of the wavevector of the electro-magnetic wave to the lateral direction due to the randomly distributed nonlinear increase in the refractive index. (author)

An approximate method for nonlinear diffusion applied to enzyme inactivation during drying

NARCIS (Netherlands)

Liou, J.K.

1982-01-01

An approximate model was developed for nonlinear diffusion with a power-function variation of the diffusion coefficient with concentration. This model may serve for the computation of desorption times and concentration profiles in non-shrinking or shrinking slabs, cylinders or spheres, under

Robust and fast nonlinear optimization of diffusion MRI microstructure models.

Science.gov (United States)

Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A

2017-07-15

Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of

Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

CERN Document Server

Cherniha, Roman

2017-01-01

This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception,...

Super Nonlinear Electrodeposition-Diffusion-Controlled Thin-Film Selector.

Science.gov (United States)

Ji, Xinglong; Song, Li; He, Wei; Huang, Kejie; Yan, Zhiyuan; Zhong, Shuai; Zhang, Yishu; Zhao, Rong

2018-03-28

Selector elements with high nonlinearity are an indispensable part in constructing high density, large-scale, 3D stackable emerging nonvolatile memory and neuromorphic network. Although significant efforts have been devoted to developing novel thin-film selectors, it remains a great challenge in achieving good switching performance in the selectors to satisfy the stringent electrical criteria of diverse memory elements. In this work, we utilized high-defect-density chalcogenide glass (Ge 2 Sb 2 Te 5 ) in conjunction with high mobility Ag element (Ag-GST) to achieve a super nonlinear selective switching. A novel electrodeposition-diffusion dynamic selector based on Ag-GST exhibits superior selecting performance including excellent nonlinearity (<5 mV/dev), ultra-low leakage (<10 fA), and bidirectional operation. With the solid microstructure evidence and dynamic analyses, we attributed the selective switching to the competition between the electrodeposition and diffusion of Ag atoms in the glassy GST matrix under electric field. A switching model is proposed, and the in-depth understanding of the selective switching mechanism offers an insight of switching dynamics for the electrodeposition-diffusion-controlled thin-film selector. This work opens a new direction of selector designs by combining high mobility elements and high-defect-density chalcogenide glasses, which can be extended to other materials with similar properties.

Nonlinear analysis of a reaction-diffusion system: Amplitude equations

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

2012-10-15

A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

Exact analytical solutions for nonlinear reaction-diffusion equations

International Nuclear Information System (INIS)

Liu Chunping

2003-01-01

By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

Some applications of nonlinear diffusion to processing of dynamic evolution images

International Nuclear Information System (INIS)

Goltsov, Alexey N.; Nikishov, Sergey A.

1997-01-01

Model nonlinear diffusion equation with the most simple Landau-Ginzburg free energy functional was applied to locate boundaries between meaningful regions of low-level images. The method is oriented to processing images of objects that are a result of dynamic evolution: images of different organs and tissues obtained by radiography and NMR methods, electron microscope images of morphogenesis fields, etc. In the methods developed by us, parameters of the nonlinear diffusion model are chosen on the basis of the preliminary treatment of the images. The parameters of the Landau-Ginzburg free energy functional are extracted from the structure factor of the images. Owing to such a choice of the model parameters, the image to be processed is located in the vicinity of the steady-state of the diffusion equation. The suggested method allows one to separate distinct structures having specific space characteristics from the whole image. The method was applied to processing X-ray images of the lung

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

Science.gov (United States)

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

Science.gov (United States)

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Multi-diffusive nonlinear Fokker–Planck equation

International Nuclear Information System (INIS)

Ribeiro, Mauricio S; Casas, Gabriela A; Nobre, Fernando D

2017-01-01

Nonlinear Fokker–Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker–Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker–Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker–Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution. (paper)

On the integrability of the generalized Fisher-type nonlinear diffusion equations

International Nuclear Information System (INIS)

Wang Dengshan; Zhang Zhifei

2009-01-01

In this paper, the geometric integrability and Lax integrability of the generalized Fisher-type nonlinear diffusion equations with modified diffusion in (1+1) and (2+1) dimensions are studied by the pseudo-spherical surface geometry method and prolongation technique. It is shown that the (1+1)-dimensional Fisher-type nonlinear diffusion equation is geometrically integrable in the sense of describing a pseudo-spherical surface of constant curvature -1 only for m = 2, and the generalized Fisher-type nonlinear diffusion equations in (1+1) and (2+1) dimensions are Lax integrable only for m = 2. This paper extends the results in Bindu et al 2001 (J. Phys. A: Math. Gen. 34 L689) and further provides the integrability information of (1+1)- and (2+1)-dimensional Fisher-type nonlinear diffusion equations for m = 2

Pattern formation due to non-linear vortex diffusion

Science.gov (United States)

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.

A family of analytical solutions of a nonlinear diffusion-convection equation

Science.gov (United States)

Hayek, Mohamed

2018-01-01

Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.

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.

A numerical study of one-dimensional replicating patterns in reaction-diffusion systems with non-linear diffusion coefficients

International Nuclear Information System (INIS)

Ferreri, J. C.; Carmen, A. del

1998-01-01

A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs

A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.

Science.gov (United States)

Joy, Ajin; Paul, Joseph Suresh

2018-03-07

Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained. © 2018 International Society for Magnetic Resonance in Medicine.

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

Directory of Open Access Journals (Sweden)

Ervin K. Lenzi

2017-01-01

Full Text Available We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.

Nonlinear Diffusion and Transient Osmosis

International Nuclear Information System (INIS)

Igarashi, Akira; Rondoni, Lamberto; Botrugno, Antonio; Pizzi, Marco

2011-01-01

We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call ''transient osmosis . We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

International Nuclear Information System (INIS)

Arkhincheev, V.E.

2001-04-01

To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

Nonlinear degenerate cross-diffusion systems with nonlocal interaction

OpenAIRE

Di Francesco, M.; Esposito, A.; Fagioli, S.

2017-01-01

We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove g...

Nonlinear diffusion problem arising in plasma physics

International Nuclear Information System (INIS)

Berryman, J.G.; Holland, C.J.

1978-01-01

In earlier studies of plasma diffusion with Okuda-Dawson scaling (D approx. n/sup -1/2/), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separation solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toeard the separable solution is summarized. Rigorous bounds on the decay time are also presented

Nonlinear flow model for well production in an underground formation

Directory of Open Access Journals (Sweden)

J. C. Guo

2013-05-01

Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

A mixed finite element method for nonlinear diffusion equations

KAUST Repository

Burger, Martin; Carrillo, José ; Wolfram, Marie-Therese

2010-01-01

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

Science.gov (United States)

Fiorina, B.; Lele, S. K.

2007-03-01

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

A strongly nonlinear reaction-diffusion model for a deterministic diffusive epidemic

International Nuclear Information System (INIS)

Kirane, M.; Kouachi, S.

1992-10-01

In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the diffusivities. (author). 7 refs

Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach.

Science.gov (United States)

Tredenick, Eloise C; Farrell, Troy W; Forster, W Alison; Psaltis, Steven T P

2017-01-01

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.

Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach

Directory of Open Access Journals (Sweden)

Eloise C. Tredenick

2017-05-01

Full Text Available The agricultural industry requires improved efficacy of sprays being applied to crops and weeds in order to reduce their environmental impact and deliver improved financial returns. Enhanced foliar uptake is one means of improving efficacy. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The usefulness of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted previously in the literature, as the results of each uptake experiment are specific to each formulation of active ingredient, plant species and environmental conditions. In this work we develop a mathematical model and numerical simulation for the uptake of hydrophilic ionic agrochemicals through aqueous pores in plant cuticles. We propose a novel, nonlinear, porous diffusion model for ionic agrochemicals in isolated cuticles, which extends simple diffusion through the incorporation of parameters capable of simulating: plant species variations, evaporation of surface droplet solutions, ion binding effects on the cuticle surface and swelling of the aqueous pores with water. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms. Major influencing factors have been found to be cuticle structure, including tortuosity and density of the aqueous pores, and to a lesser extent humidity and cuticle surface ion binding effects.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

Science.gov (United States)

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

Models of diffuse solar radiation

Energy Technology Data Exchange (ETDEWEB)

Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Brown, Bruce [Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546 (Singapore)

2008-04-15

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19-32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103-16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions. Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. (author)

Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

Indian Academy of Sciences (India)

constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Science.gov (United States)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

International Nuclear Information System (INIS)

Indekeu, Joseph O; Smets, Ruben

2017-01-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

Exact solutions of some coupled nonlinear diffusion-reaction ...

Indian Academy of Sciences (India)

certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

Energy Technology Data Exchange (ETDEWEB)

Schunert, Sebastian; Hammer, Hans; Lou, Jijie; Wang, Yaqi; Ortensi, Javier; Gleicher, Frederick; Baker, Benjamin; DeHart, Mark; Martineau, Richard

2016-11-01

The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA

Differential constraints and exact solutions of nonlinear diffusion equations

International Nuclear Information System (INIS)

Kaptsov, Oleg V; Verevkin, Igor V

2003-01-01

The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

Science.gov (United States)

Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-02-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

Nonlinear diffusion in the presence of a time-dependent external electric field

International Nuclear Information System (INIS)

Lima e Silva, T. de; Galvao, R.M.O.

1987-09-01

The influence of a time-dependent external electric field on the nonlinear diffusion process of weakly ionized plasmas is investigated. A new solution of the diffusion equation is obtained for the case when electron-ion collisions can be neglected. (author) [pt

Fractional Diffusion Equations and Anomalous Diffusion

Science.gov (United States)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

3-D Model of Broadband Emission from Supernova Remnants Undergoing Non-linear Diffusive Shock Acceleration

Energy Technology Data Exchange (ETDEWEB)

Lee, Shiu-Hang; Kamae, Tuneyoshi; Ellison, Donald C.

2008-07-02

We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occurring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to develop a flexible platform, which can be generalized to include effects such as MFA, and which can be easily adapted to various SNR environments, including Type Ia SNRs, which explode in a constant density medium, and Type II SNRs, which explode in a pre-supernova wind. When applied to a specific SNR, our model will predict cosmic-ray spectra and multi-wavelength morphology in projected images for instruments with varying spatial and spectral resolutions. We show examples of these spectra and images and emphasize the importance of measurements in the hard X-ray, GeV, and TeV gamma-ray bands for investigating key ingredients in the acceleration mechanism, and for deducing whether or not TeV emission is produced by IC from electrons or pion-decay from protons.

Analytically solvable models of reaction-diffusion systems

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)

2004-05-01

We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.

Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

Science.gov (United States)

Liu, Ping; Shi, Junping

2018-01-01

The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.

Diffuse-interface model for rapid phase transformations in nonequilibrium systems.

Science.gov (United States)

Galenko, Peter; Jou, David

2005-04-01

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

Directory of Open Access Journals (Sweden)

Ida de Bonis

2017-09-01

Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

Science.gov (United States)

Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

2017-05-01

The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

Nonlinear theory of diffusive acceleration of particles by shock waves

Energy Technology Data Exchange (ETDEWEB)

Malkov, M.A. [University of California at San Diego, La Jolla, CA (United States)]. E-mail: mmalkov@ucsd.edu; Drury, L. O' C. [Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2 (Ireland)

2001-04-01

Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data. (author)

Application of nonlinear nodal diffusion generalized perturbation theory to nuclear fuel reload optimization

International Nuclear Information System (INIS)

Maldonado, G.I.; Turinsky, P.J.

1995-01-01

The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

Polyanin, A. D.; Sorokin, V. G.

2017-12-01

The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

Science.gov (United States)

Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

2016 CIME Course on Nonlocal and Nonlinear Diffusions and Interactions : New Methods and Directions

CERN Document Server

Grillo, Gabriele

2017-01-01

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.

Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

International Nuclear Information System (INIS)

Qu Changzheng; Kang Jing

2008-01-01

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

Moderately nonlinear diffuse-charge dynamics under an ac voltage.

Science.gov (United States)

Stout, Robert F; Khair, Aditya S

2015-09-01

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

Moderately nonlinear diffuse-charge dynamics under an ac voltage

Science.gov (United States)

Stout, Robert F.; Khair, Aditya S.

2015-09-01

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of Vo/(kBT /e ) , where Vo is the amplitude of the driving voltage and kBT /e is the thermal voltage with kB as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D /λDL , where D is the ion diffusivity, λD is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O (Vo3) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in Vo. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing Vo. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior

KAUST Repository

Markowich, Peter

2010-06-01

We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty with respect to previous papers in the literature lies in the presence of nonlinear porous-medium-like diffusion in the equation for the density n of the bacteria, motivated by a finite size effect. We prove that, under the constraint m ε (3/2, 2] for the adiabatic exponent, such system features global in time solutions in two space dimensions for large data. Moreover, in the case m = 2 we prove that solutions converge to constant states in the large-time limit. The proofs rely on standard energy methods and on a basic entropy estimate which cannot be achieved in the case m = 1. The case m = 2 is very special as we can provide a Lyapounov functional. We generalize our results to the three-dimensional case and obtain a smaller range of exponents m ε (m*, 2] with m* > 3/2, due to the use of classical Sobolev inequalities.

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

Science.gov (United States)

Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

2009-01-01

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Nonlinear drift-diffusion model of gating in K and nACh ion channels

Energy Technology Data Exchange (ETDEWEB)

Vaccaro, S.R. [Department of Physics, University of Adelaide, Adelaide, South Australia 5005 (Australia)], E-mail: svaccaro@physics.adelaide.edu.au

2007-09-03

The configuration of a sensor regulates the transition between the closed and open states of both voltage and ligand gated channels. The closed state dwell-time distribution f{sub c}(t) derived from a Fokker-Planck equation with a nonlinear diffusion coefficient is in good agreement with experimental data and can account for the power law approximation to f{sub c}(t) for a delayed rectifier K channel and a nicotinic acetylcholine (nACh) ion channel. The solution of a master equation which approximates the Fokker-Planck equation provides a better description of the small time behaviour of the dwell-time distribution and can account for the empirical rate-amplitude correlation for these ion channels.

Modelling of diffuse solar fraction with multiple predictors

Energy Technology Data Exchange (ETDEWEB)

Ridley, Barbara; Boland, John [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Lauret, Philippe [Laboratoire de Physique du Batiment et des Systemes, University of La Reunion, Reunion (France)

2010-02-15

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia. Boland et al. developed a validated model for Australian conditions. Boland et al. detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model. (author)

A non-Linear transport model for determining shale rock characteristics

Science.gov (United States)

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

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Science.gov (United States)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Directory of Open Access Journals (Sweden)

Shahid Hasnain

2017-07-01

Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

New variable separation approach: application to nonlinear diffusion equations

International Nuclear Information System (INIS)

Zhang Shunli; Lou, S Y; Qu Changzheng

2003-01-01

The concept of the derivative-dependent functional separable solution (DDFSS), as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the DDFSS is obtained and some exact solutions to the resulting equations are described

On Diffusive Climatological Models.

Science.gov (United States)

Griffel, D. H.; Drazin, P. G.

1981-11-01

A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.

Numerical solution of non-linear diffusion problems

International Nuclear Information System (INIS)

Carmen, A. del; Ferreri, J.C.

1998-01-01

This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

Nonlinear variational models for reaction and diffusion systems

International Nuclear Information System (INIS)

Tanyi, G.E.

1983-08-01

There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

International Nuclear Information System (INIS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-01-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

Science.gov (United States)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

Recent advances in modelling diffuse radiation

Energy Technology Data Exchange (ETDEWEB)

Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, Univ. of South Australia, Mawson Lakes, SA (Australia)

2008-07-01

Boland et al (2001) developed a validated model for Australian conditions, using a logistic function instead of piecewise linear or simple nonlinear functions. Recently, Jacovides et al (2006) have verified that this model performs well for locations in Cyprus. Their analysis includes using moving average techniques to demonstrate the form of the relationship, which corresponds well to a logistic relationship. We have made significant advances in both the intuitive and theoretical justification of the use of the logistic function. In the theoretical development of the model utilising advanced non-parametric statistical methods. We have also constructed a method of identifying values that are likely to be erroneous. Using quadratic programming, we can eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. Additionally, this is a first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors (see Boland and Ridley 2007). Our more recent investigations focus on examining the effects of adding additional explanatory variables to enhance the predictability of the model. Examples for Australian and other locations will be presented. (orig.)

A Detailed Analytical Study of Non-Linear Semiconductor Device Modelling

Directory of Open Access Journals (Sweden)

Umesh Kumar

1995-01-01

junction diode have been developed. The results of computer simulated examples have been presented in each case. The non-linear lumped model for Gunn is a unified model as it describes the diffusion effects as the-domain traves from cathode to anode. An additional feature of this model is that it describes the domain extinction and nucleation phenomena in Gunn dioder with the help of a simple timing circuit. The non-linear lumped model for SCR is general and is valid under any mode of operation in any circuit environment. The memristive circuit model for p-n junction diodes is capable of simulating realistically the diode’s dynamic behavior under reverse, forward and sinusiodal operating modes. The model uses memristor, the charge-controlled resistor to mimic various second-order effects due to conductivity modulation. It is found that both storage time and fall time of the diode can be accurately predicted.

A synchrotron radiation study of nonlinear diffusion in Cu-Au

International Nuclear Information System (INIS)

Menon, E.S.K.; Huang, P.; Kraitchman, M.; deFontaine, D.; Hoyt, J.J.; Chow, P.

1992-01-01

This paper reports a study in which alternate layers of pure copper and gold were vapor deposited on a sodium chloride substrate, the average concentration of the films being Cu-16 at% Au and the layering periodicity (modulation wavelength) being 3.31 nm. The composition modulation gives rise to satellite diffraction peaks around the (200) Bragg reelections. Synchrotron radiation at SSRL was able to detect u to third order satellite intensity the evolution of which was measured as a function of annealing time at 515 K. although the first order satellite intensity decayed as expected exponentially with time, intensities of both second and third order satellites decreased very rapidly at first, then increased before decaying exponentially. These results are in conformity with theoretical models of satellite evolution during annealing in a one-dimensional modulated system governed by a nonlinear diffusion equation

Turing and Non-Turing patterns in diffusive plankton model

Directory of Open Access Journals (Sweden)

N. K. Thakur

2015-03-01

Full Text Available In this paper, we investigate a Rosenzweig-McAurthur model and its variant for phytoplankton, zooplankton and fish population dynamics with Holling type II and III functional responses. We present the theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The choice of parameter values is important to study the effect of diffusion, also it depends more on the nonlinearity of the system. With the help of numerical simulations, we observe the formation of spatiotemporal patterns both inside and outside the Turing space.

Size effects in non-linear heat conduction with flux-limited behaviors

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

Science.gov (United States)

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Microscopic modeling of the Raman diffusion

International Nuclear Information System (INIS)

Benisti, D.; Morice, O.; Gremillet, L.; Strozzi, D.

2010-01-01

In the typical conditions of density and electronic temperature of the Laser Megajoule (LMJ), a quantitative assessment of the Raman reflectivity requires an accurate calculation of the non-linear movement of each electron submitted to the waves propagating in the plasma. The interaction of a laser beam with a plasma generates an electronic wave shifted in frequency (that can be back-scattered) and an electron plasma wave (OPE). The OPE can give to the electrons a strongly non-linear movement by trapping them in a potential well. This non-linearity of microscopic origin has an impact on the plasma electronic density. We have succeeded in computing this plasma electronic density in a very accurate way by combining the principles of a perturbative approach with those of an adiabatic theory. Results show that the Raman diffusion can grow on temperature and density ranges more important than expected. We have predicted the threshold and the behavior of the Raman diffusion above this threshold as accurately as we had done it with a Vlasov code but by being 10000 times more rapid. (A.C.)

Diffusion properties of a guiding center plasma in a model electrostatic turbulence

International Nuclear Information System (INIS)

Pettini, M.; Vulpiani, A.; Misguich, J.H.; Balescu, R.; De Leener, M.; Orban, J.

1986-01-01

Numerical simulations have been performed to calculate the diffusion coefficient of several hundreds of charged particles across a strong magnetic field B, due to a known spectrum of electrostatic fluctuations. The results have been compared with the turbulent diffusion theory proposed by Misguich et al. The equation of motion is solved with a model electrostatic potential. This potential is also the Hamiltonian of this chaotic non-autonomous system: positive Lyapunov exponents are found in qualitative agreement with theoretical predictions. The absolute diffusion coefficients found in two different models exhibit a transition between two scaling regions: a classical scaling at low amplitudes (D ∼ E 2 /B 2 ), and a Bohm scaling at higher amplitudes (D ∼ E/B), in agreement with the predictions for these models. The value of the diffusion coefficient obtained in the isotropic model shows a satisfactory agreement with the theory. The study of the relative diffusion of initially close particles yields a clear quantitative confirmation of the clump effect and of the validity of the theoretical treatment of such nonlinearities. (26 fig, 20 refs)

Homotopy perturbation transform method for pricing under pure diffusion models with affine coefficients

Directory of Open Access Journals (Sweden)

Claude Rodrigue Bambe Moutsinga

2018-01-01

Full Text Available Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique, a combination of Laplace transform and homotopy perturbation methods is considered as an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is applied to solving stiff diffusion model problems that include interest rates models as well as two and three-factor stochastic volatility models. We show that the present approach is relatively easy, efficient and highly accurate.

Differences in Gaussian diffusion tensor imaging and non-Gaussian diffusion kurtosis imaging model-based estimates of diffusion tensor invariants in the human brain.

Science.gov (United States)

Lanzafame, S; Giannelli, M; Garaci, F; Floris, R; Duggento, A; Guerrisi, M; Toschi, N

2016-05-01

An increasing number of studies have aimed to compare diffusion tensor imaging (DTI)-related parameters [e.g., mean diffusivity (MD), fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD)] to complementary new indexes [e.g., mean kurtosis (MK)/radial kurtosis (RK)/axial kurtosis (AK)] derived through diffusion kurtosis imaging (DKI) in terms of their discriminative potential about tissue disease-related microstructural alterations. Given that the DTI and DKI models provide conceptually and quantitatively different estimates of the diffusion tensor, which can also depend on fitting routine, the aim of this study was to investigate model- and algorithm-dependent differences in MD/FA/RD/AD and anisotropy mode (MO) estimates in diffusion-weighted imaging of human brain white matter. The authors employed (a) data collected from 33 healthy subjects (20-59 yr, F: 15, M: 18) within the Human Connectome Project (HCP) on a customized 3 T scanner, and (b) data from 34 healthy subjects (26-61 yr, F: 5, M: 29) acquired on a clinical 3 T scanner. The DTI model was fitted to b-value =0 and b-value =1000 s/mm(2) data while the DKI model was fitted to data comprising b-value =0, 1000 and 3000/2500 s/mm(2) [for dataset (a)/(b), respectively] through nonlinear and weighted linear least squares algorithms. In addition to MK/RK/AK maps, MD/FA/MO/RD/AD maps were estimated from both models and both algorithms. Using tract-based spatial statistics, the authors tested the null hypothesis of zero difference between the two MD/FA/MO/RD/AD estimates in brain white matter for both datasets and both algorithms. DKI-derived MD/FA/RD/AD and MO estimates were significantly higher and lower, respectively, than corresponding DTI-derived estimates. All voxelwise differences extended over most of the white matter skeleton. Fractional differences between the two estimates [(DKI - DTI)/DTI] of most invariants were seen to vary with the invariant value itself as well as with MK

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

Directory of Open Access Journals (Sweden)

Narcisa Apreutesei

2014-05-01

Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

LDRD report nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Segalman, D.; Heinstein, M.

1997-09-01

The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

Science.gov (United States)

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

Yunying Zheng

2011-01-01

Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

Science.gov (United States)

Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

2018-07-01

We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

Science.gov (United States)

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Non-linear diffusion and pattern formation in vortex matter

Science.gov (United States)

Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Griessen, R.; Einfeld, J.; Woerdenweber, R.

2000-03-01

Penetration of magnetic flux in YBa_2Cu_3O7 superconducting thin films and crystals in externally applied magnetic fields is visualized with a magneto-optical technique. A variety of flux patterns due to non-linear vortex behavior is observed: 1. Roughening of the flux front^1 with scaling exponents identical to those observed in burning paper^2. Two regimes are found where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. 2. Roughening of the flux profile similar to the Oslo model for rice-piles. 3. Fractal penetration of flux^3 with Hausdorff dimension depending on the critical current anisotropy. 4. Penetration as 'flux-rivers'. 5. The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori^4. By comparison with numerical simulations, it is shown that most of the observed behavior can be explained in terms of non-linear diffusion of vortices. ^1R. Surdeanu, R.J. Wijngaarden, E. Visser, J.M. Huijbregtse, J.H. Rector, B. Dam and R. Griessen, Phys.Rev. Lett. 83 (1999) 2054 ^2J. Maunuksela, M. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M.J. Alava, T. Ala-Nissila, Phys. Rev. Lett. 79, 1515 (1997) ^3R. Surdeanu, R.J. Wijngaarden, B. Dam, J. Rector, R. Griessen, C. Rossel, Z.F. Ren and J.H. Wang, Phys Rev B 58 (1998) 12467 ^4C. Reichhardt, C.J. Olson and F. Nori, Phys. Rev. B 58, 6534 (1998)

Thermodynamic modelling of fast dopant diffusion in Si

Science.gov (United States)

Saltas, V.; Chroneos, A.; Vallianatos, F.

2018-04-01

In the present study, nickel and copper fast diffusion in silicon is investigated in the framework of the cBΩ thermodynamic model, which connects point defect parameters with the bulk elastic and expansion properties. All the calculated point defect thermodynamic properties (activation Gibbs free energy, activation enthalpy, activation entropy, and activation volume) exhibit temperature dependence due to the non-linear anharmonic behavior of the isothermal bulk modulus of Si. Calculated activation enthalpies (0.15-0.16 eV for Ni and 0.17-0.19 eV for Cu) are in agreement with the reported experimental results. Small values of calculated activation volumes for both dopants (˜4% of the mean atomic volume) are consistent with the interstitial diffusion of Ni and Cu in Si.

Computing diffusivities from particle models out of equilibrium

Science.gov (United States)

Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia

2018-04-01

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.

Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models

KAUST Repository

Lewis, Mark A.

2012-08-15

How growth, mortality, and dispersal in a species affect the species\\' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species\\' spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results. © 2012 Society for Mathematical Biology.

Generalized Nonlinear Yule Models

OpenAIRE

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-01-01

With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth...

Modeling nonlinearities in MEMS oscillators.

Science.gov (United States)

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Modelling of a diffusion-sorption experiment on sandstone

International Nuclear Information System (INIS)

Smith, P.A.

1989-11-01

The results of a diffusion-sorption experiment on a sample of Darley Dale sandstone, using simulated groundwater spiked with a mixture of 125 I, 85 Sr and 137 Cs, are modelled by a one-dimensional porous medium approach in which sorption is described by Freundlich isotherms. The governing equations are solved analytically for the special case of a linear isotherm, and numerically using the computer code RANCHDIFF for non-linear isotherms. A set of time-dependent, ordinary differential equations is obtained using the Lagrange interpolation technique and integrated by Gear's variable order predictor-corrector method. It is shown that the sorption behaviour of 85 Sr can be modelled successfully by a linear isotherm, using a sorption parameter consistent with batch-sorption tests. The behaviour of 137 Cs may be modelled by a non-linear isotherm, but the amount of 137 Cs sorbed is less than that anticipated from batch-sorption tests. 125 I is assumed to be non-sorbing and is used to determine the porosity of the sandstone. (author) 10 figs., 4 tabs., 6 refs

Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

International Nuclear Information System (INIS)

Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.

1996-01-01

This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

Science.gov (United States)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Regression-based model of skin diffuse reflectance for skin color analysis

Science.gov (United States)

Tsumura, Norimichi; Kawazoe, Daisuke; Nakaguchi, Toshiya; Ojima, Nobutoshi; Miyake, Yoichi

2008-11-01

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.

A diffusion model of protected population on bilocal habitat with generalized resource

Science.gov (United States)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Understanding of flux-limited behaviors of heat transport in nonlinear regime

Energy Technology Data Exchange (ETDEWEB)

Guo, Yangyu, E-mail: yangyuhguo@gmail.com [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China); Jou, David, E-mail: david.jou@uab.es [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Wang, Moran, E-mail: mrwang@tsinghua.edu [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China)

2016-01-28

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit. - Highlights: • Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models. • Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters. • Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

Modelling of Innovation Diffusion

Directory of Open Access Journals (Sweden)

Arkadiusz Kijek

2010-01-01

Full Text Available Since the publication of the Bass model in 1969, research on the modelling of the diffusion of innovation resulted in a vast body of scientific literature consisting of articles, books, and studies of real-world applications of this model. The main objective of the diffusion model is to describe a pattern of spread of innovation among potential adopters in terms of a mathematical function of time. This paper assesses the state-of-the-art in mathematical models of innovation diffusion and procedures for estimating their parameters. Moreover, theoretical issues related to the models presented are supplemented with empirical research. The purpose of the research is to explore the extent to which the diffusion of broadband Internet users in 29 OECD countries can be adequately described by three diffusion models, i.e. the Bass model, logistic model and dynamic model. The results of this research are ambiguous and do not indicate which model best describes the diffusion pattern of broadband Internet users but in terms of the results presented, in most cases the dynamic model is inappropriate for describing the diffusion pattern. Issues related to the further development of innovation diffusion models are discussed and some recommendations are given. (original abstract

Nonlinear Modeling by Assembling Piecewise Linear Models

Science.gov (United States)

Yao, Weigang; Liou, Meng-Sing

2013-01-01

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Traveling waves in a diffusive predator-prey model with holling type-III functional response

International Nuclear Information System (INIS)

Li Wantong; Wu Shiliang

2008-01-01

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system in the traveling wave variable. The methods used to prove the results are the shooting argument, invariant manifold theory and the Hopf bifurcation theorem

Adaptive regression for modeling nonlinear relationships

CERN Document Server

Knafl, George J

2016-01-01

This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...

A clutter removal method for the Doppler ultrasound signal based on a nonlinear diffusion equation

International Nuclear Information System (INIS)

Li Peng; Xin Pengcheng; Bian Zhengzhong; Yu Gang

2008-01-01

Strong clutter components produced by stationary and slow-moving tissue structures render the lower frequency part of the spectrogram useless and degrade the accuracy of clinical ultrasound indices. An adaptive method based on the nonlinear forward-and-backward diffusion equation (FAB-DE) is proposed to remove strong clutter components from the contaminated Doppler signal. The clutter signal is extracted first by the FAB-DE accurately, in which the nonlinear diffusion coefficient function of the FAB-DE locally adjusts according to signal features and the diffusion adaptively switches between forward and backward mode. The present method has been validated by simulated and realistic pulse wave Doppler signals, and compared with the conventional high pass filter and the matching pursuit method. The simulation results, including spectrogram, mean velocity error, standard deviation of mean velocity and signal-to-clutter ratio of a decontaminated signal, demonstrate that the present FAB-DE method can remove clutter sufficiently and retain more low blood components simultaneously as compared with the other two methods. Results of the realistic Doppler blood signal, including spectrogram and low-frequency part of the spectrum, support the conclusion drawn from simulation cases

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

Science.gov (United States)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

Energy Technology Data Exchange (ETDEWEB)

Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)

2014-09-25

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.

Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

International Nuclear Information System (INIS)

Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar

2014-01-01

Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range

Scaling of chaos in strongly nonlinear lattices.

Science.gov (United States)

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Diffusion and sorption on hardened cement pastes - experiments and modelling results

Energy Technology Data Exchange (ETDEWEB)

Jakob, A.; Sarott, F.-A.; Spieler, P.

1999-08-01

Large parts of repositories for low and intermediate level radioactive waste consist of cementitious materials. Radionuclides are transported by diffusion in the cement matrix or, in case of fractured or highly permeable cement, by advection and dispersion. In this work we aim at a mechanistic understanding of diffusion processes of some reactive tracers. On the laboratory scale, ten through-diffusion experiments were performed to study these processes for Cl{sup -}, I{sup -}, Cs{sup +} and Ni{sup 2+} ions in a Sulphate Resisting Portland Cement (SRPC) equilibrated with an artificial pore water. Some of the experiments continued up to nearly three years with daily measurements. In all the experiments, a cement disk initially saturated with an artificial pore water was exposed on one side to a highly diluted solution containing the species of interest. On the second side, a near-zero concentration boundary was maintained to drive through-diffusion of the tracer. The changes of concentrations on both sides of the samples were monitored, allowing careful mass balances. From these data, values of the diffusive flux and the mass of tracer taken up by the cementitious material were determined as a function of time. In the subsequent modelling, the time histories of these tracer breakthroughs were fitted using five different models. The simplest model neglects all retarding mechanisms except pure diffusion. More complex models either account for instantaneous equilibrium sorption in form of linear or non-linear (Freundlich) sorption or for first-order sorption kinetics where the forward reaction may be linear or non-linear according to the Freundlich isotherm, while the back-reaction is linear. Hence, the analysis allows the extraction of the diffusion coefficient and parameter values for the sorption isotherm or rate-constants for sorption and desorption. The fits to the experimental data were carried out by an automated Marquardt-Levenberg procedure yielding error

Generalized Nonlinear Yule Models

Science.gov (United States)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Correction of Gradient Nonlinearity Bias in Quantitative Diffusion Parameters of Renal Tissue with Intra Voxel Incoherent Motion.

Science.gov (United States)

Malyarenko, Dariya I; Pang, Yuxi; Senegas, Julien; Ivancevic, Marko K; Ross, Brian D; Chenevert, Thomas L

2015-12-01

Spatially non-uniform diffusion weighting bias due to gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from magnet isocenter. Our previously-described approach allowed effective removal of spatial ADC bias from three orthogonal DWI measurements for mono-exponential media of arbitrary anisotropy. The present work evaluates correction feasibility and performance for quantitative diffusion parameters of the two-component IVIM model for well-perfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T MRI scanner near isocenter and offset superiorly. Spatially non-uniform diffusion weighting due to GNL resulted both in shift and broadening of perfusion-suppressed ADC histograms for off-center DWI relative to unbiased measurements close to isocenter. Direction-average DW-bias correctors were computed based on the known gradient design provided by vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gel-flood phantom. Both phantom and renal tissue ADC bias for off-center measurements was effectively removed by applying pre-computed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b -maps and DWI intensities in presence of IVIM perfusion. No significant bias impact was observed for IVIM perfusion fraction.

Nonlinear acceleration of transport criticality problems

International Nuclear Information System (INIS)

Park, H.; Knoll, D.A.; Newman, C.K.

2011-01-01

We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system. (author)

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

Science.gov (United States)

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Nonlinear models for autoregressive conditional heteroskedasticity

DEFF Research Database (Denmark)

Teräsvirta, Timo

This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation are discu...

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D; Keesman, K.J.; Zwart, Heiko J.

In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D.; Keesman, K.J.; Zwart, H.

2006-01-01

Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state

Second generation diffusion model of interacting gravity waves on the surface of deep fluid

Directory of Open Access Journals (Sweden)

A. Pushkarev

2004-01-01

Full Text Available We propose a second generation phenomenological model for nonlinear interaction of gravity waves on the surface of deep water. This model takes into account the effects of non-locality of the original Hasselmann diffusion equation still preserving important properties of the first generation model: physically consistent scaling, adherence to conservation laws and the existence of Kolmogorov-Zakharov solutions. Numerical comparison of both models with the original Hasselmann equation shows that the second generation models improves the angular distribution in the evolving wave energy spectrum.

Application of nonlinear nodal diffusion method for a small research reactor

International Nuclear Information System (INIS)

Jaradat, Mustafa K.; Alawneh, Luay M.; Park, Chang Je; Lee, Byungchul

2014-01-01

Highlights: • We applied nonlinear unified nodal method for 10 MW IAEA MTR benchmark problem. • TRITION–NEWT system was used to obtain two-group burnup dependent cross sections. • The criticality and power distribution compared with reference (IAEA-TECDOC-233). • Comparison between different fuel materials was conducted. • Satisfactory results were provided using UNM for MTR core calculations. - Abstract: Nodal diffusion methods are usually used for LWR calculations and rarely used for research reactor calculations. A unified nodal method with an implementation of the coarse mesh finite difference acceleration was developed for use in plate type research reactor calculations. It was validated for two PWR benchmark problems and then applied for IAEA MTR benchmark problem for static calculations to check the validity and accuracy of the method. This work was conducted to investigate the unified nodal method capability to treat material testing reactor cores. A 10 MW research reactor core is considered with three calculation cases for low enriched uranium fuel depending on the core burnup status of fresh, beginning-of-life, and end-of-life cores. The validation work included criticality calculations, flux distribution, and power distribution; in addition, a comparison between different fuel materials with the same uranium content was conducted. The homogenized two-group cross sections were generated using the TRITON–NEWT system. The results were compared with a reference, which was taken from IAEA-TECDOC-233. The unified nodal method provides satisfactory results for an all-rod out case, and the three-dimensional, two-group diffusion model can be considered accurate enough for MTR core calculations

Stochastic development regression on non-linear manifolds

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

From spiking neuron models to linear-nonlinear models.

Science.gov (United States)

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Finite element model for nonlinear shells of revolution

International Nuclear Information System (INIS)

Cook, W.A.

1979-01-01

Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials

Numerical simulation of a PSA system using a pore diffusion model

Energy Technology Data Exchange (ETDEWEB)

Raghavan, N S; Hassan, M M; Ruthven, D M

1986-01-01

A mathematical model has been developed for a pressure swing adsorption (PSA) system (heatless drier) in which the controlling resistance to mass transfer is diffusion within the pores of the adsorbent particles. The model equations are solved numerically by the method of orthogonal collocation. By comparing the solutions from this model with the solutions derived from the simpler linear driving force model it is shown that the simpler model provides an acceptable approximation provided that the coefficient (omega in eq. (1)) is chosen correctly. The appropriate value of omega depends on the cycle time and to a lesser extent on the degree of isotherm non-linearity and the nature of the diffusion mechanism, varying from about 40 at low cycle times to 15 or even lower at large cycle times. However, over a fairly wide range of conditions typical of PSA operation the linear driving force model with omega = 40 provides an acceptable approximation, except in the initial region of the transient. The value of omega recommended by Glueckauf for modelling of a fixed bed (omega = 15) is approached only at rather large cycle times and is clearly inappropriate for a PSA system under most practical conditions.

Superspace formulation of new nonlinear sigma models

International Nuclear Information System (INIS)

Gates, S.J. Jr.

1983-07-01

The superspace formulation of two classes of supersymmetric nonlinear σ-models are presented. Two alternative N=1 superspace formulations are given for the d=2 supersymmetric nonlinear σ-models with Killing vector potentials: (a) formulation uses an active central charge and, (b) formulation uses a spurion superfield without inducing a classical breakdown of supersymmetry. The N=2 vector multiplet is used to construct a new class of d=4 nonlinear σ-models which when reduced to d=2 possess N=4 supersymmetry. Implications of these two classes of nonlinear σ-models for N>=4 superfield supergravity are discussed. (author)

An extended five-stream model for diffusion of ion-implanted dopants in monocrystalline silicon

International Nuclear Information System (INIS)

Khina, B.B.

2007-01-01

Low-energy high-dose ion implantation of different dopants (P, Sb, As, B and others) into monocrystalline silicon with subsequent thermal annealing is used for the formation of ultra-shallow p-n junctions in modern VLSI circuit technology. During annealing, dopant activation and diffusion in silicon takes place. The experimentally observed phenomenon of transient enhanced diffusion (TED), which is typically ascribed to the interaction of diffusing species with non-equilibrium point defects accumulated in silicon due to ion damage, and formation of small clusters and extended defects, hinders further down scaling of p-n junctions in VLSI circuits. TED is currently a subject of extensive experimental and theoretical investigation in many binary and multicomponent systems. However, the state-of-the-art mathematical models of dopant diffusion, which are based on the so-called 'five-stream' approach, and modern TCAD software packages such as SUPREM-4 (by Silvaco Data Systems, Ltd.) that implement these models encounter severe difficulties in describing TED. Solving the intricate problem of TED suppression and development of novel regimes of ion implantation and rapid thermal annealing is impossible without elaboration of new mathematical models and computer simulation of this complex phenomenon. In this work, an extended five-stream model for diffusion in silicon is developed which takes into account all possible charge states of point defects (vacancies and silicon self-interstitials) and diffusing pairs 'dopant atom-vacancy' and 'dopant atom-silicon self-interstitial'. The model includes the drift terms for differently charged point defects and pairs in the internal electric field and the kinetics of interaction between unlike 'species' (generation and annihilation of pairs and annihilation of point defects). Expressions for diffusion coefficients and numerous sink/source terms that appear in the non-linear, non-steady-state reaction-diffusion equations are derived

Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

Science.gov (United States)

Das, T.; Panda, S.; Panda, B. K.

2018-05-01

Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.

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...

Traveling wave solutions of a biological reaction-convection-diffusion equation model by using $(G'/G$ expansion method

Directory of Open Access Journals (Sweden)

Shahnam Javadi

2013-07-01

Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.

Forecasting with nonlinear time series models

DEFF Research Database (Denmark)

Kock, Anders Bredahl; Teräsvirta, Timo

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...

Clinical system model for monitoring the physiological status of jaundice by extracting bilirubin components from skin diffuse reflectance spectra

Science.gov (United States)

Kumar, Alla S.; Clark, Joseph; Beyette, Fred R., Jr.

2009-02-01

Neonatal jaundice is a medical condition which occurs in newborns as a result of an imbalance between the production and elimination of bilirubin. The excess bilirubin in the blood stream diffuses into the surrounding tissue leading to a yellowing of the skin. As the bilirubin levels rise in the blood stream, there is a continuous exchange between the extra vascular bilirubin and bilirubin in the blood stream. Exposure to phototherapy alters the concentration of bilirubin in the vascular and extra vascular regions by causing bilirubin in the skin layers to be broken down. Thus, the relative concentration of extra vascular bilirubin is reduced leading to a diffusion of bilirubin out of the vascular region. Diffuse reflectance spectra from human skin contains physiological and structural information of the skin and nearby tissue. A diffuse reflectance spectrum must be captured before and after blanching in order to isolate the intravascular and extra vascular bilirubin. A new mathematical model is proposed with extra vascular bilirubin concentration taken into consideration along with other optical parameters in defining the diffuse reflectance spectrum from human skin. A nonlinear optimization algorithm has been adopted to extract the optical properties (including bilirubin concentration) from the skin reflectance spectrum. The new system model and nonlinear algorithm have been combined to enable extraction of Bilirubin concentrations within an average error of 10%.

Fuzzy model-based servo and model following control for nonlinear systems.

Science.gov (United States)

Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O

2009-12-01

This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

Directory of Open Access Journals (Sweden)

Roman Cherniha

2018-04-01

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

Nonlinear traveling waves in rotating Rayleigh-Bacute enard convection: Stability boundaries and phase diffusion

International Nuclear Information System (INIS)

Liu, Y.; Ecke, R.E.

1999-01-01

We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bacute enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio Γ=5. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates 60<Ω<420. The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for Ω=274. The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated. copyright 1999 The American Physical Society

Identification of nonlinear anelastic models

International Nuclear Information System (INIS)

Draganescu, G E; Bereteu, L; Ercuta, A

2008-01-01

A useful nonlinear identification technique applied to the anelastic and rheologic models is presented in this paper. First introduced by Feldman, the method is based on the Hilbert transform, and is currently used for identification of the nonlinear vibrations

Relation between nonlinear models and gauge ambiguities

International Nuclear Information System (INIS)

Balachandran, A.P.; Ramachandran, R.; Rupertsberger, H.; Skagerstam, B.S.

1980-01-01

We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear sigma-models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group). (orig.)

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

Simple Analytical Forms of the Perpendicular Diffusion Coefficient for Two-component Turbulence. III. Damping Model of Dynamical Turbulence

Energy Technology Data Exchange (ETDEWEB)

Gammon, M.; Shalchi, A., E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada)

2017-10-01

In several astrophysical applications one needs analytical forms of cosmic-ray diffusion parameters. Some examples are studies of diffusive shock acceleration and solar modulation. In the current article we explore perpendicular diffusion based on the unified nonlinear transport theory. While we focused on magnetostatic turbulence in Paper I, we included the effect of dynamical turbulence in Paper II of the series. In the latter paper we assumed that the temporal correlation time does not depend on the wavenumber. More realistic models have been proposed in the past, such as the so-called damping model of dynamical turbulence. In the present paper we derive analytical forms for the perpendicular diffusion coefficient of energetic particles in two-component turbulence for this type of time-dependent turbulence. We present new formulas for the perpendicular diffusion coefficient and we derive a condition for which the magnetostatic result is recovered.

Nonlinear resonance islands and modulational effects in a proton synchrotron

International Nuclear Information System (INIS)

Satogata, T.J.

1993-01-01

The authors examine one-dimensional and two-dimensional nonlinear resonance islands created in the transverse phase space of a proton synchrotron by nonlinear magnets. The authors examine application of the theoretical framework constructed to the phenomenon of modulational diffusion in a collider model of the Fermilab Tevatron. For the one-dimensional resonance island system, the authors examine the effects of two types of modulational perturbations on the stability of these resonance islands: Tune modulation and beta function modulation. Hamiltonian models are presented which predict stability boundaries that depend on only three parameters: The strength and frequency of the modulation and the frequency of small oscillations inside the resonance island. The tune modulation model is successfully tested in experiment, where frequency domain analysis coupled with tune modulation is demonstrated to be useful in measuring the strength of a nonlinear resonance. Nonlinear resonance islands are examined in two transverse dimensions in the presence of coupling and linearly independent crossing resonances. The authors present a first-order Hamiltonian model which predicts fixed point locations, but does not reproduce small oscillation frequencies seen in tracking. Particle tracking is presented which shows evidence of two-dimensional persistent signals, and the authors make suggestions on methods for observing such signals in future experiment. The authors apply the tune modulation stability diagram to the explicitly two-dimensional phenomenon of modulational diffusion in the Fermilab Tevatron with beam-beam kicks as the source of nonlinearity. The amplitude growth created by this mechanism in simulation is exponential rather than root-time as predicted by modulational diffusion models. The authors comment upon the luminosity and lifetime limitations such a mechanism implies in a proton storage ring

Formation of universal and diffusion regions of non-linear spectra of relativistic electrons in spatially limited sources

International Nuclear Information System (INIS)

Kontorovich, V.M.; Kochanov, A.E.

1980-01-01

It is demonstrated that in the case of hard injection of relativistic electrons accompanied by the joint action of synchrotron (Compton) losses and energy-dependent spatial diffusion, a spectrum with 'breaks' is formed containing universal (with index γ = 2) and diffusion regions, both independent of the injection spectrum. The effect from non-linearity of the electron spectrum is considered in averaged electromagnetic spectra for various geometries of sources (sphere, disk, arm). It is shown that an universal region (with index α = 0.5) can occur in the radiation spectrum. (orig.)

Physics constrained nonlinear regression models for time series

International Nuclear Information System (INIS)

Majda, Andrew J; Harlim, John

2013-01-01

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

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...

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 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 thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....

Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

OpenAIRE

Fagioli, Simone; Radici, Emanuela

2018-01-01

We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegative initial data in $L^{\\infty} \\cap BV$ away from vacuum and supported in a closed interval with zero-velocity boundary conditions. The main novelti...

A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

Directory of Open Access Journals (Sweden)

Pratibha Joshi

2014-12-01

Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

Science.gov (United States)

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

International Nuclear Information System (INIS)

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-01-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

Energy Technology Data Exchange (ETDEWEB)

Nedialkova, Lilia V.; Amat, Miguel A. [Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de [Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544 (United States); Hummer, Gerhard, E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de [Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Str. 3, 60438 Frankfurt am Main (Germany)

2014-09-21

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

Energy Technology Data Exchange (ETDEWEB)

Garcia Velarde, M

1977-07-01

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

International Nuclear Information System (INIS)

Garcia Velarde, M.

1977-01-01

Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

International Nuclear Information System (INIS)

Garcia Velarde, M.

1977-01-01

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

Modeling of Volatility with Non-linear Time Series Model

OpenAIRE

Kim Song Yon; Kim Mun Chol

2013-01-01

In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.

Nonlinear spherical perturbations in quintessence models of dark energy

Science.gov (United States)

Pratap Rajvanshi, Manvendra; Bagla, J. S.

2018-06-01

Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from ‑1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.

Image classification using multiscale information fusion based on saliency driven nonlinear diffusion filtering.

Science.gov (United States)

Hu, Weiming; Hu, Ruiguang; Xie, Nianhua; Ling, Haibin; Maybank, Stephen

2014-04-01

In this paper, we propose saliency driven image multiscale nonlinear diffusion filtering. The resulting scale space in general preserves or even enhances semantically important structures such as edges, lines, or flow-like structures in the foreground, and inhibits and smoothes clutter in the background. The image is classified using multiscale information fusion based on the original image, the image at the final scale at which the diffusion process converges, and the image at a midscale. Our algorithm emphasizes the foreground features, which are important for image classification. The background image regions, whether considered as contexts of the foreground or noise to the foreground, can be globally handled by fusing information from different scales. Experimental tests of the effectiveness of the multiscale space for the image classification are conducted on the following publicly available datasets: 1) the PASCAL 2005 dataset; 2) the Oxford 102 flowers dataset; and 3) the Oxford 17 flowers dataset, with high classification rates.

Amplitude equations for a sub-diffusive reaction-diffusion system

International Nuclear Information System (INIS)

Nec, Y; Nepomnyashchy, A A

2008-01-01

A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points

Comparing coefficients of nested nonlinear probability models

DEFF Research Database (Denmark)

Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders

2011-01-01

In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...

A two-layered diffusion model traces the dynamics of information processing in the valuation-and-choice circuit of decision making.

Science.gov (United States)

Piu, Pietro; Fargnoli, Francesco; Innocenti, Alessandro; Rufa, Alessandra

2014-01-01

A circuit of evaluation and selection of the alternatives is considered a reliable model in neurobiology. The prominent contributions of the literature to this topic are reported. In this study, valuation and choice of a decisional process during Two-Alternative Forced-Choice (TAFC) task are represented as a two-layered network of computational cells, where information accrual and processing progress in nonlinear diffusion dynamics. The evolution of the response-to-stimulus map is thus modeled by two linked diffusive modules (2LDM) representing the neuronal populations involved in the valuation-and-decision circuit of decision making. Diffusion models are naturally appropriate for describing accumulation of evidence over the time. This allows the computation of the response times (RTs) in valuation and choice, under the hypothesis of ex-Wald distribution. A nonlinear transfer function integrates the activities of the two layers. The input-output map based on the infomax principle makes the 2LDM consistent with the reinforcement learning approach. Results from simulated likelihood time series indicate that 2LDM may account for the activity-dependent modulatory component of effective connectivity between the neuronal populations. Rhythmic fluctuations of the estimate gain functions in the delta-beta bands also support the compatibility of 2LDM with the neurobiology of DM.

Nonlinear Control of Heartbeat Models

Directory of Open Access Journals (Sweden)

Witt Thanom

2011-02-01

Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

A simplified model exploration research of new anisotropic diffuse radiation model

International Nuclear Information System (INIS)

Yao, Wanxiang; Li, Zhengrong; Wang, Xiao; Zhao, Qun; Zhang, Zhigang; Lin, Lin

2016-01-01

Graphical abstract: The specific process of measured diffuse radiation data. - Highlights: • Simplified diffuse radiation model is extremely important for solar radiation simulation and energy simulation. • A new simplified anisotropic diffuse radiation model (NSADR model) is proposed. • The accuracy of existing models and NSADR model is compared based on the measured values. • The accuracy of the NSADR model is higher than that of the existing models, and suitable for calculating diffuse radiation. - Abstract: More accurate new anisotropic diffuse radiation model (NADR model) has been proposed, but the parameters and calculation process of NADR model used in the process are complex. So it is difficult to widely used in the simulation software and engineering calculation. Based on analysis of the diffuse radiation model and measured diffuse radiation data, this paper put forward three hypotheses: (1) diffuse radiation from sky horizontal region is concentrated in a very thin layer which is close to the line source; (2) diffuse radiation from circumsolar region is concentrated in the point of the sun; (3) diffuse radiation from orthogonal region is concentrated in the point located at 90 degree angles with the Sun. Based on these hypotheses, NADR model is simplified to a new simplified anisotropic diffuse radiation model (NSADR model). Then the accuracy of NADR model and its simplified model (NSADR model) are compared with existing models based on the measured values, and the result shows that Perez model and its simplified model are relatively accurate among existing models. However, the accuracy of these two models is lower than the NADR model and NSADR model due to neglect the influence of the orthogonal diffuse radiation. The accuracy of the NSADR model is higher than that of the existing models, meanwhile, another advantage is that the NSADR model simplifies the process of solution parameters and calculation. Therefore it is more suitable for

Double diffusivity model under stochastic forcing

Science.gov (United States)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

Nonlinear theory of collisionless trapped ion modes

International Nuclear Information System (INIS)

Hahm, T.S.; Tang, W.M.

1996-01-01

A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level δn/n 0 is lower than the conventional mixing length estimate, Δr/L n (ii) the ion temperature fluctuation level δT i /T i significantly exceeds the density fluctuation level δn/n 0 ; and (iii) the parallel ion velocity fluctuation level δv iparallel /v Ti is expected to be negligible

Applying DTI white matter orientations to finite element head models to examine diffuse TBI under high rotational accelerations.

LENUS (Irish Health Repository)

Colgan, Niall C

2010-12-01

The in-vivo mechanical response of neural tissue during impact loading of the head is simulated using geometrically accurate finite element (FE) head models. However, current FE models do not account for the anisotropic elastic material behaviour of brain tissue. In soft biological tissue, there is a correlation between internal microscopic structure and macroscopic mechanical properties. Therefore, constitutive equations are important for the numerical analysis of the soft biological tissues. By exploiting diffusion tensor techniques the anisotropic orientation of neural tissue is incorporated into a non-linear viscoelastic material model for brain tissue and implemented in an explicit FE analysis. The viscoelastic material parameters are derived from published data and the viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. The constitutive model was applied in the University College Dublin brain trauma model (UCDBTM) (i.e. three-dimensional finite element head model) to predict the mechanical response of the intra-cranial contents due to rotational injury.

Analysis of nonlinear systems using ARMA [autoregressive moving average] models

International Nuclear Information System (INIS)

Hunter, N.F. Jr.

1990-01-01

While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs

Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior

KAUST Repository

Markowich, Peter; Lorz, Alexander; Francesco, Marco

2010-01-01

We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through

Nonlinear System Identification and Its Applications in Fault Detection and Diagnosis

DEFF Research Database (Denmark)

Sun, Zhen

equation, the ISDE model generally consists of not only a structured deterministic part called drift term, but also a structured random part called diffusion term. The model can describe the system in which the random features are correlated with system states (inputs, outputs) and this relationship can......Interest in nonlinear system identification has grown significantly in recent years. It is much more difficult to develop general results than the concern for linear models since the nonlinear model structures are often much more complicated. As a consequence, the thesis only considers two...... different kinds of models, one is a type of state space model which is described by Itô Stochastic Differential Equations (ISDE), the other one is a nonlinear First Order Plus Dead Time (FOPDT) model. This thesis aims to investigate these two different kinds of nonlinear models and to propose...

Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

Directory of Open Access Journals (Sweden)

Jun Yan

2013-01-01

Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Global asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological models

International Nuclear Information System (INIS)

Wu Shiliang; Li Wantong

2009-01-01

This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.

Model of diffusers / permeators for hydrogen processing

International Nuclear Information System (INIS)

Jacobs, W. D.; Hang, T.

2008-01-01

Palladium-silver (Pd-Ag) diffusers are mainstays of hydrogen processing. Diffusers separate hydrogen from inert species such as nitrogen, argon or helium. The tubing becomes permeable to hydrogen when heated to more than 250 C and a differential pressure is created across the membrane. The hydrogen diffuses better at higher temperatures. Experimental or experiential results have been the basis for determining or predicting a diffuser's performance. However, the process can be mathematically modeled, and comparison to experimental or other operating data can be utilized to improve the fit of the model. A reliable model-based diffuser system design is the goal which will have impacts on tritium and hydrogen processing. A computer model has been developed to solve the differential equations for diffusion given the operating boundary conditions. The model was compared to operating data for a low pressure diffuser system. The modeling approach and the results are presented in this paper. (authors)

Modeling the diffusion of scientific publications

NARCIS (Netherlands)

D. Fok (Dennis); Ph.H.B.F. Franses (Philip Hans)

2005-01-01

textabstractThis paper illustrates that salient features of a panel of time series of annual citations can be captured by a Bass type diffusion model. We put forward an extended version of this diffusion model, where we consider the relation between key characteristics of the diffusion process and

NONLINEAR PLANT PIECEWISE-CONTINUOUS MODEL MATRIX PARAMETERS ESTIMATION

Directory of Open Access Journals (Sweden)

Roman L. Leibov

2017-09-01

Full Text Available This paper presents a nonlinear plant piecewise-continuous model matrix parameters estimation technique using nonlinear model time responses and random search method. One of piecewise-continuous model application areas is defined. The results of proposed approach application for aircraft turbofan engine piecewisecontinuous model formation are presented

The effect of a realistic thermal diffusivity on numerical model of a subducting slab

Science.gov (United States)

Maierova, P.; Steinle-Neumann, G.; Cadek, O.

2010-12-01

A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the

Study of the nonlinear imperfect software debugging model

International Nuclear Information System (INIS)

Wang, Jinyong; Wu, Zhibo

2016-01-01

In recent years there has been a dramatic proliferation of research on imperfect software debugging phenomena. Software debugging is a complex process and is affected by a variety of factors, including the environment, resources, personnel skills, and personnel psychologies. Therefore, the simple assumption that debugging is perfect is inconsistent with the actual software debugging process, wherein a new fault can be introduced when removing a fault. Furthermore, the fault introduction process is nonlinear, and the cumulative number of nonlinearly introduced faults increases over time. Thus, this paper proposes a nonlinear, NHPP imperfect software debugging model in consideration of the fact that fault introduction is a nonlinear process. The fitting and predictive power of the NHPP-based proposed model are validated through related experiments. Experimental results show that this model displays better fitting and predicting performance than the traditional NHPP-based perfect and imperfect software debugging models. S-confidence bounds are set to analyze the performance of the proposed model. This study also examines and discusses optimal software release-time policy comprehensively. In addition, this research on the nonlinear process of fault introduction is significant given the recent surge of studies on software-intensive products, such as cloud computing and big data. - Highlights: • Fault introduction is a nonlinear changing process during the debugging phase. • The assumption that the process of fault introduction is nonlinear is credible. • Our proposed model can better fit and accurately predict software failure behavior. • Research on fault introduction case is significant to software-intensive products.

Heterotic sigma models and non-linear strings

International Nuclear Information System (INIS)

Hull, C.M.

1986-01-01

The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)

Stability, diffusion and interactions of nonlinear excitations in a many body system

Science.gov (United States)

Coste, Christophe; Jean, Michel Saint; Dessup, Tommy

2017-04-01

When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.

Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems

International Nuclear Information System (INIS)

Ma, Z.; Whitley, R.D.; Wang, N.H.L.

1996-01-01

A generalized parallel pore and surface diffusion model for multicomponent adsorption and liquid chromatography is formulated and solved numerically. Analytical solution for first- and second-order central moments for a pulse on a plateau input is used as benchmarks for the numerical solutions. Theoretical predictions are compared with experimental data for two systems: ion-exchange of strontium, sodium, and calcium in a zeolite and competitive adsorption of two organics on activated carbon. In a linear isotherm region of single-component systems, both surface and pore diffusion cause symmetric spreading in breakthrough curves. In a highly nonlinear isotherm region, however, surface diffusion causes pronounced tailing in breakthrough curves; the larger the step change in concentration, the more pronounced tailing, in contrast to relatively symmetric breakthroughs due to pore diffusion. If only a single diffusion mechanism is assumed in analyzing the data of parallel diffusion systems, a concentration-dependent apparent surface diffusivity or pore diffusivity results; for a convex isotherm, the apparent surface diffusivity increases, whereas the apparent pore diffusivity decreases with increasing concentration. For a multicomponent nonlinear system, elution order can change if pore diffusion dominates for a low-affinity solute, whereas surface diffusion dominates for a high-affinity solute

Diffusion of multiple species with excluded-volume effects

KAUST Repository

Bruna, Maria; Chapman, S. Jonathan

2012-01-01

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results. © 2012 American Institute of Physics.

From conservative to reactive transport under diffusion-controlled conditions

Science.gov (United States)

Babey, Tristan; de Dreuzy, Jean-Raynald; Ginn, Timothy R.

2016-05-01

We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions.

Nonlinear distortion in wireless systems modeling and simulation with Matlab

CERN Document Server

Gharaibeh, Khaled M

2011-01-01

This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems

Model and Comparative Study for Flow of Viscoelastic Nanofluids with Cattaneo-Christov Double Diffusion.

Directory of Open Access Journals (Sweden)

Tasawar Hayat

Full Text Available Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

Science.gov (United States)

Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent

2018-03-01

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

Nonlinear Dynamics of a Diffusing Interface

Science.gov (United States)

Duval, Walter M. B.

2001-01-01

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Stochastic development regression on non-linear manifolds

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....

Model reduction of nonlinear systems subject to input disturbances

KAUST Repository

Ndoye, Ibrahima

2017-07-10

The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.

Non-linear Growth Models in Mplus and SAS

Science.gov (United States)

Grimm, Kevin J.; Ram, Nilam

2013-01-01

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. PMID:23882134

Cosmic ray diffusion: report of the workshop in cosmic ray diffusion theory

International Nuclear Information System (INIS)

Birmingham, T.J.; Jones, F.C.

1975-02-01

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory. (auth)

Nonlinear analysis on power reactor dynamics

International Nuclear Information System (INIS)

Konno, H.; Hayashi, K.

1997-01-01

We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)

Parameter estimation in fractional diffusion models

CERN Document Server

Kubilius, Kęstutis; Ralchenko, Kostiantyn

2017-01-01

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

Science.gov (United States)

Barsi, C; Fleischer, J W

2015-09-21

We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

Modeling dendrite density from magnetic resonance diffusion measurements

DEFF Research Database (Denmark)

Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif

2007-01-01

in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.......e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides......Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal...

Nonlinear model predictive control theory and algorithms

CERN Document Server

Grüne, Lars

2017-01-01

This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

Parameter Estimation of Nonlinear Models in Forestry.

OpenAIRE

Fekedulegn, Desta; Mac Siúrtáin, Máirtín Pádraig; Colbert, Jim J.

1999-01-01

Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard’s nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinnin...

A micro-macro constitutive model for finite-deformation viscoelasticity of elastomers with nonlinear viscosity

Science.gov (United States)

Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.

2018-01-01

Elastomers are known to exhibit viscoelastic behavior under deformation, which is linked to the diffusion processes of the highly mobile and flexible polymer chains. Inspired by the theories of polymer dynamics, a micro-macro constitutive model is developed to study the viscoelastic behaviors and the relaxation process of elastomeric materials under large deformation, in which the material parameters all have a microscopic foundation or a microstructural justification. The proposed model incorporates the nonlinear material viscosity into the continuum finite-deformation viscoelasticity theories which represent the polymer networks of elastomers with an elastic ground network and a few viscous subnetworks. The developed modeling framework is capable of adopting most of strain energy density functions for hyperelastic materials and thermodynamics evolution laws of viscoelastic solids. The modeling capacity of the framework is outlined by comparing the simulation results with the experimental data of three commonly used elastomeric materials, namely, VHB4910, HNBR50 and carbon black (CB) filled elastomers. The comparison shows that the stress responses and some typical behaviors of filled and unfilled elastomers can be quantitatively predicted by the model with suitable strain energy density functions. Particularly, the strain-softening effect of elastomers could be explained by the deformation-dependent (nonlinear) viscosity of the polymer chains. The presented modeling framework is expected to be useful as a modeling platform for further study on the performance of different type of elastomeric materials.

Numerical solution of a reaction-diffusion equation

International Nuclear Information System (INIS)

Moyano, Edgardo A.; Scarpettini, Alberto F.

2000-01-01

The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

A Simple Model for Nonlinear Confocal Ultrasonic Beams

Science.gov (United States)

Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

2007-01-01

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander; Haskovec, Jan; Markowich, Peter A.

2014-01-01

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative

Probabilistic transport models for plasma transport in the presence of critical thresholds: Beyond the diffusive paradigm

International Nuclear Information System (INIS)

Sanchez, R.; Milligen, B.Ph. van; Carreras, B.A.

2005-01-01

It is argued that the modeling of plasma transport in tokamaks may benefit greatly from extending the usual local paradigm to accommodate scale-free transport mechanisms. This can be done by combining Levy distributions and a nonlinear threshold condition within the continuous time random walk concept. The advantages of this nonlocal, nonlinear extension are illustrated by constructing a simple particle density transport model that, as a result of these ideas, spontaneously exhibits much of nondiffusive phenomenology routinely observed in tokamaks. The fluid limit of the system shows that the kind of equations that are appropriate to capture these dynamics are based on fractional differential operators. In them, effective diffusivities and pinch velocities are found that are dynamically set by the system in response to the specific characteristics of the fueling source and external perturbations. This fact suggests some dramatic consequences for the extrapolation of these transport properties to larger size systems

Direct diffusion tensor estimation using a model-based method with spatial and parametric constraints.

Science.gov (United States)

Zhu, Yanjie; Peng, Xi; Wu, Yin; Wu, Ed X; Ying, Leslie; Liu, Xin; Zheng, Hairong; Liang, Dong

2017-02-01

To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue. © 2016 American Association of Physicists in Medicine.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Science.gov (United States)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

A tracer diffusion model derived from microstructure

International Nuclear Information System (INIS)

Lehikoinen, Jarmo; Muurinen, Arto; Olin, Markus

2012-01-01

Document available in extended abstract form only. Full text of publication follows: Numerous attempts have been made to explain the tracer diffusion of various solutes in compacted clays. These attempts have commonly suffered from an inability to describe the diffusion of uncharged and charged solutes with a single unified model. Here, an internally consistent approach to describing the diffusion of solutes in a heterogeneous porous medium, such as compacted bentonite, in terms of its microstructure is presented. The microstructure is taken to be represented by a succession of unit cells, which consist of two consecutive regions (Do, 1996). In the first region, the diffusion is viewed to occur in two parallel paths: one through microcrystalline units (micropores) and the other through meso-pores between the microcrystalline units. Solutes exiting these two paths are then joined together to continue diffusing through the second, disordered, region, connecting the two adjacent microcrystalline units. Adsorption (incl. co-ion exclusion) is thought to occur in the micropores, whereas meso-pores and the disordered region accommodate free species alone. Co-ions are also assumed to experience transfer resistance into and out of the micropores, which is characterized in the model by a transmission coefficient. Although the model is not new per se, its application to compacted clays has never been attempted before. It is shown that in the limit of strong adsorption, the effective diffusivity is limited from above only by the microstructural parameters of the model porous medium. As intuitive and logical as this result may appear, it has not been proven before. In the limit of vanishing disordered region, the effective diffusivity is no longer explicitly constrained by any of the model parameters. The tortuosity of the diffusion path, i.e. the quotient of the actual diffusion path length in the porous-medium coordinates and the characteristic length of the laboratory frame

Nonlinear Kalman Filtering in Affine Term Structure Models

DEFF Research Database (Denmark)

Christoffersen, Peter; Dorion, Christian; Jacobs, Kris

When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... the potential of the unscented Kalman …filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman …filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive...

Deterministic Diffusion in Delayed Coupled Maps

International Nuclear Information System (INIS)

Sozanski, M.

2005-01-01

Coupled Map Lattices (CML) are discrete time and discrete space dynamical systems used for modeling phenomena arising in nonlinear systems with many degrees of freedom. In this work, the dynamical and statistical properties of a modified version of the CML with global coupling are considered. The main modification of the model is the extension of the coupling over a set of local map states corresponding to different time iterations. The model with both stochastic and chaotic one-dimensional local maps is studied. Deterministic diffusion in the CML under variation of a control parameter is analyzed for unimodal maps. As a main result, simple relations between statistical and dynamical measures are found for the model and the cases where substituting nonlinear lattices with simpler processes is possible are presented. (author)

Mathematical aspects of reacting and diffusing systems

CERN Document Server

Fife, Paul C

1979-01-01

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...

Nonlinear Growth Models in M"plus" and SAS

Science.gov (United States)

Grimm, Kevin J.; Ram, Nilam

2009-01-01

Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

Di Francesco, M.

2008-12-08

We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

Modeling the reemergence of information diffusion in social network

Science.gov (United States)

Yang, Dingda; Liao, Xiangwen; Shen, Huawei; Cheng, Xueqi; Chen, Guolong

2018-01-01

Information diffusion in networks is an important research topic in various fields. Existing studies either focus on modeling the process of information diffusion, e.g., independent cascade model and linear threshold model, or investigate information diffusion in networks with certain structural characteristics such as scale-free networks and small world networks. However, there are still several phenomena that have not been captured by existing information diffusion models. One of the prominent phenomena is the reemergence of information diffusion, i.e., a piece of information reemerges after the completion of its initial diffusion process. In this paper, we propose an optimized information diffusion model by introducing a new informed state into traditional susceptible-infected-removed model. We verify the proposed model via simulations in real-world social networks, and the results indicate that the model can reproduce the reemergence of information during the diffusion process.

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes

DEFF Research Database (Denmark)

Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan

2013-01-01

The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...

Topological approximation of the nonlinear Anderson model

Science.gov (United States)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

A non-linear state space approach to model groundwater fluctuations

NARCIS (Netherlands)

Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.

2006-01-01

A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual

Augmented twin-nonlinear two-box behavioral models for multicarrier LTE power amplifiers.

Science.gov (United States)

Hammi, Oualid

2014-01-01

A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.

Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks

Science.gov (United States)

Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming

2018-04-01

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.

Diffusion-type model of the global carbon cycle for the estimation of dose to the world population from releases of carbon-14 to the atmosphere

International Nuclear Information System (INIS)

Killough, G.G.

1977-05-01

A nonlinear dynamic model of the exchange of carbon among the atmosphere, terrestrial biosphere, and ocean is described and applied to estimating the radiation dose to the world's population from the release of 14 C to the atmosphere from the nuclear power industry. A computer implementation of the model, written in the IBM Continuous System Modeling Program III (CSMP III) simulation language, is presented. The model treats the ocean as a diffusive medium with respect to vertical transport of carbon, and the nonlinear variation of CO 2 partial pressure with the total inorganic carbon concentration in surface waters is taken into account in calculating the transfer rate from ocean to atmosphere. Transfers between the atmosphere and terrestrial biosphere are represented by nonlinear equations which consider CO 2 fertilization and impose a constraint on the ultimate total carbon mass in the biosphere

A nonlinear model for AC induced corrosion

Directory of Open Access Journals (Sweden)

N. Ida

2012-09-01

Full Text Available The modeling of corrosion poses particular difficulties. The understanding of corrosion as an electrochemical process has led to simple capacitive-resistive models that take into account the resistance of the electrolytic cell and the capacitive effect of the surface potential at the interface between conductors and the electrolyte. In some models nonlinear conduction effects have been added to account for more complex observed behavior. While these models are sufficient to describe the behavior in systems with cathodic protection, the behavior in the presence of induced AC currents from power lines and from RF sources cannot be accounted for and are insufficient to describe the effects observed in the field. Field observations have shown that a rectifying effect exists that affects the cathodic protection potential and this effect is responsible for corrosion in the presence of AC currents. The rectifying effects of the metal-corrosion interface are totally missing from current models. This work proposes a nonlinear model based on finite element analysis that takes into account the nonlinear behavior of the metal-oxide interface and promises to improve modeling by including the rectification effects at the interface.

Diffusion coefficient adaptive correction in Lagrangian puff model

International Nuclear Information System (INIS)

Tan Wenji; Wang Dezhong; Ma Yuanwei; Ji Zhilong

2014-01-01

Lagrangian puff model is widely used in the decision support system for nuclear emergency management. The diffusion coefficient is one of the key parameters impacting puff model. An adaptive method was proposed in this paper, which could correct the diffusion coefficient in Lagrangian puff model, and it aimed to improve the accuracy of calculating the nuclide concentration distribution. This method used detected concentration data, meteorological data and source release data to estimate the actual diffusion coefficient with least square method. The diffusion coefficient adaptive correction method was evaluated by Kincaid data in MVK, and was compared with traditional Pasquill-Gifford (P-G) diffusion scheme method. The results indicate that this diffusion coefficient adaptive correction method can improve the accuracy of Lagrangian puff model. (authors)

Diffusion Influenced Adsorption Kinetics.

Science.gov (United States)

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

Science.gov (United States)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low

A non-linear dimension reduction methodology for generating data-driven stochastic input models

International Nuclear Information System (INIS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-01-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R n . An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R d (d<< n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology

Comparison of a nonlinear dynamic model of a piping system to test data

International Nuclear Information System (INIS)

Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

1983-01-01

Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

On some applications of diffusion processes for image processing

International Nuclear Information System (INIS)

Morfu, S.

2009-01-01

We propose a new algorithm inspired by the properties of diffusion processes for image filtering. We show that purely nonlinear diffusion processes ruled by Fisher equation allows contrast enhancement and noise filtering, but involves a blurry image. By contrast, anisotropic diffusion, described by Perona and Malik algorithm, allows noise filtering and preserves the edges. We show that combining the properties of anisotropic diffusion with those of nonlinear diffusion provides a better processing tool which enables noise filtering, contrast enhancement and edge preserving.

3D early embryogenesis image filtering by nonlinear partial differential equations.

Science.gov (United States)

Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

2010-08-01

We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which

Background field method for nonlinear σ-model in stochastic quantization

International Nuclear Information System (INIS)

Nakazawa, Naohito; Ennyu, Daiji

1988-01-01

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model. (orig.)

A spatial structural derivative model for ultraslow diffusion

Directory of Open Access Journals (Sweden)

Xu Wei

2017-01-01

Full Text Available This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function ex is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function ex in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.

Modeling Non-Linear Material Properties in Composite Materials

Science.gov (United States)

2016-06-28

Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions

Probabilistic transport models for plasma transport in the presence of critical thresholds: Beyond the diffusive paradigma)

Science.gov (United States)

Sánchez, R.; van Milligen, B. Ph.; Carreras, B. A.

2005-05-01

It is argued that the modeling of plasma transport in tokamaks may benefit greatly from extending the usual local paradigm to accommodate scale-free transport mechanisms. This can be done by combining Lévy distributions and a nonlinear threshold condition within the continuous time random walk concept. The advantages of this nonlocal, nonlinear extension are illustrated by constructing a simple particle density transport model that, as a result of these ideas, spontaneously exhibits much of nondiffusive phenomenology routinely observed in tokamaks. The fluid limit of the system shows that the kind of equations that are appropriate to capture these dynamics are based on fractional differential operators. In them, effective diffusivities and pinch velocities are found that are dynamically set by the system in response to the specific characteristics of the fueling source and external perturbations. This fact suggests some dramatic consequences for the extrapolation of these transport properties to larger size systems.

Time-delayed feedback control of diffusion in random walkers

Science.gov (United States)

Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U.

2017-07-01

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model

Filamentary structures of the cosmic web and the nonlinear Schroedinger type equation

International Nuclear Information System (INIS)

Tigrak, E; Weygaert, R van de; Jones, B J T

2011-01-01

We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schroedinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation.

Modeling of immision from power plants using stream-diffusion model

International Nuclear Information System (INIS)

Kanevce, Lj.; Kanevce, G.; Markoski, A.

1996-01-01

Analyses of simple empirical and integral immision models, comparing with complex three dimensional differential models is given. Complex differential models needs huge computer power, so they can't be useful for practical engineering calculations. In this paper immision modeling, using stream-diffusion approach is presented. Process of dispersion is divided into two parts. First part is called stream part, it's near the source of the pollutants, and it's presented with defected turbulent jet in wind field. This part finished when the velocity of stream (jet) becomes equal with wind speed. Boundary conditions in the end of the first part, are initial for the second, called diffusion part, which is modeling with tri dimensional diffusion equation. Gradient of temperature, wind speed profile and coefficient of diffusion in this model must not be constants, they can change with the height. Presented model is much simpler than the complete meteorological differential models which calculates whole fields of meteorological parameters. Also, it is more complex and gives more valuable results for dispersion of pollutants from widely used integral and empirical models

Stability of Gradient Field Corrections for Quantitative Diffusion MRI

OpenAIRE

Rogers, Baxter P.; Blaber, Justin; Welch, E. Brian; Ding, Zhaohua; Anderson, Adam W.; Landman, Bennett A.

2017-01-01

In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fie...

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

Science.gov (United States)

Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich

2018-04-01

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

Science.gov (United States)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

A deep belief network with PLSR for nonlinear system modeling.

Science.gov (United States)

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2017-10-31

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

An efficient method for model refinement in diffuse optical tomography

Science.gov (United States)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process

Directory of Open Access Journals (Sweden)

Dazi Li

2015-01-01

Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.

Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials

International Nuclear Information System (INIS)

Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan

2007-01-01

A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models

Modelling effects of tree population dynamics, tree throw and pit-mound formation/diffusion on microtopography over time in different forest settings

Science.gov (United States)

Martin, Y. E.; Johnson, E. A.; Gallaway, J.; Chaikina, O.

2011-12-01

Herein we conduct a followup investigation to an earlier research project in which we developed a numerical model of tree population dynamics, tree throw, and sediment transport associated with the formation of pit-mound features for Hawk Creek watershed, Canadian Rockies (Gallaway et al., 2009). We extend this earlier work by exploring the most appropriate transport relations to simulate the diffusion over time of newly-formed pit-pound features due to tree throw. We combine our earlier model with a landscape development model that can incorporate these diffusive transport relations. Using these combined models, changes in hillslope microtopography over time associated with the formation of pit-mound features and their decay will be investigated. The following ideas have motivated this particular study: (i) Rates of pit-mound degradation remain a source of almost complete speculation, as there is almost no long-term information on process rates. Therefore, we will attempt to tackle the issue of pit-mound degradation in a methodical way that can guide future field studies; (ii) The degree of visible pit-mound topography at any point in time on the landscape is a joint function of the rate of formation of new pit-mound features due to tree death/topple and their magnitude vs. the rate of decay of pit-mound features. An example of one interesting observation that arises is the following: it appears that pit-mound topography is often more pronounced in some eastern North American forests vs. field sites along the eastern slopes of the Canadian Rockies. Why is this the case? Our investigation begins by considering whether pit-mound decay might occur by linear or nonlinear diffusion. What differences might arise depending on which diffusive approach is adopted? What is the magnitude of transport rates associated with these possible forms of transport relations? We explore linear and nonlinear diffusion at varying rates and for different sizes of pit-mound pairs using a

Lagrangian-similarity diffusion-deposition model

International Nuclear Information System (INIS)

Horst, T.W.

1979-01-01

A Lagrangian-similarity diffusion model has been incorporated into the surface-depletion deposition model. This model predicts vertical concentration profiles far downwind of the source that agree with those of a one-dimensional gradient-transfer model

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

Energy Technology Data Exchange (ETDEWEB)

Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B. [Research Department of Biomedical Engineering, Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190 (China); Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn [School of Science, Harbin Institute of Technology, Shenzhen 518055 (China)

2017-08-20

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

Science.gov (United States)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

International Nuclear Information System (INIS)

Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B.; Qin, G.

2017-01-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Anomalous spreading of a density front from an infinite continuous source in a concentration-dependent lattice gas automaton diffusion model

CERN Document Server

Kuentz, M

2003-01-01

A two-dimensional lattice gas automaton (LGA) is used for simulating concentration-dependent diffusion in a microscopically random heterogeneous structure. The heterogeneous medium is initialized at a low density rho sub 0 and then submitted to a steep concentration gradient by continuous injection of particles at a concentration rho sub 1 >rho sub 0 from a one-dimensional source to model spreading of a density front. Whereas the nonlinear diffusion equation generally used to describe concentration-dependent diffusion processes predicts a scaling law of the type phi = xt sup - sup 1 sup / sup 2 in one dimension, the spreading process is shown to deviate from the expected t sup 1 sup / sup 2 scaling. The time exponent is found to be larger than 1/2, i.e. diffusion of the density front is enhanced with respect to standard Fickian diffusion. It is also established that the anomalous time exponent decreases as time elapses: anomalous spreading is thus not a timescaling process. We demonstrate that occurrence of a...

Robust model predictive control for constrained continuous-time nonlinear systems

Science.gov (United States)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

Modelling female fertility traits in beef cattle using linear and non-linear models.

Science.gov (United States)

Naya, H; Peñagaricano, F; Urioste, J I

2017-06-01

Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2  linear models; h 2  > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.

Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

Directory of Open Access Journals (Sweden)

Nicolás Peréz Alvarez

2015-11-01

Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

Symmetries and modelling functions for diffusion processes

International Nuclear Information System (INIS)

Nikitin, A G; Spichak, S V; Vedula, Yu S; Naumovets, A G

2009-01-01

A constructive approach to the theory of diffusion processes is proposed, which is based on application of both symmetry analysis and the method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error function expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment in experimental results obtained for surface diffusion of lithium on the molybdenum (1 1 2) surface precovered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems.

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

Science.gov (United States)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

-SED - the module of the simulation of the sediment transport in which the suspended sediments are simulated on the basis of the solution of 2-D advection -diffusion equation and the bottom sediment transport calculations are provided the basis of a library of the most popular semi-empirical formulas. MORPH - the module of the simulation of the morphological transformation of coastal zone based on the mass balance equation, on the basis of the sediment fluxes, calculated in the SED module. MORPH management submodel is responsible for the execution of the model chain "waves- current- sediments - morphodynamics- waves". The open source model SWASH has been used to simulate nonlinear resonance phenomena in coastal waters. The model chain was applied to simulate the potential impact of the designed shore protection structures at the Sochi Olympic Park on coastal morphodynamics, the wave parameters and nonlinear oscillations in the new ports designed in Gelenddjik and Taman at North-East coast of the Black Sea. The modeling results are compared with the results of the physical modeling in the hydraulic flumes of Moscow University of Civil Engineering.

Perturbation analysis of nonlinear matrix population models

Directory of Open Access Journals (Sweden)

Hal Caswell

2008-03-01

Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes

Directory of Open Access Journals (Sweden)

Qi-Zhi Zhang

2005-01-01

Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.

A strongly nonlinear reaction diffusion model for a deterministic diffusive epidemic

International Nuclear Information System (INIS)

Kirane, M.; Kouachi, S.

1993-04-01

In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. Moreover the large time behaviour of the global solutions is analyzed. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the data. (author). 9 refs

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

Science.gov (United States)

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

Dissipative quantum dynamics and nonlinear sigma-model

International Nuclear Information System (INIS)

Tarasov, V.E.

1992-01-01

Sedov variational principle which is the generalization of the least action principle for the dissipative and irreversible processes and the classical dissipative mechanics in the phase space is considered. Quantum dynamics for the dissipative and irreversible processes is constructed. As an example of the dissipative quantum theory the nonlinear two-dimensional sigma-model is considered. The conformal anomaly of the energy momentum tensor trace for closed bosonic string on the affine-metric manifold is investigated. The two-loop metric beta-function for nonlinear dissipative sigma-model was calculated. The results are compared with the ultraviolet two-loop conterterms for affine-metric sigma model. 71 refs

Stochastic Modelling of the Diffusion Coefficient for Concrete

DEFF Research Database (Denmark)

Thoft-Christensen, Palle

In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

Science.gov (United States)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

Variational Boussinesq model for strongly nonlinear dispersive waves

NARCIS (Netherlands)

Lawrence, C.; Adytia, D.; van Groesen, E.

2018-01-01

For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory

International Nuclear Information System (INIS)

Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping

2015-01-01

Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.

Nonlinear Inertia Classification Model and Application

Directory of Open Access Journals (Sweden)

Mei Wang

2014-01-01

Full Text Available Classification model of support vector machine (SVM overcomes the problem of a big number of samples. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO is an evolutionary search algorithm based on the swarm intelligence, which is suitable for parameter optimization. Accordingly, a nonlinear inertia convergence classification model (NICCM is proposed after the nonlinear inertia convergence (NICPSO is developed in this paper. The velocity of NICPSO is firstly defined as the weighted velocity of the inertia PSO, and the inertia factor is selected to be a nonlinear function. NICPSO is used to optimize the kernel parameter and a punishment factor of SVM. Then, NICCM classifier is trained by using the optical punishment factor and the optical kernel parameter that comes from the optimal particle. Finally, NICCM is applied to the classification of the normal state and fault states of online power cable. It is experimentally proved that the iteration number for the proposed NICPSO to reach the optimal position decreases from 15 to 5 compared with PSO; the training duration is decreased by 0.0052 s and the recognition precision is increased by 4.12% compared with SVM.

Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

DEFF Research Database (Denmark)

Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav

model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...

Fractional diffusion models of nonlocal transport

International Nuclear Information System (INIS)

Castillo-Negrete, D. del

2006-01-01

A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments

Nonlinear Modeling of the PEMFC Based On NNARX Approach

OpenAIRE

Shan-Jen Cheng; Te-Jen Chang; Kuang-Hsiung Tan; Shou-Ling Kuo

2015-01-01

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accurac...

A finite element model for nonlinear shells of revolution

International Nuclear Information System (INIS)

Cook, W.A.

1979-01-01

A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)

Heeding the waveform inversion nonlinearity by unwrapping the model and data

KAUST Repository

Alkhalifah, Tariq Ali

2012-01-01

Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We use unwrapped-phase-based objective functions to reduce such nonlinearity in a domain in which the high-frequency component is given by the traveltime inversion. Such information is packaged in a frequency-dependent attribute (or traveltime) that can be easily manipulated at different frequencies. It unwraps the phase of the wavefield yielding far less nonlinearity in the objective function than those experienced with the conventional misfit objective function, and yet it still holds most of the critical waveform information in its frequency dependency. However, it suffers from nonlinearity introduced by the model (or reflectivity), as events interact with each other (something like cross talk). This stems from the sinusoidal nature of the band-limited reflectivity model. Unwrapping the phase for such a model can mitigate this nonlinearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced nonlinearity and, thus, make the inversion more convergent. Simple examples are used to highlight such features.

Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach

DEFF Research Database (Denmark)

Knudsen, Morten; Jensen, J.G.

1995-01-01

A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....

Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach

NARCIS (Netherlands)

Doeswijk, T.G.; Keesman, K.J.

2005-01-01

Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such

Comments on Nonlinear Sigma Models Coupled to Supergravity arXiv

CERN Document Server

Ferrara, Sergio

2017-12-10

N=1 , D=4 nonlinear sigma models, parametrized by chiral superfields, usually describe Kählerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kähler when local supersymmetry becomes nonlinearly realized through the nilpotency of the supergravity auxiliary fields. In some cases the nonlinear realization eliminates one scalar propagating degree of freedom. This happens when the sigma model conformal-frame metric has co-rank 2. In the geometry of the inflaton, this effect eliminates its scalar superpartner. We show that the sigma model metric remains semidefinite positive in all cases, due the to positivity properties of the conformal-frame sigma model metric.

Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model

OpenAIRE

T. H. Lee; J. H. Park; S. M. Lee; S. C. Lee

2010-01-01

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of ...

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

Science.gov (United States)

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

Diffusion of Finite-Size Particles in Confined Geometries

KAUST Repository

Bruna, Maria; Chapman, S. Jonathan

2013-01-01

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

Science.gov (United States)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Directory of Open Access Journals (Sweden)

Petr Stehlík

2015-01-01

Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′  (or  Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

El-Beltagy, Mohamed A.

2014-01-06

Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

El-Beltagy, Mohamed A.; Al-Mulla, Noah

2014-01-01

Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Multiphase Microfluidics The Diffuse Interface Model

CERN Document Server

2012-01-01

Multiphase flows are typically described assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. This approach breaks down whenever the lengthscale of the phenomenon that is being studied is comparable with the real interface thickness, as it happens, for example, in the coalescence and breakup of bubbles and drops, the wetting and dewetting of solid surfaces and, in general, im micro-devices. The diffuse interface model resolves these probems by assuming that all quantities can vary continuously, so that interfaces have a non-zero thickness, i.e. they are "diffuse". The contributions in this book review the theory and describe some relevant applications of the diffuse interface model for one-component, two-phase fluids and for liquid binary mixtures, to model multiphase flows in confined geometries.

Lukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

CERN Document Server

Baianu, I C

2004-01-01

A categorical and Lukasiewicz-Topos framework for Lukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Lukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Lukasiewicz Topos with an n-valued Lukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.

Nonlinear control of the Salnikov model reaction

DEFF Research Database (Denmark)

Recke, Bodil; Jørgensen, Sten Bay

1999-01-01

This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...

Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity

Directory of Open Access Journals (Sweden)

Isao Ishida

2015-01-01

Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.

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...

Nonlinear Modelling of Low Frequency Loudspeakers

DEFF Research Database (Denmark)

Olsen, Erling Sandermann

1997-01-01

In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...

Nonlinear Modelling of Low Frequency Loudspeakers

DEFF Research Database (Denmark)

Olsen, Erling Sandermann

1997-01-01

In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

A simple numerical model of a geometrically nonlinear Timoshenko beam

NARCIS (Netherlands)

Keijdener, C.; Metrikine, A.

2015-01-01

In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and

Rigorous Multicomponent Reactive Separations Modelling: Complete Consideration of Reaction-Diffusion Phenomena

International Nuclear Information System (INIS)

Ahmadi, A.; Meyer, M.; Rouzineau, D.; Prevost, M.; Alix, P.; Laloue, N.

2010-01-01

This paper gives the first step of the development of a rigorous multicomponent reactive separation model. Such a model is highly essential to further the optimization of acid gases removal plants (CO 2 capture, gas treating, etc.) in terms of size and energy consumption, since chemical solvents are conventionally used. Firstly, two main modelling approaches are presented: the equilibrium-based and the rate-based approaches. Secondly, an extended rate-based model with rigorous modelling methodology for diffusion-reaction phenomena is proposed. The film theory and the generalized Maxwell-Stefan equations are used in order to characterize multicomponent interactions. The complete chain of chemical reactions is taken into account. The reactions can be kinetically controlled or at chemical equilibrium, and they are considered for both liquid film and liquid bulk. Thirdly, the method of numerical resolution is described. Coupling the generalized Maxwell-Stefan equations with chemical equilibrium equations leads to a highly non-linear Differential-Algebraic Equations system known as DAE index 3. The set of equations is discretized with finite-differences as its integration by Gear method is complex. The resulting algebraic system is resolved by the Newton- Raphson method. Finally, the present model and the associated methods of numerical resolution are validated for the example of esterification of methanol. This archetype non-electrolytic system permits an interesting analysis of reaction impact on mass transfer, especially near the phase interface. The numerical resolution of the model by Newton-Raphson method gives good results in terms of calculation time and convergence. The simulations show that the impact of reactions at chemical equilibrium and that of kinetically controlled reactions with high kinetics on mass transfer is relatively similar. Moreover, the Fick's law is less adapted for multicomponent mixtures where some abnormalities such as counter-diffusion

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

Science.gov (United States)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Modeling and non-linear responses of MEMS capacitive accelerometer

Directory of Open Access Journals (Sweden)

Sri Harsha C.

2014-01-01

Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

Statistical comparison of models for estimating the monthly average daily diffuse radiation at a subtropical African site

International Nuclear Information System (INIS)

Bashahu, M.

2003-01-01

Nine correlations have been developed in this paper to estimate the monthly average diffuse radiation for Dakar, Senegal. A 16-year period data on the global (H) and diffuse (H d ) radiation, together with data on the bright sunshine hours (N), the fraction of the sky's (Ne/8), the water vapour pressure in the air (e) and the ambient temperature (T) have been used for that purpose. A model inter-comparison based on the MBE, RMSE and t statistical tests has shown that estimates in any of the obtained correlations are not significantly different from their measured counterparts, thus all the nine models are recommended for the aforesaid location. Three of them should be particularly selected for their simplicity, universal applicability and high accuracy. Those are simple linear correlations between K d and N/N d , Ne/8 or K t . Even presenting adequate performance, the remaining correlations are either simple but less accurate, or multiple or nonlinear regressions needing one or two input variables. (author)

Error-diffusion binarization for joint transform correlators

Science.gov (United States)

Inbar, Hanni; Mendlovic, David; Marom, Emanuel

1993-02-01

A normalized nonlinearly scaled binary joint transform image correlator (JTC) based on a 1D error-diffusion binarization method has been studied. The behavior of the error-diffusion method is compared with hard-clipping, the most widely used method of binarized JTC approaches, using a single spatial light modulator. Computer simulations indicate that the error-diffusion method is advantageous for the production of a binarized power spectrum interference pattern in JTC configurations, leading to better definition of the correlation location. The error-diffusion binary JTC exhibits autocorrelation characteristics which are superior to those of the high-clipping binary JTC over the whole nonlinear scaling range of the Fourier-transform interference intensity for all noise levels considered.

Fractional diffusion models of transport in magnetically confined plasmas

International Nuclear Information System (INIS)

Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.

2005-01-01

Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model

Lévy flight with absorption: A model for diffusing diffusivity with long tails

Science.gov (United States)

Jain, Rohit; Sebastian, K. L.

2017-03-01

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.

Simplified Model of Nonlinear Landau Damping

International Nuclear Information System (INIS)

Yampolsky, N.A.; Fisch, N.J.

2009-01-01

The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.

Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.

Science.gov (United States)

Maybank, Philip J; Whiteley, Jonathan P

2014-02-01

Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.

Modelization of highly nonlinear waves in coastal regions

Science.gov (United States)

Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

2015-04-01

The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.

A multigrid Newton-Krylov method for flux-limited radiation diffusion

International Nuclear Information System (INIS)

Rider, W.J.; Knoll, D.A.; Olson, G.L.

1998-01-01

The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques

Diffusion of Finite-Size Particles in Confined Geometries

KAUST Repository

Bruna, Maria

2013-05-10

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle\\'s dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.

Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction

International Nuclear Information System (INIS)

Upadrashta, Deepesh; Yang, Yaowen

2015-01-01

Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)

A variable-order fractal derivative model for anomalous diffusion

Directory of Open Access Journals (Sweden)

Liu Xiaoting

2017-01-01

Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.

Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition

Science.gov (United States)

Kwon, H.; Khalil, A.; Brown, C.; Lall, U.; Ahn, H.; Moon, Y.

2005-12-01

Traditionally forecasting and characterizations of hydrologic systems is performed utilizing many techniques. Stochastic linear methods such as AR and ARIMA and nonlinear ones such as statistical learning theory based tools have been extensively used. The common difficulty to all methods is the determination of sufficient and necessary information and predictors for a successful prediction. Relationships between hydrologic variables are often highly nonlinear and interrelated across the temporal scale. A new hybrid approach is proposed for the simulation of hydrologic time series combining both the wavelet transform and the nonlinear model. The present model employs some merits of wavelet transform and nonlinear time series model. The Wavelet Transform is adopted to decompose a hydrologic nonlinear process into a set of mono-component signals, which are simulated by nonlinear model. The hybrid methodology is formulated in a manner to improve the accuracy of a long term forecasting. The proposed hybrid model yields much better results in terms of capturing and reproducing the time-frequency properties of the system at hand. Prediction results are promising when compared to traditional univariate time series models. An application of the plausibility of the proposed methodology is provided and the results conclude that wavelet based time series model can be utilized for simulating and forecasting of hydrologic variable reasonably well. This will ultimately serve the purpose of integrated water resources planning and management.

Finite difference modelling of the temperature rise in non-linear medical ultrasound fields.

Science.gov (United States)

Divall, S A; Humphrey, V F

2000-03-01

Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.

Verification of atmospheric diffusion models using data of long term atmospheric diffusion experiments

International Nuclear Information System (INIS)

Tamura, Junji; Kido, Hiroko; Hato, Shinji; Homma, Toshimitsu

2009-03-01

Straight-line or segmented plume models as atmospheric diffusion models are commonly used in probabilistic accident consequence assessment (PCA) codes due to cost and time savings. The PCA code, OSCAAR developed by Japan Atomic Energy Research Institute (Present; Japan Atomic Energy Agency) uses the variable puff trajectory model to calculate atmospheric transport and dispersion of released radionuclides. In order to investigate uncertainties involved with the structure of the atmospheric dispersion/deposition model in OSCAAR, we have introduced the more sophisticated computer codes that included regional meteorological models RAMS and atmospheric transport model HYPACT, which were developed by Colorado State University, and comparative analyses between OSCAAR and RAMS/HYPACT have been performed. In this study, model verification of OSCAAR and RAMS/HYPACT was conducted using data of long term atmospheric diffusion experiments, which were carried out in Tokai-mura, Ibaraki-ken. The predictions by models and the results of the atmospheric diffusion experiments indicated relatively good agreements. And it was shown that model performance of OSCAAR was the same degree as it of RAMS/HYPACT. (author)

Separation of irradiance and reflectance from observed color images by logarithmical nonlinear diffusion process

Science.gov (United States)

Saito, Takahiro; Takahashi, Hiromi; Komatsu, Takashi

2006-02-01

The Retinex theory was first proposed by Land, and deals with separation of irradiance from reflectance in an observed image. The separation problem is an ill-posed problem. Land and others proposed various Retinex separation algorithms. Recently, Kimmel and others proposed a variational framework that unifies the previous Retinex algorithms such as the Poisson-equation-type Retinex algorithms developed by Horn and others, and presented a Retinex separation algorithm with the time-evolution of a linear diffusion process. However, the Kimmel's separation algorithm cannot achieve physically rational separation, if true irradiance varies among color channels. To cope with this problem, we introduce a nonlinear diffusion process into the time-evolution. Moreover, as to its extension to color images, we present two approaches to treat color channels: the independent approach to treat each color channel separately and the collective approach to treat all color channels collectively. The latter approach outperforms the former. Furthermore, we apply our separation algorithm to a high quality chroma key in which before combining a foreground frame and a background frame into an output image a color of each pixel in the foreground frame are spatially adaptively corrected through transformation of the separated irradiance. Experiments demonstrate superiority of our separation algorithm over the Kimmel's separation algorithm.

Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell–Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model

International Nuclear Information System (INIS)

Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A

2015-01-01

This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3–9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects. (paper)

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

Science.gov (United States)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter

Science.gov (United States)

Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç

2017-01-01

This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.

Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant

Directory of Open Access Journals (Sweden)

Xiangjie Liu

2014-01-01

Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.

Diffuse radiation models and monthly-average, daily, diffuse data for a wide latitude range

International Nuclear Information System (INIS)

Gopinathan, K.K.; Soler, A.

1995-01-01

Several years of measured data on global and diffuse radiation and sunshine duration for 40 widely spread locations in the latitude range 36° S to 60° N are used to develop and test models for estimating monthly-mean, daily, diffuse radiation on horizontal surfaces. Applicability of the clearness-index (K) and sunshine fraction (SSO) models for diffuse estimation and the effect of combining several variables into a single multilinear equation are tested. Correlations connecting the diffuse to global fraction (HdH) with K and SSO predict Hd values more accurately than their separate use. Among clearness-index and sunshine-fraction models, SSO models are found to have better accuracy if correlations are developed for wide latitude ranges. By including a term for declinations in the correlation, the accuracy of the estimated data can be marginally improved. The addition of latitude to the equation does not help to improve the accuracy further. (author)

Study of a diffusion flamelet model, with preferential diffusion effects included

NARCIS (Netherlands)

Delhaye, S.; Somers, L.M.T.; Bongers, H.; Oijen, van J.A.; Goey, de L.P.H.; Dias, V.

2005-01-01

The non-premixed flamelet model of Peters [1] (model1), which does not include preferential diffusion effects is investigated. Two similar models are presented, but without the assumption of unity Lewis numbers. One of these models was derived by Peters & Pitsch [2] (model2), while the other one was

COMBINING LONG MEMORY AND NONLINEAR MODEL OUTPUTS FOR INFLATION FORECAST

OpenAIRE

Heri Kuswanto; Irhamah Alimuhajin; Laylia Afidah

2014-01-01

Long memory and nonlinearity have been proven as two models that are easily to be mistaken. In other words, nonlinearity is a strong candidate of spurious long memory by introducing a certain degree of fractional integration that lies in the region of long memory. Indeed, nonlinear process belongs to short memory with zero integration order. The idea of the forecast is to obtain the future condition with minimum error. Some researches argued that no matter what the model is, the important thi...

Nonlinear friction model for servo press simulation

Science.gov (United States)

Ma, Ninshu; Sugitomo, Nobuhiko; Kyuno, Takunori; Tamura, Shintaro; Naka, Tetsuo

2013-12-01

The friction coefficient was measured under an idealized condition for a pulse servo motion. The measured friction coefficient and its changing with both sliding distance and a pulse motion showed that the friction resistance can be reduced due to the re-lubrication during unloading process of the pulse servo motion. Based on the measured friction coefficient and its changes with sliding distance and re-lubrication of oil, a nonlinear friction model was developed. Using the newly developed the nonlinear friction model, a deep draw simulation was performed and the formability was evaluated. The results were compared with experimental ones and the effectiveness was verified.

Mathematical models for suspension bridges nonlinear structural instability

CERN Document Server

Gazzola, Filippo

2015-01-01

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

An Improved Nonlinear Five-Point Model for Photovoltaic Modules

Directory of Open Access Journals (Sweden)

Sakaros Bogning Dongue

2013-01-01

Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.

A new model of anomalous phosphorus diffusion in silicon

International Nuclear Information System (INIS)

Budil, M.; Poetzl, H.; Stingeder, G.; Grasserbauer, M.

1989-01-01

A model is presented to describe the 'kink and tail' diffusion of phosphorus. The diffusion behaviour of phosphorus is expplained by the motion of phosphorus-interstitial and phosphorus-vacancy pairs in different charge states. The model yields the enhancement of diffusion in the tail region depending on surface concentration. Furthermore it yields the same selfdiffusion coefficient for interstitials as the gold diffusion experiments. A transformation of the diffusion equation was found to reduce the number of simulation equations. (author) 7 refs., 5 figs

Modelling of a bridge-shaped nonlinear piezoelectric energy harvester

International Nuclear Information System (INIS)

Gafforelli, G; Corigliano, A; Xu, R; Kim, S G

2013-01-01

Piezoelectric MicroElectroMechanical Systems (MEMS) energy harvesting is an attractive technology for harvesting small magnitudes of energy from ambient vibrations. Increasing the operating frequency bandwidth of such devices is one of the major issues for real world applications. A MEMS-scale doubly clamped nonlinear beam resonator is designed and developed to demonstrate very wide bandwidth and high power density. In this paper a first complete theoretical discussion of nonlinear resonating piezoelectric energy harvesting is provided. The sectional behaviour of the beam is studied through the Classical Lamination Theory (CLT) specifically modified to introduce the piezoelectric coupling and nonlinear Green-Lagrange strain tensor. A lumped parameter model is built through Rayleigh-Ritz Method and the resulting nonlinear coupled equations are solved in the frequency domain through the Harmonic Balance Method (HBM). Finally, the influence of external load resistance on the dynamic behaviour is studied. The theoretical model shows that nonlinear resonant harvesters have much wider power bandwidth than that of linear resonators but their maximum power is still bounded by the mechanical damping as is the case for linear resonating harvesters

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

International Nuclear Information System (INIS)

Adcock, T. A. A.; Taylor, P. H.

2016-01-01

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum

DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

International Nuclear Information System (INIS)

Leaf, G.K.; Minkoff, M.

1982-01-01

1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

On an adaptive time stepping strategy for solving nonlinear diffusion equations

International Nuclear Information System (INIS)

Chen, K.; Baines, M.J.; Sweby, P.K.

1993-01-01

A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs

Diffusion Based Photon Mapping

DEFF Research Database (Denmark)

Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon

2007-01-01

. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....

Diffusion Based Photon Mapping

DEFF Research Database (Denmark)

Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon

2006-01-01

. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....

Spatiotemporal drought forecasting using nonlinear models

Science.gov (United States)

Vasiliades, Lampros; Loukas, Athanasios

2010-05-01

Spatiotemporal data mining is the extraction of unknown and implicit knowledge, structures, spatiotemporal relationships, or patterns not explicitly stored in spatiotemporal databases. As one of data mining techniques, forecasting is widely used to predict the unknown future based upon the patterns hidden in the current and past data. In order to achieve spatiotemporal forecasting, some mature analysis tools, e.g., time series and spatial statistics are extended to the spatial dimension and the temporal dimension, respectively. Drought forecasting plays an important role in the planning and management of natural resources and water resource systems in a river basin. Early and timelines forecasting of a drought event can help to take proactive measures and set out drought mitigation strategies to alleviate the impacts of drought. Despite the widespread application of nonlinear mathematical models, comparative studies on spatiotemporal drought forecasting using different models are still a huge task for modellers. This study uses a promising approach, the Gamma Test (GT), to select the input variables and the training data length, so that the trial and error workload could be greatly reduced. The GT enables to quickly evaluate and estimate the best mean squared error that can be achieved by a smooth model on any unseen data for a given selection of inputs, prior to model construction. The GT is applied to forecast droughts using monthly Standardized Precipitation Index (SPI) timeseries at multiple timescales in several precipitation stations at Pinios river basin in Thessaly region, Greece. Several nonlinear models have been developed efficiently, with the aid of the GT, for 1-month up to 12-month ahead forecasting. Several temporal and spatial statistical indices were considered for the performance evaluation of the models. The predicted results show reasonably good agreement with the actual data for short lead times, whereas the forecasting accuracy decreases with

Nonlinear adaptive inverse control via the unified model neural network

Science.gov (United States)

Jeng, Jin-Tsong; Lee, Tsu-Tian

1999-03-01

In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

Science.gov (United States)

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory.

Science.gov (United States)

Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping

2015-12-15

Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber. Copyright © 2015 Elsevier B.V. All rights reserved.

Nonlinear GARCH model and 1 / f noise

Science.gov (United States)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

Model reduction of nonlinear systems subject to input disturbances

KAUST Repository

Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem

2017-01-01

The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order

Calibration of the nonlinear ring model at the Diamond Light Source

Directory of Open Access Journals (Sweden)

R. Bartolini

2011-05-01

Full Text Available Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration of the nonlinear model that can accurately reproduce the nonlinear beam dynamics in Diamond.

Modeling vector nonlinear time series using POLYMARS

NARCIS (Netherlands)

de Gooijer, J.G.; Ray, B.K.

2003-01-01

A modified multivariate adaptive regression splines method for modeling vector nonlinear time series is investigated. The method results in models that can capture certain types of vector self-exciting threshold autoregressive behavior, as well as provide good predictions for more general vector

Verification of atmospheric diffusion models with data of atmospheric diffusion experiments

International Nuclear Information System (INIS)

Hato, Shinji; Homma, Toshimitsu

2009-02-01

The atmospheric diffusion experiments were implemented by Japan Atomic Energy Research Institute (JAERI) around Mount Tsukuba in 1989 and 1990, and the tracer gas concentration were monitored. In this study, the Gauss Plume Model and RAMS/HYPACT that are meteorological forecast code and atmospheric diffusion code with detailed physical law are made a comparison between monitored concentration. In conclusion, the Gauss Plume Model is better than RAM/HYPACT even complex topography if the estimation is around tens of kilometer form release point and the change in weather is constant for short time. This reason is difference of wind between RAMS and observation. (author)

Matrix diffusion model. In situ tests using natural analogues

International Nuclear Information System (INIS)

Rasilainen, K.

1997-11-01

Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories

Likelihood-Based Inference in Nonlinear Error-Correction Models

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbæk, Anders

We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...

Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Directory of Open Access Journals (Sweden)

Zhenhua Hu

2013-01-01

Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

Application of homotopy-perturbation method to nonlinear population dynamics models

International Nuclear Information System (INIS)

Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.

2007-01-01

In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)

Diffusion Forecasting Model with Basis Functions from QR-Decomposition

Science.gov (United States)

Harlim, John; Yang, Haizhao

2017-12-01

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

Comparison of apparent diffusion coefficients (ADCs) between two-point and multi-point analyses using high-B-value diffusion MR imaging

International Nuclear Information System (INIS)

Kubo, Hitoshi; Maeda, Masayuki; Araki, Akinobu

2001-01-01

We evaluated the accuracy of calculating apparent diffusion coefficients (ADCs) using high-B-value diffusion images. Echo planar diffusion-weighted MR images were obtained at 1.5 tesla in five standard locations in six subjects using gradient strengths corresponding to B values from 0 to 3000 s/mm 2 . Estimation of ADCs was made using two methods: a nonlinear regression model using measurements from a full set of B values (multi-point method) and linear estimation using B values of 0 and max only (two-point method). A high correlation between the two methods was noted (r=0.99), and the mean percentage differences were -0.53% and 0.53% in phantom and human brain, respectively. These results suggest there is little error in estimating ADCs calculated by the two-point technique using high-B-value diffusion MR images. (author)

Diffuse solar radiation estimation models for Turkey's big cities

International Nuclear Information System (INIS)

Ulgen, Koray; Hepbasli, Arif

2009-01-01

A reasonably accurate knowledge of the availability of the solar resource at any place is required by solar engineers, architects, agriculturists, and hydrologists in many applications of solar energy such as solar furnaces, concentrating collectors, and interior illumination of buildings. For this purpose, in the past, various empirical models (or correlations) have been developed in order to estimate the solar radiation around the world. This study deals with diffuse solar radiation estimation models along with statistical test methods used to statistically evaluate their performance. Models used to predict monthly average daily values of diffuse solar radiation are classified in four groups as follows: (i) From the diffuse fraction or cloudness index, function of the clearness index, (ii) From the diffuse fraction or cloudness index, function of the relative sunshine duration or sunshine fraction, (iii) From the diffuse coefficient, function of the clearness index, and (iv) From the diffuse coefficient, function of the relative sunshine duration or sunshine fraction. Empirical correlations are also developed to establish a relationship between the monthly average daily diffuse fraction or cloudness index (K d ) and monthly average daily diffuse coefficient (K dd ) with the monthly average daily clearness index (K T ) and monthly average daily sunshine fraction (S/S o ) for the three big cities by population in Turkey (Istanbul, Ankara and Izmir). Although the global solar radiation on a horizontal surface and sunshine duration has been measured by the Turkish State Meteorological Service (STMS) over all country since 1964, the diffuse solar radiation has not been measured. The eight new models for estimating the monthly average daily diffuse solar radiation on a horizontal surface in three big cites are validated, and thus, the most accurate model is selected for guiding future projects. The new models are then compared with the 32 models available in the

Modelling of information diffusion on social networks with applications to WeChat

Science.gov (United States)

Liu, Liang; Qu, Bo; Chen, Bin; Hanjalic, Alan; Wang, Huijuan

2018-04-01

Traces of user activities recorded in online social networks open new possibilities to systematically understand the information diffusion process on social networks. From the online social network WeChat, we collected a large number of information cascade trees, each of which tells the spreading trajectory of a message/information such as which user creates the information and which users view or forward the information shared by which neighbours. In this work, we propose two heterogeneous non-linear models, one for the topologies of the information cascade trees and the other for the stochastic process of information diffusion on a social network. Both models are validated by the WeChat data in reproducing and explaining key features of cascade trees. Specifically, we apply the Random Recursive Tree (RRT) to model the growth of cascade trees. The RRT model could capture key features, i.e. the average path length and degree variance of a cascade tree in relation to the number of nodes (size) of the tree. Its single identified parameter quantifies the relative depth or broadness of the cascade trees and indicates that information propagates via a star-like broadcasting or viral-like hop by hop spreading. The RRT model explains the appearance of hubs, thus a possibly smaller average path length as the cascade size increases, as observed in WeChat. We further propose the stochastic Susceptible View Forward Removed (SVFR) model to depict the dynamic user behaviour including creating, viewing, forwarding and ignoring a message on a given social network. Beside the average path length and degree variance of the cascade trees in relation to their sizes, the SVFR model could further explain the power-law cascade size distribution in WeChat and unravel that a user with a large number of friends may actually have a smaller probability to read a message (s)he receives due to limited attention.

Linear and nonlinear susceptibilities from diffusion quantum Monte Carlo: application to periodic hydrogen chains.

Science.gov (United States)

Umari, P; Marzari, Nicola

2009-09-07

We calculate the linear and nonlinear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field--an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hypersusceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry--usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hypersusceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wave function affect the accuracy of the calculated susceptibilities.

Modelling and control of a nonlinear magnetostrictive actuator system

Science.gov (United States)

Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.

2018-04-01

This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

Science.gov (United States)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis

Directory of Open Access Journals (Sweden)

Moussa Leblouba

2016-01-01

Full Text Available Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases.

An Ensemble Nonlinear Model Predictive Control Algorithm in an Artificial Pancreas for People with Type 1 Diabetes

DEFF Research Database (Denmark)

Boiroux, Dimitri; Hagdrup, Morten; Mahmoudi, Zeinab

2016-01-01

patients with different physiological parameters and a time-varying insulin sensitivity using the Medtronic Virtual Patient (MVP) model. We augment the MVP model with stochastic diffusion terms, time-varying insulin sensitivity and noise-corrupted CGM measurements. We consider meal challenges where......This paper presents a novel ensemble nonlinear model predictive control (NMPC) algorithm for glucose regulation in type 1 diabetes. In this approach, we consider a number of scenarios describing different uncertainties, for instance meals or metabolic variations. We simulate a population of 9...... the uncertainty in meal size is ±50%. Numerical results show that the ensemble NMPC reduces the risk of hypoglycemia compared to standard NMPC in the case where the meal size is overestimated or correctly estimated at the expense of a slightly increased number of hyperglycemia. Therefore, ensemble MPC...

Diffuse ions produced by electromagnetic ion beam instabilities

International Nuclear Information System (INIS)

Winske, D.; Leroy, M.M.

1984-01-01

The evolution of the electromagnetic ions beam instability driven by the reflected ion component backstreaming away from the earth's how shock into the foreshock region is studied by means computer simulation. The linear the quasi-linear states of the instability are found to be in good agreement with known results for the resonant model propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude 8Bapprox.B, sinusoidal transverse waves and ''intermediate'' ion distribution, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and ''diffuse'' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks

Nonlinear modeling of a rotational MR damper via an enhanced Bouc–Wen model

International Nuclear Information System (INIS)

Miah, Mohammad S; Chatzi, Eleni N; Dertimanis, Vasilis K; Weber, Felix

2015-01-01

The coupling of magnetorheological (MR) dampers with semi-active control schemes has proven to be an effective and failsafe approach for vibration mitigation of low-damped structures. However, due to the nonlinearities inherently relating to such damping devices, the characterization of the associated nonlinear phenomena is still a challenging task. Herein, an enhanced phenomenological modeling approach is proposed for the description of a rotational-type MR damper, which comprises a modified Bouc–Wen model coupled with an appropriately selected sigmoid function. In a first step, parameter optimization is performed on the basis of individual models in an effort to approximate the experimentally observed response for varying current levels and actuator force characteristics. In a second step, based on the previously identified parameters, a generalized best-fit model is proposed by performing a regression analysis. Finally, model validation is carried out via implementation on different sets of experimental data. The proposed model indeed renders an improved representation of the actually observed nonlinear behavior of the tested rotational MR damper. (paper)

An analog model for quantum lightcone fluctuations in nonlinear optics

International Nuclear Information System (INIS)

Ford, L.H.; De Lorenci, V.A.; Menezes, G.; Svaiter, N.F.

2013-01-01

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable. - Highlights: ► Lightcone fluctuations, quantum fluctuations of the effective speed of light, are a feature of quantum gravity. ► Nonlinear dielectrics have a variable speed of light, analogous to the effects of gravity. ► Fluctuating electric fields create the effect of lightcone fluctuations in a nonlinear material. ► We propose to use squeezed light in a nonlinear material as an analog model of lightcone fluctuations. ► Variation in the speed of propagation of pulses is the observational signature of lightcone fluctuations.

Asymmetric diffusion model for oblique-incidence reflectometry

Institute of Scientific and Technical Information of China (English)

Yaqin Chen; Liji Cao; Liqun Sun

2011-01-01

A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectom-etry. By fitting to this asymmetric diffusion model, the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10% from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp') away from the incident point; particularly, μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10% accuracy. The method is verified by Monte Carlo simulations and experimentally tested on a phantom.%A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectometry.By fitting to this asymmetric diffusion model,the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10％ from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp')away from the incident point;particularly,μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10％ accuracy.The method is verified by Monte Carlo simulations and experimentally tested on a phantom.Knowledge about the optical properties,including the absorption coefficient (μa) and the reduced scattering coefficient (μ's =μs(1-g)),where μs is the scattering coefficient and g is the anisotropy factor of scattering,of biological tissues plays an important role for optical therapeutic and diagnostic techniques in medicine.

Self diffusion in tungsten

International Nuclear Information System (INIS)

Mundy, J.N.; Rothman, S.J.; Lam, N.Q.; Nowicki, L.J.; Hoff, H.A.

1978-01-01

The lack of understanding of self-diffusion in Group VI metals together with the wide scatter in the measured values of tungsten self-diffusion has prompted the present measurements to be made over a wide temperature range (1/2Tsub(m) to Tsub(m)). The diffusion coefficients have been measured in the temperature range 1430-2630 0 C. The present measurements show non-linear Arrhenius behavior but a reliable two-exponential fit of the data should await further measurements. (Auth.)

Modeling 2D and 3D diffusion.

Science.gov (United States)

Saxton, Michael J

2007-01-01

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.

Special class of nonlinear damping models in flexible space structures

Science.gov (United States)

Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

1991-01-01

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Asymptotic solutions of diffusion models for risk reserves

Directory of Open Access Journals (Sweden)

S. Shao

2003-01-01

Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.

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...

Nonlinear modeling and identification of a DC motor for bidirectional operation with real time experiments

International Nuclear Information System (INIS)

Kara, Tolgay; Eker, Ilyas

2004-01-01

Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed

Reflector modelization for neutronic diffusion and parameters identification

International Nuclear Information System (INIS)

Argaud, J.P.

1993-04-01

Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous. (author). 12 refs

On the nonlinear modeling of ring oscillators

KAUST Repository

Elwakil, Ahmed S.

2009-06-01

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.

On the nonlinear modeling of ring oscillators

KAUST Repository

Elwakil, Ahmed S.; Salama, Khaled N.

2009-01-01

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.

Nonlinear signal processing using neural networks: Prediction and system modelling

Energy Technology Data Exchange (ETDEWEB)

Lapedes, A.; Farber, R.

1987-06-01

The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

Wind Power in Europe. A Simultaneous Innovation-Diffusion Model

International Nuclear Information System (INIS)

Soederholm, P.; Klaassen, G.

2007-01-01

The purpose of this paper is to provide a quantitative analysis of innovation and diffusion in the European wind power sector. We derive a simultaneous model of wind power innovation and diffusion, which combines a rational choice model of technological diffusion and a learning curve model of dynamic cost reductions. These models are estimated using pooled annual time series data for four European countries (Denmark, Germany, Spain and the United Kingdom) over the time period 1986-2000. The empirical results indicate that reductions in investment costs have been important determinants of increased diffusion of wind power, and these cost reductions can in turn be explained by learning activities and public R and D support. Feed-in tariffs also play an important role in the innovation and diffusion processes. The higher the feed-in price the higher, ceteris paribus, the rate of diffusion, and we present some preliminary empirical support for the notion that the impact on diffusion of a marginal increase in the feed-in tariff will differ depending on the support system used. High feed-in tariffs, though, also have a negative effect on cost reductions as they induce wind generators to choose high-cost sites and provide fewer incentives for cost cuts. This illustrates the importance of designing an efficient wind energy support system, which not only promotes diffusion but also provides continuous incentives for cost-reducing innovations

Diffusion of hydrous species in model basaltic melt

Science.gov (United States)

Zhang, Li; Guo, Xuan; Wang, Qinxia; Ding, Jiale; Ni, Huaiwei

2017-10-01

Water diffusion in Fe-free model basaltic melt with up to 2 wt% H2O was investigated at 1658-1846 K and 1 GPa in piston-cylinder apparatus using both hydration and diffusion couple techniques. Diffusion profiles measured by FTIR are consistent with a model in which both molecular H2O (H2Om) and hydroxyl (OH) contribute to water diffusion. OH diffusivity is roughly 13% of H2Om diffusivity, showing little dependence on temperature or water concentration. Water diffusion is dominated by the motion of OH until total H2O (H2Ot) concentration reaches 1 wt%. The dependence of apparent H2Ot diffusivity on H2Ot concentration appears to be overestimated by a previous study on MORB melt, but H2Ot diffusivity at 1 wt% H2Ot in basaltic melt is still greater than those in rhyolitic to andesitic melts. The appreciable contribution of OH to water diffusion in basaltic melt can be explained by enhanced mobility of OH, probably associated with the development of free hydroxyl bonded with network-modifying cations, as well as higher OH concentration. Calculation based on the Nernst-Einstein equation demonstrates that OH may serve as an effective charge carrier in hydrous basaltic melt, which could partly account for the previously observed strong influence of water on electrical conductivity of basaltic melt.

Statistical comparison of models for estimating the monthly average daily diffuse radiation at a subtropical African site

Energy Technology Data Exchange (ETDEWEB)

Bashahu, M. [University of Burundi, Bujumbura (Burundi). Institute of Applied Pedagogy, Department of Physics and Technology

2003-07-01

Nine correlations have been developed in this paper to estimate the monthly average diffuse radiation for Dakar, Senegal. A 16-year period data on the global (H) and diffuse (H{sub d}) radiation, together with data on the bright sunshine hours (N), the fraction of the sky's (Ne/8), the water vapour pressure in the air (e) and the ambient temperature (T) have been used for that purpose. A model inter-comparison based on the MBE, RMSE and t statistical tests has shown that estimates in any of the obtained correlations are not significantly different from their measured counterparts, thus all the nine models are recommended for the aforesaid location. Three of them should be particularly selected for their simplicity, universal applicability and high accuracy. Those are simple linear correlations between K{sub d} and N/N{sub d}, Ne/8 or K{sub t}. Even presenting adequate performance, the remaining correlations are either simple but less accurate, or multiple or nonlinear regressions needing one or two input variables. (author)

A model of nonlinear strain and damage accumulation in polymer composites

Directory of Open Access Journals (Sweden)

A. N. Ruslantsev

2014-01-01

Full Text Available This paper presents a model to predict a nonlinear strain of the carbon laminate; the model is based on the relations between the theory of laminated plates and the non-linear approximation of deformation curve of unidirectional layer at the shear in the layer plane. The explicit expressions of stiffness and compliance matrices were obtained via multiplying the matrices that correspond to the elastic characteristics by the matrices, considering the non-linear properties of the laminate. The paper suggests an approximation option for the non-linear properties of the layer at the shear using an exponential function. Some considerations on damage accumulation in carbon laminates were made.

Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI.

Science.gov (United States)

Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong

2016-12-09

Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2  = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

Parametric spatiotemporal oscillation in reaction-diffusion systems.

Science.gov (United States)

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.

Matrix diffusion model. In situ tests using natural analogues

Energy Technology Data Exchange (ETDEWEB)

Rasilainen, K. [VTT Energy, Espoo (Finland)

1997-11-01

Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories. 98 refs. The thesis includes also eight previous publications by author.

Catchment Models and Management Tools for diffuse Contaminants (Sediment, Phosphorus and Pesticides): DIFFUSE Project

Science.gov (United States)

Mockler, Eva; Reaney, Simeon; Mellander, Per-Erik; Wade, Andrew; Collins, Adrian; Arheimer, Berit; Bruen, Michael

2017-04-01

The agricultural sector is the most common suspected source of nutrient pollution in Irish rivers. However, it is also often the most difficult source to characterise due to its predominantly diffuse nature. Particulate phosphorus in surface water and dissolved phosphorus in groundwater are of particular concern in Irish water bodies. Hence the further development of models and indices to assess diffuse sources of contaminants are required for use by the Irish Environmental Protection Agency (EPA) to provide support for river basin planning. Understanding connectivity in the landscape is a vital component of characterising the source-pathway-receptor relationships for water-borne contaminants, and hence is a priority in this research. The DIFFUSE Project will focus on connectivity modelling and incorporation of connectivity into sediment, nutrient and pesticide risk mapping. The Irish approach to understanding and managing natural water bodies has developed substantially in recent years assisted by outputs from multiple research projects, including modelling and analysis tools developed during the Pathways and CatchmentTools projects. These include the Pollution Impact Potential (PIP) maps, which are an example of research output that is used by the EPA to support catchment management. The PIP maps integrate an understanding of the pollution pressures and mobilisation pathways and, using the source-pathways-receptor model, provide a scientific basis for evaluation of mitigation measures. These maps indicate the potential risk posed by nitrate and phosphate from diffuse agricultural sources to surface and groundwater receptors and delineate critical source areas (CSAs) as a means of facilitating the targeting of mitigation measures. Building on this previous research, the DIFFUSE Project will develop revised and new catchment managements tools focused on connectivity, sediment, phosphorus and pesticides. The DIFFUSE project will strive to identify the state

A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

International Nuclear Information System (INIS)

Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

2013-01-01

Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

Periodic and solitary wave solutions of cubic–quintic nonlinear ...

Indian Academy of Sciences (India)

Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

Nonlinear Resonance Islands and Modulational Effects in a Proton Synchrotron

Energy Technology Data Exchange (ETDEWEB)

Satogata, Todd Jeffrey [Northwestern Univ., Evanston, IL (United States)

1993-01-01

We examine both one-dimensional and two-dimensional nonlinear resonance islands created in the transverse phase space of a proton synchrotron by nonlinear magnets. We also examine application of the theoretical framework constructed to the phenomenon of modulational diffusion in a collider model of the Fermilab Tevatron. For the one-dimensional resonance island system, we examine the effects of two types of modulational perturbations on the stability of these resonance islands: tune modulation and beta function modulation. Hamiltonian models are presented which predict stability boundaries that depend on only three paramders: the strength and frequency of the modulation and the frequency of small oscillations inside the resonance island. These. models are compared to particle tracking with excellent agreement. The tune modulation model is also successfully tested in experiment, where frequency domain analysis coupled with tune modulation is demonstrated to be useful in measuring the strength of a nonlinear resonance. Nonlinear resonance islands are also examined in two transverse dimensions in the presence of coupling and linearly independent crossing resonances. We present a first-order Hamiltonian model which predicts fixed point locations, but does not reproduce small oscillation frequencies seen in tracking; therefore in this circumstance such a model is inadequate. Particle tracking is presented which shows evidence of two-dimensional persistent signals, and we make suggestions on methods for observing such signals in future experiment.