Frost heave modelling of buried pipelines using non-linear Fourier finite elements

International Nuclear Information System (INIS)

Wan, R. G.; You, R.

1998-01-01

Numerical analysis of the response of a three-dimensional soil-pipeline system in a freezing environment using non-linear Fourier finite elements was described as an illustration of the effectiveness of this technique in analyzing plasticity problems. Plastic deformations occur when buried pipeline is under the action of non-uniform frost heave. The three-dimensional frost heave which develops over time including elastoplastic deformations of the soil and pipe are computed. The soil heave profile obtained in the numerical analysis was consistent with experimental findings for similar configurations. 8 refs., 8 figs

An efficient formulation for linear and geometric non-linear membrane elements

Directory of Open Access Journals (Sweden)

Mohammad Rezaiee-Pajand

Full Text Available Utilizing the straingradient notation process and the free formulation, an efficient way of constructing membrane elements will be proposed. This strategy can be utilized for linear and geometric non-linear problems. In the suggested formulation, the optimization constraints of insensitivity to distortion, rotational invariance and not having parasitic shear error are employed. In addition, the equilibrium equations will be established based on some constraints among the strain states. The authors' technique can easily separate the rigid body motions, and those belong to deformational motions. In this article, a novel triangular element, named SST10, is formulated. This element will be used in several plane problems having irregular mesh and complicated geometry with linear and geometrically nonlinear behavior. The numerical outcomes clearly demonstrate the efficiency of the new formulation.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

Science.gov (United States)

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

Finite Algorithms for Robust Linear Regression

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun

1990-01-01

The Huber M-estimator for robust linear regression is analyzed. Newton type methods for solution of the problem are defined and analyzed, and finite convergence is proved. Numerical experiments with a large number of test problems demonstrate efficiency and indicate that this kind of approach may...

Non-linear finite element analysis in structural mechanics

CERN Document Server

Rust, Wilhelm

2015-01-01

This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

FEAST: a two-dimensional non-linear finite element code for calculating stresses

International Nuclear Information System (INIS)

Tayal, M.

1986-06-01

The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%

Modeling of non-linear CHP efficiency curves in distributed energy systems

DEFF Research Database (Denmark)

Milan, Christian; Stadler, Michael; Cardoso, Gonçalo

2015-01-01

Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation...... for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation......, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two...

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

International Nuclear Information System (INIS)

Diaz del Coz, J.J.; Nieto, P.J. Garcia; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon

2006-01-01

The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

Energy Technology Data Exchange (ETDEWEB)

Del Coz Diaz, J.J.; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)

2006-06-15

The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown. [Author].

Non-linear thermal analysis of light concrete hollow brick walls by the finite element method and experimental validation

Energy Technology Data Exchange (ETDEWEB)

Diaz del Coz, J.J. [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)]. E-mail: juanjo@constru.uniovi.es; Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Rodriguez, A. Martin [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Martinez-Luengas, A. Lozano [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)

2006-06-15

The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown.

Non-linear effects in vortex viscous flow in superconductors-role of finite heat removal velocity

International Nuclear Information System (INIS)

Bezuglyj, A.I.; Shklovskij, V.A.

1991-01-01

The role of finite heat removal velocity in experiments on non-linear effects in vortex viscous flow in superconducting films near critical temperature was investigated. It was shown that the account of thermal effects permits to explain the experimentally observed dependence of electron energy relaxation time and current break-down in voltage-current characteristic from magnetic field value. 5 refs.; 1 fig. (author)

Non linear permanent magnets modelling with the finite element method

International Nuclear Information System (INIS)

Chavanne, J.; Meunier, G.; Sabonnadiere, J.C.

1989-01-01

In order to perform the calculation of permanent magnets with the finite element method, it is necessary to take into account the anisotropic behaviour of hard magnetic materials (Ferrites, NdFeB, SmCo5). In linear cases, the permeability of permanent magnets is a tensor. This one is fully described with the permeabilities parallel and perpendicular to the easy axis of the magnet. In non linear cases, the model uses a texture function which represents the distribution of the local easy axis of the cristallytes of the magnet. This function allows a good representation of the angular dependance of the coercitive field of the magnet. As a result, it is possible to express the magnetic induction B and the tensor as functions of the field and the texture parameter. This model has been implemented in the software FLUX3D where the tensor is used for the Newton-Raphson procedure. 3D demagnetization of a ferrite magnet by a NdFeB magnet is a suitable representative example. They analyze the results obtained for an ideally oriented ferrite magnet and a real one using a measured texture parameter

A finite element perspective on non-linear FFT-based micromechanical simulations

NARCIS (Netherlands)

Zeman, J.; de Geus, T.W.J.; Vondřejc, J.; Peerlings, R.H.J.; Geers, M.G.D.

2016-01-01

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency

Testing Linear Temporal Logic Formulae on Finite Execution Traces

Science.gov (United States)

Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)

2001-01-01

We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.

Linearized holographic isotropization at finite coupling

Energy Technology Data Exchange (ETDEWEB)

Atashi, Mahdi; Fadafan, Kazem Bitaghsir [Shahrood University of Technology, Physics Department (Iran, Islamic Republic of); Jafari, Ghadir [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of)

2017-06-15

We study holographic isotropization of an anisotropic homogeneous non-Abelian strongly coupled plasma in the presence of Gauss-Bonnet corrections. It was verified before that one can linearize Einstein's equations around the final black hole background and simplify the complicated setup. Using this approach, we study the expectation value of the boundary stress tensor. Although we consider small values of the Gauss-Bonnet coupling constant, it is found that finite coupling leads to significant increasing of the thermalization time. By including higher order corrections in linearization, we extend the results to study the effect of the Gauss-Bonnet coupling on the entropy production on the event horizon. (orig.)

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

Angela Mihai, L.

2013-03-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

Efficient EBE treatment of the dynamic far-field in non-linear FE soil-structure interaction analyses

NARCIS (Netherlands)

Crouch, R.S.; Bennett, T.

2000-01-01

This paper presents results and observations from the use of a rigorous method of treating the dynamic far-field as part of a non-linear FE analysis. The technique de-veloped by Wolf and Song (referred to as the Scaled Boundary Finite-Element Method) is incorporated into a 3-D time-domain analysis

A solution approach for non-linear analysis of concrete members

International Nuclear Information System (INIS)

Hadi, N. M.; Das, S.

1999-01-01

Non-linear solution of reinforced concrete structural members, at and beyond its maximum strength poses complex numerical problems. This is due to the fact that concrete exhibits strain softening behaviour once it reaches its maximum strength. This paper introduces an improved non-linear solution capable to overcome the numerical problems efficiently. The paper also presents a new concept of modeling discrete cracks in concrete members by using gap elements. Gap elements are placed in between two adjacent concrete elements in tensile zone. The magnitude of elongation of gap elements, which represents the width of the crack in concrete, increases edith the increase of tensile stress in those elements. As a result, transfer of local from one concrete element to adjacent elements reduces. Results of non-linear finite element analysis of three concrete beams using this new solution strategy are compared with those obtained by other researchers, and a good agreement is achieved. (authors). 13 refs. 9 figs.,

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.

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.

Quantum osp-invariant non-linear Schroedinger equation

International Nuclear Information System (INIS)

Kulish, P.P.

1985-04-01

The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2007-01-01

In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

Effect of linear and non-linear components in the temperature dependences of thermoelectric properties on the energy conversion efficiency

International Nuclear Information System (INIS)

Yamashita, Osamu

2009-01-01

The new thermal rate equations were built up by taking the linear and non-linear components in the temperature dependences of the Seebeck coefficient α, the electrical resistivity ρ and thermal conductivity κ of a thermoelectric (TE) material into the thermal rate equations on the assumption that their temperature dependences are expressed by a quadratic function of temperature T. The energy conversion efficiency η for a single TE element was formulated using the new thermal rate ones proposed here. By applying it to the high-performance half-Heusler compound, the non-linear component in the temperature dependence of α among those of the TE properties has the greatest effect on η, so that η/η 0 was increased by 11% under the condition of T = 510 K and ΔT = 440 K, where η 0 is a well-known conventional energy conversion efficiency. It was thus found that the temperature dependences of TE properties have a significant influence on η. When one evaluates the accurate achievement rate of η exp obtained experimentally for a TE generator, therefore, η exp should be compared with η the estimated from the theoretical expression proposed here, not with η 0 , particularly when there is a strong non-linearity in the temperature dependence of TE properties.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

Science.gov (United States)

Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen

2017-06-01

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

Angela Mihai, L.; Goriely, Alain

2013-01-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

DEFF Research Database (Denmark)

Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

2004-01-01

of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....

A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis

CERN Multimedia

CERN. Geneva

2000-01-01

A new method for analysing non-linear and non-stationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero crossing and extreme, and also having symmetric envelopes defined by the local maximal and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Classical non-l...

A high-accuracy optical linear algebra processor for finite element applications

Science.gov (United States)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

A New Finite Continuation Algorithm for Linear Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa

1996-01-01

We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an $\\ell_1$ minimization problem augmented with the addition of a linear term. This nondifferentiable problem is approximated...... by a smooth problem. It is shown that the minimizers of the smooth problem define a family of piecewise-linear paths as a function of a smoothing parameter. Based on this property, a finite algorithm that traces these paths to arrive at an optimal solution of the linear program is developed. The smooth...

A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

International Nuclear Information System (INIS)

Ansanay-Alex, G.

2009-01-01

The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

Science.gov (United States)

Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent

2016-04-01

Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

2008-04-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

International Nuclear Information System (INIS)

Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

2008-01-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

A comparison between linear and non-linear analysis of flexible pavements

Energy Technology Data Exchange (ETDEWEB)

Soleymani, H.R.; Berthelot, C.F.; Bergan, A.T. [Saskatchewan Univ., Saskatoon, SK (Canada). Dept. of Mechanical Engineering

1995-12-31

Computer pavement analysis programs, which are based on mathematical simulation models, were compared. The programs included in the study were: ELSYM5, an Elastic Linear (EL) pavement analysis program, MICH-PAVE, a Finite Element Non-Linear (FENL) and Finite Element Linear (FEL) pavement analysis program. To perform the analysis different tire pressures, pavement material properties and asphalt layer thicknesses were selected. Evaluation criteria used in the analysis were tensile strain in bottom of the asphalt layer, vertical compressive strain at the top of the subgrade and surface displacement. Results showed that FENL methods predicted more strain and surface deflection than the FEL and EL analysis methods. Analyzing pavements with FEL does not offer many advantages over the EL method. Differences in predicted strains between the three methods of analysis in some cases was found to be close to 100% It was suggested that these programs require more calibration and validation both theoretically and empirically to accurately correlate with field observations. 19 refs., 4 tabs., 9 figs.

Non-linear Behavior of Curved Sandwich Panels

DEFF Research Database (Denmark)

Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.

2003-01-01

In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure loa...

A multigrid solution method for mixed hybrid finite elements

Energy Technology Data Exchange (ETDEWEB)

Schmid, W. [Universitaet Augsburg (Germany)

1996-12-31

We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.

Non-Linear Dynamics and Fundamental Interactions

CERN Document Server

Khanna, Faqir

2006-01-01

The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.

Finite element modeling of nanotube structures linear and non-linear models

CERN Document Server

Awang, Mokhtar; Muhammad, Ibrahim Dauda

2016-01-01

This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.

Equivalent model construction for a non-linear dynamic system based on an element-wise stiffness evaluation procedure and reduced analysis of the equivalent system

Science.gov (United States)

Kim, Euiyoung; Cho, Maenghyo

2017-11-01

In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.

Adaptive Kronrod-Patterson integration of non-linear finite-element matrices

DEFF Research Database (Denmark)

Janssen, Hans

2010-01-01

inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...

Macroscopic and non-linear quantum games

International Nuclear Information System (INIS)

Aerts, D.; D'Hooghe, A.; Posiewnik, A.; Pykacz, J.

2005-01-01

Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)

Non-linear finite element analysis of reinforced concrete members and punching shear strength of HSC slabs

Directory of Open Access Journals (Sweden)

Nassim Kernou

2018-01-01

Full Text Available A rational three-dimensional nonlinear finite element model (NLFEAS is used for evaluating the behavior of high strength concrete slabs under monotonic transverse load. The non-linear equations of equilibrium have been solved using the incremental-iterative technique based on the modified Newton-Raphson method. The convergence of the solution was controlled by a load convergence criterion. The validity of the theoretical formulations and the program used was verified, through comparison with results obtained using ANSYS program and with available experimental test results. A parametric study was conducted to investigate the effect of different parameters on the behavior of slabs which was evaluated in terms of loaddeflection characteristics, concrete and steel stresses and strains, and failure mechanisms. Also, punching shear resistance of slabs was numerically evaluated and compared with the prediction specified by some design codes.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

Science.gov (United States)

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

PWR in-core nuclear fuel management optimization utilizing nodal (non-linear NEM) generalized perturbation theory

International Nuclear Information System (INIS)

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

1993-01-01

The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Science.gov (United States)

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Verification of Linear (In)Dependence in Finite Precision Arithmetic

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2014-01-01

Roč. 8, č. 3-4 (2014), s. 323-328 ISSN 1661-8289 Institutional support: RVO:67985807 Keywords : linear dependence * linear independence * pseudoinverse matrix * finite precision arithmetic * verification * MATLAB file Subject RIV: BA - General Mathematics

Non-linear effects and thermoelectric efficiency of quantum dot-based single-electron transistors.

Science.gov (United States)

Talbo, Vincent; Saint-Martin, Jérôme; Retailleau, Sylvie; Dollfus, Philippe

2017-11-01

By means of advanced numerical simulation, the thermoelectric properties of a Si-quantum dot-based single-electron transistor operating in sequential tunneling regime are investigated in terms of figure of merit, efficiency and power. By taking into account the phonon-induced collisional broadening of energy levels in the quantum dot, both heat and electrical currents are computed in a voltage range beyond the linear response. Using our homemade code consisting in a 3D Poisson-Schrödinger solver and the resolution of the Master equation, the Seebeck coefficient at low bias voltage appears to be material independent and nearly independent on the level broadening, which makes this device promising for metrology applications as a nanoscale standard of Seebeck coefficient. Besides, at higher voltage bias, the non-linear characteristics of the heat current are shown to be related to the multi-level effects. Finally, when considering only the electronic contribution to the thermal conductance, the single-electron transistor operating in generator regime is shown to exhibit very good efficiency at maximum power.

A parametric FE modeling of brake for non-linear analysis

Energy Technology Data Exchange (ETDEWEB)

Ahmed,Ibrahim; Fatouh, Yasser [Automotive and Tractors Technology Department, Faculty of Industrial Education, Helwan University, Cairo (Egypt); Aly, Wael [Refrigeration and Air-Conditioning Technology Department, Faculty of Industrial Education, Helwan University, Cairo (Egypt)

2013-07-01

A parametric modeling of a drum brake based on 3-D Finite Element Methods (FEM) for non-contact analysis is presented. Many parameters are examined during this study such as the effect of drum-lining interface stiffness, coefficient of friction, and line pressure on the interface contact. Firstly, the modal analysis of the drum brake is also studied to get the natural frequency and instability of the drum to facilitate transforming the modal elements to non-contact elements. It is shown that the Unsymmetric solver of the modal analysis is efficient enough to solve this linear problem after transforming the non-linear behavior of the contact between the drum and the lining to a linear behavior. A SOLID45 which is a linear element is used in the modal analysis and then transferred to non-linear elements which are Targe170 and Conta173 that represent the drum and lining for contact analysis study. The contact analysis problems are highly non-linear and require significant computer resources to solve it, however, the contact problem give two significant difficulties. Firstly, the region of contact is not known based on the boundary conditions such as line pressure, and drum and friction material specs. Secondly, these contact problems need to take the friction into consideration. Finally, it showed a good distribution of the nodal reaction forces on the slotted lining contact surface and existing of the slot in the middle of the lining can help in wear removal due to the friction between the lining and the drum. Accurate contact stiffness can give a good representation for the pressure distribution between the lining and the drum. However, a full contact of the front part of the slotted lining could occur in case of 20, 40, 60 and 80 bar of piston pressure and a partially contact between the drum and lining can occur in the rear part of the slotted lining.

Plastic limit analysis with non linear kinematic strain hardening for metalworking processes applications

International Nuclear Information System (INIS)

Chaaba, Ali; Aboussaleh, Mohamed; Bousshine, Lahbib; Boudaia, El Hassan

2011-01-01

Limit analysis approaches are widely used to deal with metalworking processes analysis; however, they are applied only for perfectly plastic materials and recently for isotropic hardening ones excluding any kind of kinematic hardening. In the present work, using Implicit Standard Materials concept, sequential limit analysis approach and the finite element method, our objective consists in extending the limit analysis application for including linear and non linear kinematic strain hardenings. Because this plastic flow rule is non associative, the Implicit Standard Materials concept is adopted as a framework of non standard plasticity modeling. The sequential limit analysis procedure which considers the plastic behavior with non linear kinematic strain hardening as a succession of perfectly plastic behavior with yielding surfaces updated after each sequence of limit analysis and geometry updating is applied. Standard kinematic finite element method together with a regularization approach is used for performing two large compression cases (cold forging) in plane strain and axisymmetric conditions

Assessment of Structural Behavior of Non-corroded and Corroded RCC Beams Using Finite Element Method

Directory of Open Access Journals (Sweden)

Anand Parande

2008-09-01

Full Text Available A three dimensional finite element model is developed to examine the structural behaviour of corroded reinforced concrete beam and non corroded reinforced concrete beam. Non linear finite element analysis is performed using the ANSYS program. SOLID 65, LINK 8 element represent concrete and discrete reinforcing steel bars, based on each component actual characteristics, non linear material properties are defined for both elements. The effect of corrosion in reinforced concrete is studied by finite element analysis; an approach is developed to model the corrosion product expansion causing concrete cover cracking for this, beam has been modeled using ANSYS and using this data the beam has been casted with M20 concrete after 28 days the beam will be tested for flexural strength. The comparison between ANSYS prediction and field data are made in terms of deflection, stress, strain, bond strength and crack pattern of concrete beam.

Linear finite element method for one-dimensional diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica

2011-07-01

We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)

Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.

Science.gov (United States)

Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko

2010-06-28

We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

Science.gov (United States)

Townsend, Molly T; Sarigul-Klijn, Nesrin

2016-01-01

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

Identification of an Equivalent Linear Model for a Non-Linear Time-Variant RC-Structure

DEFF Research Database (Denmark)

Kirkegaard, Poul Henning; Andersen, P.; Brincker, Rune

are investigated and compared with ARMAX models used on a running window. The techniques are evaluated using simulated data generated by the non-linear finite element program SARCOF modeling a 10-storey 3-bay concrete structure subjected to amplitude modulated Gaussian white noise filtered through a Kanai......This paper considers estimation of the maximum softening for a RC-structure subjected to earthquake excitation. The so-called Maximum Softening damage indicator relates the global damage state of the RC-structure to the relative decrease of the fundamental eigenfrequency in an equivalent linear...

A non-linear, finite element, heat conduction code to calculate temperatures in solids of arbitrary geometry

International Nuclear Information System (INIS)

Tayal, M.

1987-01-01

Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated

Stress Induced in Periodontal Ligament under Orthodontic Loading (Part II): A Comparison of Linear Versus Non-Linear Fem Study.

Science.gov (United States)

Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B

2015-09-01

Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. This shows that the force level required for non-linear analysis is lesser than that of linear analysis.

Optimum Performances for Non-Linear Finite Elements Model of 8/6 Switched Reluctance Motor Based on Intelligent Routing Algorithms

Directory of Open Access Journals (Sweden)

Chouaib Labiod

2017-01-01

Full Text Available This paper presents torque ripple reduction with speed control of 8/6 Switched Reluctance Motor (SRM by the determination of the optimal parameters of the turn on, turn off angles Theta_(on, Theta_(off, and the supply voltage using Particle Swarm Optimization (PSO algorithm and steady state Genetic Algorithm (ssGA. With SRM model, there is difficulty in the control relapsed into highly non-linear static characteristics. For this, the Finite Elements Method (FEM has been used because it is a powerful tool to get a model closer to reality. The mechanism used in this kind of machine control consists of a speed controller in order to determine current reference which must be produced to get the desired speed, hence, hysteresis controller is used to compare current reference with current measured up to achieve switching signals needed in the inverter. Depending on this control, the intelligent routing algorithms get the fitness equation from torque ripple and speed response so as to give the optimal parameters for better results. Obtained results from the proposed strategy based on metaheuristic methods are compared with the basic case without considering the adjustment of specific parameters. Optimized results found clearly confirmed the ability and the efficiency of the proposed strategy based on metaheuristic methods in improving the performances of the SRM control considering different torque loads.

Scattering of massless lumps and non-local charges in the two-dimensional classical non-linear sigma-model

International Nuclear Information System (INIS)

Luescher, M.; Pohlmeyer, K.

1977-09-01

Finite energy solutions of the field equations of the non-linear sigma-model are shown to decay asymptotically into massless lumps. By means of a linear eigenvalue problem connected with the field equations we then find an infinite set of dynamical conserved charges. They, however, do not provide sufficient information to decode the complicated scattering of lumps. (orig.) [de

Slope Safety Calculation With A Non-Linear Mohr Criterion Using Finite Element Method

DEFF Research Database (Denmark)

Clausen, Johan; Damkilde, Lars

2005-01-01

Safety factors for soil slopes are calculated using a non-linear Mohr envelope. The often used linear Mohr-Coulomb envelope tends to overestimate the safety as the material parameters are usually determined at much higher stress levels, than those present at slope failure. Experimental data...

Non-linear elastic thermal stress analysis with phase changes

International Nuclear Information System (INIS)

Amada, S.; Yang, W.H.

1978-01-01

The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)

Linear optical response of finite systems using multishift linear system solvers

Energy Technology Data Exchange (ETDEWEB)

Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)

2014-07-28

We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

A two-dimensional finite element model of front surface current flow in cells under non-uniform, concentrated illumination

Energy Technology Data Exchange (ETDEWEB)

Mellor, A.; Domenech-Garret, J.L.; Chemisana, D.; Rosell, J.I. [Departament de Medi Ambient i C.S., University of Lleida, Av. Alcalde Rovira Roure 191, E25198 (Spain)

2009-09-15

A two-dimensional finite element model of current flow in the front surface of a PV cell is presented. In order to validate this model we perform an experimental test. Later, particular attention is paid to the effects of non-uniform illumination in the finger direction which is typical in a linear concentrator system. Fill factor, open circuit voltage and efficiency are shown to decrease with increasing degree of non-uniform illumination. It is shown that these detrimental effects can be mitigated significantly by reoptimization of the number of front surface metallization fingers to suit the degree of non-uniformity. The behavior of current flow in the front surface of a cell operating at open circuit voltage under non-uniform illumination is discussed in detail. (author)

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

Science.gov (United States)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Linear and Nonlinear Finite Elements.

Science.gov (United States)

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

Directory of Open Access Journals (Sweden)

E. Çelebi

2012-11-01

Full Text Available The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.

Finite element historical deformation analysis in piecewise linear plasticity by mathematical programming

International Nuclear Information System (INIS)

De Donato, O.; Parisi, M.A.

1977-01-01

When loads increase proportionally beyond the elastic limit in the presence of elastic-plastic piecewise-linear constitutive laws, the problem of finding the whole evolution of the plastic strain and displacements of structures was recently shown to be amenable to a parametric linear complementary problem (PLCP) in which the parameter is represented by the load factor, the matrix is symmetric positive definite or at least semi-definite (for perfect plasticity) and the variables with a direct mechanical meaning are the plastic multipliers. With reference to plane trusses and frames with elastic-plastic linear work-hardening material behaviour numerical solutions were also fairly efficiently obtained using a recent mathematical programming algorithm (due to R.W. Cottle) which is able to provide the whole deformation history of the structure and, at the same time to rule out local unloadings along the given proportional loading process by means of 'a priori' checks carried out before each pivotal step of the procedure. Hence it becomes possible to use the holonomic (reversible, path-independent) constitutive laws in finite terms and to benefit by all the relevant numerical and computational advantages despite the non-holonomic nature of plastic behaviour. In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. (Auth.)

A proof of the Woodward-Lawson sampling method for a finite linear array

Science.gov (United States)

Somers, Gary A.

1993-01-01

An extension of the continuous aperture Woodward-Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.

Novel phenomena in one-dimensional non-linear transport in long quantum wires

International Nuclear Information System (INIS)

Morimoto, T; Hemmi, M; Naito, R; Tsubaki, K; Park, J-S; Aoki, N; Bird, J P; Ochiai, Y

2006-01-01

We have investigated the non-linear transport properties of split-gate quantum wires of various channel lengths. In this report, we present results on a resonant enhancement of the non-linear conductance that is observed near pinch-off under a finite source-drain bias voltage. The resonant phenomenon exhibits a strong dependence on temperature and in-plane magnetic field. We discuss the possible relationship of this phenomenon to the spin-polarized manybody state that has recently been suggested to occur in quasi-one dimensional systems

Non-linear electromagnetic interactions in thermal QED

International Nuclear Information System (INIS)

Brandt, F.T.; Frenkel, J.

1994-08-01

The behavior of the non-linear interactions between electromagnetic fields at high temperature is examined. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. It is argued that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T -> ∞. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action. (author). 12 refs, 1 fig

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

Science.gov (United States)

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Non-Linear Multi-Physics Analysis and Multi-Objective Optimization in Electroheating Applications

Czech Academy of Sciences Publication Activity Database

di Barba, P.; Doležel, Ivo; Mognaschi, M. E.; Savini, A.; Karban, P.

2014-01-01

Roč. 50, č. 2 (2014), s. 7016604-7016604 ISSN 0018-9464 Institutional support: RVO:61388998 Keywords : coupled multi-physics problems * finite element method * non-linear equations Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.386, year: 2014

Discretisation of the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements

Directory of Open Access Journals (Sweden)

E. D. Resende

2007-09-01

Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.

A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

Energy Technology Data Exchange (ETDEWEB)

Ansanay-Alex, G.

2009-06-17

The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

Science.gov (United States)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. non-linear model are compared to those

Mappings with closed range and finite dimensional linear spaces

International Nuclear Information System (INIS)

Iyahen, S.O.

1984-09-01

This paper looks at two settings, each of continuous linear mappings of linear topological spaces. In one setting, the domain space is fixed while the range space varies over a class of linear topological spaces. In the second setting, the range space is fixed while the domain space similarly varies. The interest is in when the requirement that the mappings have a closed range implies that the domain or range space is finite dimensional. Positive results are obtained for metrizable spaces. (author)

Three dimensional non-linear cracking analysis of prestressed concrete containment vessel

International Nuclear Information System (INIS)

Al-Obaid, Y.F.

2001-01-01

The paper gives full development of three-dimensional cracking matrices. These matrices are simulated in three-dimensional non-linear finite element analysis adopted for concrete containment vessels. The analysis includes a combination of conventional steel, the steel line r and prestressing tendons and the anisotropic stress-relations for concrete and concrete aggregate interlocking. The analysis is then extended and is linked to cracking analysis within the global finite element program OBAID. The analytical results compare well with those available from a model test. (author)

Implementation of neural network based non-linear predictive

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1998-01-01

The paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems including open loop unstable and non-minimum phase systems, but has also been proposed extended for the control of non......-linear systems. GPC is model-based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis on an efficient Quasi......-Newton optimization algorithm. The performance is demonstrated on a pneumatic servo system....

Optimal non-linear health insurance.

Science.gov (United States)

Blomqvist, A

1997-06-01

Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.

A non-linear optimal Discontinuous Petrov-Galerkin method for stabilising the solution of the transport equation

International Nuclear Information System (INIS)

Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.; Buchan, A. G.; Eaton, M. D.

2009-01-01

This paper describes a new Non-Linear Discontinuous Petrov-Galerkin (NDPG) method and application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The amount of dissipation added acts internal to each element. This is done using a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is designed to be independent of angular expansion framework. This is demonstrated for the both discrete ordinates (S N ) and spherical harmonics (P N ) descriptions of the angular variable. Results show the scheme performs consistently well in demanding time dependent and multi-dimensional radiation transport problems. (authors)

Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite-element model and experimental data.

Science.gov (United States)

Lundström, T; Jonas, T; Volkwein, A

2008-01-01

Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.

Finite rotation shells basic equations and finite elements for Reissner kinematics

CERN Document Server

Wisniewski, K

2010-01-01

This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.

Asymptotic analysis of a stochastic non-linear nuclear reactor model

International Nuclear Information System (INIS)

Rodriguez, M.A.; Sancho, J.M.

1986-01-01

The asymptotic behaviour of a stochastic non-linear nuclear reactor modelled by a master equation is analysed in two different limits: the thermodynamic limit and the zero-neutron-source limit. In the first limit a finite steady neutron density is obtained. The second limit predicts the neutron extinction. The interplay between these two limits is studied for different situations. (author)

Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact

NARCIS (Netherlands)

Brands, D.W.A.; Peters, G.W.M.; Bovendeerd, P.H.M.

2004-01-01

Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. CurrentFE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model

Efficient Estimation of Non-Linear Dynamic Panel Data Models with Application to Smooth Transition Models

DEFF Research Database (Denmark)

Gørgens, Tue; Skeels, Christopher L.; Wurtz, Allan

This paper explores estimation of a class of non-linear dynamic panel data models with additive unobserved individual-specific effects. The models are specified by moment restrictions. The class includes the panel data AR(p) model and panel smooth transition models. We derive an efficient set...... of moment restrictions for estimation and apply the results to estimation of panel smooth transition models with fixed effects, where the transition may be determined endogenously. The performance of the GMM estimator, both in terms of estimation precision and forecasting performance, is examined in a Monte...

An enhanced finite volume method to model 2D linear elastic structures

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2014-04-01

Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...

Optimization of Linear Permanent Magnet (PM Generator with Triangular-Shaped Magnet for Wave Energy Conversion using Finite Element Method

Directory of Open Access Journals (Sweden)

Aamir Hussain

2016-06-01

Full Text Available This paper presents the design optimization of linear permanent magnet (PM generator for wave energy conversion using finite element method (FEM. A linear PM generator with triangular-shaped magnet is proposed, which has higher electromagnetic characteristics, superior performance and low weight as compared to conventional linear PM generator with rectangular shaped magnet. The Individual Parameter (IP optimization technique is employed in order to optimize and achieve optimum performance of linear PM generator. The objective function, optimization variables; magnet angle,M_θ(∆ (θ, the pole-width ratio, P_w ratio(τ_p/τ_mz,, and split ratio between translator and stator, δ_a ratio(R_m/R_e, and constraints are defined. The efficiency and its main parts; copper and iron loss are computed using time-stepping FEM. The optimal values after optimization are presented which yields highest efficiency. Key

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

Science.gov (United States)

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Finite elements for non-linear analysis of pipelines

International Nuclear Information System (INIS)

Benjamim, A.C.; Ebecken, N.F.F.

1982-01-01

The application of a three-dimensional lagrangian formulation for the great dislocations analysis and great rotation of pipelines systems is studied. This formulation is derived from the soil mechanics and take into account the shear stress effects. Two finite element models are implemented. The first, of right axis, uses as interpolation functions the conventional gantry functions, defined in relation to mobile coordinates. The second, of curve axis and variable cross sections, is obtained from the degeneration of the three-dimensional isoparametric element, and uses as interpolation functions third degree polynomials. (E.G.) [pt

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

Science.gov (United States)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Non-linear sigma model on the fuzzy supersphere

International Nuclear Information System (INIS)

Kurkcuoglu, Seckin

2004-01-01

In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S (2,2) . In hep-th/0212133 Bott projectors have been used to obtain the fuzzy C P 1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super)-projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model. (author)

Non linear identification applied to PWR steam generators

International Nuclear Information System (INIS)

Poncet, B.

1982-11-01

For the precise industrial purpose of PWR nuclear power plant steam generator water level control, a natural method is developed where classical techniques seem not to be efficient enough. From this essentially non-linear practical problem, an input-output identification of dynamic systems is proposed. Through Homodynamic Systems, characterized by a regularity property which can be found in most industrial processes with balance set, state form realizations are built, which resolve the exact joining of local dynamic behaviors, in both discrete and continuous time cases, avoiding any load parameter. Specifically non-linear modelling analytical means, which have no influence on local joined behaviors, are also pointed out. Non-linear autoregressive realizations allow us to perform indirect adaptive control under constraint of an admissible given dynamic family [fr

Oracle Inequalities for Convex Loss Functions with Non-Linear Targets

DEFF Research Database (Denmark)

Caner, Mehmet; Kock, Anders Bredahl

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...... of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions...

Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

Science.gov (United States)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.

Implementation of neural network based non-linear predictive control

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1999-01-01

This paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems, including open-loop unstable and non-minimum phase systems, but has also been proposed to be extended for the control...... of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...... on an efficient quasi-Newton algorithm. The performance is demonstrated on a pneumatic servo system....

Domain of composition and finite volume schemes on non-matching grids; Decomposition de domaine et schemas volumes finis sur maillages non-conformes

Energy Technology Data Exchange (ETDEWEB)

Saas, L.

2004-05-01

This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)

Non-linear Capital Taxation Without Commitment

OpenAIRE

Emmanuel Farhi; Christopher Sleet; Iván Werning; Sevin Yeltekin

2012-01-01

We study efficient non-linear taxation of labour and capital in a dynamic Mirrleesian model incorporating political economy constraints. Policies are chosen sequentially over time, without commitment. Our main result is that the marginal tax on capital income is progressive, in the sense that richer agents face higher marginal tax rates. Copyright , Oxford University Press.

Finite-Time H∞ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations

Directory of Open Access Journals (Sweden)

Huihong Zhao

2012-01-01

Full Text Available This paper is concerned with the finite-time H∞ filtering problem for linear continuous time-varying systems with uncertain observations and ℒ2-norm bounded noise. The design of finite-time H∞ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time H∞ filtering problem is solved. A numerical example is given to illustrate the performance of the H∞ filter.

A novel recurrent neural network with finite-time convergence for linear programming.

Science.gov (United States)

Liu, Qingshan; Cao, Jinde; Chen, Guanrong

2010-11-01

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

Non-linear algorithms solved with the help of the GIBIANE macro-language

International Nuclear Information System (INIS)

Ebersolt, L.; Combescure, A.; Millard, A.; Verpeaux, P.

1987-01-01

Non linear finite element problems are often solved with the help of iteratives procedures. In the finite element program CASTEM 2000, the syntax of the dataset permits the user to derive his own algorithm and tune it to his problem. These basic ideas, simple to imagine, needed a proper frame to be materialized in a general purpose finite element program, and three concepts emerged: Operators, the Gibiane macro-language. In the two first paragraphs, we will detail these concepts, in the third paragraph, we will describe the different possibilities of the program, in the fourth paragraph, we will show, by combining operators in a proper order, how to obtain the desired algorithm. (orig./GL)

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

Science.gov (United States)

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Finite field-dependent symmetries in perturbative quantum gravity

International Nuclear Information System (INIS)

Upadhyay, Sudhaker

2014-01-01

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

Science.gov (United States)

Wienkers, A. F.; Ogilvie, G. I.

2018-04-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalises the often-used cartesian shearing box model. The numerical method is an overall second order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localise the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of "bursty" dynamics such as the superhump phenomenon.

An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

KAUST Repository

Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar

2012-01-01

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

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

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

Science.gov (United States)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

International Nuclear Information System (INIS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-01-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix

An Efficient Return Algorithm For Non-Associated Plasticity With Linear Yield Criteria In Principal Stress Space

DEFF Research Database (Denmark)

Clausen, Johan Christian; Damkilde, Lars; Andersen, Lars

2007-01-01

. The stress return and the formation of the constitutive matrix is carried out in principal stress space. Here the manipulations simplify and rely on geometrical arguments. The singularities arising at the intersection of yield planes are dealt with in a straightforward way also based on geometrical......An efficient return algorithm for stress update in numerical plasticity computations is presented. The yield criterion must be linear in principal stress space and can be composed of any number of yield planes. Each of these yield planes may have an associated or non-associated flow rule...

Linear and non-linear optics of condensed matter

International Nuclear Information System (INIS)

McLean, T.P.

1977-01-01

Part I - Linear optics: 1. General introduction. 2. Frequency dependence of epsilon(ω, k vector). 3. Wave-vector dependence of epsilon(ω, k vector). 4. Tensor character of epsilon(ω, k vector). Part II - Non-linear optics: 5. Introduction. 6. A classical theory of non-linear response in one dimension. 7. The generalization to three dimensions. 8. General properties of the polarizability tensors. 9. The phase-matching condition. 10. Propagation in a non-linear dielectric. 11. Second harmonic generation. 12. Coupling of three waves. 13. Materials and their non-linearities. 14. Processes involving energy exchange with the medium. 15. Two-photon absorption. 16. Stimulated Raman effect. 17. Electro-optic effects. 18. Limitations of the approach presented here. (author)

Biderivations of finite dimensional complex simple Lie algebras

OpenAIRE

Tang, Xiaomin

2016-01-01

In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find a class of a non-inner and non-skewsymmetric biderivations. Furthermore, we also get the forms of linear commuting maps on the finite dimensional complex simple Lie algebra or general linear Lie algebra.

Inelastic analysis of finite length and depth cracked tubes

International Nuclear Information System (INIS)

Reich, M.; Gardner, D.; Prachuktam, S.; Chang, T.Y.

1977-01-01

Steam generator tube failure can at times result in reactor safety problems and subsequent premature reactor shutdown. This paper concerns itself with the prediction of the failure pressures for typical PWR steam generator tubes with longitudinal finite length and finite depth cracks. Only local plastic overload failure is considered since the material is non-notch sensitive. Non-linear finite element analyses are carried out to determine the burst pressures of steam generator tubes containing longitudinal cracks located on the outer surface of the tubes. The non-linearities considered herein include elastic-plastic material behaviour and large deformations. A non-proprietary general purpose non-linear finite element program, NFAP was adopted for the analysis. Due to the asymmetric nature of the cracks, two-dimensional as well as three-dimensional finite element analyses, were performed. The analysis clearly shows that for short cracks axial effects play a significant role. For long cracks, they are not important since two-dimensional conditions predominate and failure is governed by circumferential or hoop stress conditions. (Auth.)

Decomposition of Riesz frames and waveletsinto a finite union of linearly independent sets

DEFF Research Database (Denmark)

Christensen, Ole; Lindner, Alexander M

2002-01-01

We characterize Riesz frames and prove that every Riesz frame is the union of a finite number of Riesz sequences. Furthermore, it is shown that for piecewise continuous wavelets with compact support, the associated regular wavelet systems can be decomposed into a finite number of linearly indepen...

From Finite Time to Finite Physical Dimensions Thermodynamics: The Carnot Engine and Onsager's Relations Revisited

Science.gov (United States)

Feidt, Michel; Costea, Monica

2018-04-01

Many works have been devoted to finite time thermodynamics since the Curzon and Ahlborn [1] contribution, which is generally considered as its origin. Nevertheless, previous works in this domain have been revealed [2], [3], and recently, results of the attempt to correlate Finite Time Thermodynamics with Linear Irreversible Thermodynamics according to Onsager's theory were reported [4]. The aim of the present paper is to extend and improve the approach relative to thermodynamic optimization of generic objective functions of a Carnot engine with linear response regime presented in [4]. The case study of the Carnot engine is revisited within the steady state hypothesis, when non-adiabaticity of the system is considered, and heat loss is accounted for by an overall heat leak between the engine heat reservoirs. The optimization is focused on the main objective functions connected to engineering conditions, namely maximum efficiency or power output, except the one relative to entropy that is more fundamental. Results given in reference [4] relative to the maximum power output and minimum entropy production as objective function are reconsidered and clarified, and the change from finite time to finite physical dimension was shown to be done by the heat flow rate at the source. Our modeling has led to new results of the Carnot engine optimization and proved that the primary interest for an engineer is mainly connected to what we called Finite Physical Dimensions Optimal Thermodynamics.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

Trend analysis using non-stationary time series clustering based on the finite element method

OpenAIRE

Gorji Sefidmazgi, M.; Sayemuzzaman, M.; Homaifar, A.; Jha, M. K.; Liess, S.

2014-01-01

In order to analyze low-frequency variability of climate, it is useful to model the climatic time series with multiple linear trends and locate the times of significant changes. In this paper, we have used non-stationary time series clustering to find change points in the trends. Clustering in a multi-dimensional non-stationary time series is challenging, since the problem is mathematically ill-posed. Clustering based on the finite element method (FEM) is one of the methods ...

Non-linear finite element model to assess the effect of tendon forces on the foot-ankle complex.

Science.gov (United States)

Morales-Orcajo, Enrique; Souza, Thales R; Bayod, Javier; Barbosa de Las Casas, Estevam

2017-11-01

A three-dimensional foot finite element model with actual geometry and non-linear behavior of tendons is presented. The model is intended for analysis of the lower limb tendon forces effect in the inner foot structure. The geometry of the model was obtained from computational tomographies and magnetic resonance images. Tendon tissue was characterized with the first order Ogden material model based on experimental data from human foot tendons. Kinetic data was employed to set the load conditions. After model validation, a force sensitivity study of the five major foot extrinsic tendons was conducted to evaluate the function of each tendon. A synergic work of the inversion-eversion tendons was predicted. Pulling from a peroneus or tibialis tendon stressed the antagonist tendons while reducing the stress in the agonist. Similar paired action was predicted for the Achilles tendon with the tibialis anterior. This behavior explains the complex control motion performed by the foot. Furthermore, the stress state at the plantar fascia, the talocrural joint cartilage, the plantar soft tissue and the tendons were estimated in the early and late midstance phase of walking. These estimations will help in the understanding of the functional role of the extrinsic muscle-tendon-units in foot pronation-supination. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

Science.gov (United States)

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

the frame of an ESA TRP study [1]. A bread-board including typical non-linearities has been designed, manufactured and tested through a typical spacecraft dynamic test campaign. The study has demonstrate the capabilities to perform non-linear dynamic test predictions on a flight representative spacecraft, the good correlation of test results with respect to Finite Elements Model (FEM) prediction and the possibility to identify modal behaviour and to characterize non-linearities characteristics from test results. As a synthesis for this study, overall guidelines have been derived on the mechanical verification process to improve level of expertise on tests involving spacecraft including non-linearity.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

Science.gov (United States)

Sasaki, Misao; Wands, David

2010-06-01

In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

A non-linear discrete transform for pattern recognition of discrete chaotic systems

International Nuclear Information System (INIS)

Karanikas, C.; Proios, G.

2003-01-01

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter

A non-linear discrete transform for pattern recognition of discrete chaotic systems

CERN Document Server

Karanikas, C

2003-01-01

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.

Finite Groups with Given Quantitative Non-Nilpotent Subgroups II

DEFF Research Database (Denmark)

Shi, Jiangtao; Zhang, Cui

2014-01-01

As an extension of Shi and Zhang's 2011 article [4], we prove that any finite group having at most 23 non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5), and any finite group having at most three conjugacy classes of non-normal non-nilpotent proper subgroups is s...

Finite-time H∞ control for linear continuous system with norm-bounded disturbance

Science.gov (United States)

Meng, Qingyi; Shen, Yanjun

2009-04-01

In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Quantitative Assessment of Arrhythmia Using Non-linear Approach: A Non-invasive Prognostic Tool

Science.gov (United States)

Chakraborty, Monisha; Ghosh, Dipak

2018-04-01

Accurate prognostic tool to identify severity of Arrhythmia is yet to be investigated, owing to the complexity of the ECG signal. In this paper, we have shown that quantitative assessment of Arrhythmia is possible using non-linear technique based on "Hurst Rescaled Range Analysis". Although the concept of applying "non-linearity" for studying various cardiac dysfunctions is not entirely new, the novel objective of this paper is to identify the severity of the disease, monitoring of different medicine and their dose, and also to assess the efficiency of different medicine. The approach presented in this work is simple which in turn will help doctors in efficient disease management. In this work, Arrhythmia ECG time series are collected from MIT-BIH database. Normal ECG time series are acquired using POLYPARA system. Both time series are analyzed in thelight of non-linear approach following the method "Rescaled Range Analysis". The quantitative parameter, "Fractal Dimension" (D) is obtained from both types of time series. The major finding is that Arrhythmia ECG poses lower values of D as compared to normal. Further, this information can be used to access the severity of Arrhythmia quantitatively, which is a new direction of prognosis as well as adequate software may be developed for the use of medical practice.

Non-linear triangle-based polynomial expansion nodal method for hexagonal core analysis

International Nuclear Information System (INIS)

Cho, Jin Young; Cho, Byung Oh; Joo, Han Gyu; Zee, Sung Qunn; Park, Sang Yong

2000-09-01

This report is for the implementation of triangle-based polynomial expansion nodal (TPEN) method to MASTER code in conjunction with the coarse mesh finite difference(CMFD) framework for hexagonal core design and analysis. The TPEN method is a variation of the higher order polynomial expansion nodal (HOPEN) method that solves the multi-group neutron diffusion equation in the hexagonal-z geometry. In contrast with the HOPEN method, only two-dimensional intranodal expansion is considered in the TPEN method for a triangular domain. The axial dependence of the intranodal flux is incorporated separately here and it is determined by the nodal expansion method (NEM) for a hexagonal node. For the consistency of node geometry of the MASTER code which is based on hexagon, TPEN solver is coded to solve one hexagonal node which is composed of 6 triangular nodes directly with Gauss elimination scheme. To solve the CMFD linear system efficiently, stabilized bi-conjugate gradient(BiCG) algorithm and Wielandt eigenvalue shift method are adopted. And for the construction of the efficient preconditioner of BiCG algorithm, the incomplete LU(ILU) factorization scheme which has been widely used in two-dimensional problems is used. To apply the ILU factorization scheme to three-dimensional problem, a symmetric Gauss-Seidel Factorization scheme is used. In order to examine the accuracy of the TPEN solution, several eigenvalue benchmark problems and two transient problems, i.e., a realistic VVER1000 and VVER440 rod ejection benchmark problems, were solved and compared with respective references. The results of eigenvalue benchmark problems indicate that non-linear TPEN method is very accurate showing less than 15 pcm of eigenvalue errors and 1% of maximum power errors, and fast enough to solve the three-dimensional VVER-440 problem within 5 seconds on 733MHz PENTIUM-III. In the case of the transient problems, the non-linear TPEN method also shows good results within a few minute of

Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

Science.gov (United States)

Hurtado, Daniel E.; Rojas, Guillermo

2018-04-01

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.

Non-linear optical materials

CERN Document Server

Saravanan, R

2018-01-01

Non-linear optical materials have widespread and promising applications, but the efforts to understand the local structure, electron density distribution and bonding is still lacking. The present work explores the structural details, the electron density distribution and the local bond length distribution of some non-linear optical materials. It also gives estimation of the optical band gap, the particle size, crystallite size, and the elemental composition from UV-Visible analysis, SEM, XRD and EDS of some non-linear optical materials respectively.

The Para-Bose oscillator in a finite linear space

International Nuclear Information System (INIS)

Campos, R.G.

1987-01-01

The harmonic oscillator whose canonical variables satisfy the generalized commutation relations proposed by Wigner is studied in a finite linear space of dimension N by elementary methods. The eigenvalue problems of the Hamiltonian and position operators are worked out and it is found that, when N tends to infinity, the H-eigenvectors tend to the two solutions obtained by Ohnuki Kamefuchi evaluated in the X eigenpoints as N is odd or even. Beside this, the P-representative in the finite X-basis resembles the form that it has in the continuous case and the X-eigenvalues satisfy a minimal property. In this context, some properties of the associated Laguerre polynomials and their zeros (some of them already studied) are derived

Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces

International Nuclear Information System (INIS)

Robinson, James C

2009-01-01

This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X − X is finite, d H (X − X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2d B (X). A related argument shows that if the Assouad dimension of X − X is finite and k > d A (X − X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L ∞ (X)

Extension of non-linear beam models with deformable cross sections

Science.gov (United States)

Sokolov, I.; Krylov, S.; Harari, I.

2015-12-01

Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.

Linearity and Non-linearity of Photorefractive effect in Materials ...

African Journals Online (AJOL)

In this paper we have studied the Linearity and Non-linearity of Photorefractive effect in materials using the band transport model. For low light beam intensities the change in the refractive index is proportional to the electric field for linear optics while for non- linear optics the change in refractive index is directly proportional ...

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

Science.gov (United States)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Non-parametric data predistortion for non-linear channels with memory

OpenAIRE

Piazza, Roberto; Shankar, Bhavani; Ottersten, Björn

2013-01-01

With the growing application of high order modulation techniques, the mitigation of the non-linear distortions introduced by the power amplification, has become a major issue in telecommunication. More sophisticated techniques to counteract the strong generated interferences need to be investigated in order to achieve the desired power and spectral efficiency. This work proposes a novel approach for the definition of a transmitter technique (predistortion) that outperforms the standard method...

Useful tools for non-linear systems: Several non-linear integral inequalities

Czech Academy of Sciences Publication Activity Database

Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

2013-01-01

Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

Science.gov (United States)

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

Core seismic behaviour: linear and non-linear models

International Nuclear Information System (INIS)

Bernard, M.; Van Dorsselaere, M.; Gauvain, M.; Jenapierre-Gantenbein, M.

1981-08-01

The usual methodology for the core seismic behaviour analysis leads to a double complementary approach: to define a core model to be included in the reactor-block seismic response analysis, simple enough but representative of basic movements (diagrid or slab), to define a finer core model, with basic data issued from the first model. This paper presents the history of the different models of both kinds. The inert mass model (IMM) yielded a first rough diagrid movement. The direct linear model (DLM), without shocks and with sodium as an added mass, let to two different ones: DLM 1 with independent movements of the fuel and radial blanket subassemblies, and DLM 2 with a core combined movement. The non-linear (NLM) ''CORALIE'' uses the same basic modelization (Finite Element Beams) but accounts for shocks. It studies the response of a diameter on flats and takes into account the fluid coupling and the wrapper tube flexibility at the pad level. Damping consists of one modal part of 2% and one part due to shocks. Finally, ''CORALIE'' yields the time-history of the displacements and efforts on the supports, but damping (probably greater than 2%) and fluid-structures interaction are still to be precised. The validation experiments were performed on a RAPSODIE core mock-up on scale 1, in similitude of 1/3 as to SPX 1. The equivalent linear model (ELM) was developed for the SPX 1 reactor-block response analysis and a specified seismic level (SB or SM). It is composed of several oscillators fixed to the diagrid and yields the same maximum displacements and efforts than the NLM. The SPX 1 core seismic analysis with a diagrid input spectrum which corresponds to a 0,1 g group acceleration, has been carried out with these models: some aspects of these calculations are presented here

Linear and Non-Linear Control Techniques Applied to Actively Lubricated Journal Bearings

DEFF Research Database (Denmark)

Nicoletti, Rodrigo; Santos, Ilmar

2003-01-01

The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can count with the conventional hydrodynamic lubrication. For furt......The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can count with the conventional hydrodynamic lubrication....... For further reduction of shaft vibrations one can count with the active lubrication action, which is based on injecting pressurised oil into the bearing gap through orifices machined in the bearing sliding surface. The design and efficiency of some linear (PD, PI and PID) and non-linear controllers, applied...... vibration reduction of unbalance response of a rigid rotor, where the PD and the non-linear P controllers show better performance for the frequency range of study (0 to 80 Hz). The feasibility of eliminating rotor-bearing instabilities (phenomena of whirl) by using active lubrication is also investigated...

Asymptotic method for non-linear magnetosonic waves in an isothermal plasma with a finite conductivity

Energy Technology Data Exchange (ETDEWEB)

Fusco, D [Messina Univ. (Italy). Instituto de Matematica

1979-01-01

The paper is concerned with a three-dimensional theory of non-linear magnetosonic waves in a turbulent plasma. A perturbation method is used that allows a transport equation, like Burgers equation but with a variable coefficient to be obtained.

Genetic design of interpolated non-linear controllers for linear plants

International Nuclear Information System (INIS)

Ajlouni, N.

2000-01-01

The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)

Designing Non-linear Frequency Modulated Signals For Medical Ultrasound Imaging

DEFF Research Database (Denmark)

Gran, Fredrik; Jensen, Jørgen Arendt

2006-01-01

In this paper a new method for designing non-linear frequency modulated (NLFM) waveforms for ultrasound imaging is proposed. The objective is to control the amplitude spectrum of the designed waveform and still keep a constant transmit amplitude, so that the transmitted energy is maximized....... The signal-to-noise-ratio can in this way be optimized. The waveform design is based on least squares optimization. A desired amplitude spectrum is chosen, hereafter the phase spectrum is chosen, so that the instantaneous frequency takes on the form of a third order polynomial. The finite energy waveform...

Efficient Linear and Non-Linear Finite Element Formulation using a New Local Enhancement of Displacement Fields for Triangular Elements

DEFF Research Database (Denmark)

Damkilde, Lars; Pedersen, Ronnie

2012-01-01

This paper describes a new triangular plane element which can be considered as a linear strain triangular element (LST) extended with incompatible displacement modes. The extended element will have a full cubic interpolation of strains and stresses. The extended LST-element is connected with other...... elements similar to the LST-element i.e. through three corner nodes and three mid-side nodes. The incompatible modes are associated with two displacement gradients at each mid-side node and displacements in the central node. The element passes the patch test and converges to the exact solution. The element...... often show a very slow convergence, and the numerical solutions will in general overestimate the bearing capacity and underestimate the displacements. The examples show that the extended incompatible element behaves much better than the corresponding compatible elements especially for coarse meshes....

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

Science.gov (United States)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

Energy Technology Data Exchange (ETDEWEB)

Melboe, Hallgeir

2001-10-01

This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

Non-linear aeroelastic prediction for aircraft applications

Science.gov (United States)

de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.

2007-05-01

in this domain. This is set within the context of a generic industrial process and the requirements of UK and US aeroelastic qualification. A range of test cases, from simple small DOF cases to full aircraft, have been used to evaluate and validate the non-linear methods developed and to make comparison with the linear methods in everyday use. These have focused mainly on aerodynamic non-linearity, although some results for structural non-linearity are also presented. The challenges associated with time domain (coupled computational fluid dynamics-computational structural model (CFD-CSM)) methods have been addressed through the development of grid movement, fluid-structure coupling, and control surface movement technologies. Conclusions regarding the accuracy and computational cost of these are presented. The computational cost of time-domain methods, despite substantial improvements in efficiency, remains high. However, significant advances have been made in reduced order methods, that allow non-linear behaviour to be modelled, but at a cost comparable with that of the regular linear methods. Of particular note is a method based on Hopf bifurcation that has reached an appropriate maturity for deployment on real aircraft configurations, though only limited results are presented herein. Results are also presented for dynamically linearised CFD approaches that hold out the possibility of non-linear results at a fraction of the cost of time coupled CFD-CSM methods. Local linearisation approaches (higher order harmonic balance and continuation method) are also presented; these have the advantage that no prior assumption of the nature of the aeroelastic instability is required, but currently these methods are limited to low DOF problems and it is thought that these will not reach a level of maturity appropriate to real aircraft problems for some years to come. Nevertheless, guidance on the most likely approaches has been derived and this forms the basis for ongoing

An introduction to the UNCLE finite element scheme

International Nuclear Information System (INIS)

Enderby, J.A.

1983-01-01

UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)

An introduction to the UNCLE finite element scheme

Energy Technology Data Exchange (ETDEWEB)

Enderby, J A [UK Atomic Energy Authority, Northern Division, Risley Nuclear Power Development Establishment, Risley, Warrington (United Kingdom)

1983-05-01

UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)

Finite time thermodynamic analysis and optimization of solar-dish Stirling heat engine with regenerative losses

Directory of Open Access Journals (Sweden)

Sharma Arjun

2011-01-01

Full Text Available The present study investigates the performance of the solar-driven Stirling engine system to maximize the power output and thermal efficiency using the non-linearized heat loss model of the solar dish collector and the irreversible cycle model of the Stirling engine. Finite time thermodynamic analysis has been done for combined system to calculate the finite-rate heat transfer, internal heat losses in the regenerator, conductive thermal bridging losses and finite regeneration process time. The results indicate that exergy efficiency of dish system increases as the effectiveness of regenerator increases but decreases with increase in regenerative time coefficient. It is also found that optimal range of collector temperature and corresponding concentrating ratio are 1000 K~1400 K and 1100~1400, respectively in order to get maximum value of exergy efficiency. It is reported that the exergy efficiency of this dish system can reach the maximum value when operating temperature and concentrating ratio are 1150 K and 1300, respectively.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

Science.gov (United States)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties

Linear and non-linear simulation of joints contact surface using ...

African Journals Online (AJOL)

The joint modelling including non-linear effects needs accurate and precise study of their behaviors. When joints are under the dynamic loading, micro, macro- slip happens in contact surface which is non-linear reason of the joint contact surface. The non-linear effects of joint contact surface on total behavior of structure are ...

Infrared reduction, an efficient method to control the non-linear optical property of graphene oxide in femtosecond regime

Science.gov (United States)

Bhattacharya, S.; Maiti, R.; Saha, S.; Das, A. C.; Mondal, S.; Ray, S. K.; Bhaktha, S. B. N.; Datta, P. K.

2016-04-01

Graphene Oxide (GO) has been prepared by modified Hummers method and it has been reduced using an IR bulb (800-2000 nm). Both as grown GO and reduced graphene oxide (RGO) have been characterized using Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Raman spectra shows well documented Dband and G-band for both the samples while blue shift of G-band confirms chemical functionalization of graphene with different oxygen functional group. The XPS result shows that the as-prepared GO contains 52% of sp2 hybridized carbon due to the C=C bonds and 33% of carbon atoms due to the C-O bonds. As for RGO, increment of the atomic % of the sp2 hybridized carbon atom to 83% and rapid decrease in atomic % of C=O bonds confirm an efficient reduction with infrared radiation. UV-Visible absorption spectrum also confirms increment of conjugation with increased reduction. Non-linear optical properties of both GO and RGO are measured using single beam open aperture Z-Scan technique in femtosecond regime. Intensity dependent nonlinear phenomena are observed. Depending upon the intensity, both saturable absorption and two photon absorption contribute to the non-linearity of both the samples. Saturation dominates at low intensity (~ 127 GW/cm2) while two photon absorption become prominent at higher intensities (from 217 GW/cm2 to 302 GW/cm2). We have calculated the two-photon absorption co-efficient and saturation intensity for both the samples. The value of two photon absorption co-efficient (for GO~ 0.0022-0.0037 cm/GW and for RGO~ 0.0128-0.0143 cm/GW) and the saturation intensity (for GO~57 GW/cm2 and for RGO~ 194GW/cm2) is increased with reduction. Increase in two photon absorption coefficient with increasing intensity can also suggest that there may be multi-photon absorption is taking place.

Finite element analyses of a linear-accelerator electron gun

Science.gov (United States)

Iqbal, M.; Wasy, A.; Islam, G. U.; Zhou, Z.

2014-02-01

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.

Finite element analyses of a linear-accelerator electron gun

Energy Technology Data Exchange (ETDEWEB)

Iqbal, M., E-mail: muniqbal.chep@pu.edu.pk, E-mail: muniqbal@ihep.ac.cn [Centre for High Energy Physics, University of the Punjab, Lahore 45590 (Pakistan); Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Wasy, A. [Department of Mechanical Engineering, Changwon National University, Changwon 641773 (Korea, Republic of); Islam, G. U. [Centre for High Energy Physics, University of the Punjab, Lahore 45590 (Pakistan); Zhou, Z. [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China)

2014-02-15

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.

Finite element analyses of a linear-accelerator electron gun

International Nuclear Information System (INIS)

Iqbal, M.; Wasy, A.; Islam, G. U.; Zhou, Z.

2014-01-01

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator

Development of non-linear TWB parts

Energy Technology Data Exchange (ETDEWEB)

Lee, J.; Yoon, C.S.; Lim, J.D. [Hyundai Motor Company and Kia Motors Corp. (Korea). Advanced Technology Center; Park, H.C. [Hyundai Hysco (Korea). Technical Research Lab.

2005-07-01

New manufacturing methods have applied for automotive parts to reduce total weight of car, resulting in improvement of fuel efficiency. TWB technique is applied to auto body parts, especially door inner, side inner and outer panel, and center floor panel to accomplish this goal. We applied non-linear (circular welded) TWB to shock absorber housing (to reduce total weight of shock absorber housing assembly). Welding line and shape of blank were determined by FEM analysis. High formability steel sheet and 440MPa grade high strength steel sheet were laser welded and press formed to final shock absorber housing (S/ABS HSG) panel and assembled with other sub parts. As a result, more than 10% of total weight of shock absorber housing assembly could be reduced compared with the mass of same part manufactured by conventional method. Also circular welding technique made it possible to design optimum welding line of TWB part. This paper is about result of FEM analysis and development procedure of non-linear TWB part (shock absorber housing assembly). (orig.)

Analysis of noncoplanar pressurized laminations in X2 steel pipes by non-linear finite element

Energy Technology Data Exchange (ETDEWEB)

Morales, Alfredo [Instituto Tecnologico de Puebla (Mexico). Dept. de Posgrado; Gonzalez, Jorge L.; Hallen, Jose M. [Instituto Politecnico Nacional (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE). Dept. de Ingenieria Metalurgica

2005-07-01

Hydrogen induced cracking is of great interest in the mechanical integrity assessment of sour gas pipelines. Multiple stepwise cracks with internal pressure called laminations are often observed in pipelines and their interaction and coalescence may significantly affect the residual strength of the pipes. In this work, the interacting fields of non coplanar pressurized laminations in the wall of a pipe under pressure are analyzed by non-lineal finite element, considering an isotropic hardening law and the real tensile properties of the X52 steel. The results are presented as the evolution of the stress fields in the interlaminar region as a function of the pressure inside the laminations. It is found that for two approaching stepwise laminations the critical pressure follows a hyperbolic type law, thus the effect of the lamination length is principal for greater lengths and for shorter lengths the effect is minimum. The critical pressure is defined as pressure inside the lamination that causes plastification of the interlaminar region. (author)

Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics

International Nuclear Information System (INIS)

Nazem, M; Carter, J P; Airey, D W

2010-01-01

In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.

Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

Directory of Open Access Journals (Sweden)

Songlin Wo

2014-01-01

Full Text Available The finite-time stability (FTS problem of discrete-time linear singular systems (DTLSS is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

Finite-element semi-discretization of linearized compressible and resistive MHD

International Nuclear Information System (INIS)

Kerner, W.; Jakoby, A.; Lerbinger, K.

1985-08-01

The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)

Perfect commuting-operator strategies for linear system games

Science.gov (United States)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels

Science.gov (United States)

Colera, Manuel; Pérez-Saborid, Miguel

2017-09-01

A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

Computer codes for three dimensional mass transport with non-linear sorption

International Nuclear Information System (INIS)

Noy, D.J.

1985-03-01

The report describes the mathematical background and data input to finite element programs for three dimensional mass transport in a porous medium. The transport equations are developed and sorption processes are included in a general way so that non-linear equilibrium relations can be introduced. The programs are described and a guide given to the construction of the required input data sets. Concluding remarks indicate that the calculations require substantial computer resources and suggest that comprehensive preliminary analysis with lower dimensional codes would be important in the assessment of field data. (author)

Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction

International Nuclear Information System (INIS)

Dubois-Boudesocque, Carine

2000-01-01

The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

Science.gov (United States)

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

International Nuclear Information System (INIS)

Liolios, A.A.; Boglou, A.K.

2003-01-01

The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-θ method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-convex linear complementarity problem is solved with a reduced number of unknowns

Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model

Directory of Open Access Journals (Sweden)

Oluwaseun Egbelowo

2017-05-01

Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.

Linear versus non-linear supersymmetry, in general

Energy Technology Data Exchange (ETDEWEB)

Ferrara, Sergio [Theoretical Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati,Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics and Astronomy, UniversityC.L.A.,Los Angeles, CA 90095-1547 (United States); Kallosh, Renata [SITP and Department of Physics, Stanford University,Stanford, California 94305 (United States); Proeyen, Antoine Van [Institute for Theoretical Physics, Katholieke Universiteit Leuven,Celestijnenlaan 200D, B-3001 Leuven (Belgium); Wrase, Timm [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria)

2016-04-12

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM’s: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.

Linear versus non-linear supersymmetry, in general

International Nuclear Information System (INIS)

Ferrara, Sergio; Kallosh, Renata; Proeyen, Antoine Van; Wrase, Timm

2016-01-01

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM’s: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

Science.gov (United States)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Inelastic analysis of finite length and depth cracked tubes

International Nuclear Information System (INIS)

Reich, M.; Gardner, D.; Prachuktam, S.; Chang, T.Y.

1977-01-01

Steam generator tube failure can at times result in reactor safety problems and subsequent premature reactor shutdowns. This paper concerns itself with the prediction of the failure pressures for typical PWR steam generator tubes with longitudinal finite length and finite depth cracks. Only local plastic overload failure is considered since the material is non-notch sensitive. Non-linear finite element analyses are carried out to determine the burst pressures of steam generator tubes containing longitudinal cracks located on the outer surface of the tubes. The non-linearities considered herein include elastic-plastic material behavior and large deformations. A non-proprietary general purpose non-linear finite element program, NFAP was adopted for the analysis. Due to the asymmetric nature of the cracks, two-dimensional, as well as three-dimensional finite element analyses, were performed. The two-dimensional element and its formulations are similar to those of NONSAP. The three-dimensional isoparametric element with elastic-plastic material characteristics together with the large deformation formulations used in NFAP are described in the Report BNL-20684. The numerical accuracy of the program was investigated and checked with known solutions of benchmark problems. In addition to the three-dimensional element which was specifically inserted into NFAP for this problem, other features such as direct pressure inputs for isoparametric elements, automatic load increment adjustments for convergent non-linear solutions, and automatic bandwidth reduction schemes are incorporated into the program thus allowing for a more economical evaluation of three-dimensional inelastic analysis. In summary the analysis clearly shows that for short cracks axial effects play a significant role. For long cracks, they are not important since two-dimensional conditions predominate and failure is governed by circumferential or hoop stress conditions

Efficient Searching with Linear Constraints

DEFF Research Database (Denmark)

Agarwal, Pankaj K.; Arge, Lars Allan; Erickson, Jeff

2000-01-01

We show how to preprocess a set S of points in d into an external memory data structure that efficiently supports linear-constraint queries. Each query is in the form of a linear constraint xd a0+∑d−1i=1 aixi; the data structure must report all the points of S that satisfy the constraint. This pr...

Gyrokinetic simulation of finite-β plasmas on parallel architectures

International Nuclear Information System (INIS)

Reynders, J.V.W.

1993-01-01

Much research exists on the linear and non-linear properties of plasma microinstabilities induced by density and temperature gradients. There has been an interest in the electromagnetic or finite-β effects on these microinstabilities. This thesis focuses on the finite-β modification of an ion temperature gradient (ITG) driven microinstability in a two-dimensional shearless and sheared-slab geometries. A gyrokinetic model is employed in the numerical and analytic studies of this instability. Chapter 1 introduces the electromagnetic gyrokinetic model employed in the numerical and analytic studies of the ITG instability. Some discussion of the Klimontovich particle representation of the gyrokinetic Vlasov equation and a multiple scale model of the background plasma gradient is presented. Chapter 2 details the computational issues facing an electromagnetic gyrokinetic particle simulation of the ITG mode. An electromagnetic extension of the partially linearized algorithm is presented with a comparison of quiet particle initialization routines. Chapter 3 presents and compares algorithms for the gyrokinetic particle simulation technique on SIMD and MIMD computing platforms. Chapter 4 discusses electromagnetic gyrokinetic fluctuation theory and provides a comparison of analytic and numerical results. Chapter 5 contains a linear and a non-linear three-wave coupling analysis of the finite-β modified ITG mode in a shearless slab geometry. Comparisons are made with linear and partially linearized gyrokinetic simulation results. Chapter 6 presents results from a finite-β modified ITG mode in a sheared slab geometry. The linear dispersion relation is derived and results from an integral eigenvalue code are presented. Comparisons are made with the gyrokinetic particle code in a variety of limits with both adiabatic and non-adiabatic electrons. Evidence of ITG driven microtearing is presented

Non-linear numerical studies of the tearing mode

International Nuclear Information System (INIS)

Schnack, D.D. Jr.

1978-01-01

A non-linear, time dependent, hydromagnetic model is developed and applied to the tearing mode, one of a class of instabilities which can occur in a magnetically confined plasma when the constraint of infinite conductivity is relaxed. The model is based on the eight partial differential equations of resistive magnetohydrodynamics (MHD). The equations are expressed as a set of conservation laws which conserves magnetic flux, momentum, mass, and total energy. These equations are then written in general, orthogonal, curvilinear coordinates in two space dimensions, so that the model can readily be applied to a variety of geometries. No assumption about the ordering of terms is made. The resulting equations are then solved by the method of finite differences on an Eulerian mesh. The model is applied to several geometries

Coupled Analytical-Finite Element Methods for Linear Electromagnetic Actuator Analysis

Directory of Open Access Journals (Sweden)

K. Srairi

2005-09-01

Full Text Available In this paper, a linear electromagnetic actuator with moving parts is analyzed. The movement is considered through the modification of boundary conditions only using coupled analytical and finite element analysis. In order to evaluate the dynamic performance of the device, the coupling between electric, magnetic and mechanical phenomena is established. The displacement of the moving parts and the inductor current are determined when the device is supplied by capacitor discharge voltage.

Few-photon Non-linearities in Nanophotonic Devices for Quantum Information Technology

DEFF Research Database (Denmark)

Nysteen, Anders

In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices...... the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic...... by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between...

Non-linear osmosis

Science.gov (United States)

Diamond, Jared M.

1966-01-01

1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254

Revisiting linear plasma waves for finite value of the plasma parameter

Science.gov (United States)

Grismayer, Thomas; Fahlen, Jay; Decyk, Viktor; Mori, Warren

2010-11-01

We investigate through theory and PIC simulations the Landau-damping of plasma waves with finite plasma parameter. We concentrate on the linear regime, γφB, where the waves are typically small and below the thermal noise. We simulate these condition using 1,2,3D electrostatic PIC codes (BEPS), noting that modern computers now allow us to simulate cases where (nλD^3 = [1e2;1e6]). We study these waves by using a subtraction technique in which two simulations are carried out. In the first, a small wave is initialized or driven, in the second no wave is excited. The results are subtracted to provide a clean signal that can be studied. As nλD^3 is decreased, the number of resonant electrons can be small for linear waves. We show how the damping changes as a result of having few resonant particles. We also find that for small nλD^3 fluctuations can cause the electrons to undergo collisions that eventually destroy the initial wave. A quantity of interest is the the life time of a particular mode which depends on the plasma parameter and the wave number. The life time is estimated and then compared with the numerical results. A surprising result is that even for large values of nλD^3 some non-Vlasov discreteness effects appear to be important.

A penalized framework for distributed lag non-linear models.

Science.gov (United States)

Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G

2017-09-01

Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Quantum associative memory with linear and non-linear algorithms for the diagnosis of some tropical diseases.

Science.gov (United States)

Tchapet Njafa, J-P; Nana Engo, S G

2018-01-01

This paper presents the QAMDiagnos, a model of Quantum Associative Memory (QAM) that can be a helpful tool for medical staff without experience or laboratory facilities, for the diagnosis of four tropical diseases (malaria, typhoid fever, yellow fever and dengue) which have several similar signs and symptoms. The memory can distinguish a single infection from a polyinfection. Our model is a combination of the improved versions of the original linear quantum retrieving algorithm proposed by Ventura and the non-linear quantum search algorithm of Abrams and Lloyd. From the given simulation results, it appears that the efficiency of recognition is good when particular signs and symptoms of a disease are inserted given that the linear algorithm is the main algorithm. The non-linear algorithm helps confirm or correct the diagnosis or give some advice to the medical staff for the treatment. So, our QAMDiagnos that has a friendly graphical user interface for desktop and smart-phone is a sensitive and a low-cost diagnostic tool that enables rapid and accurate diagnosis of four tropical diseases. Copyright © 2017 Elsevier Ltd. All rights reserved.

Solving non-linear Horn clauses using a linear Horn clause solver

DEFF Research Database (Denmark)

Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre

2016-01-01

In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....

Effects of vortex-like and non-thermal ion distributions on non-linear dust-acoustic waves

International Nuclear Information System (INIS)

Mamun, A.A.; Cairns, R.A.; Shukla, P.K.

1996-01-01

The effects of vortex-like and non-thermal ion distributions are incorporated in the study of nonlinear dust-acoustic waves in an unmagnetized dusty plasma. It is found that owing to the departure from the Boltzmann ion distribution to a vortex-like phase space distribution, the dynamics of small but finite amplitude dust-acoustic waves is governed by a modified Kortweg endash de Vries equation. The latter admits a stationary dust-acoustic solitary wave solution, which has larger amplitude, smaller width, and higher propagation velocity than that involving adiabatic ions. On the other hand, consideration of a non-thermal ion distribution provides the possibility of coexistence of large amplitude rarefactive as well as compressive dust-acoustic solitary waves, whereas these structures appear independently when the wave amplitudes become infinitely small. The present investigation should help us to understand the salient features of the non-linear dust-acoustic waves that have been observed in a recent numerical simulation study. copyright 1996 American Institute of Physics

Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

International Nuclear Information System (INIS)

Gelebart, Lionel; Mondon-Cancel, Romain

2013-01-01

FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted to periodic boundary conditions, which is of a great interest in the context of numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously to use Conjugate Gradient based solvers in order to improve the convergence properties (when compared to the basic scheme, proposed initially in 1994). The purpose of the paper is to extend this idea to the case of non-linear behaviors. The proposed method is based on a Newton-Raphson algorithm and can be applied to various kinds of behaviors (time dependant or independent, with or without internal variables) through a conventional integration procedure as used in finite element codes. It must be pointed out that this approach is fundamentally different from the traditional FFT-based approaches which rely on a fixed-point algorithm (e.g. basic scheme, Eyre and Milton accelerated scheme, Augmented Lagrangian scheme, etc.). The method is compared to the basic scheme on the basis of a simple application (a linear elastic spherical inclusion within a non-linear elastic matrix): a low sensitivity to the reference material and an improved efficiency, for a soft or a stiff inclusion, are observed. At first proposed for a prescribed macroscopic strain, the method is then extended to mixed loadings. (authors)

Distributed Leader-Following Finite-Time Consensus Control for Linear Multiagent Systems under Switching Topology

Science.gov (United States)

Xu, Xiaole; Chen, Shengyong

2014-01-01

This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach. PMID:24883367

Linear Algebraic Method for Non-Linear Map Analysis

International Nuclear Information System (INIS)

Yu, L.; Nash, B.

2009-01-01

We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH

Directory of Open Access Journals (Sweden)

Q. A. HASAN

2017-11-01

Full Text Available The paper presents Finite Element Analysis to determine the ultimate shear capacity of tapered composite plate girder. The effect of degree of taper on the ultimate shear capacity of tapered steel-concrete composite plate girder with a nonlinear varying web depth, effect of slenderness ratio on the ultimate shear capacity, and effect of flange stiffness on the ductility were considered as the parametric studies. Effect of concrete slab on the ultimate shear capacity of tapered plate girders was also considered and it was found to be so effective on the ultimate shear capacity of the tapered plate girder compared with the steel one. The accuracy of the finite element method is established by comparing the finite element with the results existing in the literature. The study was conducted using nonlinear finite element modelling with computer software LUSAS 14.7.

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin

2010-10-28

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel

2010-01-01

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

Linear theory of a cold relativistic beam in a strongly magnetized finite-geometry plasma

International Nuclear Information System (INIS)

Gagne, R.R.J.; Shoucri, M.M.

1976-01-01

The linear theory of a finite-geometry cold relativistic beam propagating in a cold homogeneous finite-geometry plasma, is investigated in the case of a strongly magnetized plasma. The beam is assumed to propagate parallel to the external magnetic field. It is shown that the instability which takes place at the Cherenkov resonance ωapprox. =k/subz/v/subb/ is of the convective type. The effect of the finite geometry on the instability growth rate is studied and is shown to decrease the growth rate, with respect to the infinite geometry, by a factor depending on the ratio of the beam-to-plasma radius

Finite-dimensional linear algebra

CERN Document Server

Gockenbach, Mark S

2010-01-01

Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq

Non-linear finite element analyses of wide plate fracture mechanics experiments

International Nuclear Information System (INIS)

Harrop, L.P.; Gibson, S.

1988-06-01

A series of centre-cracked, wide plate fracture mechanics tests is being conducted with plates made from 0.36% carbon steel. This report gives an account of post-test finite element analyses performed to compare with the results of one of these tests (designated CSTP4) and a pre-test analysis of the next test which has a slightly different geometry (CSTP5). The plates are relatively thick (75mm) and have a width of 1.62m. The finite element analyses use a two-dimensional plane stress mesh. The work shows good agreement between the post-test analysis results and the overall experimental results for CSTP4. It is not expected that the analysis results will be accurate within the dimensions of the process zone ahead of the crack tip; the mesh is not sufficient for this. A vital ingredient in attaining the good overall agreement is the representation of the actual stress-strain curve of the material. The predicted response of test CSTP5 is markedly different from that of CSTP4 even though the only change is the increase in the height of the plate. In particular the shape and size of the plastic zone ahead of the crack tip is quite different in the two tests at the same nominal remote applied load. (author)

Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

Energy Technology Data Exchange (ETDEWEB)

Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

1996-12-31

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

Non-linear dielectric monitoring of biological suspensions

International Nuclear Information System (INIS)

Treo, E F; Felice, C J

2007-01-01

Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response

A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

International Nuclear Information System (INIS)

Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

2011-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

International Nuclear Information System (INIS)

Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

2010-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

2010-12-22

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

Locally supersymmetric D=3 non-linear sigma models

International Nuclear Information System (INIS)

Wit, B. de; Tollsten, A.K.; Nicolai, H.

1993-01-01

We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is riemannian or Kaehler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it generally decomposes, into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N=5, 6, 8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N=9, 10, 12 and 16, associated with coset spaces with the exceptional isometry groups F 4(-20) , E 6(-14) , E 7(-5) and E 8(+8) , respectively. For N=3 and N ≥ 5 the D=2 theories obtained by dimensional reduction are two-loop finite. (orig.)

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.

2017-01-01

. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

Non-linear models for the detection of impaired cerebral blood flow autoregulation.

Science.gov (United States)

Chacón, Max; Jara, José Luis; Miranda, Rodrigo; Katsogridakis, Emmanuel; Panerai, Ronney B

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

Directory of Open Access Journals (Sweden)

Songlin Wo

2018-01-01

Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Linear and non-linear energy barriers in systems of interacting single-domain ferromagnetic particles

International Nuclear Information System (INIS)

Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru

2011-01-01

A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.

Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

CERN Document Server

Liolios, A

2003-01-01

The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-theta method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-c...

Non linear system become linear system

Directory of Open Access Journals (Sweden)

Petre Bucur

2007-01-01

Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.

Application of Linear Viscoelastic Properties in Semianalytical Finite Element Method with Recursive Time Integration to Analyze Asphalt Pavement Structure

Directory of Open Access Journals (Sweden)

Pengfei Liu

2018-01-01

Full Text Available Traditionally, asphalt pavements are considered as linear elastic materials in finite element (FE method to save computational time for engineering design. However, asphalt mixture exhibits linear viscoelasticity at small strain and low temperature. Therefore, the results derived from the elastic analysis will inevitably lead to discrepancies from reality. Currently, several FE programs have already adopted viscoelasticity, but the high hardware demands and long execution times render them suitable primarily for research purposes. Semianalytical finite element method (SAFEM was proposed to solve the abovementioned problem. The SAFEM is a three-dimensional FE algorithm that only requires a two-dimensional mesh by incorporating the Fourier series in the third dimension, which can significantly reduce the computational time. This paper describes the development of SAFEM to capture the viscoelastic property of asphalt pavements by using a recursive formulation. The formulation is verified by comparison with the commercial FE software ABAQUS. An application example is presented for simulations of creep deformation of the asphalt pavement. The investigation shows that the SAFEM is an efficient tool for pavement engineers to fast and reliably predict asphalt pavement responses; furthermore, the SAFEM provides a flexible, robust platform for the future development in the numerical simulation of asphalt pavements.

Linearity and Non-linearity of Photorefractive effect in Materials ...

African Journals Online (AJOL)

Linearity and Non-linearity of Photorefractive effect in Materials using the Band transport ... For low light beam intensities the change in the refractive index is ... field is spatially phase shifted by /2 relative to the interference fringe pattern, which ...

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang

2010-01-01

Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo

2010-01-01

Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

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....

Subroutine MLTGRD: a multigrid algorithm based on multiplicative correction and implicit non-stationary iteration

International Nuclear Information System (INIS)

Barry, J.M.; Pollard, J.P.

1986-11-01

A FORTRAN subroutine MLTGRD is provided to solve efficiently the large systems of linear equations arising from a five-point finite difference discretisation of some elliptic partial differential equations. MLTGRD is a multigrid algorithm which provides multiplicative correction to iterative solution estimates from successively reduced systems of linear equations. It uses the method of implicit non-stationary iteration for all grid levels

CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

International Nuclear Information System (INIS)

Benzley, S.E.; Beisinger, Z.E.

1981-01-01

1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

A Non-Linear Finite Element Model for the LHC Main Dipole Coil Cross-Section

CERN Document Server

Pojer, M; Scandale, Walter

2006-01-01

The production of the dipole magnets for the Large Hadron Collider is at its final stage. Nevertheless, some mechanical instabilities are still observed for which no clear explanation has been found yet. A FE modelization of the dipole cold mass cross-section had already been developed at CERN, mainly for magnetic analysis, taking into account conductor blocks and a frictionless behavior. This paper describes a new ANSYS® model of the dipole coil cross-section, featuring individual turns inside conductor blocks, and implementing friction and the mechanical non-linear behavior of insulated cables. Preliminary results, comparison with measurements performed in industry and ongoing developments are discussed.

An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element

Directory of Open Access Journals (Sweden)

Litesh N. Sulbhewar

Full Text Available The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section.

Solving wave propagation within finite-sized composite media with linear embedding via Green's operators

NARCIS (Netherlands)

Lancellotti, V.; Tijhuis, A.G.

2012-01-01

The calculation of electromagnetic (EM) fields and waves inside finite-sized structures comprised of different media can benefit from a diakoptics method such as linear embedding via Green's operators (LEGO). Unlike scattering problems, the excitation of EM waves within the bulk dielectric requires

Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

KAUST Repository

Dujardin, G. M.

2009-08-12

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.

Fourier imaging of non-linear structure formation

Energy Technology Data Exchange (ETDEWEB)

Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)

2017-04-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Fourier imaging of non-linear structure formation

International Nuclear Information System (INIS)

Brandbyge, Jacob; Hannestad, Steen

2017-01-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Algorithms for non-linear M-estimation

DEFF Research Database (Denmark)

Madsen, Kaj; Edlund, O; Ekblom, H

1997-01-01

In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

Non-linear realization of α0 -extended supersymmetry

International Nuclear Information System (INIS)

Nishino, Hitoshi

2000-01-01

As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the global non-linear supersymmetry. As an interesting consequence, we find a non-linear supersymmetric Born-Infeld action for a non-Abelian gauge group for arbitrary D and N , which coincides with the linearly supersymmetric Born-Infeld action in D=10 at the lowest order. For the gauge group U(N) for M(atrix)-theory, this model has N 2 -extended non-linear supersymmetries, so that its large N limit corresponds to the infinitely many (α 0 ) supersymmetries. We also perform a duality transformation from F μν into its Hodge dual N μ 1 ctdot μD-2 . We next point out that any Chern-Simons action for any (super)groups has the non-linear supersymmetry as a hidden symmetry. Subsequently, we present a superspace formulation for the component results. We further find that as long as superspace supergravity is consistent, this generalized Volkov-Akulov action can further accommodate such curved superspace backgrounds with local supersymmetry, as a super p -brane action with fermionic kappa-symmetry. We further elaborate these results to what we call 'simplified' (Supersymmetry) 2 -models, with both linear and non-linear representations of supersymmetries in superspace at the same time. Our result gives a proof that there is no restriction on D or N for global non-linear supersymmetry. We also see that the non-linear realization of supersymmetry in 'curved' space-time can be interpreted as 'non-perturbative' effect starting with the 'flat' space-time

The Transfer efficiency analysis and modeling technology of new non - contact power transmission equipment

Directory of Open Access Journals (Sweden)

Cao Shi

2017-01-01

Full Text Available Due to the shortcomings of current power transmission which is used in ultrasound - assisted machining and the different transfer efficiency caused by the related parameters of the electromagnetic converter, this paper proposes an analysis model of the new non-contact power transmission device with more stable output and higher transmission efficiency. Then By utilizing Maxwell finite element analysis software, this paper studies the law of the transfer efficiency of the new non-contact transformer and compares new type with traditional type with the method of setting the boundary conditions of non-contact power supply device. At last, combining with the practical application, the relevant requirements which have a certain reference value in the application are put forward in the actual processing.

Neural Networks for Non-linear Control

DEFF Research Database (Denmark)

Sørensen, O.

1994-01-01

This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....

Non-Linear Approximation of Bayesian Update

KAUST Repository

Litvinenko, Alexander

2016-01-01

We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

Non-Linear Approximation of Bayesian Update

KAUST Repository

Litvinenko, Alexander

2016-06-23

We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

Optimising Reactive Control in non-ideal Efficiency Wave Energy Converters

DEFF Research Database (Denmark)

Strager, Thomas; Lopez, Pablo Fernandez; Giorgio, Giuseppe

2014-01-01

When analytically optimising the control strategy in wave energy converters which use a point absorber, the efficiency aspect is generally neglected. The results presented in this paper provide an analytical expression for the mean harvested electrical power in non-ideal efficiency situations....... These have been derived under the assumptions of monochromatic incoming waves and linear system behaviour. This allows to establish the power factor of a system with non-ideal efficiency. The locus of the optimal reactive control parameters is then studied and an alternative method of representation...... is developed to model the optimal control parameters. Ultimately we present a simple method of choosing optimal control parameters for any combination of efficiency and wave frequency....

The linear-non-linear frontier for the Goldstone Higgs

International Nuclear Information System (INIS)

Gavela, M.B.; Saa, S.; Kanshin, K.; Machado, P.A.N.

2016-01-01

The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)

The linear-non-linear frontier for the Goldstone Higgs

Energy Technology Data Exchange (ETDEWEB)

Gavela, M.B.; Saa, S. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Kanshin, K. [Universita di Padova, Dipartimento di Fisica e Astronomia ' G. Galilei' , Padua (Italy); INFN, Padova (Italy); Machado, P.A.N. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Fermi National Accelerator Laboratory, Theoretical Physics Department, Batavia, IL (United States)

2016-12-15

The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)

Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

International Nuclear Information System (INIS)

Van Aert, S.; Chen, J.H.; Van Dyck, D.

2010-01-01

A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has

Non-linear soil-structure interaction

International Nuclear Information System (INIS)

Wolf, J.P.

1984-01-01

The basic equation of motion to analyse the interaction of a non-linear structure and an irregular soil with the linear unbounded soil is formulated in the time domain. The contribution of the unbounded soil involves convolution integrals of the dynamic-stiffness coefficients in the time domain and the corresponding motions. As another possibility, a flexibility formulation fot the contribution of the unbounded soil using the dynamic-flexibility coefficients in the time domain, together with the direct-stiffness method for the structure and the irregular soil can be applied. As an example of a non-linear soil-structure-interaction analysis, the partial uplift of the basemat of a structure is examined. (Author) [pt

Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

Science.gov (United States)

Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

2017-12-27

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

Contributions to micromechanical model of the non linear behavior of the Callovo-Oxfordian argillite

International Nuclear Information System (INIS)

Abou-Chakra Guery, A.

2007-12-01

This work is performed in the general context of the project of underground disposal of radioactive waste, undertaken by the French National Radioactive Waste Management Agency (ANDRA). Due to its strong density and weak permeability, the formation of Callovo-Oxfordian argillite is chosen as one of possible geological barriers to radionuclides. The objective of the study to develop and validate a non linear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modelled as a composite constituted of an elasto(visco)plastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill. The derived model is first compared to Finite Element calculations on unit cell. It is then validated and applied for the prediction of the macroscopic stress-strain responses of the argillite at different geological depths. Finally, the micromechanical model is implemented in a commercial finite element code (Abaqus) for the simulation of a vertical shaft of the underground laboratory. This allows predicting the distribution of damage state and plastic strains and characterizing the excavation damage zone (EDZ). (author)

Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps

Directory of Open Access Journals (Sweden)

Deep Parikh

2015-08-01

Full Text Available This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current motors used in quad-copter UAV (Unmanned Aerial Vehicles. The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM.  Traditionally, quad-copter BLDC motor speed control uses simple linear motor-control map defined by the motor-constant specification. However, practical BLDC motors show non-linear characteristic, particularly when operated across wide operating speed-range as is commonly required in quad-copter UAV flight operations. In this paper, our investigations to compare performance of linear versus non-linear motor-control maps are presented. The investigations cover simulation-based and experimental study of BLDC motor speed control systems for  quad-copter vehicle available. First the non-linear map relating rotor RPM to motor voltage for quad-copter BLDC motor is obtained experimentally using an optical speed encoder. The performance of the linear versus non-linear motor-control-maps for the speed control are studied. The investigations also cover study of time-responses for various standard test input-signals e.g. step, ramp and pulse inputs, applied as the reference speed-commands. Also, simple 2-degree of freedom test-bed is developed in our laboratory to help test the open-loop and closed-loop experimental investigations. The non-linear motor-control map is found to perform better in BLDC motor speed tracking control performance and thereby helping achieve better quad-copter roll-angle attitude control.

Three dimensional finite element linear analysis of reinforced concrete structures

International Nuclear Information System (INIS)

Inbasakaran, M.; Pandarinathan, V.G.; Krishnamoorthy, C.S.

1979-01-01

A twenty noded isoparametric reinforced concrete solid element for the three dimensional linear elastic stress analysis of reinforced concrete structures is presented. The reinforcement is directly included as an integral part of the element thus facilitating discretization of the structure independent of the orientation of reinforcement. Concrete stiffness is evaluated by taking 3 x 3 x 3 Gauss integration rule and steel stiffness is evaluated numerically by considering three Gaussian points along the length of reinforcement. The numerical integration for steel stiffness necessiates the conversion of global coordiantes of the Gaussian points to nondimensional local coordinates and this is done by Newton Raphson iterative method. Subroutines for the above formulation have been developed and added to SAP and STAP routines for solving the examples. The validity of the reinforced concrete element is verified by comparison of results from finite element analysis and analytical results. It is concluded that this finite element model provides a valuable analytical tool for the three dimensional elastic stress analysis of concrete structures like beams curved in plan and nuclear containment vessels. (orig.)

Non-linear collective phenomena in dusty plasmas

International Nuclear Information System (INIS)

Tsytovich, V N; Morfill, G E

2004-01-01

Dusty plasmas are unusual states of matter where the interactions between the dust grains can be collective and are not a sum of all pair particle interactions. This state of matter is appropriate to form non-linear dissipative collective self-organized structures. It is found that the potential around the grains can be over-screened leading to a new phenomenon-collective attraction of pairs of large charge grains of equal sign. The grain clouds can self-contract and their collapse is terminated at distances where the interaction becomes repulsive. The homogeneous dusty plasma distribution is universally unstable to form structures. The potential of the collective attraction is proportional to the square of the dimensionless parameter P = n d Z d /n i , where n d and n i are the average dust and ion densities, respectively, and Z d is the dust charge in units of electron charge. The collective attraction is determined by finite grain size and by the presence of absorption of plasma flux on grains. The physics of attraction is related to the space charge accumulation caused by collective flux disturbances. The collective attraction operates for systems with size larger than the mean free path for ion-dust absorption, the condition met in many existing low temperature dusty plasma experiments, in edge plasmas of fusion devices and in space dusty plasmas. The collective attraction exceeds the previously known non-collective attraction such as shadow attraction or wake attraction. The collective attraction can be responsible for pairing of dust grains (this process is completely classical in contrast to the known pairing in superconductivity) and can serve as the main process for the formation of more complicated dust complexes up to dust-plasma crystals. The equilibrium structures formed by collective attraction have universal properties and can exist in a limited domain of parameters (similar to the equilibrium balance known for stars). The balance conditions for

Study of the linear and non-linear coupling of the LH wave to the tokamak plasmas

International Nuclear Information System (INIS)

Preynas, M.

2012-10-01

In order to achieve long pulse operation with a tokamak, additional heating and current drive systems are necessary. High frequency antennas, which deliver several megawatts of power to the plasma, are currently used in several tokamaks. Moreover, a good control of the coupling of the wave launched by the antenna to the edge plasma is required to optimize the efficiency of heating and current drive LH systems. However, non-linear effects which depend on the level of injected power in the plasma strongly damage the coupling of the LH wave at particular edge parameters (density and temperature profiles). Results presented in the manuscript deal with the study of the linear and non-linear coupling of the LH wave to the plasma. In the framework of the commissioning of the Passive Active Multijunction antenna in 2009 on the Tore Supra tokamak aiming at validating the LH system suggested for ITER, the characterisation of its coupling properties was realized from low power experiments. The experimental results, which are compared with the linear coupling code ALOHA, have validated the theoretical predictions of good coupling at edge plasma density around the cut-off density. Besides, the ponderomotive effect is clearly identified as responsible for the deterioration in the coupling of the wave, which is measured under particular edge plasma conditions. A theoretical model combining the coupling of the LH wave with the ponderomotive force is suggested to explain the experimental observations. Thus, a new full wave code (named PICCOLO-2D) was developed and results from simulations validate the working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling on Tore Supra. (author)

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

Science.gov (United States)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

An efficient linear power generator - Linear motor for oscillating piston machines; Effizienter Lineargenerator / Linearmotor fuer Kolbenmaschine - Schlussbericht

Energy Technology Data Exchange (ETDEWEB)

Lindegger, M.

2008-07-01

When an oscillating piston interacts with an electrical generator or motor, it is obvious that the electrical machine should also have linear motion, eliminating the disadvantage of a crankshaft. This work has two parts: construction of an efficient linear generator for a Stirling engine with a free piston and a theoretical study of the efficiency of linear motors for driving compressors. The Stirling engine and the linear generator have a continuous power of 1.3 kW{sub el}. With thermal peak power the planned 1.5 kW{sub el} are attained. The Project 'Stirling Free Piston Generator' for cogeneration will continue. Smaller linear motors with permanent magnets function without electronic control from single-phase AC net. The theoretical study shows how linear motors can be led out by linking the electric vector diagram with the pressure-volume diagram of the compressor. At a power level exceeding a few kW, a three-phase system with power electronics is more suitable. The frequency of oscillation is variable and lower than 50 Hz. The efficiency of the simulated linear motors lies in the range of efficiency class EFF1 of standard motors. The very high efficiencies of rotating motors with permanent magnets are not attained. The combination of the linear motor with an optimised thermal process leads to advantages regarding the efficiency. If a heat pump with linear drive system can operate with hot lubricating oil the losses in the heat exchangers are reduced. The Competence Center for Thermal Machines at Lucerne University of Applied Sciences and Arts shows great interest to pursue the project of a linear heat pump for small temperature differences. (author)

A linear evolution for non-linear dynamics and correlations in realistic nuclei

International Nuclear Information System (INIS)

Levin, E.; Lublinsky, M.

2004-01-01

A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sums the 'fan' diagrams. For the amplitude this equation is equivalent to the non-linear Balitsky-Kovchegov equation. The second equation is a generalization of the Balitsky-Kovchegov non-linear equation to interactions with realistic nuclei. It includes a new correlation parameter which incorporates, in a model-dependent way, correlations inside the nuclei. The third equation is a non-linear equation for QCD generating functional (and for scattering amplitude) that in addition to the 'fan' diagrams sums the Glauber-Mueller multiple rescatterings

Non-linear realizations and bosonic branes

International Nuclear Information System (INIS)

West, P.

2001-01-01

In this very short note, following hep-th/0001216, we express the well known bosonic brane as a non-linear realization. The reader may also consult hep-th/9912226, 0001216 and 0005270 where the branes of M theory are constructed as a non-linear realisation. The automorphisms of the supersymmetry algebra play an essential role. (author)

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.

GDTM-Padé technique for the non-linear differential-difference equation

Directory of Open Access Journals (Sweden)

Lu Jun-Feng

2013-01-01

Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

Spatial linear flows of finite length with nonuniform intensity distribution

Directory of Open Access Journals (Sweden)

Mikhaylov Ivan Evgrafovich

2014-02-01

Full Text Available Irrotational flows produced by spatial linear flows of finite length with different uneven lows of discharge over the flow length are represented in cylindrical coordinate system. Flows with the length 2a are placed in infinite space filled with ideal (inviscid fluid. In “А” variant discharge is fading linearly downward along the length of the flow. In “B” variant in upper half of the flow (length a discharge is fading linearly downward, in lower half of the flow discharge is fading linearly from the middle point to lower end. In “C” variant discharge of the flow is growing linearly from upper and lower ends to middle point.Equations for discharge distribution along the length of the flow are provided for each variant. Equations consist of two terms and include two dimensional parameters and current coordinate that allows integrating on flow length. Analytical expressions are derived for speed potential functions and flow speed components for flow speeds produced by analyzed flows. These analytical expressions consist of dimensional parameters of discharge distribution patterns along the length of the flow. Flow lines equation (meridional sections of flow surfaces for variants “A”, “B”, “C” is unsolvable in quadratures. Flow lines plotting is proposed to be made by finite difference method. Equations for flow line plotting are provided for each variant. Calculations of these equations show that the analyzed flows have the following flow lines: “A” has confocal hyperbolical curves, “B” and “C” have confocal hyperboles. Flow surfaces are confocal hyperboloids produced by rotation of these hyperboles about the axis passing through the flows. In “A” variant the space filled with fluid is separated by vividly horizontal flow surface in two parts. In upper part that includes the smaller part of the flow length flow lines are oriented downward, in lower part – upward. The equation defining coordinate of

A finite element thermohydrodynamic analyis of profile bore bearing

International Nuclear Information System (INIS)

Shah Nor bin Basri

1994-01-01

A finite element-based method is presented for analysing the thermohydrodynamic (THD) behaviour of profile bore bearing. A variational statement for the governing equation is derived and used to formulate a non-linear quadrilateral finite element of serendipity family. The predicted behaviour is compared with experimental evidence where possible and favorable correlation is obtained

Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

Energy Technology Data Exchange (ETDEWEB)

Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

2011-01-15

The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Directory of Open Access Journals (Sweden)

Armando Martínez-Pérez

2017-10-01

Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

Assessment of non-linear analysis finite element program (NONSAP) for inelastic analysis

International Nuclear Information System (INIS)

Chang, T.Y.; Prachuktam, S.; Reich, M.

1976-11-01

An assessment on a nonlinear structural analysis finite element program called NONSAP is given with respect to its inelastic analysis capability for pressure vessels and components. The assessment was made from the review of its theoretical basis and bench mark problem runs. It was found that NONSAP has only limited capability for inelastic analysis. However, the program was written flexible enough that it can be easily extended or modified to suit the user's need. Moreover, some of the numerical difficulties in using NONSAP are pointed out

Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data

KAUST Repository

Cheng, Guang

2014-02-01

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based on a spline approximation of the nonparametric part of the model and the generalized estimating equations (GEE). Although the model in consideration is natural and useful in many practical applications, the literature on this model is very limited because of challenges in dealing with dependent data for nonparametric additive models. We show that the proposed estimators are consistent and asymptotically normal even if the covariance structure is misspecified. An explicit consistent estimate of the asymptotic variance is also provided. Moreover, we derive the semiparametric efficiency score and information bound under general moment conditions. By showing that our estimators achieve the semiparametric information bound, we effectively establish their efficiency in a stronger sense than what is typically considered for GEE. The derivation of our asymptotic results relies heavily on the empirical processes tools that we develop for the longitudinal/clustered data. Numerical results are used to illustrate the finite sample performance of the proposed estimators. © 2014 ISI/BS.

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

Dyson-Schwinger equations for the non-linear σ-model

International Nuclear Information System (INIS)

Drouffe, J.M.; Flyvbjerg, H.

1989-08-01

Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived. They are polynomials in N, hence 1/N-expanded ab initio. A finite, closed set of equations is obtained by keeping only the leading term and the first correction term in this 1/N-series. These equations are solved numerically in two dimensions on square lattices measuring 50x50, 100x100, 200x200, and 400x400. They are also solved analytically at strong coupling and at weak coupling in a finite volume. In these two limits the solution is asymptotically identical to the exact strong- and weak-coupling series through the first three terms. Between these two limits, results for the magnetic susceptibility and the mass gap are identical to the Monte Carlo results available for N=3 and N=4 within a uniform systematic error of O(1/N 3 ), i.e. the results seem good to O(1/N 2 ), though obtained from equations that are exact only to O(1/N). This is understood by seeing the results as summed infinite subseries of the 1/N-series for the exact susceptibility and mass gap. We conclude that the kind of 1/N-expansion presented here converges as well as one might ever hope for, even for N as small as 3. (orig.)

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

Science.gov (United States)

Franzen, J.

1994-01-01

The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd

Vectorized Matlab Codes for Linear Two-Dimensional Elasticity

Directory of Open Access Journals (Sweden)

Jonas Koko

2007-01-01

Full Text Available A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

A non-linear kinematic hardening function

International Nuclear Information System (INIS)

Ottosen, N.S.

1977-05-01

Based on the classical theory of plasticity, and accepting the von Mises criterion as the initial yield criterion, a non-linear kinematic hardening function applicable both to Melan-Prager's and to Ziegler's hardening rule is proposed. This non-linear hardening function is determined by means of the uniaxial stress-strain curve, and any such curve is applicable. The proposed hardening function considers the problem of general reversed loading, and a smooth change in the behaviour from one plastic state to another nearlying plastic state is obtained. A review of both the kinematic hardening theory and the corresponding non-linear hardening assumptions is given, and it is shown that material behaviour is identical whether Melan-Prager's or Ziegler's hardening rule is applied, provided that the von Mises yield criterion is adopted. (author)

On natural frequencies of non-uniform beams modulated by finite periodic cells

International Nuclear Information System (INIS)

Xu, Yanlong; Zhou, Xiaoling; Wang, Wei; Wang, Longqi; Peng, Fujun; Li, Bin

2016-01-01

It is well known that an infinite periodic beam can support flexural wave band gaps. However, in real applications, the number of the periodic cells is always limited. If a uniform beam is replaced by a non-uniform beam with finite periodicity, the vibration changes are vital by mysterious. This paper employs the transfer matrix method (TMM) to study the natural frequencies of the non-uniform beams with modulation by finite periodic cells. The effects of the amounts, cross section ratios, and arrangement forms of the periodic cells on the natural frequencies are explored. The relationship between the natural frequencies of the non-uniform beams with finite periodicity and the band gap boundaries of the corresponding infinite periodic beam is also investigated. Numerical results and conclusions obtained here are favorable for designing beams with good vibration control ability. - Highlights: • The transfer matrix method to study the natural frequencies of the finite periodic non-uniform beams is derived. • The transfer matrix method to study the band gaps of the infinite periodic non-uniform beams is derived. • The effects of the periodic cells on the natural frequencies are explored. • The relationships of the natural frequencies and band gap boundaries are investigated.

On natural frequencies of non-uniform beams modulated by finite periodic cells

Energy Technology Data Exchange (ETDEWEB)

Xu, Yanlong, E-mail: xuyanlong@nwpu.edu.cn [School of Aeronautics, Northwestern Polytechnical University, Xi' an 710072, Shaanxi (China); Zhou, Xiaoling [Shanghai Institute of Aerospace System Engineering, Shanghai 201109 (China); Wang, Wei [School of Aeronautics, Northwestern Polytechnical University, Xi' an 710072, Shaanxi (China); Wang, Longqi [School of Civil & Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Peng, Fujun [Shanghai Institute of Aerospace System Engineering, Shanghai 201109 (China); Li, Bin [School of Aeronautics, Northwestern Polytechnical University, Xi' an 710072, Shaanxi (China)

2016-09-23

It is well known that an infinite periodic beam can support flexural wave band gaps. However, in real applications, the number of the periodic cells is always limited. If a uniform beam is replaced by a non-uniform beam with finite periodicity, the vibration changes are vital by mysterious. This paper employs the transfer matrix method (TMM) to study the natural frequencies of the non-uniform beams with modulation by finite periodic cells. The effects of the amounts, cross section ratios, and arrangement forms of the periodic cells on the natural frequencies are explored. The relationship between the natural frequencies of the non-uniform beams with finite periodicity and the band gap boundaries of the corresponding infinite periodic beam is also investigated. Numerical results and conclusions obtained here are favorable for designing beams with good vibration control ability. - Highlights: • The transfer matrix method to study the natural frequencies of the finite periodic non-uniform beams is derived. • The transfer matrix method to study the band gaps of the infinite periodic non-uniform beams is derived. • The effects of the periodic cells on the natural frequencies are explored. • The relationships of the natural frequencies and band gap boundaries are investigated.

Chiral symmetry and finite temperature effects in quantum theories

International Nuclear Information System (INIS)

Larsen, Aa.

1987-01-01

A computer simulation of the harmonic oscillator at finite temperature has been carried out, using the Monte Carlo Metropolis algorithm. Accurate results for the energy and fluctuations have been obtained, with special attention to the manifestation of the temperature effects. Varying the degree of symmetry breaking, the finite temperature behaviour of the asymmetric linear model in a linearized mean field approximation has been studied. In a study of the effects of chiral symmetry on baryon mass splittings, reasonable agreement with experiment has been obtained in a non-relativistic harmonic oscillator model

Non-linear wave loads and ship responses by a time-domain strip theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

Galois towers over non-prime finite fields

DEFF Research Database (Denmark)

Bassa, Alp; Beelen, Peter; Garcia, Arnaldo

2014-01-01

In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field Fℓ; i.e., we construct sequences of function fields N=(N1⊂N2⊂⋯) over Fℓ of increasing genus, such that all the extensions Ni/N1 are Galois extensions and the number of rational places of these...

Non-linear dynamics of wind turbine wings

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2006-01-01

The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced...

Automated, non-linear registration between 3-dimensional brain map and medical head image

International Nuclear Information System (INIS)

Mizuta, Shinobu; Urayama, Shin-ichi; Zoroofi, R.A.; Uyama, Chikao

1998-01-01

In this paper, we propose an automated, non-linear registration method between 3-dimensional medical head image and brain map in order to efficiently extract the regions of interest. In our method, input 3-dimensional image is registered into a reference image extracted from a brain map. The problems to be solved are automated, non-linear image matching procedure, and cost function which represents the similarity between two images. Non-linear matching is carried out by dividing the input image into connected partial regions, transforming the partial regions preserving connectivity among the adjacent images, evaluating the image similarity between the transformed regions of the input image and the correspondent regions of the reference image, and iteratively searching the optimal transformation of the partial regions. In order to measure the voxelwise similarity of multi-modal images, a cost function is introduced, which is based on the mutual information. Some experiments using MR images presented the effectiveness of the proposed method. (author)

Non-linear seismic analysis of structures coupled with fluid

International Nuclear Information System (INIS)

Descleve, P.; Derom, P.; Dubois, J.

1983-01-01

This paper presents a method to calculate non-linear structure behaviour under horizontal and vertical seismic excitation, making possible the full non-linear seismic analysis of a reactor vessel. A pseudo forces method is used to introduce non linear effects and the problem is solved by superposition. Two steps are used in the method: - Linear calculation of the complete model. - Non linear analysis of thin shell elements and calculation of seismic induced pressure originating from linear and non linear effects, including permanent loads and thermal stresses. Basic aspects of the mathematical formulation are developed. It has been applied to axi-symmetric shell element using a Fourier series solution. For the fluid interaction effect, a comparison is made with a dynamic test. In an example of application, the displacement and pressure time history are given. (orig./GL)

Effects of the time delays in a non linear pendular Fabry-Perot

International Nuclear Information System (INIS)

Tourrenc, P.; Deruelle, N.

1985-01-01

We study a one arm pendular Fabry-Perot interferometer with specifications corresponding to the two arms interferometers designed to detect gravitational radiation. We consider the non linearities originating from the radiation force and the effects of time delays due to the finite length of the arm. We derive the exact and the associated ''predictivised'' equations for the motion of the suspended mirror. We show that effects of time delays increase considerably the stability of the device when the optical relaxation time is of the order of the period of the pendulum, a case of relevance when light is recycled. However the thermal noise does not seem to be much modified when calculated within a simple approximation scheme

The Cauchy problem for non-linear Klein-Gordon equations

International Nuclear Information System (INIS)

Simon, J.C.H.; Taflin, E.

1993-01-01

We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

Non-Linear Rheological Properties and Neutron Scattering Investigation on Dilute Ring-Linear Blends

DEFF Research Database (Denmark)

Pyckhout-Hintzen, W.; Bras, A.R.; Wischnewski, A.

in a filament stretching rheometer, followed by quenching, strong anisotropic scattering patterns were obtained which were described by affinely deformed rings which function as giant, polymeric chemical crosslinks or sliplinks and more or less isotropic topological contributions from the entangling...... with interpenetrating linear chains. At the same time the non-linear rheological and mechanical data fit to a non-affine slip-tube model as for moderately crosslinked networks and to interchain pressure models or a modified non-linear Doi-Edwards description for the observed strain hardening during the extensional...

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...

Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

Science.gov (United States)

Rosenberg, D. E.; Alafifi, A.

2016-12-01

Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one

Finite orbit energetic particle linear response to toroidal Alfven eigenmodes

International Nuclear Information System (INIS)

Berk, H.L.; Ye Huanchun; Breizman, B.N.

1992-01-01

The linear response of energetic particles of the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width; when the banana width Δ b is much larger than the mode thickness Δ m , we obtain a new compact expression for the linear power transfer. When Δ m /Δ b m /Δ b from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balanced-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (vertical strokev parallel vertical stroke=v A ) is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (vertical strokev parallel vertical stroke=v A /(2l-1) with l≥2) is substantially reduced. (orig.)

A Stream Function Theory Based Calculation of Wave Kinematics for Very Steep Waves Using a Novel Non-linear Stretching Technique

DEFF Research Database (Denmark)

Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak

2016-01-01

A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei

2012-07-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

Science.gov (United States)

Rosu, Grigore; Havelund, Klaus

2001-01-01

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

Applicability of linear and non-linear potential flow models on a Wavestar float

DEFF Research Database (Denmark)

Bozonnet, Pauline; Dupin, Victor; Tona, Paolino

2017-01-01

as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...

Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2012-07-01

Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...

How many accelerograms to use and how to deal with scattering for transient non-linear seismic computations?

International Nuclear Information System (INIS)

Viallet, E.; Heinfling, G.

2005-01-01

Due to increased potentialities of computers, it is nowadays possible to perform dynamic non-linear computation of structures to evaluate their ultimate behavior under seismic loads using refined finite element models. Nevertheless, one key parameter for such complex computations is the input load (i.e. input time histories) which may lead to important discrepancies in the results and therefore difficulties to deal with for engineering purpose (variability, number of time histories to use...). In this situation, the number of accelerograms to be used and the way to deal with the results is to be carefully assessed. The objective of this study is to give some elements concerning (i) the number of accelerograms to be used for transient non-linear computations and (ii) the way to account for scattering of results. For this purpose, some simplified non-linear models are used. These models represent characteristic types of non-linearities such as : - Reinforce concrete (RC) structure model (with plastic non-linearity), - PWR core model (with impact non-linearity). For each type of non-linearity, different sets of accelerograms are used (artificial and natural ones). Each set is composed of a relatively high number of accelerograms in order to get proper trends. The results are expressed in term of average and standard deviation values of the characteristic parameters for each non-linearity (i.e. ductility drift for RC structure model and impact force for PWR core model). The results show that, a relatively large number of time histories may be necessary to get proper predictions of the average value of the characteristic non-linear parameter under consideration. In that situation, it should be difficult to deal with such a result for complex studies on reel structures. Nevertheless, it may be necessarily to perform transient non-linear seismic computations for design analyses but with a reduced number of calculations. For this purpose, the previous results are analyzed

A Linear Electromagnetic Piston Pump

Science.gov (United States)

Hogan, Paul H.

Advancements in mobile hydraulics for human-scale applications have increased demand for a compact hydraulic power supply. Conventional designs couple a rotating electric motor to a hydraulic pump, which increases the package volume and requires several energy conversions. This thesis investigates the use of a free piston as the moving element in a linear motor to eliminate multiple energy conversions and decrease the overall package volume. A coupled model used a quasi-static magnetic equivalent circuit to calculate the motor inductance and the electromagnetic force acting on the piston. The force was an input to a time domain model to evaluate the mechanical and pressure dynamics. The magnetic circuit model was validated with finite element analysis and an experimental prototype linear motor. The coupled model was optimized using a multi-objective genetic algorithm to explore the parameter space and maximize power density and efficiency. An experimental prototype linear pump coupled pistons to an off-the-shelf linear motor to validate the mechanical and pressure dynamics models. The magnetic circuit force calculation agreed within 3% of finite element analysis, and within 8% of experimental data from the unoptimized prototype linear motor. The optimized motor geometry also had good agreement with FEA; at zero piston displacement, the magnetic circuit calculates optimized motor force within 10% of FEA in less than 1/1000 the computational time. This makes it well suited to genetic optimization algorithms. The mechanical model agrees very well with the experimental piston pump position data when tuned for additional unmodeled mechanical friction. Optimized results suggest that an improvement of 400% of the state of the art power density is attainable with as high as 85% net efficiency. This demonstrates that a linear electromagnetic piston pump has potential to serve as a more compact and efficient supply of fluid power for the human scale.

Non linear structures seismic analysis by modal synthesis

International Nuclear Information System (INIS)

Aita, S.; Brochard, D.; Guilbaud, D.; Gibert, R.J.

1987-01-01

The structures submitted to a seismic excitation, may present a great amplitude response which induces a non linear behaviour. These non linearities have an important influence on the response of the structure. Even in this case (local shocks) the modal synthesis method remains attractive. In this paper we will present the way of taking into account, a local non linearity (shock between structures) in the seismic response of structures, by using the modal synthesis method [fr

On conjugacy growth of linear groups

OpenAIRE

Breuillard, Emmanuel; de Cornulier, Yves; Lubotzky, Alexander; Meiri, Chen

2011-01-01

We investigate the conjugacy growth of finitely generated linear groups. We show that finitely generated non-virtually-solvable subgroups of GL_d have uniform exponential conjugacy growth and in fact that the number of distinct polynomials arising as characteristic polynomials of the elements of the ball of radius n for the word metric has exponential growth rate bounded away from 0 in terms of the dimension d only.

Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements

Directory of Open Access Journals (Sweden)

Jesus M. de la Cruz

2012-02-01

Full Text Available This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.

Generalized non-linear Schroedinger hierarchy

International Nuclear Information System (INIS)

Aratyn, H.; Gomes, J.F.; Zimerman, A.H.

1994-01-01

The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Q i can be associated to a Hamiltonian, defining a time evolution related to to a time t i through the Hamilton equation ∂A/∂t i =[A,Q i ]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy

Finite-size effect on optimal efficiency of heat engines.

Science.gov (United States)

Tajima, Hiroyasu; Hayashi, Masahito

2017-07-01

The optimal efficiency of quantum (or classical) heat engines whose heat baths are n-particle systems is given by the strong large deviation. We give the optimal work extraction process as a concrete energy-preserving unitary time evolution among the heat baths and the work storage. We show that our optimal work extraction turns the disordered energy of the heat baths to the ordered energy of the work storage, by evaluating the ratio of the entropy difference to the energy difference in the heat baths and the work storage, respectively. By comparing the statistical mechanical optimal efficiency with the macroscopic thermodynamic bound, we evaluate the accuracy of the macroscopic thermodynamics with finite-size heat baths from the statistical mechanical viewpoint. We also evaluate the quantum coherence effect on the optimal efficiency of the cycle processes without restricting their cycle time by comparing the classical and quantum optimal efficiencies.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

Science.gov (United States)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Convergence of hybrid methods for solving non-linear partial ...

African Journals Online (AJOL)

This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

Implicit finite-difference simulations of seismic wave propagation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

Implicit finite-difference simulations of seismic wave propagation

KAUST Repository

Chu, Chunlei

2012-03-01

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

Non linear seismic analysis of charge/discharge machine

International Nuclear Information System (INIS)

Dostal, M.; Trbojevic, V.M.; Nobile, M.

1987-01-01

The main conclusions of the seismic analysis of the Latina CDM are: i. The charge machine has been demonstrated to be capable of withstanding the effects of a 0.1 g earthquake. Stresses and displacements were all within allowable limits and the stability criteria were fully satisfied for all positions of the cross-travel bogie on the gantry. ii. Movements due to loss of friction between the cross-travel bogie wheels and the rail was found to be small, i.e. less than 2 mm for all cases considered. The modes of rocking of the fixed and hinged legs preclude any possibility of excessive movement between the long travel bogie wheels and the rail. iii. The non-linear analysis incorporating contact and friction has given more realistic results than any of the linear verification analyses. The method of analysis indicates that even the larger structures can be efficiently solved on a mini computer for a long forcing input (16 s). (orig.)

Construction of local and non-local conservation laws for non-linear field equations

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1984-08-01

A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)

A Design of a Hybrid Non-Linear Control Algorithm

Directory of Open Access Journals (Sweden)

Farinaz Behrooz

2017-11-01

Full Text Available One of the high energy consuming devices in the buildings is the air-conditioning system. Designing a proper controller to consider the thermal comfort and simultaneously control the energy usage of the device will impact on the system energy efficiency and its performance. The aim of this study was to design a Multiple-Input and Multiple-Output (MIMO, non-linear, and intelligent controller on direct expansion air-conditioning system The control algorithm uses the Fuzzy Cognitive Map method as a main controller and the Generalized Predictive Control method is used for assigning the initial weights of the main controller. The results of the proposed controller shows that the controller was successfully designed and works in set point tracking and under disturbance rejection tests. The obtained results of the Generalized Predictive Control-Fuzzy Cognitive Map controller are compared with the previous MIMO Linear Quadratic Gaussian control design on the same direct expansion air-conditioning system under the same conditions. The comparative results indicate energy savings would be achieved with the proposed controller with long-term usage. Energy efficiency and thermal comfort conditions are achieved by the proposed controller.

Linear and non-linear autoregressive models for short-term wind speed forecasting

International Nuclear Information System (INIS)

Lydia, M.; Suresh Kumar, S.; Immanuel Selvakumar, A.; Edwin Prem Kumar, G.

2016-01-01

Highlights: • Models for wind speed prediction at 10-min intervals up to 1 h built on time-series wind speed data. • Four different multivariate models for wind speed built based on exogenous variables. • Non-linear models built using three data mining algorithms outperform the linear models. • Autoregressive models based on wind direction perform better than other models. - Abstract: Wind speed forecasting aids in estimating the energy produced from wind farms. The soaring energy demands of the world and minimal availability of conventional energy sources have significantly increased the role of non-conventional sources of energy like solar, wind, etc. Development of models for wind speed forecasting with higher reliability and greater accuracy is the need of the hour. In this paper, models for predicting wind speed at 10-min intervals up to 1 h have been built based on linear and non-linear autoregressive moving average models with and without external variables. The autoregressive moving average models based on wind direction and annual trends have been built using data obtained from Sotavento Galicia Plc. and autoregressive moving average models based on wind direction, wind shear and temperature have been built on data obtained from Centre for Wind Energy Technology, Chennai, India. While the parameters of the linear models are obtained using the Gauss–Newton algorithm, the non-linear autoregressive models are developed using three different data mining algorithms. The accuracy of the models has been measured using three performance metrics namely, the Mean Absolute Error, Root Mean Squared Error and Mean Absolute Percentage Error.

Non deterministic finite automata for power systems fault diagnostics

Directory of Open Access Journals (Sweden)

LINDEN, R.

2009-06-01

Full Text Available This paper introduces an application based on finite non-deterministic automata for power systems diagnosis. Automata for the simpler faults are presented and the proposed system is compared with an established expert system.

Noise and non-linearities in high-throughput data

International Nuclear Information System (INIS)

Nguyen, Viet-Anh; Lió, Pietro; Koukolíková-Nicola, Zdena; Bagnoli, Franco

2009-01-01

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets

An efficient linear approach in the reservoirs operation for electric power generation; Uma eficiente abordagem linear na operacao de reservatorios para geracao de energia eletrica

Energy Technology Data Exchange (ETDEWEB)

Zambon, Katia Livia

1997-07-01

A new approach for the Scheduling of Hydrothermal Systems, with a formulation that allows the solution of the problem through the linear programming techniques, otherwise the original form, which is complex and difficult is presented. The models were developed through a linear form for the generation function of hydroelectric plants, successive of the linearization of the cost function of the problem. The linear techniques used were the Simplex Method, with some modification that is is efficient, fast and simple. The important physical aspects of the system were preserved, like the individual representation of the hydroelectric plant, the features of cost function with the exponential increase and the head effect. Besides, this formulation can lead to stochastic approaches. All the optimization methods were implemented for the solution of the problem. The performance obtained were compared with each other and with that obtained through the non linear techniques. The algorithms showed to be efficient, with good results and very near to the optimal behavior of the reservoir operation planning obtained by traditional methods. (author)

A finite integration method for conformal, structured-grid, electromagnetic simulation

International Nuclear Information System (INIS)

Cooke, S.J.; Shtokhamer, R.; Mondelli, A.A.; Levush, B.

2006-01-01

We describe a numerical scheme for solving Maxwell's equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwell's equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwell's equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faraday's law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Ampere's law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwell's equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295-319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi-Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401-425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi

Return-Volatility Relationship: Insights from Linear and Non-Linear Quantile Regression

NARCIS (Netherlands)

D.E. Allen (David); A.K. Singh (Abhay); R.J. Powell (Robert); M.J. McAleer (Michael); J. Taylor (James); L. Thomas (Lyn)

2013-01-01

textabstractThe purpose of this paper is to examine the asymmetric relationship between price and implied volatility and the associated extreme quantile dependence using linear and non linear quantile regression approach. Our goal in this paper is to demonstrate that the relationship between the

A novel efficient coupled polynomial field interpolation scheme for higher order piezoelectric extension mode beam finite elements

International Nuclear Information System (INIS)

Sulbhewar, Litesh N; Raveendranath, P

2014-01-01

An efficient piezoelectric smart beam finite element based on Reddy’s third-order displacement field and layerwise linear potential is presented here. The present formulation is based on the coupled polynomial field interpolation of variables, unlike conventional piezoelectric beam formulations that use independent polynomials. Governing equations derived using a variational formulation are used to establish the relationship between field variables. The resulting expressions are used to formulate coupled shape functions. Starting with an assumed cubic polynomial for transverse displacement (w) and a linear polynomial for electric potential (φ), coupled polynomials for axial displacement (u) and section rotation (θ) are found. This leads to a coupled quadratic polynomial representation for axial displacement (u) and section rotation (θ). The formulation allows accommodation of extension–bending, shear–bending and electromechanical couplings at the interpolation level itself, in a variationally consistent manner. The proposed interpolation scheme is shown to eliminate the locking effects exhibited by conventional independent polynomial field interpolations and improve the convergence characteristics of HSDT based piezoelectric beam elements. Also, the present coupled formulation uses only three mechanical degrees of freedom per node, one less than the conventional formulations. Results from numerical test problems prove the accuracy and efficiency of the present formulation. (paper)

Seismic analysis of equipment system with non-linearities such as gap and friction using equivalent linearization method

International Nuclear Information System (INIS)

Murakami, H.; Hirai, T.; Nakata, M.; Kobori, T.; Mizukoshi, K.; Takenaka, Y.; Miyagawa, N.

1989-01-01

Many of the equipment systems of nuclear power plants contain a number of non-linearities, such as gap and friction, due to their mechanical functions. It is desirable to take such non-linearities into account appropriately for the evaluation of the aseismic soundness. However, in usual design works, linear analysis method with rough assumptions is applied from engineering point of view. An equivalent linearization method is considered to be one of the effective analytical techniques to evaluate non-linear responses, provided that errors to a certain extent are tolerated, because it has greater simplicity in analysis and economization in computing time than non-linear analysis. The objective of this paper is to investigate the applicability of the equivalent linearization method to evaluate the maximum earthquake response of equipment systems such as the CANDU Fuelling Machine which has multiple non- linearities

Non-linear dynamics in Parkinsonism

Directory of Open Access Journals (Sweden)

Olivier eDarbin

2013-12-01

Full Text Available Over the last 30 years, the functions (and dysfunctions of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the "rate hypothesis" and the "oscillatory hypothesis". In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively.More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e. parkinsonism, dyskinesia, healthy control and are responsive to treatments (i.e. L-DOPA,DBS. A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG, muscular activities (EMG or kinetic of motor symptoms (tremor, gait of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity and hypokinesia.

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.

An Efficient Explicit Finite-Difference Scheme for Simulating Coupled Biomass Growth on Nutritive Substrates

Directory of Open Access Journals (Sweden)

G. F. Sun

2015-01-01

Full Text Available A novel explicit finite-difference (FD method is presented to simulate the positive and bounded development process of a microbial colony subjected to a substrate of nutrients, which is governed by a nonlinear parabolic partial differential equations (PDE system. Our explicit FD scheme is uniquely designed in such a way that it transfers the nonlinear terms in the original PDE into discrete sets of linear ones in the algebraic equation system that can be solved very efficiently, while ensuring the stability and the boundedness of the solution. This is achieved through (1 a proper design of intertwined FD approximations for the diffusion function term in both time and spatial variations and (2 the control of the time-step through establishing theoretical stability criteria. A detailed theoretical stability analysis is conducted to reveal that our FD method is indeed stable. Our examples verified the fact that the numerical solution can be ensured nonnegative and bounded to simulate the actual physics. Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme. The present scheme is applicable for solving similar systems of PDEs in the investigation of the dynamics of biological films.

Development op finite volume methods for fluid dynamics

International Nuclear Information System (INIS)

Delcourte, S.

2007-09-01

We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)

Non-linear dynamics in galactic disks: the spiral-warps connection

International Nuclear Information System (INIS)

Masset, Frederic

1997-01-01

After a recall on warp theories and on warp waves, this research thesis reports a linear study of warp waves with an assessment of the role of gas compressibility when taking the galactic disk thickness into account. Then, the author reports an analytical study of the non-linear coupling between warp waves and density waves, in order to calculate coupling efficiency, to identify areas of the galactic disk in which it is efficient, and to discuss concurrent physical processes (such as Landau absorption) and the validity of assumptions made to perform the calculations. The next part reports numerical simulations which have been performed to check the coupling mechanism. The author notably comments evolutions brought to existing codes, and finally presents the three-dimensional version of the developed code, and discusses choices made for this code (presence of gas, choice of hydrodynamics algorithms and of gas mesh geometry, and so on). Numerical results are then presented and discussed: they actually show the existence of a coupling between density waves and warp waves [fr

The BL-QMR algorithm for non-Hermitian linear systems with multiple right-hand sides

Energy Technology Data Exchange (ETDEWEB)

Freund, R.W. [AT& T Bell Labs., Murray Hill, NJ (United States)

1996-12-31

Many applications require the solution of multiple linear systems that have the same coefficient matrix, but differ in their right-hand sides. Instead of applying an iterative method to each of these systems individually, it is potentially much more efficient to employ a block version of the method that generates iterates for all the systems simultaneously. However, it is quite intricate to develop robust and efficient block iterative methods. In particular, a key issue in the design of block iterative methods is the need for deflation. The iterates for the different systems that are produced by a block method will, in general, converge at different stages of the block iteration. An efficient and robust block method needs to be able to detect and then deflate converged systems. Each such deflation reduces the block size, and thus the block method needs to be able to handle varying block sizes. For block Krylov-subspace methods, deflation is also crucial in order to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences. An added difficulty arises for Lanczos-type block methods for non-Hermitian systems, since they involve two different block Krylov sequences. In these methods, deflation can now occur independently in both sequences, and consequently, the block sizes in the two sequences may become different in the course of the iteration, even though they were identical at the beginning. We present a block version of Freund and Nachtigal`s quasi-minimal residual method for the solution of non-Hermitian linear systems with single right-hand sides.

Non-linear heat transfer computer code by finite element method

International Nuclear Information System (INIS)

Nagato, Kotaro; Takikawa, Noboru

1977-01-01

The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)

The importance of non-linearities in modern proton synchrotrons

International Nuclear Information System (INIS)

Wilson, E.J.N.

1977-01-01

The paper outlines the physics and mathematics of non-linear field errors in the quide fields of accelerators, with particular reference to large accelerators such as the SPS. These non-linearities give rise to closed orbital distortions and non-linear resonances or stopbands. Both of these effects are briefly discussed and the use of resonances for slow beam extraction is also described. Another problem considered is that of chromaticity of the particle beam. The use of sextupoles to correct chromaticity and the Landau damping of beam instabilities using octupoles are also discussed. In the final section the application of Hamiltonian mechanics to non-linearities is demonstrated. The author concludes that the effect of non-linearities on particle dynamics may place a more severe limit on intensity and storage time in large rings than any other effect in transverse phase space. (B.D.)

Diomres (k,m): An efficient method based on Krylov subspaces to solve big, dispersed, unsymmetrical linear systems

Energy Technology Data Exchange (ETDEWEB)

de la Torre Vega, E. [Instituto de Investigaciones Electricas, Cuernavaca (Mexico); Cesar Suarez Arriaga, M. [Universidad Michoacana SNH, Michoacan (Mexico)

1995-03-01

In geothermal simulation processes, MULKOM uses Integrated Finite Differences to solve the corresponding partial differential equations. This method requires to resolve efficiently big linear dispersed systems of non-symmetrical nature on each temporal iteration. The order of the system is usually greater than one thousand its solution could represent around 80% of CPU total calculation time. If the elapsed time solving this class of linear systems is reduced, the duration of numerical simulation decreases notably. When the matrix is big (N{ge}500) and with holes, it is inefficient to handle all the system`s elements, because it is perfectly figured out by its elements distinct of zero, quantity greatly minor than N{sup 2}. In this area, iteration methods introduce advantages with respect to gaussian elimination methods, because these last replenish matrices not having any special distribution of their non-zero elements and because they do not make use of the available solution estimations. The iterating methods of the Conjugated Gradient family, based on the subspaces of Krylov, possess the advantage of improving the convergence speed by means of preconditioning techniques. The creation of DIOMRES(k,m) method guarantees the continuous descent of the residual norm, without incurring in division by zero. This technique converges at most in N iterations if the system`s matrix is symmetrical, it does not employ too much memory to converge and updates immediately the approximation by using incomplete orthogonalization and adequate restarting. A preconditioned version of DIOMRES was applied to problems related to unsymmetrical systems with 1000 unknowns and less than five terms per equation. We found that this technique could reduce notably the time needful to find the solution without requiring memory increment. The coupling of this method to geothermal versions of MULKOM is in process.

3D CSEM inversion based on goal-oriented adaptive finite element method

Science.gov (United States)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

FINITE TIME THERMODYNAMIC MODELING AND ANALYSIS FOR AN IRREVERSIBLE ATKINSON CYCLE

Directory of Open Access Journals (Sweden)

Yanlin Ge

2010-01-01

Full Text Available Performance of an air-standard Atkinson cycle is analyzed by using finite-time thermodynamics. The irreversible cycle model which is more close to practice is founded. In this model, the non-linear relation between the specific heats of working fluid and its temperature, the friction loss computed according to the mean velocity of the piston, the internal irreversibility described by using the compression and expansion efficiencies, and heat transfer loss are considered. The relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between power output and the efficiency of the cycle are derived by detailed numerical examples. Moreover, the effects of internal irreversibility, heat transfer loss and friction loss on the cycle performance are analyzed. The results obtained in this paper may provide guidelines for the design of practical internal combustion engines.

Non-linear wave packet dynamics of coherent states

Indian Academy of Sciences (India)

In recent years, the non-linear quantum dynamics of these states have revealed some striking features. It was found that under the action of a Hamil- tonian which is a non-linear function of the photon operator(s) only, an initial coherent state loses its coherent structure quickly due to quantum dephasing induced by the non-.

Confining dyon gas with finite-volume effects under control

Energy Technology Data Exchange (ETDEWEB)

Bruckmann, Falk [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Dinter, Simon [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ilgenfritz, Ernst-Michael [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Maier, Benjamin; Mueller-Preussker, Michael [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Wagner, Marc [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik

2011-11-15

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature Tnon-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles. (orig.)

Confining dyon gas with finite-volume effects under control

International Nuclear Information System (INIS)

Bruckmann, Falk; Maier, Benjamin; Mueller-Preussker, Michael; Wagner, Marc; Frankfurt Univ.

2011-11-01

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T c , we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles. (orig.)

Development of an efficient iterative solver for linear systems in FE structural analysis

International Nuclear Information System (INIS)

Saint-Georges, P.; Warzee, G.; Beauwens, R.; Notay, Y.

1993-01-01

The preconditioned conjugate gradient is a well-known and powerful method to solve sparse symmetric positive definite systems of linear equations. Such systems are generated by the finite element discretization in structural analysis but users of finite element in this context generally still rely on direct methods. It is our purpose in the present paper to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method is more performant than any direct method. (author)

Hybrid Spectral Unmixing: Using Artificial Neural Networks for Linear/Non-Linear Switching

Directory of Open Access Journals (Sweden)

Asmau M. Ahmed

2017-07-01

Full Text Available Spectral unmixing is a key process in identifying spectral signature of materials and quantifying their spatial distribution over an image. The linear model is expected to provide acceptable results when two assumptions are satisfied: (1 The mixing process should occur at macroscopic level and (2 Photons must interact with single material before reaching the sensor. However, these assumptions do not always hold and more complex nonlinear models are required. This study proposes a new hybrid method for switching between linear and nonlinear spectral unmixing of hyperspectral data based on artificial neural networks. The neural networks was trained with parameters within a window of the pixel under consideration. These parameters are computed to represent the diversity of the neighboring pixels and are based on the Spectral Angular Distance, Covariance and a non linearity parameter. The endmembers were extracted using Vertex Component Analysis while the abundances were estimated using the method identified by the neural networks (Vertex Component Analysis, Fully Constraint Least Square Method, Polynomial Post Nonlinear Mixing Model or Generalized Bilinear Model. Results show that the hybrid method performs better than each of the individual techniques with high overall accuracy, while the abundance estimation error is significantly lower than that obtained using the individual methods. Experiments on both synthetic dataset and real hyperspectral images demonstrated that the proposed hybrid switch method is efficient for solving spectral unmixing of hyperspectral images as compared to individual algorithms.

Finite orbit energetic particle linear response to toroidal Alfven eigenmodes

International Nuclear Information System (INIS)

Berk, H.L.; Ye, Huanchun; Breizman, B.N.

1991-07-01

The linear response of energetic particles to the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width: when the banana width triangle b is much larger than the mode thickness triangle m , we obtain a new compact expression for the linear power transfer. When triangle m /triangle b much-lt 1, the banana orbit effect reduces the power transfer by a factor of triangle m /triangle b from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balance-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (|υ parallel | = υ A is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (|υ parallel |) = υ A /(2 ell - 1) with ell ≥ 2) is substantially reduced. 10 refs

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

Energy Technology Data Exchange (ETDEWEB)

Lindesay, James V

2001-05-11

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.

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.)

Probabilistic finite elements for transient analysis in nonlinear continua

Science.gov (United States)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

DIESYS—dynamically non-linear dielectric elastomer energy generating synergetic structures: perspectives and challenges

International Nuclear Information System (INIS)

Antoniadis, I A; Venetsanos, D T; Papaspyridis, F G

2013-01-01

Dielectric elastomer based generators (DEGs) offer some unique properties over energy generators based on other materials. These properties include high energy density, high efficiency over a broad range of frequencies, low compliance, the ability to produce high strain, large area, low cost films with no toxic materials and wide range environmental tolerance. As further shown in this paper, DEG materials can also exhibit a non-linear dynamic behavior, enhancing broad-band energy transfer. More specifically, dielectric elastomer (DE) energy generating synergetic structures (DIESYS) are considered as dynamic energy absorbers. Two elementary characteristic DIESYS design concepts are examined, leading to a typical antagonistic configuration for in-plane oscillations and a typical synagonistic configuration for out-of-plane oscillations. Originally, all the DE elements of the structure are assumed to be always in tension during all the phases of the harvesting cycle, conforming to the traditional concept of operation of DE structures. As shown in this paper, the traditional always-in-tension concept results in a linear dynamic system response, despite the fact that the implemented (DE) parts are considered to have been made of a non-linear (hyperelastic) material. In contrast, the proposed loose-part concept ensures the appearance of a non-linear broad-band system response, enhancing energy transfer from the environmental source. (paper)

Linear and non-linear Modified Gravity forecasts with future surveys

Science.gov (United States)

Casas, Santiago; Kunz, Martin; Martinelli, Matteo; Pettorino, Valeria

2017-12-01

Modified Gravity theories generally affect the Poisson equation and the gravitational slip in an observable way, that can be parameterized by two generic functions (η and μ) of time and space. We bin their time dependence in redshift and present forecasts on each bin for future surveys like Euclid. We consider both Galaxy Clustering and Weak Lensing surveys, showing the impact of the non-linear regime, with two different semi-analytical approximations. In addition to these future observables, we use a prior covariance matrix derived from the Planck observations of the Cosmic Microwave Background. In this work we neglect the information from the cross correlation of these observables, and treat them as independent. Our results show that η and μ in different redshift bins are significantly correlated, but including non-linear scales reduces or even eliminates the correlation, breaking the degeneracy between Modified Gravity parameters and the overall amplitude of the matter power spectrum. We further apply a Zero-phase Component Analysis and identify which combinations of the Modified Gravity parameter amplitudes, in different redshift bins, are best constrained by future surveys. We extend the analysis to two particular parameterizations of μ and η and consider, in addition to Euclid, also SKA1, SKA2, DESI: we find in this case that future surveys will be able to constrain the current values of η and μ at the 2-5% level when using only linear scales (wavevector k < 0 . 15 h/Mpc), depending on the specific time parameterization; sensitivity improves to about 1% when non-linearities are included.

Existence of entire solutions of some non-linear differential-difference equations.

Science.gov (United States)

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

Validity of purchasing power parity for selected Latin American countries: Linear and non-linear unit root tests

Directory of Open Access Journals (Sweden)

Claudio Roberto Fóffano Vasconcelos

2016-01-01

Full Text Available The aim of this study is to examine empirically the validity of PPP in the context of unit root tests based on linear and non-linear models of the real effective exchange rate of Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela. For this purpose, we apply the Harvey et al. (2008 linearity test and the non-linear unit root test (Kruse, 2011. The results show that the series with linear characteristics are Argentina, Brazil, Chile, Colombia and Peru and those with non-linear characteristics are Mexico and Venezuela. The linear unit root tests indicate that the real effective exchange rate is stationary for Chile and Peru, and the non-linear unit root tests evidence that Mexico is stationary. In the period analyzed, the results show support for the validity of PPP in only three of the seven countries.

Evaluation of non-linear blending in dual-energy computed tomography

International Nuclear Information System (INIS)

Holmes, David R.; Fletcher, Joel G.; Apel, Anja; Huprich, James E.; Siddiki, Hassan; Hough, David M.; Schmidt, Bernhard; Flohr, Thomas G.; Robb, Richard; McCollough, Cynthia; Wittmer, Michael; Eusemann, Christian

2008-01-01

Dual-energy CT scanning has significant potential for disease identification and classification. However, it dramatically increases the amount of data collected and therefore impacts the clinical workflow. One way to simplify image review is to fuse CT datasets of different tube energies into a unique blended dataset with desirable properties. A non-linear blending method based on a modified sigmoid function was compared to a standard 0.3 linear blending method. The methods were evaluated in both a liver phantom and patient study. The liver phantom contained six syringes of known CT contrast which were placed in a bovine liver. After scanning at multiple tube currents (45, 55, 65, 75, 85, 95, 105, and 115 mAs for the 140-kV tube), the datasets were blended using both methods. A contrast-to-noise (CNR) measure was calculated for each syringe. In addition, all eight scans were normalized using the effective dose and statistically compared. In the patient study, 45 dual-energy CT scans were retrospectively mixed using the 0.3 linear blending and modified sigmoid blending functions. The scans were compared visually by two radiologists. For the 15, 45, and 64 HU syringes, the non-linear blended images exhibited similar CNR to the linear blended images; however, for the 79, 116, and 145 HU syringes, the non-linear blended images consistently had a higher CNR across dose settings. The radiologists qualitatively preferred the non-linear blended images of the phantom. In the patient study, the radiologists preferred non-linear blending in 31 of 45 cases with a strong preference in bowel and liver cases. Non-linear blending of dual energy data can provide an improvement in CNR over linear blending and is accompanied by a visual preference for non-linear blended images. Further study on selection of blending parameters and lesion conspicuity in non-linear blended images is being pursued

Non-linear stochastic response of a shallow cable

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2004-01-01

The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two...

Linear and Non-Linear Piezoresistance Coefficients in Cubic Semiconductors. I. Theoretical Formulations

Science.gov (United States)

Durand, S.; Tellier, C. R.

1996-02-01

This paper constitutes the first part of a work devoted to applications of piezoresistance effects in germanium and silicon semiconductors. In this part, emphasis is placed on a formal explanation of non-linear effects. We propose a brief phenomenological description based on the multi-valleys model of semiconductors before to adopt a macroscopic tensorial model from which general analytical expressions for primed non-linear piezoresistance coefficients are derived. Graphical representations of linear and non-linear piezoresistance coefficients allows us to characterize the influence of the two angles of cut and of directions of alignment. The second part will primarily deal with specific applications for piezoresistive sensors. Cette publication constitue la première partie d'un travail consacré aux applications des effets piézorésistifs dans les semiconducteurs germanium et silicium. Cette partie traite essentiellement de la modélisation des effets non-linéaires. Après une description phénoménologique à partir du modèle de bande des semiconducteurs nous développons un modèle tensoriel macroscopique et nous proposons des équations générales analytiques exprimant les coefficients piézorésistifs non-linéaires dans des repères tournés. Des représentations graphiques des variations des coefficients piézorésistifs linéaires et non-linéaires permettent une pré-caractérisation de l'influence des angles de coupes et des directions d'alignement avant l'étude d'applications spécifiques qui feront l'objet de la deuxième partie.

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

Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

Directory of Open Access Journals (Sweden)

Fei Chen

2013-01-01

Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

Implementation of thermo-viscoplastic constitutive equations into the finite element code ABAQUS

International Nuclear Information System (INIS)

Youn, Sam Son; Lee, Soon Bok; Kim, Jong Bum; Lee, Hyeong Yeon; Yoo, Bong

1998-01-01

Sophisticated viscoplatic constitutive laws describing material behavior at high temperature have been implemented in the general-purpose finite element code ABAQUS to predict the viscoplastic response of structures to cyclic loading. Because of the complexity of viscoplastic constitutive equation, the general implementation methods are developed. The solution of the non-linear system of algebraic equations arising from time discretization is determined using line-search and back-tracking in combination with Newton method. The time integration method of the constitutive equations is based on semi-implicit method with efficient time step control. For numerical examples, the viscoplastic model proposed by Chaboche is implemented and several applications are illustrated

Application of linear and non-linear low-Re k-ε models in two-dimensional predictions of convective heat transfer in passages with sudden contractions

International Nuclear Information System (INIS)

Raisee, M.; Hejazi, S.H.

2007-01-01

This paper presents comparisons between heat transfer predictions and measurements for developing turbulent flow through straight rectangular channels with sudden contractions at the mid-channel section. The present numerical results were obtained using a two-dimensional finite-volume code which solves the governing equations in a vertical plane located at the lateral mid-point of the channel. The pressure field is obtained with the well-known SIMPLE algorithm. The hybrid scheme was employed for the discretization of convection in all transport equations. For modeling of the turbulence, a zonal low-Reynolds number k-ε model and the linear and non-linear low-Reynolds number k-ε models with the 'Yap' and 'NYP' length-scale correction terms have been employed. The main objective of present study is to examine the ability of the above turbulence models in the prediction of convective heat transfer in channels with sudden contraction at a mid-channel section. The results of this study show that a sudden contraction creates a relatively small recirculation bubble immediately downstream of the channel contraction. This separation bubble influences the distribution of local heat transfer coefficient and increases the heat transfer levels by a factor of three. Computational results indicate that all the turbulence models employed produce similar flow fields. The zonal k-ε model produces the wrong Nusselt number distribution by underpredicting heat transfer levels in the recirculation bubble and overpredicting them in the developing region. The linear low-Re k-ε model, on the other hand, returns the correct Nusselt number distribution in the recirculation region, although it somewhat overpredicts heat transfer levels in the developing region downstream of the separation bubble. The replacement of the 'Yap' term with the 'NYP' term in the linear low-Re k-ε model results in a more accurate local Nusselt number distribution. Moreover, the application of the non-linear k

PWR control system design using advanced linear and non-linear methodologies

International Nuclear Information System (INIS)

Rabindran, N.; Whitmarsh-Everiss, M.J.

2004-01-01

Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)

Resource-efficient generation of linear cluster states by linear optics with postselection

International Nuclear Information System (INIS)

Uskov, D B; Alsing, P M; Fanto, M L; Szep, A; Smith, A M; Kaplan, L; Kim, R

2015-01-01

We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon–photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups that are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability for each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that the maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to (1/2) n−1 ; an m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of (1/4) m−1 . (paper)

Non-linear second-order periodic systems with non-smooth potential

Indian Academy of Sciences (India)

In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...

Non-linear second-order periodic systems with non-smooth potential

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...

Sensitivity Analysis of Multicarrier Digital Pre-distortion/ Equalization Techniques for Non-linear Satellite Channels

OpenAIRE

Piazza, Roberto; Shankar, Bhavani; Zenteno, Efrain; Ronnow, Daniel; Liolis, Kostantinos; Zimmer, Frank; Grasslin, Michael; Berheide, Tobias; Cioni, Stefano

2013-01-01

On-board joint power amplification of multiple-carrier DVB-S2 signals using a single High-Power Amplifier (HPA) is an emerging configuration that aims to reduce flight hardware and weight. However, effects specific to such a scenario degrade power and spectral efficiencies with increased Adjacent Channel Interference caused by non-linear characteristic of the HPA and power efficiency loss due to the increased Peak to Average Power Ratio (PAPR). The paper studies signal processing techniques ...

Robust non-gradient C subroutines for non-linear optimization

DEFF Research Database (Denmark)

Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun

2004-01-01

This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems, where gradient information is not required. The intention is that the routines should use the currently best algorithms available. All routines have...... subroutines are obtained by changing 0 to 1. The present report is a new and updated version of a previous report NI-91-04 with the title Non-gradient c Subroutines for Non- Linear Optimization, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated...... from Fortran to C. The reason for writing the present report is that some of the C subroutines have been replaced by more e ective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modified to some extent...

Optimization of piezoelectric cantilever energy harvesters including non-linear effects

International Nuclear Information System (INIS)

Patel, R; McWilliam, S; Popov, A A

2014-01-01

This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations. (paper)

Primordial black holes in linear and non-linear regimes

Energy Technology Data Exchange (ETDEWEB)

Allahyari, Alireza; Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2017-06-01

We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.

On fully multidimensional and high order non oscillatory finite volume methods, I

International Nuclear Information System (INIS)

Lafon, F.

1992-11-01

A fully multidimensional flux formulation for solving nonlinear conservation laws of hyperbolic type is introduced to perform calculations on unstructured grids made of triangular or quadrangular cells. Fluxes are computed across dual median cells with a multidimensional 2D Riemann Solver (R2D Solver) whose intermediate states depend on either a three (on triangle R2DT solver) of four (on quadrangle, R2DQ solver) state solutions prescribed on the three or four sides of a gravity cell. Approximate Riemann solutions are computed via a linearization process of Roe's type involving multidimensional effects. Moreover, a monotonous scheme using stencil and central Lax-Friedrichs corrections on sonic curves are built in. Finally, high order accurate ENO-like (Essentially Non Oscillatory) reconstructions using plane and higher degree polynomial limitations are defined in the set up of finite element Lagrange spaces P k and Q k for k≥0, on triangles and quadrangles, respectively. Numerical experiments involving both linear and nonlinear conservation laws to be solved on unstructured grids indicate the ability of our techniques when dealing with strong multidimensional effects. An application to Euler's equations for the Mach three step problem illustrates the robustness and usefulness of our techniques using triangular and quadrangular grids. (Author). 33 refs., 13 figs

Reactivity-induced time-dependencies of EBR-II linear and non-linear feedbacks

International Nuclear Information System (INIS)

Grimm, K.N.; Meneghetti, D.

1988-01-01

Time-dependent linear feedback reactivities are calculated for stereotypical subassemblies in the EBR-II reactor. These quantities are calculated from nodal reactivities obtained from a kinetic code analysis of an experiment in which the change in power resulted from the dropping of a control rod. Shown with these linear reactivities are the reactivity associated with the control-rod shaft contraction and also time-dependent non-linear (mainly bowing) component deduced from the inverse kinetics of the experimentally measured fission power and the calculated linear reactivities. (author)

Non-linear absorption for concentrated solar energy transport

Energy Technology Data Exchange (ETDEWEB)

Jaramillo, O. A; Del Rio, J.A; Huelsz, G [Centro de Investigacion de Energia, UNAM, Temixco, Morelos (Mexico)

2000-07-01

In order to determine the maximum solar energy that can be transported using SiO{sub 2} optical fibers, analysis of non-linear absorption is required. In this work, we model the interaction between solar radiation and the SiO{sub 2} optical fiber core to determine the dependence of the absorption of the radioactive intensity. Using Maxwell's equations we obtain the relation between the refractive index and the electric susceptibility up to second order in terms of the electric field intensity. This is not enough to obtain an explicit expression for the non-linear absorption. Thus, to obtain the non-linear optical response, we develop a microscopic model of an harmonic driven oscillators with damp ing, based on the Drude-Lorentz theory. We solve this model using experimental information for the SiO{sub 2} optical fiber, and we determine the frequency-dependence of the non-linear absorption and the non-linear extinction of SiO{sub 2} optical fibers. Our results estimate that the average value over the solar spectrum for the non-linear extinction coefficient for SiO{sub 2} is k{sub 2}=10{sup -}29m{sup 2}V{sup -}2. With this result we conclude that the non-linear part of the absorption coefficient of SiO{sub 2} optical fibers during the transport of concentrated solar energy achieved by a circular concentrator is negligible, and therefore the use of optical fibers for solar applications is an actual option. [Spanish] Con el objeto de determinar la maxima energia solar que puede transportarse usando fibras opticas de SiO{sub 2} se requiere el analisis de absorcion no linear. En este trabajo modelamos la interaccion entre la radiacion solar y el nucleo de la fibra optica de SiO{sub 2} para determinar la dependencia de la absorcion de la intensidad radioactiva. Mediante el uso de las ecuaciones de Maxwell obtenemos la relacion entre el indice de refraccion y la susceptibilidad electrica hasta el segundo orden en terminos de intensidad del campo electrico. Esto no es

Advanced analysis technique for the evaluation of linear alternators and linear motors

Science.gov (United States)

Holliday, Jeffrey C.

1995-01-01

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

Analytical exact solution of the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

2011-01-01

Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

Non-linear characteristics and long-range correlations in Asian stock markets

Science.gov (United States)

Jiang, J.; Ma, K.; Cai, X.

2007-05-01

We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

International Nuclear Information System (INIS)

Hoelzl, M; Merkel, P; Lackner, K; Strumberger, E; Huijsmans, G T A; Aleynikova, K; Liu, F; Atanasiu, C; Nardon, E; Fil, A; McAdams, R; Chapman, I

2014-01-01

The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described

Efficient non-linear two-photon effects from the Cesium 6D manifold

Science.gov (United States)

Haluska, Nathan D.; Perram, Glen P.; Rice, Christopher A.

2018-02-01

We report several non-linear process that occur when two-photon pumping the cesium 6D states. Cesium vapor possess some of the largest two-photon pump cross sections in nature. Pumping these cross sections leads to strong amplified spontaneous emission that we observe on over 17 lasing lines. These new fields are strong enough to couple with the pump to create additional tunable lines. We use a heat pipe with cesium densities of 1014 to 1016 cm-3 and 0 to 5 Torr of helium buffer gas. The cesium 6D States are interrogated by both high energy pulses and low power CW sources. We observe four-wave mixing, six-wave mixing, potential two-photon lasing, other unknown nonlinear processes, and the persistence of some processes at low thresholds. This system is also uniquely qualified to support two-photon lasing under the proper conditions.

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

Non-linear dynamic response of reactor containment

International Nuclear Information System (INIS)

Takemori, T.; Sotomura, K.; Yamada, M.

1975-01-01

A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

A simple method for non-linear analysis of steel fiber reinforced concrete - 10.4025/actascitechnol.v32i4.7249

Directory of Open Access Journals (Sweden)

Leandro Vanalli

2010-12-01

Full Text Available This paper proposes a physical non-linear formulation to deal with steel fiber reinforced concrete by the finite element method. The proposed formulation allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix. The most important feature of the formulation is that no additional degree of freedom is introduced in the pre-existent finite element numerical system to consider any distribution or quantity of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic of the formulation is the reduced work required by the user to introduce reinforcements, avoiding "rebar" elements, node by node geometrical definitions or even complex mesh generation. Bounded connection between long fibers and continuum is considered, for short fibers a simplified approach is proposed to consider splitting. Non-associative plasticity is adopted for the continuum and one dimensional plasticity is adopted to model fibers. Examples are presented in order to show the capabilities of the formulation.

PRINCIPAL STRESSES IN NON-LINEAR ANALYSIS OF BAKUN CONCRETE FACED ROCKFILL DAM

Directory of Open Access Journals (Sweden)

Mohd Hilton Ahmad

2017-11-01

Full Text Available With rapid population growth and accelerating economic development, much of the world’s WATER which requires urgent attention to ensure sustainable use. Nowadays, Concrete Faced Rockfill Dam (CFRD is preferred among dam consultant due to its advantages. They are designed to withstand all applied loads; namely gravity load due to its massive weight and hydrostatic load due to water thrust from the reservoir. Bakun CFRD, which ranks as the second highest CFRD in the world when completed, is analyzed to its safety due to both loads mentioned earlier by using Finite Element Method. 2-D plane strain finite element analysis of non-linear Duncan-Chang hyperbolic Model which formulated by Duncan and Chang is used to study the structural response of the dam in respect to the deformation and stresses of Main dam of Bakun’s CFRD project. Dead-Birth-Ghost element technique was used to simulate sequences of construction of the dam as well as during reservoir fillings. The comparison of rigid and flexible foundation on the behaviour of the dam was discussed. The maximum and minimum principal stresses are the maximum and minimum possible values of the normal stresses. The maximum principal stress controls brittle fracture. In the finite element modeling the concrete slab on the upstream was represented through six-noded element, while the interface characteristic between dam body and concrete slab was modeled using interface element. The maximum settlement and stresses of the cross section was founded and the distribution of them were discussed and tabulated in form of contours.

Application of non-linear discretetime feedback regulators with assignable closed-loop dynamics

Directory of Open Access Journals (Sweden)

Dubljević Stevan

2003-01-01

Full Text Available In the present work the application of a new approach is demonstrated to a discrete-time state feedback regulator synthesis with feedback linearization and pole-placement for non-linear discrete-time systems. Under the simultaneous implementation of a non-linear coordinate transformation and a non-linear state feedback law computed through the solution of a system of non-linear functional equations, both the feedback linearization and pole-placement design objectives were accomplished. The non-linear state feedback regulator synthesis method was applied to a continuous stirred tank reactor (CSTR under non-isothermal operating conditions that exhibits steady-state multiplicity. The control objective was to regulate the reactor at the middle unstable steady state by manipulating the rate of input heat in the reactor. Simulation studies were performed to evaluate the performance of the proposed non-linear state feedback regulator, as it was shown a non-linear state feedback regulator clearly outperformed a standard linear one, especially in the presence of adverse disturbance under which linear regulation at the unstable steady state was not feasible.

Graded associative conformal algebras of finite type

OpenAIRE

Kolesnikov, Pavel

2011-01-01

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\\simeq \\Gamma $. A classification of simple...

On structural identifiability analysis of the cascaded linear dynamic systems in isotopically non-stationary 13C labelling experiments.

Science.gov (United States)

Lin, Weilu; Wang, Zejian; Huang, Mingzhi; Zhuang, Yingping; Zhang, Siliang

2018-06-01

The isotopically non-stationary 13C labelling experiments, as an emerging experimental technique, can estimate the intracellular fluxes of the cell culture under an isotopic transient period. However, to the best of our knowledge, the issue of the structural identifiability analysis of non-stationary isotope experiments is not well addressed in the literature. In this work, the local structural identifiability analysis for non-stationary cumomer balance equations is conducted based on the Taylor series approach. The numerical rank of the Jacobian matrices of the finite extended time derivatives of the measured fractions with respect to the free parameters is taken as the criterion. It turns out that only one single time point is necessary to achieve the structural identifiability analysis of the cascaded linear dynamic system of non-stationary isotope experiments. The equivalence between the local structural identifiability of the cascaded linear dynamic systems and the local optimum condition of the nonlinear least squares problem is elucidated in the work. Optimal measurements sets can then be determined for the metabolic network. Two simulated metabolic networks are adopted to demonstrate the utility of the proposed method. Copyright © 2018 Elsevier Inc. All rights reserved.

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

Non-linear realizations of supersymmetry with off-shell central charges

International Nuclear Information System (INIS)

Santos Filho, P.B.; Oliveira Rivelles, V. de.

1985-01-01

A new class of non-linear realizations of the extended supersymmetry algebra with central charges is presented. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as is the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. It is worked in two dimensions and its extension to higher dimensions is discussed. (Author) [pt

Non-linear finite element modelling and analysis of the effect of gasket creep-relaxation on circular bolted flange connections

International Nuclear Information System (INIS)

Luyt, P.C.B.; Theron, N.J.; Pietra, F.

2017-01-01

It is well known that gasket creep-relaxation results in a reduction of contact pressure between the surface of a gasket and the face of a flange over an extended period of time. This reduction may result in the subsequent failure of the circular bolted flange connection due to leakage. In this paper a pair of flat and raised face integral flanges, PN 10 DN 50 (in accordance with the European EN 1092-1 standard), with non-asbestos compressed fibre ring gaskets with aramid and a nitrile rubber binder were considered. Finite element modelling and analyses were done, for both the circular bolted flange configurations, during the seating condition. The results of the finite element analyses were experimentally validated. It was found that the number of bolt tightening increments as well as the time between the bolt tightening increments had a significant impact on the effect which gasket creep-relaxation had after the seating condition. An increase in either the number of bolting increments or the time between the bolting increments will reduce the effect which gasket creep-relaxation has once the bolts had been fastened. Based on these results it is possible to develop an optimisation scheme to minimize the effect which gasket creep-relaxation has on the contact pressure between the face of the flange and the gasket, after seating, by either increasing or decreasing the number of bolt tightening increments or the time between the bolt tightening increments. - Highlights: • Number of bolt tightening increments and time between bolt tightening increments had significant impact on effect of gasket creep-relaxation after the seating condition. • Impact of gasket creep-relaxation during seating and operating phases investigated by means of finite element analysis and experimentally verified. • Possible to develop optimisation scheme to minimize effect ofh gasket creep-relaxation on contact pressure between flange face and gasket. • Knowing the contact pressure is

The algebra of non-local charges in non-linear sigma models

International Nuclear Information System (INIS)

Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.

1993-07-01

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower. (author). 22 refs, 5 figs

A computationally efficient 3D finite-volume scheme for violent liquid–gas sloshing

CSIR Research Space (South Africa)

Oxtoby, Oliver F

2015-10-01

Full Text Available We describe a semi-implicit volume-of-fluid free-surface-modelling methodology for flow problems involving violent free-surface motion. For efficient computation, a hybrid-unstructured edge-based vertex-centred finite volume discretisation...

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Total and Differential Efficiencies for a Circular Detector Viewing a Circular Radiator of Finite Thickness

Energy Technology Data Exchange (ETDEWEB)

Lauber, A; Tollander, B

1967-08-15

Total and differential detection efficiencies have been computed for a circular detector viewing a circular radiator of finite thickness. Isotropic, cosines and n-p scattering angular emission distributions of the radiated particles are considered. Tables are given for the total efficiencies as well as for the differential efficiencies in the n-p scattering case.

Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

KAUST Repository

Dujardin, G. M.

2009-01-01

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Dilna, N.; Rontó, András

2010-01-01

Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

Neural Generalized Predictive Control of a non-linear Process

DEFF Research Database (Denmark)

Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

1998-01-01

The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability qu...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem.......The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...

Non-linear punctual kinetics applied to PWR reactors simulation

International Nuclear Information System (INIS)

Cysne, F.S.

1978-11-01

In order to study some kinds of nuclear reactor accidents, a simulation is made using the punctual kinetics model for the reactor core. The following integration methods are used: Hansen's method in which a linearization is made and CSMP using a variable interval fourth-order Runge Kutta method. The results were good and were compared with those obtained by the code Dinamica I which uses a finite difference integration method of backward kind. (Author) [pt

Non-linear thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM

International Nuclear Information System (INIS)

Coz Diaz, J.J. del; Garcia Nieto, P.J.; Suarez Sierra, J.L.; Penuelas Sanchez, I.

2008-01-01

The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed

Non-linear thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM

Energy Technology Data Exchange (ETDEWEB)

Coz Diaz, J.J. del [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain)], E-mail: juanjo@constru.uniovi.es; Garcia Nieto, P.J. [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Suarez Sierra, J.L.; Penuelas Sanchez, I. [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain)

2008-06-15

The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed.

A non conforming finite element method for computing eigenmodes of resonant cavities

International Nuclear Information System (INIS)

Touze, F.; Le Meur, G.

1990-06-01

We present here a non conforming finite element in R 3 . This finite element, built on tetrahedrons, is particularly suited for computing eigenmodes. The main advantage of this element is that it preserves some structural properties of the space in which the solutions of the Maxwell's equations are to be found. Numerical results are presented for both two-dimensional and three-dimensional cases

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

Directory of Open Access Journals (Sweden)

MC. Souza

Full Text Available Leaf area estimation is an important biometrical trait for evaluating leaf development and plant growth in field and pot experiments. We developed a non-destructive model to estimate the leaf area (LA of Vernonia ferruginea using the length (L and width (W leaf dimensions. Different combinations of linear equations were obtained from L, L2, W, W2, LW and L2W2. The linear regressions using the product of LW dimensions were more efficient to estimate the LA of V. ferruginea than models based on a single dimension (L, W, L2 or W2. Therefore, the linear regression “LA=0.463+0.676WL” provided the most accurate estimate of V. ferruginea leaf area. Validation of the selected model showed that the correlation between real measured leaf area and estimated leaf area was very high.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Application of finite-element method to three-dimensional nuclear reactor analysis

International Nuclear Information System (INIS)

Cheung, K.Y.

1985-01-01

The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired

A finite element method for SSI time history calculation

International Nuclear Information System (INIS)

Ni, X.; Gantenbein, F.; Petit, M.

1989-01-01

The method which is proposed is based on a finite element modelization for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method is presented, then applications are given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior are described

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...

INTRANS. A computer code for the non-linear structural response analysis of reactor internals under transient loads

International Nuclear Information System (INIS)

Ramani, D.T.

1977-01-01

The 'INTRANS' system is a general purpose computer code, designed to perform linear and non-linear structural stress and deflection analysis of impacting or non-impacting nuclear reactor internals components coupled with reactor vessel, shield building and external as well as internal gapped spring support system. This paper describes in general a unique computational procedure for evaluating the dynamic response of reactor internals, descretised as beam and lumped mass structural system and subjected to external transient loads such as seismic and LOCA time-history forces. The computational procedure is outlined in the INTRANS code, which computes component flexibilities of a discrete lumped mass planar model of reactor internals by idealising an assemblage of finite elements consisting of linear elastic beams with bending, torsional and shear stiffnesses interacted with external or internal linear as well as non-linear multi-gapped spring support system. The method of analysis is based on the displacement method and the code uses the fourth-order Runge-Kutta numerical integration technique as a basis for solution of dynamic equilibrium equations of motion for the system. During the computing process, the dynamic response of each lumped mass is calculated at specific instant of time using well-known step-by-step procedure. At any instant of time then, the transient dynamic motions of the system are held stationary and based on the predicted motions and internal forces of the previous instant. From which complete response at any time-step of interest may then be computed. Using this iterative process, the relationship between motions and internal forces is satisfied step by step throughout the time interval

Finite-volume effects due to spatially non-local operators arXiv

CERN Document Server

Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.

Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\\pi (L- \\xi)} $, where $m_\\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \\xi|^n$ that can lead to enhanced volume effects. These ...

Towers of Function Fields over Non-prime Finite Fields

DEFF Research Database (Denmark)

Bassa, Alp; Beelen, Peter; Garcia, Arnaldo

2015-01-01

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pn with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modu...

Non-linear Imaging using an Experimental Synthetic Aperture Real Time Ultrasound Scanner

DEFF Research Database (Denmark)

Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt

2011-01-01

This paper presents the first non-linear B-mode image of a wire phantom using pulse inversion attained via an experimental synthetic aperture real-time ultrasound scanner (SARUS). The purpose of this study is to implement and validate non-linear imaging on SARUS for the further development of new...... non-linear techniques. This study presents non-linear and linear B-mode images attained via SARUS and an existing ultrasound system as well as a Field II simulation. The non-linear image shows an improved spatial resolution and lower full width half max and -20 dB resolution values compared to linear...

Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities

NARCIS (Netherlands)

van Rooij, A.C.L.M.

2017-01-01

Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities

Three-dimensional linear fracture mechanics analysis by a displacement-hybrid finite-element model

International Nuclear Information System (INIS)

Atluri, S.N.; Kathiresan, K.; Kobayashi, A.S.

1975-01-01

This paper deals with a finite-element procedures for the calculation of modes I, II and III stress intensity factors, which vary, along an arbitrarily curved three-dimensional crack front in a structural component. The finite-element model is based on a modified variational principle of potential energy with relaxed continuity requirements for displacements at the inter-element boundary. The variational principle is a three-field principle, with the arbitrary interior displacements for the element, interelement boundary displacements, and element boundary tractions as variables. The unknowns in the final algebraic system of equations, in the present displacement hybrid finite element model, are the nodal displacements and the three elastic stress intensity factors. Special elements, which contain proper square root and inverse square root crack front variations in displacements and stresses, respectively, are used in a fixed region near the crack front. Interelement displacement compatibility is satisfied by assuming an independent interelement boundary displacement field, and using a Lagrange multiplier technique to enforce such interelement compatibility. These Lagrangean multipliers, which are physically the boundary tractions, are assumed from an equilibrated stress field derived from three-dimensional Beltrami (or Maxwell-Morera) stress functions that are complete. However, considerable care should be exercised in the use of these stress functions such that the stresses produced by any of these stress function components are not linearly dependent

Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

Science.gov (United States)

Sahin, Rubina; Tapadia, Kavita

2015-01-01

The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

Frequency-domain full-waveform inversion with non-linear descent directions

Science.gov (United States)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a

Pulse height non-linearity in LaBr3:Ce crystal for gamma ray spectrometry and imaging

International Nuclear Information System (INIS)

Pani, R.; Cinti, M.N.; Pellegrini, R.; Bennati, P.; Ridolfi, S.; Scafe, R.; Orsolini Cencelli, V.; De Notaristefani, F.; Fabbri, A.; Navarria, F.L.; Lanconelli, N.; Moschini, G.; Boccaccio, P.

2011-01-01

In this paper the response in term of pulse height linearity of two Hamamatsu photomultipliers is investigated, when coupled to a LaBr 3 :Ce scintillation crystal. The two photodetectors have high quantum efficiency and in particular 30% for R6231-01 and 42% for R7600-200 tube. The substantial difference is in the dynode structure, linear focused and metal channel for R6231 and R7600 respectively. In this work in order to verify the non-linearity effects on the pulse height distribution, due principally to the high and fast light production of LaBr 3 :Ce scintillator, we propose a 'peak by peak' procedure to calibrate the pulse height distribution. Utilizing a specific fragmentation of the calibration curve in subsets, the calculated energy values are very similar for both PMTs. This result confirmed the potentiality of the procedure to highlight the non-linearity effects on pulse height distribution.

Non-linear optics of nano-scale pentacene thin film

Science.gov (United States)

Yahia, I. S.; Alfaify, S.; Jilani, Asim; Abdel-wahab, M. Sh.; Al-Ghamdi, Attieh A.; Abutalib, M. M.; Al-Bassam, A.; El-Naggar, A. M.

2016-07-01

We have found the new ways to investigate the linear/non-linear optical properties of nanostructure pentacene thin film deposited by thermal evaporation technique. Pentacene is the key material in organic semiconductor technology. The existence of nano-structured thin film was confirmed by atomic force microscopy and X-ray diffraction. The wavelength-dependent transmittance and reflectance were calculated to observe the optical behavior of the pentacene thin film. It has been observed the anomalous dispersion at wavelength λ 800. The non-linear refractive index of the deposited films was investigated. The linear optical susceptibility of pentacene thin film was calculated, and we observed the non-linear optical susceptibility of pentacene thin film at about 6 × 10-13 esu. The advantage of this work is to use of spectroscopic method to calculate the liner and non-liner optical response of pentacene thin films rather than expensive Z-scan. The calculated optical behavior of the pentacene thin films could be used in the organic thin films base advanced optoelectronic devices such as telecommunications devices.

Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity

Science.gov (United States)

Rand, J. L.; Wakefield, D. S.

Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may

Non-linear Q-clouds around Kerr black holes

International Nuclear Information System (INIS)

Herdeiro, Carlos; Radu, Eugen; Rúnarsson, Helgi

2014-01-01

Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

Science.gov (United States)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

SPORTS - a simple non-linear thermalhydraulic stability code

International Nuclear Information System (INIS)

Chatoorgoon, V.

1986-01-01

A simple code, called SPORTS, has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers. (orig.)

Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

International Nuclear Information System (INIS)

Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

2009-01-01

The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

Non-linearity aspects in the design of submarine pipelines

NARCIS (Netherlands)

Fernández, M.L.

1981-01-01

An arbitrary attempt has been made to classify and discuss some non-linearity aspects related to design, construction and operation of submarine pipelines. Non-linearities usually interrelate and take part of a comprehensive design, making difficult to quantify their individual influence or

Non-Linear Dynamics of Saturn's Rings

Science.gov (United States)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

OpenAIRE

Nakamura, Gen; Vashisth, Manmohan

2017-01-01

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

Mathematical problems in non-linear Physics: some results

International Nuclear Information System (INIS)

1979-01-01

The basic results presented in this report are the following: 1) Characterization of the range and Kernel of the variational derivative. 2) Determination of general conservation laws in linear evolution equations, as well as bounds for the number of polynomial conserved densities in non-linear evolution equations in two independent variables of even order. 3) Construction of the most general evolution equation which has a given family of conserved densities. 4) Regularity conditions for the validity of the Lie invariance method. 5) A simple class of perturbations in non-linear wave equations. 6) Soliton solutions in generalized KdV equations. (author)

Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

International Nuclear Information System (INIS)

Cook, W.A.

1978-10-01

Nuclear Material shipping containers have shells of revolution as a basic structural component. 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. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented

Non-linear failure analysis of HCPB blanket for DEMO taking into account high dose irradiation

Energy Technology Data Exchange (ETDEWEB)

Aktaa, J., E-mail: jarir.aktaa@kit.edu [Karlsruhe Institute of Technology (KIT), Institute for Applied Materials, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Kecskés, S.; Pereslavtsev, P.; Fischer, U.; Boccaccini, L.V. [Karlsruhe Institute of Technology (KIT), Institute for Neutron Physics and Reactor Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany)

2014-10-15

Highlights: • First non-linear structural analysis for the European Helium Cooled Pebble Bed Blanket Module taking into account high dose irradiation. • Most critical areas were identified and analyzed with regard to the effect of irradiation on predicted damage at these areas. • Despite the extensive computing time 100 cycles were simulated by using the sub-modelling technique investigating damage at most critical area. • The results show a positive effect of irradiation on calculated damage which is mainly attributed to the irradiation induced hardening. - Abstract: For the European helium cooled pebble bed (HCPB) blanket of DEMO the reduced activation ferritic martensitic steel EUROFER has been selected as structural material. During operation the HCPB blanket will be subjected to complex thermo-mechanical loadings and high irradiation doses. Taking into account the material and structural behaviour under these conditions is a precondition for a reliable blanket design. For considering high dose irradiation in structural analysis of the DEMO blanket, the coupled deformation damage model, extended recently taking into account the influence of high dose irradiation on the material behaviour of EUROFER and implemented in the finite element code ABAQUS, has been used. Non-linear finite element (FE) simulations of the DEMO HCPB blanket have been performed considering the design of the HCPB Test Blanket Module (TBM) as reference and the thermal and mechanical boundary conditions of previous analyses. The irradiation dose rate required at each position in the structure as an additional loading parameter is estimated by extrapolating the results available for the TBM in ITER scaling the value calculated in neutronics and activation analysis for ITER boundary conditions to the DEMO boundary conditions. The results of the FE simulations are evaluated considering damage at most critical highly loaded areas of the structure and discussed with regard to the impact of

Non-linear failure analysis of HCPB blanket for DEMO taking into account high dose irradiation

International Nuclear Information System (INIS)

Aktaa, J.; Kecskés, S.; Pereslavtsev, P.; Fischer, U.; Boccaccini, L.V.

2014-01-01

Highlights: • First non-linear structural analysis for the European Helium Cooled Pebble Bed Blanket Module taking into account high dose irradiation. • Most critical areas were identified and analyzed with regard to the effect of irradiation on predicted damage at these areas. • Despite the extensive computing time 100 cycles were simulated by using the sub-modelling technique investigating damage at most critical area. • The results show a positive effect of irradiation on calculated damage which is mainly attributed to the irradiation induced hardening. - Abstract: For the European helium cooled pebble bed (HCPB) blanket of DEMO the reduced activation ferritic martensitic steel EUROFER has been selected as structural material. During operation the HCPB blanket will be subjected to complex thermo-mechanical loadings and high irradiation doses. Taking into account the material and structural behaviour under these conditions is a precondition for a reliable blanket design. For considering high dose irradiation in structural analysis of the DEMO blanket, the coupled deformation damage model, extended recently taking into account the influence of high dose irradiation on the material behaviour of EUROFER and implemented in the finite element code ABAQUS, has been used. Non-linear finite element (FE) simulations of the DEMO HCPB blanket have been performed considering the design of the HCPB Test Blanket Module (TBM) as reference and the thermal and mechanical boundary conditions of previous analyses. The irradiation dose rate required at each position in the structure as an additional loading parameter is estimated by extrapolating the results available for the TBM in ITER scaling the value calculated in neutronics and activation analysis for ITER boundary conditions to the DEMO boundary conditions. The results of the FE simulations are evaluated considering damage at most critical highly loaded areas of the structure and discussed with regard to the impact of

Identification of Non-Linear Structures using Recurrent Neural Networks

DEFF Research Database (Denmark)

Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.

Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....

Identification of Non-Linear Structures using Recurrent Neural Networks

DEFF Research Database (Denmark)

Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.

1995-01-01

Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....

The non-linear Perron-Frobenius theorem : Perturbations and aggregation

NARCIS (Netherlands)

Dietzenbacher, E

The dominant eigenvalue and the corresponding eigenvector (or Perron vector) of a non-linear eigensystem are considered. We discuss the effects upon these, of perturbations and of aggregation of the underlying mapping. The results are applied to study the sensivity of the outputs in a non-linear

A finite element method for SSI time history calculations

International Nuclear Information System (INIS)

Ni, X.M.; Gantenbein, F.; Petit, M.

1989-01-01

The method which is proposed is based on a finite element modelisation for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method will be presented, then applications will be given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior will be described

Non-linear effects in transition edge sensors for X-ray detection

International Nuclear Information System (INIS)

Bandler, S.R.; Figueroa-Feliciano, E.; Iyomoto, N.; Kelley, R.L.; Kilbourne, C.A.; Murphy, K.D.; Porter, F.S.; Saab, T.; Sadleir, J.

2006-01-01

In a microcalorimeter that uses a transition-edge sensor to detect energy depositions, the small signal energy resolution improves with decreasing heat capacity. This improvement remains true up to the point where non-linear and saturation effects become significant. This happens when the energy deposition causes a significant change in the sensor resistance. Not only does the signal size become a non-linear function of the energy deposited, but also the noise becomes non-stationary over the duration of the pulse. Algorithms have been developed that can calculate the optimal performance given this non-linear behavior that typically requires significant processing and calibration work-both of which are impractical for space missions. We have investigated the relative importance of the various non-linear effects, with the hope that a computationally simple transformation can overcome the largest of the non-linear and non-stationary effects, producing a highly linear 'gain' for pulse-height versus energy, and close to the best energy resolution at all energies when using a Wiener filter

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Science.gov (United States)

Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe

2009-08-01

In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.

SYSTEMATIC SAMPLING FOR NON - LINEAR TREND IN MILK YIELD DATA

OpenAIRE

Tanuj Kumar Pandey; Vinod Kumar

2014-01-01

The present paper utilizes systematic sampling procedures for milk yield data exhibiting some non-linear trends. The best fitted mathematical forms of non-linear trend present in the milk yield data are obtained and the expressions of average variances of the estimators of population mean under simple random, usual systematic and modified systematic sampling procedures have been derived for populations showing non-linear trend. A comparative study is made among the three sampli...

Preisach hysteresis model for non-linear 2D heat diffusion

International Nuclear Information System (INIS)

Jancskar, Ildiko; Ivanyi, Amalia

2006-01-01

This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way

Scaling versus asymptotic scaling in the non-linear σ-model in 2D. Continuum version

International Nuclear Information System (INIS)

Flyvbjerg, H.

1990-01-01

The two-point function of the O(N)-symmetric non-linear σ-model in two dimensions is large-N expanded and renormalized, neglecting terms of O(1/N 2 ). At finite cut-off, universal, analytical expressions relate the magnetic susceptibility and the dressed mass to the bare coupling. Removing the cut-off, a similar relation gives the renormalized coupling as a function of the mass gap. In the weak-coupling limit these relations reproduce the results of renormalization group improved weak-coupling perturbation theory to two-loop order. The constant left unknown, when the renormalization group is integrated, is determined here. The approach to asymptotic scaling is studied for various values of N. (orig.)

Development of non-linear vibration analysis code for CANDU fuelling machine

International Nuclear Information System (INIS)

Murakami, Hajime; Hirai, Takeshi; Horikoshi, Kiyomi; Mizukoshi, Kaoru; Takenaka, Yasuo; Suzuki, Norio.

1988-01-01

This paper describes the development of a non-linear, dynamic analysis code for the CANDU 600 fuelling machine (F-M), which includes a number of non-linearities such as gap with or without Coulomb friction, special multi-linear spring connections, etc. The capabilities and features of the code and the mathematical treatment for the non-linearities are explained. The modeling and numerical methodology for the non-linearities employed in the code are verified experimentally. Finally, the simulation analyses for the full-scale F-M vibration testing are carried out, and the applicability of the code to such multi-degree of freedom systems as F-M is demonstrated. (author)

Non-Gaussian Stochastic Radiation Transfer in Finite Planar Media with Quadratic Scattering

International Nuclear Information System (INIS)

Sallah, M.

2016-01-01

The stochastic radiation transfer is considered in a participating planar finite continuously fluctuating medium characterized by non-Gaussian variability. The problem is considered for diffuse-reflecting boundaries with quadratic Rayleigh scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions that are represented by the probability-density function (PDF) of the solution process. RVT algorithm applies a simple integral transformation to the input stochastic process (the extinction function of the medium). This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the radiation transfer equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity, transmissivity and partial heat fluxes at the medium boundaries. Numerical results are represented graphically for different non-Gaussian probability distribution functions that compared with the corresponding Gaussian PDF.

TITUS: a general finite element system

International Nuclear Information System (INIS)

Bougrelle, P.

1983-01-01

TITUS is a general finite element structural analysis system which performs linear/non-linear, static/dynamic analyses of heat-transfer/thermo-mechanical problems. One of the major features of TITUS is that it was designed by engineers, to address engineers in an industrial environment. This has resulted in an easy to use system, with a high-level free-formatted problem oriented language, a large selection of pre- and post processors and sophisticated graphic capabilities. TITUS has many references in civil, mechanical and nuclear engineering applications. The TITUS system is available on various types of machines, from large mainframes to mini computers

The role of dendritic non-linearities in single neuron computation

Directory of Open Access Journals (Sweden)

Boris Gutkin

2014-05-01

Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.

Transition to turbulence for flows without linear criticality

International Nuclear Information System (INIS)

Nagata, Masato

2010-01-01

It is well known that plane Couette flow (PCF) and pipe flow (PF) are linearly stable against arbitrary three-dimensional perturbations at any finite Reynolds number, so that transitions from the basic laminar states, if they exist, must be abrupt. Due to this lack of linear criticality, weakly nonlinear analysis does not work in general and numerical approaches must be resorted to. It is only recently that non-trivial nonlinear states for these flows have been discovered numerically at finite Reynolds number as solutions bifurcating from infinity. The onset of turbulence in a subcritical transition is believed to be related to the appearance of steady/travelling wave states caused by disturbances of finite amplitude that take the flows out of the basin of attraction of the laminar state in phase space. In this paper, we introduce other flows that, in a similar way to PCF and PF, exhibit no linear critical point for the laminar states, namely flow in a square duct and sliding Couette flow in an annulus with a certain range of gap ratio. We shall show our recent numerical investigations on these flows where nonlinear travelling wave states are found for the first time by a homotopy approach. We believe that these states constitute the skeleton around which a time-dependent trajectory in the phase space is organized and help in understanding non-equilibrium turbulent processes.

Linear combination of forecasts with numerical adjustment via MINIMAX non-linear programming

Directory of Open Access Journals (Sweden)

Jairo Marlon Corrêa

2016-03-01

Full Text Available This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

Directory of Open Access Journals (Sweden)

Elias D. Nino-Ruiz

2018-03-01

Full Text Available In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

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.

Non-linear thermal and structural analysis of a typical spent fuel silo

International Nuclear Information System (INIS)

Alvarez, L.M.; Mancini, G.R.; Spina, O.A.F.; Sala, G.; Paglia, F.

1993-01-01

A numerical method for the non-linear structural analysis of a typical reinforced concrete spent fuel silo under thermal loads is proposed. The numerical time integration was performed by means of a time explicit axisymmetric finite-difference numerical operator. An analysis was made of influences by heat, viscoelasticity and cracking upon the concrete behaviour between concrete pouring stage and the first period of the silo's normal operation. The following parameters were considered for the heat generation and transmission process: Heat generated during the concrete's hardening stage, Solar radiation effects, Natural convection, Spent-fuel heat generation. For the modelling of the reinforced concrete behaviour, use was made of a simplified formulation of: Visco-elastic effects, Thermal cracking, Steel reinforcement. A comparison between some experimental temperature characteristic values obtained from the numerical integration process and empirical data obtained from a 1:1 scaled prototype was also carried out. (author)

The non-linear power spectrum of the Lyman alpha forest

International Nuclear Information System (INIS)

Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo; Cen, Renyue

2015-01-01

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate the comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula

Classical and quantum non-linear optical applications using the Mach-Zehnder interferometer

Science.gov (United States)

Prescod, Andru

Mach Zehnder (MZ) modulators are widely employed in a variety of applications, such as optical communications, optical imaging, metrology and encryption. In this dissertation, we explore two non-linear MZ applications; one classified as classical and one as quantum, in which the Mach Zehnder interferometer is used. In the first application, a classical non-linear application, we introduce and study a new electro-optic highly linear (e.g., >130 dB) modulator configuration. This modulator makes use of a phase modulator (PM) in one arm of the MZ interferometer (MZI) and a ring resonator (RR) located on the other arm. The modulator performance is obtained through the control of a combination of internal and external parameters. These parameters include the RR-coupling ratio (internal parameter); the RF power split ratio and the RF phase bias (external parameters). Results show the unique and superior features, such as high linearity (SFDR˜133 dB), modulation bandwidth extension (as much as 70%) over the previously proposed and demonstrated Resonator-Assisted Mach Zehnder (RAMZ) design. Furthermore the proposed electro-optic modulator of this dissertation also provides an inherent SFDR compensation capability, even in cases where a significant waveguide optical loss exists. This design also shows potential for increased flexibility, practicality and ease of use. In the second application, a quantum non-linear application, we experimentally demonstrate quantum optical coherence tomography (QOCT) using a type II non-linear crystal (periodically-poled potassium titanyl phosphate (KTiOPO4) or PPKTP). There have been several publications discussing the merits and disadvantages of QOCT compared to OCT and other imaging techniques. First, we discuss the issues and solutions for increasing the efficiency of the quantum entangled photons. Second, we use a free space QOCT experiment to generate a high flux of these quantum entangled photons in two orthogonal polarizations, by

Use of personal computers in performing a linear modal analysis of a large finite-element model

International Nuclear Information System (INIS)

Wagenblast, G.R.

1991-01-01

This paper presents the use of personal computers in performing a dynamic frequency analysis of a large (2,801 degrees of freedom) finite-element model. Large model linear time history dynamic evaluations of safety related structures were previously restricted to mainframe computers using direct integration analysis methods. This restriction was a result of the limited memory and speed of personal computers. With the advances in memory capacity and speed of the personal computers, large finite-element problems now can be solved in the office in a timely and cost effective manner. Presented in three sections, this paper describes the procedure used to perform the dynamic frequency analysis of the large (2,801 degrees of freedom) finite-element model on a personal computer. Section 2.0 describes the structure and the finite-element model that was developed to represent the structure for use in the dynamic evaluation. Section 3.0 addresses the hardware and software used to perform the evaluation and the optimization of the hardware and software operating configuration to minimize the time required to perform the analysis. Section 4.0 explains the analysis techniques used to reduce the problem to a size compatible with the hardware and software memory capacity and configuration

Non linear characterisation of optical components of a high power laser chain

International Nuclear Information System (INIS)

Santran, Stephane

2000-01-01

This work concerns the realisation of non linear properties measurement prototypes in glasses in the near infrared and in the visible range. The various devices are time resolved colinear pump probe experiments in which the non linear susceptibility is deduced by the probe beam intensity variations induced by the pump probe coupled in the material. The sensitivity of these experiments allows us to observe unexpected variations, greater than 30%, of several fused silica non linear indexes. As well, this allow us to analyse the origin of the promising oxide glasses non linearity for all optical applications and to understand an d measure non linear processes in the two photons photodiodes. Finally, an original structure for the non linear index measurement in non degenerated configuration by a probe pulse phase measurement approach with a Sagnac interferometer is demonstrated and analysed. (author) [fr

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.

Advanced non-linear flow-induced vibration and fretting-wear analysis capabilities

Energy Technology Data Exchange (ETDEWEB)

Toorani, M.; Pan, L.; Li, R.; Idvorian, N. [Babcock and Wilcox Canada Ltd., Cambridge, Ontario (Canada); Vincent, B.

2009-07-01

Fretting wear is a potentially significant degradation mechanism in nuclear steam generators and other shell and tube heat transfer equipment as well. This paper presents an overview of the recently developed code FIVDYNA which is used for the non-linear flow-induced vibration and fretting wear analysis for operating steam generators (OTSG and RSG) and shell-and-tube heat exchangers. FIVDYNA is a non-linear time-history Flow-Induced Vibration (FIV) analysis computer program that has been developed by Babcock and Wilcox Canada to advance the understanding of tube vibration and tube to tube-support interaction. In addition to the dynamic fluid induced forces the program takes into account other tube static forces due to axial and lateral tube preload and thermal interaction loads. The program is capable of predicting the location where the fretting wear is most likely to occur and its magnitude taking into account the support geometry including gaps. FIVDYNA uses the general purpose finite element computer code ABAQUS as its solver. Using ABAQUS gives the user the flexibility to add additional forces to the tube ranging from tube preloads and the support offsets to thermal loads. The forces currently being modeled in FIVDYNA are the random turbulence, steady drag force, fluid-elastic forces, support offset and pre-strain force (axial loads). This program models the vibration of tubes and calculates the structural dynamic characteristics, and interaction forces between the tube and the tube supports. These interaction forces are then used to calculate the work rate at the support and eventually the predicted depth of wear scar on the tube. A very good agreement is found with experiments and also other computer codes. (author)

Non-linear imaging condition to image fractures as non-welded interfaces

NARCIS (Netherlands)

Minato, S.; Ghose, R.

2014-01-01

Hydraulic properties of a fractured reservoir are often controlled by large fractures. In order to seismically detect and characterize them, a high-resolution imaging method is necessary. We apply a non-linear imaging condition to image fractures, considered as non-welded interfaces. We derive the

Non-perturbative Debye mass in finite-T QCD

CERN Document Server

Kajantie, Keijo; Peisa, J; Rajantie, A; Rummukainen, K; Shaposhnikov, Mikhail E

1997-01-01

Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.

Decoding Algorithms for Random Linear Network Codes

DEFF Research Database (Denmark)

Heide, Janus; Pedersen, Morten Videbæk; Fitzek, Frank

2011-01-01

We consider the problem of efficient decoding of a random linear code over a finite field. In particular we are interested in the case where the code is random, relatively sparse, and use the binary finite field as an example. The goal is to decode the data using fewer operations to potentially...... achieve a high coding throughput, and reduce energy consumption.We use an on-the-fly version of the Gauss-Jordan algorithm as a baseline, and provide several simple improvements to reduce the number of operations needed to perform decoding. Our tests show that the improvements can reduce the number...

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

Science.gov (United States)

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Linearization and efficiency enhancement of power amplifiers using digital predistortion

Energy Technology Data Exchange (ETDEWEB)

Safari, Nima

2008-07-01

Today, demand of higher spectral efficiency forces wireless communication systems to employ non-constant envelope modulation schemes such as Quadrature Amplitude Modulations (QAM), Code Division Multiple Access (CDMA) and Orthogonal Frequency-Division Multiplexing (OFDM) schemes. These modulation techniques generate signals with wide range of envelope fluctuation. This property makes these schemes sensitive to nonlinear amplifications. Nonlinearities introduced by Power Amplifiers (PA) cause both a distortion of the signal and an increased out of band output spectrum, which leads to a rise in adjacent channel interference. Thus, in order to ensure a high spectral efficiency and to avoid spectral regrowth, a linearization technique is required. Among all the linearization techniques, basedband Digital Predistortion (DPD) is one of the commonly used linearization techniques, which is characterized by robust operation, low implementation cost and high accuracy. In the first chapter of this thesis, an introduction on the motivation and necessity of using PA linearization techniques is presented. Digital Predistortion as a popular linearization technique aims to improve the efficiency and linearity of RF power amplifiers. The scope of the thesis, the goals to be achieved and the contributions are also discussed in chapter one. Chapter two, mainly discusses sample-by-sample updating algorithm in Digital Predistorters to adaptively linearize the PA memoryless nonlinearities. Look-up Table (LUT) and polynomial approaches are studied and implemented in Hardware using a test-bed provided by Nera Research. The experimental results together with a discussion are then given. A new DPD algorithm based on block estimation is proposed in chapter three to avoid realtime signal processing, reduce the complexity and also avoid the bad performance during the slow adaptation of adaptive the Adjacent Channel Power Ratio (ACPR) and the Error Vector Magnitude (EVM) requirements. In

The role of different linear and non-linear channels of relaxation in scintillator non-proportionality

Energy Technology Data Exchange (ETDEWEB)

Bizarri, G.; Moses, W.W. [Lawrence Berkeley Laboratory, Berkeley, CA 94720-8119 (United States); Singh, J. [Faculty of EHS, B-41, Charles Darwin University, Darwin NT 0909 (Australia); Vasil' ev, A.N., E-mail: anvasiliev@rambler.r [Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation); Williams, R.T. [Department of Physics, Wake Forest University, Winston-Salem, NC 27109 (United States)

2009-12-15

The non-proportional dependence of a scintillator's light yield on primary particle energy is believed to be influenced crucially by the interplay of non-linear kinetic terms in the radiative and non-radiative decay of excitations versus locally deposited excitation density. A calculation of energy deposition, -dE/dx, along the electron track for NaI is presented for an energy range from several electron-volt to 1 MeV. Such results can be used to specify an initial excitation distribution, if diffusion is neglected. An exactly solvable two-channel (exciton and hole(electron)) model containing 1st and 2nd order kinetic terms is constructed and used to illustrate important features seen in non-proportional light-yield curves, including a dependence on pulse shaping (detection gate width).

The role of different linear and non-linear channels of relaxation in scintillator non-proportionality

International Nuclear Information System (INIS)

Bizarri, G.; Moses, W.W.; Singh, J.; Vasil'ev, A.N.; Williams, R.T.

2009-01-01

The non-proportional dependence of a scintillator's light yield on primary particle energy is believed to be influenced crucially by the interplay of non-linear kinetic terms in the radiative and non-radiative decay of excitations versus locally deposited excitation density. A calculation of energy deposition, -dE/dx, along the electron track for NaI is presented for an energy range from several electron-volt to 1 MeV. Such results can be used to specify an initial excitation distribution, if diffusion is neglected. An exactly solvable two-channel (exciton and hole(electron)) model containing 1st and 2nd order kinetic terms is constructed and used to illustrate important features seen in non-proportional light-yield curves, including a dependence on pulse shaping (detection gate width).

Linear and non-linear calculations of the hose instability in the ion-focused regime

International Nuclear Information System (INIS)

Buchanan, H.L.

1982-01-01

A simple model is adopted to study the hose instability of an intense relativistic electron beam in a partially neutralized, low density ion channel (ion focused regime). Equations of motion for the beam and the channel are derived and linearized to obtain an approximate dispersion relation. The non-linear equations of motion are then solved numerically and the results compared to linearized data

Effect of analysis parameters on non-linear implicit finite element analysis of marine corroded steel plate

Science.gov (United States)

Islam, Muhammad Rabiul; Sakib-Ul-Alam, Md.; Nazat, Kazi Kaarima; Hassan, M. Munir

2017-12-01

FEA results greatly depend on analysis parameters. MSC NASTRAN nonlinear implicit analysis code has been used in large deformation finite element analysis of pitted marine SM490A steel rectangular plate. The effect of two types actual pit shape on parameters of integrity of structure has been analyzed. For 3-D modeling, a proposed method for simulation of pitted surface by probabilistic corrosion model has been used. The result has been verified with the empirical formula proposed by finite element analysis of steel surface generated with different pitted data where analyses have been carried out by the code of LS-DYNA 971. In the both solver, an elasto-plastic material has been used where an arbitrary stress versus strain curve can be defined. In the later one, the material model is based on the J2 flow theory with isotropic hardening where a radial return algorithm is used. The comparison shows good agreement between the two results which ensures successful simulation with comparatively less energy and time.

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

Science.gov (United States)

Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.

2018-06-01

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

Electron non-linearities in Langmuir waves with application to beat-wave experiments

International Nuclear Information System (INIS)

Bell, A.R.; Gibbon, P.

1988-01-01

Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)

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.

On the nucleon-nucleon potential obtained from non-linear coupling

International Nuclear Information System (INIS)

El Ghabaty, S.S.

1975-07-01

The static limit of a pseudoscalar symmetric meson theory of nuclear forces is examined. The Born-Oppenheimer potential is determined for the case of two very heavy nucleons exchanging pseudoscalar isovector pions with non-linear coupling. It is found that the non-linear terms induced by the γ 5 coupling are cancelled by the additional pion-nucleon coupling of the non-linear sigma model. The nucleon-nucleon potential thus obtained is the same as the Yukava potential except for strength at different separations between the two nucleons

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.

On the stability of non-linear systems

International Nuclear Information System (INIS)

Guelman, M.

1968-09-01

A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr

Finite Element Study on Continuous Rotating versus Reciprocating Nickel-Titanium Instruments.

Science.gov (United States)

El-Anwar, Mohamed I; Yousief, Salah A; Kataia, Engy M; El-Wahab, Tarek M Abd

2016-01-01

In the present study, GTX and ProTaper as continuous rotating endodontic files were numerically compared with WaveOne reciprocating file using finite element analysis, aiming at having a low cost, accurate/trustworthy comparison as well as finding out the effect of instrument design and manufacturing material on its lifespan. Two 3D finite element models were especially prepared for this comparison. Commercial engineering CAD/CAM package was used to model full detailed flute geometries of the instruments. Multi-linear materials were defined in analysis by using real strain-stress data of NiTi and M-Wire. Non-linear static analysis was performed to simulate the instrument inside root canal at a 45° angle in the apical portion and subjected to 0.3 N.cm torsion. The three simulations in this study showed that M-Wire is slightly more resistant to failure than conventional NiTi. On the other hand, both materials are fairly similar in case of severe locking conditions. For the same instrument geometry, M-Wire instruments may have longer lifespan than the conventional NiTi ones. In case of severe locking conditions both materials will fail similarly. Larger cross sectional area (function of instrument taper) resisted better to failure than the smaller ones, while the cross sectional shape and its cutting angles could affect instrument cutting efficiency.

Non-linear thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM

Energy Technology Data Exchange (ETDEWEB)

Del Coz Diaz, J.J.; Suarez Sierra, J.L.; Penuelas Sanchez, I. [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain); Garcia Nieto, P.J. [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)

2008-06-15

The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed. (author)

Some aspects of non-linear semi-groups

International Nuclear Information System (INIS)

Plant, A.T.

1976-01-01

Some simpler theorems in the theory of non-linear semi-groups of non-reflexive Banach spaces are proved, with the intention to introduce the reader to this active field of research. Flow invariance, in particular for Lipschitz generators, and contraction semi-groups are discussed in some detail. (author)

Non-linear simulations of ELMs in ASDEX upgrade

Energy Technology Data Exchange (ETDEWEB)

Lessig, Alexander; Hoelzl, Matthias; Orain, Francois; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstrasse 2, 85748 Garching (Germany); Becoulet, Marina; Huysmans, Guido [CEA-IRFM, Cadarache, 13108 Saint-Paul-Lez-Durance (France); Collaboration: the ASDEX Upgrade Team

2016-07-01

Large edge localized modes (ELMs) are a severe concern for the operation of future tokamak devices like ITER or DEMO due to the high transient heat loads induced on divertor targets and wall structures. It is therefore important to study ELMs both theoretically and experimentally in order to obtain a comprehensive understanding of the underlying mechanisms which is necessary for the prediction of ELM properties and the design of ELM mitigation systems. Using the non-linear MHD code JOREK, we have performed first simulations of full ELM crashes in ASDEX Upgrade, taking into account a large number of toroidal Fourier harmonics. The evolution of the toroidal mode spectrum has been investigated. In particular, we confirm the previously observed non-linear drive of linearly sub-dominant low-n components in the early non-linear phase of the ELM crash. Preliminary comparisons of the simulations with experimental observations regarding heat and particle losses, pedestal evolution and heat deposition patterns are shown. On the long run we aim at code validation as well as an improved understanding of the ELM dynamics and possibly a better characterization of different ELM types.

Non-local quasi-linear parabolic equations

International Nuclear Information System (INIS)

Amann, H

2005-01-01

This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

International Nuclear Information System (INIS)

Voznyuk, I; Litman, A; Tortel, H

2015-01-01

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database. (paper)

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

International Nuclear Information System (INIS)

Das, R.N.

1980-01-01

The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)

Non-linear effects in the Snoek relaxation of Nb-O

International Nuclear Information System (INIS)

Hermida, E.B.; Povolo, F.

1996-01-01