Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft

Directory of Open Access Journals (Sweden)

Yuma Fukushima

2015-01-01

Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.

Artificial dissipation models applied to Euler equations for analysis of supersonic flow of helium gas around a geometric configurations ramp and diffusor type

Energy Technology Data Exchange (ETDEWEB)

Rocha, Jussiê S., E-mail: jussie.soares@ifpi.edu.br [Instituto Federal do Piauí (IFPI), Valença, PI (Brazil); Maciel, Edisson Sávio de Góes, E-mail: edissonsavio@yahoo.com.br [Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos, SP (Brazil); Lira, Carlos A.B.O., E-mail: cabol@ufpe.edu.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil); Sousa, Pedro A.S.; Neto, Raimundo N.C., E-mail: augusto.96pedro@gmail.com, E-mail: r.correia17@hotmail.com [Instituto Federal do Piauí (IFPI), Teresina, PI (Brazil)

2017-07-01

Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added security. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in using the DISSIPA2D{sub E}ULER code, to solve the Euler equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic flow along a ramp and diffusor configurations is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipation model linear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is obtain computational tools for flow analysis through the study the cited dissipation model and describe their characteristics in relation to the overall quality of the solution, as well as obtain preliminary results for the development of computational tools of dynamic analysis of helium gas flow in gas-cooled reactors. (author)

Refinement of RAIM via Implementation of Implicit Euler Method

Energy Technology Data Exchange (ETDEWEB)

Lee, Yoonhee; Kim, Han-Chul [Korea Institute of Nuclear and Safety, Daejeon (Korea, Republic of)

2016-10-15

The first approach is a mechanistic approach which is used in LIRIC in which more than 200 reactions are modeled in detail. This approach enables to perform the detailed analysis. However, it requires huge computation burden. The other approach is a simplified model approach which is used in the IMOD, ASTEC/IODE, and etc. Recently, KINS has developed RAIM (Radio-Active Iodine chemistry Model) based on the simplified model approach. Since the numerical analysis module in RAIM is based on the explicit Euler method, there are major issues on the stability of the module. Therefore, implementation of a stable numerical method becomes essential. In this study, RAIM is refined via implementation of implicit Euler method in which the Newton method is used to find the solutions at each time step. The refined RAIM is tested by comparing to RAIM based on the explicit Euler method. In this paper, RAIM was refined by implementing the implicit Euler method. At each time step of the method in the refined RAIM, the reaction kinetics equations are solved by the Newton method in which elements of the Jacobian matrix are expressed analytically. With the results of OECD-BIP P10T2 test, the refined RAIM was compared to RAIM with the explicit Euler method. The refined RAIM shows better agreement with the experimental data than those from the explicit Euler method. For the rapid change of pH during the experiment, the refined RAIM gives more realistic changes in the concentrations of chemical species than those from the explicit Euler method. In addition, in terms of computing time, the refined RAIM shows comparable computing time to that with explicit Euler method. These comparisons are attributed to ⁓10 times larger time step size used in the implicit Euler method, even though computation burden at each time step in the refined RAIM is much higher than that of the explicit Euler method. Compared to the experimental data, the refined RAIM still shows discrepancy, which are attributed

Refinement of RAIM via Implementation of Implicit Euler Method

International Nuclear Information System (INIS)

Lee, Yoonhee; Kim, Han-Chul

2016-01-01

The first approach is a mechanistic approach which is used in LIRIC in which more than 200 reactions are modeled in detail. This approach enables to perform the detailed analysis. However, it requires huge computation burden. The other approach is a simplified model approach which is used in the IMOD, ASTEC/IODE, and etc. Recently, KINS has developed RAIM (Radio-Active Iodine chemistry Model) based on the simplified model approach. Since the numerical analysis module in RAIM is based on the explicit Euler method, there are major issues on the stability of the module. Therefore, implementation of a stable numerical method becomes essential. In this study, RAIM is refined via implementation of implicit Euler method in which the Newton method is used to find the solutions at each time step. The refined RAIM is tested by comparing to RAIM based on the explicit Euler method. In this paper, RAIM was refined by implementing the implicit Euler method. At each time step of the method in the refined RAIM, the reaction kinetics equations are solved by the Newton method in which elements of the Jacobian matrix are expressed analytically. With the results of OECD-BIP P10T2 test, the refined RAIM was compared to RAIM with the explicit Euler method. The refined RAIM shows better agreement with the experimental data than those from the explicit Euler method. For the rapid change of pH during the experiment, the refined RAIM gives more realistic changes in the concentrations of chemical species than those from the explicit Euler method. In addition, in terms of computing time, the refined RAIM shows comparable computing time to that with explicit Euler method. These comparisons are attributed to ⁓10 times larger time step size used in the implicit Euler method, even though computation burden at each time step in the refined RAIM is much higher than that of the explicit Euler method. Compared to the experimental data, the refined RAIM still shows discrepancy, which are attributed

Strong-stability-preserving additive linear multistep methods

KAUST Repository

Hadjimichael, Yiannis; Ketcheson, David I.

2018-01-01

The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed

Three dimensional steady subsonic Euler flows in bounded nozzles

Science.gov (United States)

Chen, Chao; Xie, Chunjing

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.

Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

Directory of Open Access Journals (Sweden)

Ma Yanfeng

2016-10-01

Full Text Available An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.

Chaotic dynamics of flexible Euler-Bernoulli beams

Energy Technology Data Exchange (ETDEWEB)

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl [Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland and Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw (Poland); Krysko, A. V., E-mail: anton.krysko@gmail.com [Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation); Kutepov, I. E., E-mail: iekutepov@gmail.com; Zagniboroda, N. A., E-mail: tssrat@mail.ru; Dobriyan, V., E-mail: Dobriy88@yandex.ru; Krysko, V. A., E-mail: tak@san.ru [Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation)

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

An algebraic method to develop well-posed PML models Absorbing layers, perfectly matched layers, linearized Euler equations

International Nuclear Information System (INIS)

Rahmouni, Adib N.

2004-01-01

In 1994, Berenger [Journal of Computational Physics 114 (1994) 185] proposed a new layer method: perfectly matched layer, PML, for electromagnetism. This new method is based on the truncation of the computational domain by a layer which absorbs waves regardless of their frequency and angle of incidence. Unfortunately, the technique proposed by Berenger (loc. cit.) leads to a system which has lost the most important properties of the original one: strong hyperbolicity and symmetry. We present in this paper an algebraic technique leading to well-known PML model [IEEE Transactions on Antennas and Propagation 44 (1996) 1630] for the linearized Euler equations, strongly well-posed, preserving the advantages of the initial method, and retaining symmetry. The technique proposed in this paper can be extended to various hyperbolic problems

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Science.gov (United States)

Batina, John T.

1990-01-01

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Numerical solution of Euler's equation by perturbed functionals

Science.gov (United States)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Euler systems (AM-147)

CERN Document Server

Rubin, Karl

2014-01-01

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic G

Observable algebras for the rational and trigonometric Euler-Calogero-Moser Models

International Nuclear Information System (INIS)

Avan, J.; Billey, E.

1995-01-01

We construct polynomial Poisson algebras of observables for the classical Euler-Calogero-Moser (ECM) models. Their structure connects them to flavour-indexed non-linear W ∞ algebras, albeit with qualitative differences. The conserved Hamiltonians and symmetry algebras derived in a previous work are subsets of these algebra. We define their linear, N →∞ limits, realizing W ∞ type algebras coupled to current algebras. ((orig.))

Drawing Euler Diagrams with Circles: The Theory of Piercings.

Science.gov (United States)

Stapleton, Gem; Leishi Zhang; Howse, John; Rodgers, Peter

2011-07-01

Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Euler diagram, it is computationally expensive to generate the diagram. Moreover, the generated diagrams represent sets by polygons, sometimes with quite irregular shapes that make the diagrams less comprehensible. In this paper, we address these two issues by developing the theory of piercings, where we define single piercing curves and double piercing curves. We prove that if a diagram can be built inductively by successively adding piercing curves under certain constraints, then it can be drawn with circles, which are more esthetically pleasing than arbitrary polygons. The theory of piercings is developed at the abstract level. In addition, we present a Java implementation that, given an inductively pierced abstract description, generates an Euler diagram consisting only of circles within polynomial time.

Stability analysis of the Backward Euler time discretization for the pin-resolved transport transient reactor calculation

International Nuclear Information System (INIS)

Zhu, Ang; Xu, Yunlin; Downar, Thomas

2016-01-01

Three-dimensional, full core transport modeling with pin-resolved detail for reactor dynamic simulation is important for some multi-physics reactor applications. However, it can be computationally intensive due to the difficulty in maintaining accuracy while minimizing the number of time steps. A recently proposed Transient Multi-Level (TML) methodology overcomes this difficulty by use multi-level transient solvers to capture the physical phenomenal in different time domains and thus maximize the numerical accuracy and computational efficiency. One major problem with the TML method is the negative flux/precursor number density generated using large time steps for the MOC solver, which is due to the Backward Euler discretization scheme. In this paper, the stability issue of Backward Euler discretization is first investigated using the Point Kinetics Equations (PKEs), and the predicted maximum allowed time step for SPERT test 60 case is shown to be less than 10 ms. To overcome this difficulty, linear and exponential transformations are investigated using the PKEs. The linear transformation is shown to increase the maximum time step by a factor of 2, and the exponential transformation is shown to increase the maximum time step by a factor of 5, as well as provide unconditionally stability above a specified threshold. The two sets of transformations are then applied to TML scheme in the MPACT code, and the numerical results presented show good agreement for standard, linear transformed, and exponential transformed maximum time step between the PKEs model and the MPACT whole core transport solution for three different cases, including a pin cell case, a 3D SPERT assembly case and a row of assemblies (“striped assembly case”) from the SPERT model. Finally, the successful whole transient execution of the stripe assembly case shows the ability of the exponential transformation method to use 10 ms and 20 ms time steps, which all failed using the standard method.

Artificial dissipation models applied to Euler equations for analysis of supersonic flow of helium gas around a geometric configurations ramp and diffusor type

International Nuclear Information System (INIS)

Rocha, Jussiê S.; Maciel, Edisson Sávio de Góes; Lira, Carlos A.B.O.; Sousa, Pedro A.S.; Neto, Raimundo N.C.

2017-01-01

Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added security. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in using the DISSIPA2D E ULER code, to solve the Euler equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic flow along a ramp and diffusor configurations is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipation model linear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is obtain computational tools for flow analysis through the study the cited dissipation model and describe their characteristics in relation to the overall quality of the solution, as well as obtain preliminary results for the development of computational tools of dynamic analysis of helium gas flow in gas-cooled reactors. (author)

ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.

On Euler's problem

International Nuclear Information System (INIS)

Egorov, Yurii V

2013-01-01

We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.

The most precise computations using Euler's method in standard floating-point arithmetic applied to modelling of biological systems.

Science.gov (United States)

Kalinina, Elizabeth A

2013-08-01

The explicit Euler's method is known to be very easy and effective in implementation for many applications. This article extends results previously obtained for the systems of linear differential equations with constant coefficients to arbitrary systems of ordinary differential equations. Optimal (providing minimum total error) step size is calculated at each step of Euler's method. Several examples of solving stiff systems are included. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Equivariant analogues of the Euler characteristic and Macdonald type equations

Science.gov (United States)

Gusein-Zade, S. M.

2017-02-01

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representations of the group or as an element of the Burnside ring of the group. From physics came the notion of the orbifold Euler characteristic, and this was generalized to orbifold Euler characteristics of higher orders. The main property of the Euler characteristic (defined in terms of the cohomology with compact support) is its additivity. On some classes of spaces there are additive invariants other than the Euler characteristic, and they can be regarded as generalized Euler characteristics. For example, the class of a variety in the Grothendieck ring of complex quasi-projective varieties is a universal additive invariant on the class of complex quasi-projective varieties. Generalized analogues of the Euler characteristic can also be defined in the equivariant setting. There is a simple formula — the Macdonald equation — for the generating series of the Euler characteristics of the symmetric powers of a space: it is equal to the series (1-t)-1=1+t+t^2+\\cdots independent of the space, raised to a power equal to the Euler characteristic of the space itself. Equations of a similar kind for other invariants (`equivariant and generalized Euler characteristics') are called Macdonald type equations. This survey discusses different versions of the Euler characteristic in the equivariant setting and describes some of their properties and Macdonald type equations. Bibliography: 59 titles.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

KAUST Repository

De Pascalis, Riccardo

2010-07-22

Euler\\'s celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young\\'s modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson\\'s ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

International Nuclear Information System (INIS)

Bokhari, Ashfaque H.; Zaman, F. D.; Mahomed, F. M.

2010-01-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

Numerical computation of linear instability of detonations

Science.gov (United States)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

Euler and His Contribution Number Theory

Science.gov (United States)

Len, Amy; Scott, Paul

2004-01-01

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

Diffusive limits for linear transport equations

International Nuclear Information System (INIS)

Pomraning, G.C.

1992-01-01

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

EULER - A Real Virtual Library for Mathematics

CERN Document Server

Jost, Michael

2004-01-01

The EULER project completed its work in November 2002. It forms the last part of a very successful project in the specialized but global discipline of mathematics. After a successful RTD project had created the technology, a take-up project has effectively exploited it to the point where its future is assured through a not-for-profit consortium. EULER is a European based, world class, real virtual library for mathematics with up-to-date technological solutions, well accepted by users. In particular, EULER provides a world reference and delivery service, transparent to the end user and offering full coverage of the mathematics literature world-wide, including bibliographic data, peer reviews and/or abstracts, indexing, classification and search, transparent access to library services, co-operation with commercial information providers (publishers, bookstores). The EULER services provide a gateway to the electronic catalogues and repositories of participating institutions, while the latter retain complete respo...

Non-linear belt transient analysis. A hybrid model for numerical belt conveyor simulation

Energy Technology Data Exchange (ETDEWEB)

Harrison, A. [Scientific Solutions, Inc., Aurora, CO (United States)

2008-07-01

Frictional and rolling losses along a running conveyor are discussed due to their important influence on wave propagation during starting and stopping. Hybrid friction models allow belt rubber losses and material flexing to be included in the initial tension calculations prior to any dynamic analysis. Once running tensions are defined, a numerical integration method using non-linear stiffness gradients is used to generate transient forces during starting and stopping. A modified Euler integration technique is used to simulate the entire starting and stopping cycle in less than 0.1 seconds. The procedure enables a faster scrutiny of unforeseen conveyor design issues such as low belt tension zones and high forces at drives. (orig.)

Analogues of Euler and Poisson Summation Formulae

Indian Academy of Sciences (India)

... f ( n ) have been obtained in a unified manner, where (()) is a periodic complex sequence; () is the divisor function and () is a sufficiently smooth function on [, ]. We also state a generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables.

Euler Strut: A Mechanical Analogy for Dynamics in the Vicinity of a Critical Point

Science.gov (United States)

Bobnar, Jaka; Susman, Katarina; Parsegian, V. Adrian; Rand, Peter R.; Cepic, Mojca; Podgornik, Rudolf

2011-01-01

An anchored elastic filament (Euler strut) under an external point load applied to its free end is a simple model for a second-order phase transition. In the static case, a load greater than the critical load causes a Euler buckling instability, leading to a change in the filament's shape. The analysis of filament dynamics with an external point…

Variational problems with fractional derivatives: Euler-Lagrange equations

International Nuclear Information System (INIS)

Atanackovic, T M; Konjik, S; Pilipovic, S

2008-01-01

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense

Development of Euler's ideas at the Moscow State Regional University

Science.gov (United States)

Vysikaylo, P. I.; Belyaev, V. V.

2018-03-01

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

Analysis of A Uniform Bernoulli – Euler Beam on Winkler Foundation ...

African Journals Online (AJOL)

ADOWIE PERE

2018-03-09

Mar 9, 2018 ... method to analyze Winkler foundation subjected to a harmonic moving load on a uniform Bernoulli – Euler Beam. MATLAB software was used to implement the Newmark time integration method to ... A lot of engineering structures under moving loads .... Because numerical procedure produce stability issue,.

Combinatorial Aspects of the Generalized Euler's Totient

Directory of Open Access Journals (Sweden)

Nittiya Pabhapote

2010-01-01

Full Text Available A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.

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...

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

International Nuclear Information System (INIS)

Greenough, J.A.; Rider, W.J.

2004-01-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the 'peak' shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

Science.gov (United States)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are

Conservation of energy for the Euler-Korteweg equations

KAUST Repository

Dębiec, Tomasz

2017-12-30

In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The result applies to the system of Quantum Hydrodynamics.

Conservation of energy for the Euler-Korteweg equations

KAUST Repository

Dębiec, Tomasz; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka; Tzavaras, Athanasios

2017-01-01

In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The result applies to the system of Quantum Hydrodynamics.

Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations

Science.gov (United States)

Agrawal, S.; Barnett, R. M.; Robinson, B. A.

1991-01-01

A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.

Euler European Libraries and Electronic Resources in Mathematical Sciences

CERN Document Server

The Euler Project. Karlsruhe

The European Libraries and Electronic Resources (EULER) Project in Mathematical Sciences provides the EulerService site for searching out "mathematical resources such as books, pre-prints, web-pages, abstracts, proceedings, serials, technical reports preprints) and NetLab (for Internet resources), this outstanding engine is capable of simple, full, and refined searches. It also offers a browse option, which responds to entries in the author, keyword, and title fields. Further information about the Project is provided at the EULER homepage.

On Euler's problem

Energy Technology Data Exchange (ETDEWEB)

Egorov, Yurii V [Institute de Mathematique de Toulouse, Toulouse (France)

2013-04-30

We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.

Leonhard Euler and the mechanics of rigid bodies

Science.gov (United States)

Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J.

2017-01-01

In this work we present the original ideas and the construction of the rigid bodies theory realised by Leonhard Euler between 1738 and 1775. The number of treatises written by Euler on this subject is enormous, including the most notorious Scientia Navalis (1749), Decouverte d’un noveau principe de mecanique (1752), Du mouvement de rotation des corps solides autour d’un axe variable (1765), Theoria motus corporum solidorum seu rigidorum (1765) and Nova methodus motu corporum rigidorum determinandi (1776), in which he developed the ideas of the instantaneous rotation axis, the so-called Euler equations and angles, the components of what is now known as the inertia tensor, the principal axes of inertia, and, finally, the generalisation of the translation and rotation movement equations for any system. Euler, the man who ‘put most of mechanics into its modern form’ (Truesdell 1968 Essays in the History of Mechanics (Berlin: Springer) p 106).

Remarks on Heisenberg-Euler-type electrodynamics

Science.gov (United States)

Kruglov, S. I.

2017-05-01

We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb’s law at r →∞ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at r →∞. Corrections to the Reissner-Nordström solution are obtained.

Dr. Euler's fabulous formula Cures many mathematical ills

CERN Document Server

Nahin, Paul J

2006-01-01

I used to think math was no fun'Cause I couldn't see how it was doneNow Euler's my heroFor I now see why zeroEquals e[pi] i+1--Paul Nahin, electrical engineer In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the seque

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

Science.gov (United States)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Euler-Poincare reduction for discrete field theories

International Nuclear Information System (INIS)

Vankerschaver, Joris

2007-01-01

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

Determination of regional Euler pole parameters for Eastern Austria

Science.gov (United States)

Umnig, Elke; Weber, Robert; Schartner, Matthias; Brueckl, Ewald

2017-04-01

The horizontal motion of lithospheric plates can be described as rotations around a rotation axes through the Earth's center. The two possible points where this axes intersects the surface of the Earth are called Euler poles. The rotation is expressed by the Euler parameters in terms of angular velocities together with the latitude and longitude of the Euler pole. Euler parameters were calculated from GPS data for a study area in Eastern Austria. The observation network is located along the Mur-Mürz Valley and the Vienna Basin. This zone is part of the Vienna Transfer Fault, which is the major fault system between the Eastern Alps and the Carpathians. The project ALPAACT (seismological and geodetic monitoring of ALpine-PAnnonian ACtive Tectonics) investigated intra plate tectonic movements within the Austrian part in order to estimate the seismic hazard. Precise site coordinate time series established from processing 5 years of GPS observations are available for the regional network spanning the years from 2010.0 to 2015.0. Station velocities with respect to the global reference frame ITRF2008 have been computed for 23 sites. The common Euler vector was estimated on base of a subset of reliable site velocities, for stations directly located within the area of interest. In a further step a geokinematic interpretation shall be carried out. Therefore site motions with respect to the Eurasian Plate are requested. To obtain this motion field different variants are conceivable. In a simple approach the mean ITRF2008 velocity of IGS site GRAZ can be adopted as Eurasian rotational velocity. An improved alternative is to calculate site-specific velocity differences between the Euler rotation and the individual site velocities. In this poster presentation the Euler parameters, the residual motion field as well as first geokinematic interpretation results are presented.

Symmetries of the Euler compressible flow equations for general equation of state

Energy Technology Data Exchange (ETDEWEB)

Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-10-15

The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

Science.gov (United States)

Micallef, Luana; Rodgers, Peter

2014-01-01

Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

Directory of Open Access Journals (Sweden)

Luana Micallef

Full Text Available Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

Stability properties of the Euler-Korteweg system with nonmonotone pressures

KAUST Repository

Giesselmann, Jan

2016-12-21

We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy to show that solutions of Euler-Korteweg with convex energy converge to solutions of the Euler system in the vanishing capillarity limit, as long as the latter admits sufficiently regular strong solutions.

Leonhard Euler's Wave Theory of Light

DEFF Research Database (Denmark)

Pedersen, Kurt Møller

2008-01-01

is wrong. Most of his mathematical arguments were, however, guesswork without any solid physical reasoning. Guesswork is not always a bad thing in physics if it leads to new experiments or makes the theory coherent with other theories. And Euler tried to find such experiments. He saw the construction......Euler's wave theory of light developed from a mere description of this notion based on an analogy between sound and light to a more and more mathematical elaboration on that notion. He was very successful in predicting the shape of achromatic lenses based on a new dispersion law that we now know...

Euler numbers of four-dimensional rotating black holes with the Euclidean signature

International Nuclear Information System (INIS)

Ma Zhengze

2003-01-01

For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number to which it is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2, which is in accordance with its topology

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R

Directory of Open Access Journals (Sweden)

Boutros Paul C

2011-01-01

Full Text Available Abstract Background Visualization of orthogonal (disjoint or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. Results The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. Conclusions The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R.

Science.gov (United States)

Chen, Hanbo; Boutros, Paul C

2011-01-26

Visualization of orthogonal (disjoint) or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.

Euler polynomials and identities for non-commutative operators

Science.gov (United States)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

Numerical solutions of the linearized Euler equations for unsteady vortical flows around lifting airfoils

Science.gov (United States)

Scott, James R.; Atassi, Hafiz M.

1990-01-01

A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.

Additivity for parametrized topological Euler characteristic and Reidemeister torsion

OpenAIRE

Badzioch, Bernard; Dorabiala, Wojciech

2005-01-01

Dwyer, Weiss, and Williams have recently defined the notions of parametrized topological Euler characteristic and parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and Reidemeister torsion of finite CW-complexes.

Euler-Lagrange Equations of Networks with Higher-Order Elements

Directory of Open Access Journals (Sweden)

Z. Biolek

2017-06-01

Full Text Available The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (α, β elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.

An experiment for determining the Euler load by direct computation

Science.gov (United States)

Thurston, Gaylen A.; Stein, Peter A.

1986-01-01

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length, therefore the experimental data allows a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross-section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.

3D GIS spatial operation based on extended Euler operators

Science.gov (United States)

Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing

2008-10-01

The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.

Euler Polynomials and Identities for Non-Commutative Operators

OpenAIRE

De Angelis, V.; Vignat, C.

2015-01-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...

An efficient iteration strategy for the solution of the Euler equations

Science.gov (United States)

Walters, R. W.; Dwoyer, D. L.

1985-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Euler's pioneering equation the most beautiful theorem in mathematics

CERN Document Server

Wilson, Robin

2018-01-01

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

Nilakantha, Euler and 1t

Indian Academy of Sciences (India)

It is not hard to show that the series converges, for by com- bining pairs of terms it can be ..... not escape Euler's attention-but then few things did!) We consider the function ... the proof. In particular there is no such thing as an unrig- orous proof.

Iterative methods for compressible Navier-Stokes and Euler equations

Energy Technology Data Exchange (ETDEWEB)

Tang, W.P.; Forsyth, P.A.

1996-12-31

This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.

Euler's fluid equations: Optimal control vs optimization

International Nuclear Information System (INIS)

Holm, Darryl D.

2009-01-01

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.

Free vibration of Euler and Timoshenko nanobeams using boundary characteristic orthogonal polynomials

Science.gov (United States)

Behera, Laxmi; Chakraverty, S.

2014-03-01

Vibration analysis of nonlocal nanobeams based on Euler-Bernoulli and Timoshenko beam theories is considered. Nonlocal nanobeams are important in the bending, buckling and vibration analyses of beam-like elements in microelectromechanical or nanoelectromechanical devices. Expressions for free vibration of Euler-Bernoulli and Timoshenko nanobeams are established within the framework of Eringen's nonlocal elasticity theory. The problem has been solved previously using finite element method, Chebyshev polynomials in Rayleigh-Ritz method and using other numerical methods. In this study, numerical results for free vibration of nanobeams have been presented using simple polynomials and orthonormal polynomials in the Rayleigh-Ritz method. The advantage of the method is that one can easily handle the specified boundary conditions at the edges. To validate the present analysis, a comparison study is carried out with the results of the existing literature. The proposed method is also validated by convergence studies. Frequency parameters are found for different scaling effect parameters and boundary conditions. The study highlights that small scale effects considerably influence the free vibration of nanobeams. Nonlocal frequency parameters of nanobeams are smaller when compared to the corresponding local ones. Deflection shapes of nonlocal clamped Euler-Bernoulli nanobeams are also incorporated for different scaling effect parameters, which are affected by the small scale effect. Obtained numerical solutions provide a better representation of the vibration behavior of short and stubby micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant.

Local existence of solutions to the Euler-Poisson system, including densities without compact support

Science.gov (United States)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

On the Euler Function of the Catalan Numbers

Science.gov (United States)

2012-02-26

ON THE EULER FUNCTION OF THE CATALAN NUMBERS FLORIAN LUCA AND PANTELIMON STĂNICĂ Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r...where r is a fixed rational number , Ck is the kth Catalan number and φ is the Euler function. We note that the number r = 4 is special for this...observation concerning φ(Cn+1)/φ(Cn) For a positive integer n, let (1) Cn = 1 n+ 1 ( 2n n ) be the n-th Catalan number . For a positive integer m we put φ(m) for

A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams

Science.gov (United States)

Andreaus, Ugo; Spagnuolo, Mario; Lekszycki, Tomasz; Eugster, Simon R.

2018-04-01

We present a finite element discrete model for pantographic lattices, based on a continuous Euler-Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler-Bernoulli beam is described by using nonlinear interpolation functions, a Green-Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler-Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures.

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

Science.gov (United States)

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

Stability of numerical method for semi-linear stochastic pantograph differential equations

Directory of Open Access Journals (Sweden)

Yu Zhang

2016-01-01

Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

Bernoulli and Euler Numbers

Directory of Open Access Journals (Sweden)

Dae San Kim

2012-01-01

Full Text Available We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x∈ℚ[x]∣deg p(x≤n} be the (n+1-dimensional vector space over ℚ. Then we show that {H0(x,H1(x,…,Hn(x} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications.

Extrapolating an Euler class

NARCIS (Netherlands)

Van der Kallen, Wilberd|info:eu-repo/dai/nl/117156108

2015-01-01

Let R be a noetherian ring of dimension d and let n be an integer so that n≤d≤2n-3. Let (a1,..., an+1) be a unimodular row so that the ideal J=(a1,..., an) has height n. Jean Fasel has associated to this row an element [(J, ωJ)] in the Euler

IMPROVED ENTROPY-ULTRA-BEE SCHEME FOR THE EULER SYSTEM OF GAS DYNAMICS

Institute of Scientific and Technical Information of China (English)

Rongsan Chen; Dekang Mao

2017-01-01

The Entropy-Ultra-Bee scheme was developed for the linear advection equation and extended to the Euler system of gas dynamics in [13].It was expected that the technology be applied only to the second characteristic field of the system and the computation in the other two nonlinear fields be implemented by the Godunov scheme.However,the numerical experiments in [13] showed that the scheme,though having improved the wave resolution in the second field,produced numerical oscillations in the other two nonlinear fields.Sophisticated entropy increaser was designed to suppress the spurious oscillations by increasing the entropy when there are waves in the two nonlinear fields presented.However,the scheme is then not efficient neither robust with problem-related parameters.The purpose of this paper is to fix this problem.To this end,we first study a 3 × 3 linear system and apply the technology precisely to its second characteristic field while maintaining the computation in the other two fields be implemented by the Godunov scheme.We then follow the discussion for the linear system to apply the Entropy-Ultra-Bee technology to the second characteristic field of the Euler system in a linearlized field-byfield fashion to develop a modified Entropy-Ultra-Bee scheme for the system.Meanwhile a remark is given to explain the problem of the previous Entropy-Ultra-Bee scheme in [13].A reference solution is constructed for computing the numerical entropy,which maintains the feature of the density and flats the velocity and pressure to constants.The numerical entropy is then computed as the entropy cell-average of the reference solution.Several limitations are adopted in the construction of the reference solution to further stabilize the scheme.Designed in such a way,the modified Entropy-Ultra-Bee scheme has a unified form with no problem-related parameters.Numerical experiments show that all the spurious oscillations in smooth regions are gone and the results are better than that

Euler-Poincare Reduction of a Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2005-01-01

|If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system afected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems......-known Euler-Poincare reduction to a rigid body motion with forcing....

Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations

International Nuclear Information System (INIS)

Yuen, Manwai

2011-01-01

In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu → =0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. -- Highlights: → We construct a new class of solutions to the 3D compressible or incompressible Euler and Navier-Stokes equations. → The constructed solutions are similar to the famous Arnold-Beltrami-Childress flow. → The solutions with infinite energy can exhibit the interesting behaviors locally.

A new fractional nonlocal model and its application in free vibration of Timoshenko and Euler-Bernoulli beams

Science.gov (United States)

Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun

2017-11-01

The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.

Fractional Euler Limits and Their Applications

OpenAIRE

MacNamara, Shev; Henry, Bruce I; McLean, William

2016-01-01

Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.

Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

Science.gov (United States)

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

Closure relations for the multi-species Euler system. Construction and study of relaxation schemes for the multi-species and multi-components Euler systems; Relations de fermeture pour le systeme des equations d'Euler multi-especes. Construction et etude de schemas de relaxation en multi-especes et en multi-constituants

Energy Technology Data Exchange (ETDEWEB)

Dellacherie, St. [CEA Saclay, Dir. de l' Energie Nucleaire DEN/SFNME/LMPE, Lab. de Modelisation Physique et de l' Enrichissement, 91 - Gif sur Yvette (France); Rency, N. [Paris-11 Univ., CNRS UMR 8628, 91 - Orsay (France)

2001-07-01

After having recalled the formal convergence of the semi-classical multi-species Boltzmann equations toward the multi-species Euler system (i.e. mixture of gases having the same velocity), we generalize to this system the closure relations proposed by B. Despres and by F. Lagoutiere for the multi-components Euler system (i.e. mixture of non miscible fluids having the same velocity). Then, we extend the energy relaxation schemes proposed by F. Coquel and by B. Perthame for the numerical resolution of the mono-species Euler system to the multi-species isothermal Euler system and to the multi-components isobar-isothermal Euler system. This allows to obtain a class of entropic schemes under a CFL criteria. In the multi-components case, this class of entropic schemes is perhaps a way for the treatment of interface problems and, then, for the treatment of the numerical mixture area by using a Lagrange + projection scheme. Nevertheless, we have to find a good projection stage in the multi-components case. At last, in the last chapter, we discuss, through the study of a dynamical system, about a system proposed by R. Abgrall and by R. Saurel for the numerical resolution of the multi-components Euler system.

Stability analysis of the Euler discretization for SIR epidemic model

International Nuclear Information System (INIS)

Suryanto, Agus

2014-01-01

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart

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. linear model are compared to those

Leonhard Euler's Wave Theory of Light

DEFF Research Database (Denmark)

Pedersen, Kurt Møller

2008-01-01

Euler's wave theory of light developed from a mere description of this notion based on an analogy between sound and light to a more and more mathematical elaboration on that notion. He was very successful in predicting the shape of achromatic lenses based on a new dispersion law that we now know...... of achromatic lenses, the explanation of colors of thin plates and of the opaque bodies as proof of his theory. When it came to the fundamental issues, the correctness of his dispersion law and the prediction of frequencies of light he was not at all successful. His wave theory degenerated, and it was not until...... is wrong. Most of his mathematical arguments were, however, guesswork without any solid physical reasoning. Guesswork is not always a bad thing in physics if it leads to new experiments or makes the theory coherent with other theories. And Euler tried to find such experiments. He saw the construction...

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

Science.gov (United States)

Batina, John T.

1991-01-01

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

Science.gov (United States)

Walters, Robert W.; Dwoyer, Douglas L.

1987-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

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.

Analysis of gravity data beneath Endut geothermal prospect using horizontal gradient and Euler deconvolution

Science.gov (United States)

Supriyanto, Noor, T.; Suhanto, E.

2017-07-01

The Endut geothermal prospect is located in Banten Province, Indonesia. The geological setting of the area is dominated by quaternary volcanic, tertiary sediments and tertiary rock intrusion. This area has been in the preliminary study phase of geology, geochemistry, and geophysics. As one of the geophysical study, the gravity data measurement has been carried out and analyzed in order to understand geological condition especially subsurface fault structure that control the geothermal system in Endut area. After precondition applied to gravity data, the complete Bouguer anomaly have been analyzed using advanced derivatives method such as Horizontal Gradient (HG) and Euler Deconvolution (ED) to clarify the existance of fault structures. These techniques detected boundaries of body anomalies and faults structure that were compared with the lithologies in the geology map. The analysis result will be useful in making a further realistic conceptual model of the Endut geothermal area.

Intra- and interobserver reliability of glenoid fracture classifications by Ideberg, Euler and AO.

Science.gov (United States)

Gilbert, F; Eden, L; Meffert, R; Konietschke, F; Lotz, J; Bauer, L; Staab, W

2018-03-27

Representing 3%-5% of shoulder girdle injuries scapula fractures are rare. Furthermore, approximately 1% of scapula fractures are intraarticularfractures of the glenoid fossa. Because of uncertain fracture morphology and limited experience, the treatment of glenoid fossa fractures is difficult. The glenoid fracture classification by Ideberg (1984) and Euler (1996) is still commonly used in literature. In 2013 a new glenoid fracture classification was introduced by the AO. The purpose of this study was to examine the new AO classification in clinical practice in comparison with the classifications by Ideberg and Euler. In total CT images of 84 patients with glenoid fossa fractures from 2005 to 2018 were included. Parasagittal, paracoronary and axial reconstructions were examined according to the classifications of Ideberg, Euler and the AO by 3 investigators (orthopedic surgeon, radiologist, student of medicine) at three individual time settings. Inter- and intraobserver reliability of the three classification systems were ascertained by computing Inter- and Intraclass (ICCs) correlation coefficients using Spearman's rank correlation coefficient, 95%-confidence intervals as well as F-tests for correlation coefficients. Inter- and intraobserver reliability for the AO classification showed a perspicuous coherence (R = 0.74 and R = 0.79). Low to moderate intraobserver reliability for Ideberg (R = 0.46) and Euler classification (R = 0.41) was found. Furthermore, data show a low Interobserver reliability for both Ideberg and Euler classification (R reliability using AO is significantly higher than those using Ideberg and Euler (p reliable grading of glenoid fossa fractures with high inter- and intraobserver reliability in 84 patients using CT images. It should possibly be applied in order to enable a valid, reliable and consistent academic description of glenoid fossa fractures. The established classifications by Euler and Ideberg are not capable of

The matrix Euler-Fermat theorem

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2004-01-01

We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem

Dynamic modelling and control of a rotating Euler-Bernoulli beam

Science.gov (United States)

Yang, J. B.; Jiang, L. J.; Chen, D. CH.

2004-07-01

Flexible motion of a uniform Euler-Bernoulli beam attached to a rotating rigid hub is investigated. Fully coupled non-linear integro-differential equations, describing axial, transverse and rotational motions of the beam, are derived by using the extended Hamilton's principle. The centrifugal stiffening effect is included in the derivation. A finite-dimensional model, including couplings of axial and transverse vibrations, and of elastic deformations and rigid motions, is obtained by the finite element method. By neglecting the axial motion, a simplified modelling, suitable for studying the transverse vibration and control of a beam with large angle and high-speed rotation, is presented. And suppressions of transverse vibrations of a rotating beam are simulated with the model by combining positive position feedback and momentum exchange feedback control laws. It is indicated that an improved performance for vibration control can be achieved with the method.

Explicit time marching methods for the time-dependent Euler computations

International Nuclear Information System (INIS)

Tai, C.H.; Chiang, D.C.; Su, Y.P.

1997-01-01

Four explicit type time marching methods, including one proposed by the authors, are examined. The TVD conditions of this method are analyzed with the linear conservation law as the model equation. Performance of these methods when applied to the Euler equations are numerically tested. Seven examples are tested, the main concern is the performance of the methods when discontinuities with different strengths are encountered. When the discontinuity is getting stronger, spurious oscillation shows up for three existing methods, while the method proposed by the authors always gives the results with satisfaction. The effect of the limiter is also investigated. To put these methods in the same basis for the comparison the same spatial discretization is used. Roe's solver is used to evaluate the fluxes at the cell interface; spatially second-order accuracy is achieved by the MUSCL reconstruction. 19 refs., 8 figs

A New Euler's Formula for DNA Polyhedra

Science.gov (United States)

Hu, Guang; Qiu, Wen-Yuan; Ceulemans, Arnout

2011-01-01

DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components , of crossings , and of Seifert circles are related by a simple and elegant formula: . This formula connects the topological aspects of the DNA cage to the Euler characteristic of the underlying polyhedron. It implies that Seifert circles can be used as effective topological indices to describe polyhedral links. Our study demonstrates that, the new Euler's formula provides a theoretical framework for the stereo-chemistry of DNA polyhedra, which can characterize enzymatic transformations of DNA and be used to characterize and design novel cages with higher genus. PMID:22022596

Euler-Poincare Reduction of Externall Forced Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2004-01-01

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....

Euler-Poincaré Reduction of a Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2004-01-01

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....

NEWTON'S SECOND LAW OF MOTION, F=MA; EULER'S OR NEWTON'S?

OpenAIRE

Ajay Sharma

2017-01-01

Objective: F =ma is taught as Newton’s second law of motion all over the world. But it was given by Euler in 1775, forty-eight years after the death of Newton. It is debated here with scientific logic. Methods/Statistical analysis: The discussion partially deals with history of science so various aspects are quoted from original references. Newton did not give any equation in the Principia for second, third laws motion and law of gravitation. Conceptually, in Newton’s time, neither accele...

Exploitation of ISAR Imagery in Euler Parameter Space

National Research Council Canada - National Science Library

Baird, Christopher; Kersey, W. T; Giles, R; Nixon, W. E

2005-01-01

.... The Euler parameters have potential value in target classification but have historically met with limited success due to ambiguities that arise in decomposition as well as the parameters' sensitivity...

Difference Discrete Variational Principle,EULER-Lagrange Cohomology and Symplectic, Multisymplectic Structures

OpenAIRE

Guo, H. Y.; Li, Y. Q.; Wu, K.; Wang, S. K.

2001-01-01

We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory. We also explore the difference discrete versions for the Euler...

On the Linear Stability of the Fifth-Order WENO Discretization

KAUST Repository

Motamed, Mohammad

2010-10-03

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.

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.

Euler's fluid equations: Optimal control vs optimization

Energy Technology Data Exchange (ETDEWEB)

Holm, Darryl D., E-mail: d.holm@ic.ac.u [Department of Mathematics, Imperial College London, SW7 2AZ (United Kingdom)

2009-11-23

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.

Discretization vs. Rounding Error in Euler's Method

Science.gov (United States)

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

Euler Polynomials, Fourier Series and Zeta Numbers

DEFF Research Database (Denmark)

Scheufens, Ernst E

2012-01-01

Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....

Euler-Poincaré Reduction of Externally Forced Rigid Body Motion

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2004-01-01

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

Science.gov (United States)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

Gain scheduling for non-linear time-delay systems using approximated model

NARCIS (Netherlands)

Pham, H.T.; Lim, J.T

2012-01-01

The authors investigate a regulation problem of non-linear systems driven by an exogenous signal and time-delay in the input. In order to compensate for the input delay, they propose a reduction transformation containing the past information of the control input. Then, by utilising the Euler

Cavitation Modeling in Euler and Navier-Stokes Codes

Science.gov (United States)

Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.

1993-01-01

Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.

Perturbational blowup solutions to the compressible Euler equations with damping.

Science.gov (United States)

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

KAUST Repository

De Pascalis, Riccardo; Destrade, Michel; Goriely, Alain

2010-01-01

Euler's celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson's ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Measure-valued solutions to the complete Euler system revisited

Science.gov (United States)

Březina, Jan; Feireisl, Eduard

2018-06-01

We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier-Stokes-Fourier system. Our main result states that any sequence of weak solutions to the Navier-Stokes-Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

Directory of Open Access Journals (Sweden)

Zeki Kasap

2015-01-01

Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

PID position regulation in one-degree-of-freedom Euler-Lagrange systems actuated by a PMSM

Science.gov (United States)

Verastegui-Galván, J.; Hernández-Guzmán, V. M.; Orrante-Sakanassi, J.

2018-02-01

This paper is concerned with position regulation in one-degree-of-freedom Euler-Lagrange Systems. We consider that the mechanical subsystem is actuated by a permanent magnet synchronous motor (PMSM). Our proposal consists of a Proportional-Integral-Derivative (PID) controller for the mechanical subsystem and a slight variation of field oriented control for the PMSM. We take into account the motor electric dynamics during the stability analysis. We present, for the first time, a global asymptotic stability proof for such a control scheme without requiring the mechanical subsystem to naturally possess viscous friction. Finally, as a corollary of our main result we prove global asymptotic stability for output feedback PID regulation of one-degree-of-freedom Euler-Lagrange systems when generated torque is considered as the system input, i.e. when the electric dynamics of PMSM's is not taken into account.

Entropy viscosity method applied to Euler equations

International Nuclear Information System (INIS)

Delchini, M. O.; Ragusa, J. C.; Berry, R. A.

2013-01-01

The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

International Nuclear Information System (INIS)

Shin, Young Jae; Yun, Jong Hak; Seong, Kyeong Youn; Kim, Jae Ho; Kang, Sung Hwang

2006-01-01

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Winkler foundation and Euler-Bernoulli beam on Paster nak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.; Castro, Cristó bal E.; Bok Jik, Lee

2015-01-01

Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both

Conservative numerical schemes for Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada

1999-05-01

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

Euler angles for G2

International Nuclear Information System (INIS)

Cacciatori, Sergio L.; Cerchiai, Bianca L.; Della Vedova, Alberto; Ortenzi, Giovanni; Scotti, Antonio

2005-01-01

We provide a simple coordinatization for the group G 2 , which is analogous to the Euler coordinatization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G 2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G 2 . Moreover, as a by-product it yields a concrete realization and an Einstein metric for H

Vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundations using differential transformation method and generalized differential quadrature method

International Nuclear Information System (INIS)

Shin, Young Jae; Hwang, Ki Sup; Yun, Jong Hak

2006-01-01

The main purpose of this paper is to apply Differential Transformation Method(DTM) and Generalized Differential Quadrature Method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results

Investigation of source location determination from Magsat magnetic anomalies: The Euler method approach

Science.gov (United States)

Ravat, Dhananjay

1996-01-01

The applicability of the Euler method of source location determination was investigated on several model situations pertinent to satellite-data scale situations as well as Magsat data of Europe. Our investigations enabled us to understand the end-member cases for which the Euler method will work with the present satellite magnetic data and also the cases for which the assumptions implicit in the Euler method will not be met by the present satellite magnetic data. These results have been presented in one invited lecture at the Indo-US workshop on Geomagnetism in Studies of the Earth's Interior in August 1994 in Pune, India, and at one presentation at the 21st General Assembly of the IUGG in July 1995 in Boulder, CO. A new method, called Anomaly Attenuation Rate (AAR) Method (based on the Euler method), was developed during this study. This method is scale-independent and is appropriate to locate centroids of semi-compact three dimensional sources of gravity and magnetic anomalies. The method was presented during 1996 Spring AGU meeting and a manuscript describing this method is being prepared for its submission to a high-ranking journal. The grant has resulted in 3 papers and presentations at national and international meetings and one manuscript of a paper (to be submitted shortly to a reputable journal).

An improved front tracking method for the Euler equations

NARCIS (Netherlands)

Witteveen, J.A.S.; Koren, B.; Bakker, P.G.

2007-01-01

An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as

Canonical form of Euler-Lagrange equations and gauge symmetries

Energy Technology Data Exchange (ETDEWEB)

Geyer, B [Naturwissenschaftlich-Theoretisches Zentrum und Institut fuer Theoretische Physik, Universitaet Leipzig, Leipzig (Germany); Gitman, D M [Institute of Physics, University of Sao Paulo, Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

2003-06-13

The structure of the Euler-Lagrange equations for a general Lagrangian theory (e.g. singular, with higher derivatives) is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter the right-hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proved that for local theories all the gauge generators are local in time operators.

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.

New form of the Euler-Bernoulli rod equation applied to robotic systems

Directory of Open Access Journals (Sweden)

Filipović Mirjana

2008-01-01

Full Text Available This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime in accordance with the complexity requirements of motion of an elastic robot system. The elastic line equation mode of link of a complex elastic robot system is defined based on the so-called 'Euler-Bernoulli Approach' (EBA. It is shown that the equation of equilibrium of all forces present at mode tip point ('Lumped-mass approach' (LMA follows directly from the elastic line equation for specified boundary conditions. This, in turn, proves the essential relationship between LMA and EBA approaches. In the defined mathematical model of a robotic system with multiple DOF (degree of freedom in the presence of the second mode, the phenomenon of elasticity of both links and joints are considered simultaneously with the presence of the environment dynamics - all based on the previously presented theoretical premises. Simulation results are presented. .

Using Euler buckling springs for vibration isolation

CERN Document Server

Winterflood, J; Blair, D G

2002-01-01

Difficulties in obtaining ideal vertical vibration isolation with mechanical springs are identified as being due to the mass of the elastic element which is in turn due to its energy storage requirement. A new technique to minimize this energy is presented - being an Euler column undergoing elastic buckling. The design of a high performance vertical vibration isolation stage based on this technique is presented together with its measured performance.

Using Euler buckling springs for vibration isolation

International Nuclear Information System (INIS)

Winterflood, J; Barber, T; Blair, D G

2002-01-01

Difficulties in obtaining ideal vertical vibration isolation with mechanical springs are identified as being due to the mass of the elastic element which is in turn due to its energy storage requirement. A new technique to minimize this energy is presented - being an Euler column undergoing elastic buckling. The design of a high performance vertical vibration isolation stage based on this technique is presented together with its measured performance

On the Local Type I Conditions for the 3D Euler Equations

Science.gov (United States)

Chae, Dongho; Wolf, Jörg

2018-05-01

We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution {v\\in L^∞ (-1,0; L^2 ( B(x_0,r)))\\cap L^∞_{loc} (-1,0; W^{1, ∞} (B(x_0, r)))} of the 3D Euler equations, where {B(x_0,r)} is the ball with radius r and the center at x 0, if the limiting values of certain scale invariant quantities for a solution v(·, t) as {t\\to 0} are small enough, then { \

Multi-dimensional Fuzzy Euler Approximation

Directory of Open Access Journals (Sweden)

Yangyang Hao

2017-05-01

Full Text Available Multi-dimensional Fuzzy differential equations driven by multi-dimen-sional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differential equations. The multi-dimensional fuzzy Taylor expansion is given, based on this expansion, a numerical method which is designed for giving the solution of multi-dimensional fuzzy differential equation via multi-dimensional Euler method will be presented, and its local convergence also will be discussed.

Euler y la Conjetura de Fermat sobre Números Triangulares

Directory of Open Access Journals (Sweden)

José Manuel Sánchez Muñoz

2011-04-01

Full Text Available Este artículo describe la historia de como Euler demostró la existencia de infinitos números triangulares bicuadráticos, desde su correspondencia con su amigo Christian Goldbach hasta la publicación de sus resultados en la Academia de San Petesburgo.

Multipliers for the Absolute Euler Summability of Fourier Series

Indian Academy of Sciences (India)

In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.

Development of a Three-Dimensional Unstructured Euler Solver for High-Speed Flows

Directory of Open Access Journals (Sweden)

Tudorel Petronel AFILIPOAE

2015-12-01

Full Text Available This paper addresses the solution of the compressible Euler equations on hexahedral meshes for supersonic and hypersonic flows. Spatial discretization is accomplished by a cell-centered finite-volume formulation which employs two different upwind schemes for the computation of convective fluxes. Second-order solutions are attained through a linear state reconstruction technique that yields highly resolved flows in smooth regions while providing a sharp and clean resolution of shocks. The solution gradients required for the higher-order spatial discretization are estimated by a least-square method while Venkatakrishnan limiter is employed to preserve monotonicity and avoid oscillations in the presence of shocks. Furthermore, solutions are advanced in time by an explicit third-order Runge-Kutta scheme and convergence to steady state is accelerated using implicit residual smoothing. Flow around a circular arc in a channel and flow past a circular cylinder are studied and results are presented for various Mach numbers together with comparisons to theoretical and experimental data where possible.

A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift

DEFF Research Database (Denmark)

Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef

2014-01-01

The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations...

Contact discontinuities in multi-dimensional isentropic Euler equations

Czech Academy of Sciences Publication Activity Database

Březina, J.; Chiodaroli, E.; Kreml, Ondřej

2018-01-01

Roč. 2018 (2018), č. článku 94. ISSN 1072-6691 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : isentropic Euler equations * non-uniqueness * Riemann problem Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/94/abstr.html

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

Science.gov (United States)

Chertock, Alina; Cui, Shumo; Kurganov, Alexander; Özcan, Şeyma Nur; Tadmor, Eitan

2018-04-01

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.

Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected ...

African Journals Online (AJOL)

This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the ...

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.

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.

Performance prediction and flow-field analysis of rotors in hover using a coupled Euler/boundary layer method; Previsions des performances et de l`ecoulement pour des rotors en vol stationnaire par une methode couplee Euler/couche limite

Energy Technology Data Exchange (ETDEWEB)

Beaumier, P. [ONERA, 92 - Chatillon (France); Castellin, C.; Arnaud, G. [Eurocopter France, 13 - Marignane (France)

1998-12-31

The performance prediction of helicopter in hover is of key importance for manufacturers because hover is a design configuration for the definition of a rotor-craft. A lot of efforts have been made for more than 10 years all over the world in order to develop and validate numerical methods based on CFD. An Euler method (WAVES) developed by ONERA and coupled with a boundary layer code (MI3DI) is presented, validated and applied to compute the total performance of rotors with different tip shapes. A new boundary condition for the Euler code has been tested and enables better calculation by eliminating `numerical` recirculation. The code has demonstrated its ability to rank two rotors with different planforms in good agreement with experiment. Under industrial requirements new grid strategies have been studied and should allow to reduce CPU time consumption. It is shown that WAVES/MI3DI can be efficiently used in the aerodynamic design process of a new rotor. (authors) 7 refs.

The symplectic structure of Euler-Lagrange superequations and Batalin-Vilkoviski formalism

CERN Document Server

Monterde, J

2003-01-01

We study the graded Euler-Lagrange equations from the viewpoint of graded Poincare-Cartan forms. An application to a certain class of solutions of the Batalin-Vilkoviski master equation is also given.

Generalized force in classical field theory. [Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-02-01

The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.

Newton's Laws, Euler's Laws and the Speed of Light

Science.gov (United States)

Whitaker, Stephen

2009-01-01

Chemical engineering students begin their studies of mechanics in a department of physics where they are introduced to the mechanics of Newton. The approach presented by physicists differs in both perspective and substance from that encountered in chemical engineering courses where Euler's laws provide the foundation for studies of fluid and solid…

A Short Proof of Euler's Inequality R ≥ 2r Theorem. Let ∆ ABC be an ...

Indian Academy of Sciences (India)

IAS Admin

A Short Proof of Euler's Inequality R ≥ 2r. Theorem. Let ∆ ABC be an arbitrary triangle with circumradius R and inradius r. Then R ≥ 2r with equality holding if and only if ∆ABC is equilateral. This was first published by Euler in 1765. Since then several proofs have followed, some geometric and some algebraic. We will use ...

Parallel computation of Euler and Navier-Stokes flows

International Nuclear Information System (INIS)

Swisshelm, J.M.; Johnson, G.M.; Kumar, S.P.

1986-01-01

A multigrid technique useful for accelerating the convergence of Euler and Navier-Stokes flow computations has been restructured to improve its performance on both SIMD and MIMD computers. The new algorithm allows both the construction of longer coarse-grid vectors and the multitasking of entire grids. Computational results are presented for the CDC Cyber 205, Cray X-MP, and Denelcor HEP I. 15 references

Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions

Directory of Open Access Journals (Sweden)

R. Naz

2015-01-01

Full Text Available We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass density g(x, and the applied load denoted by f(u, a function of transverse displacement u(t,x. The complete Lie group classification is obtained for different forms of the variable lineal mass density g(x and applied load f(u. The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms of g(x. For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature when g(x is constant with variable applied load f(u. For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.

Stability properties of the Euler-Korteweg system with nonmonotone pressures

KAUST Repository

Giesselmann, Jan; Tzavaras, Athanasios

2016-01-01

We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy

Large Scale Simulations of the Euler Equations on GPU Clusters

KAUST Repository

Liebmann, Manfred; Douglas, Craig C.; Haase, Gundolf; Horvá th, Zoltá n

2010-01-01

The paper investigates the scalability of a parallel Euler solver, using the Vijayasundaram method, on a GPU cluster with 32 Nvidia Geforce GTX 295 boards. The aim of this research is to enable large scale fluid dynamics simulations with up to one

Classical mechanics on the GL(n, R) group and Euler-Calogero-Sutherland model

International Nuclear Information System (INIS)

Khvedelidze, A.M.; Mladenov, D.M.

2002-01-01

Relations between free motion on the GL + (n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with a pairwise 1/sinh 2 x 'potential' (Euler-Calogero-Sutherland model) are discussed within a Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: that which is due to continuous invariance and that which is due to discrete symmetry. It is shown that, upon projecting onto the corresponding invariant manifolds, the resulting Hamiltonian system represents the Euler-Calogero-Sutherland model in both cases

Euler-Vector Clustering of GPS Velocities Defines Microplate Geometry in Southwest Japan

Science.gov (United States)

Savage, J. C.

2018-02-01

I have used Euler-vector clustering to assign 469 GEONET stations in southwest Japan to k clusters (k = 2, 3,..., 9) so that, for any k, the velocities of stations within each cluster are most consistent with rigid-block motion on a sphere. That is, I attempt to explain the raw (i.e., uncorrected for strain accumulation), 1996-2006 velocities of those 469 Global Positioning System stations by rigid motion of k clusters on the surface of a spherical Earth. Because block geometry is maintained as strain accumulates, Euler-vector clustering may better approximate the block geometry than the values of the associated Euler vectors. The microplate solution for each k is constructed by merging contiguous clusters that have closely similar Euler vectors. The best solution consists of three microplates arranged along the Nankaido Trough-Ryukyu Trench between the Amurian and Philippine Sea Plates. One of these microplates, the South Kyushu Microplate (an extension of the Ryukyu forearc into the southeast corner of Kyushu), had previously been identified from paleomagnetic rotations. Relative to ITRF2000 the three microplates rotate at different rates about neighboring poles located close to the northwest corner of Shikoku. The microplate model is identical to that proposed in the block model of Wallace et al. (2009, https://doi.org/10.1130/G2522A.1) except in southernmost Kyushu. On Shikoku and Honshu, but not Kyushu, the microplate model is consistent with that proposed in the block models of Nishimura and Hashimoto (2006, https://doi.org/10.1016/j.tecto.2006.04.017) and Loveless and Meade (2010, https://doi.org/10.1029/2008JB006248) without the low-slip-rate boundaries proposed in the latter.

Gain scheduled linear quadratic control for quadcopter

Science.gov (United States)

Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

2017-12-01

This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

Analysis of stability for stochastic delay integro-differential equations.

Science.gov (United States)

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2015-01-01

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.

Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method; Diferentes semillas para solucionar las ecuaciones de la cinetica puntual estocastica empleando el metodo de Euler-Maruyama

Energy Technology Data Exchange (ETDEWEB)

Suescun D, D.; Oviedo T, M., E-mail: daniel.suescun@usco.edu.co [Universidad Surcolombiana, Av. Pastrana Borrero - Carrera 1, Neiva, Huila (Colombia)

2017-09-15

In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and

Regularity and energy conservation for the compressible Euler equations

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.; Wiedemann, E.

2017-01-01

Roč. 223, č. 3 (2017), s. 1375-1395 ISSN 0003-9527 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler equations Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.392, year: 2016 http://link.springer.com/article/10.1007%2Fs00205-016-1060-5

Weak solutions for Euler systems with non-local interactions

Czech Academy of Sciences Publication Activity Database

Carrillo, J. A.; Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.

2017-01-01

Roč. 95, č. 3 (2017), s. 705-724 ISSN 0024-6107 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * dissipative solutions * Newtonian interaction Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.895, year: 2016 http://onlinelibrary.wiley.com/doi/10.1112/jlms.12027/abstract

Euler-Lagrange modeling of the hydrodynamics of dense multiphase flows

NARCIS (Netherlands)

Padding, J.T.; Deen, N.G.; Peters, E. A. J. F.; Kuipers, J. A. M.

2015-01-01

The large-scale hydrodynamic behavior of relatively dense dispersed multiphase flows, such as encountered in fluidized beds, bubbly flows, and liquid sprays, can be predicted efficiently by use of Euler-Lagrange models. In these models, grid-averaged equations for the continuous-phase flow field are

Leonhardi Euleri Opera omnia: Editing the works and correspondence of Leonhard Euler

Directory of Open Access Journals (Sweden)

Andreas KLEINERT

2015-12-01

Full Text Available The paper gives an overview on the history and present state of the edition of the complete works of Leonhard Euler (1707–1783. After several failed initiatives in the 19th century, the project began in 1907 with the edition of Euler’s printed works. The works were divided into three series: I. Mathematics (29 volumes; II. Mechanics and Astronomy (31 volumes; and III. Physics and Miscellaneous (12 volumes. After several ups and downs due to two World Wars and economic problems, the publication of the printed works with a total of 72 volumes is nearly finished. Only two volumes on perturbation theory in astronomy are still missing. The publication of series IV (manuscripts and correspondence started in 1967 as a joint project of the Swiss and the Soviet academies of sciences. The manuscript edition was postponed, and the project focussed on Euler’s correspondence which contains approximately 3000 letters, 1000 of them written by Euler. The correspondents include famous mathematicians of the 18th century like d’Alembert, Clairaut and the Bernoullis, but also many less-known people with whom Euler corresponded on a great variety of subjects. A major problem is to find and to finance appropriate editors who are able to read French, Latin, and the old German handwriting, and who are acquainted with history, culture and science of the 18th century. During the last 50 years, the editors gathered copies or scans of most of the preserved Euler’s letters. The original letters addressed to Euler were made available to the editorial group in Switzerland by the Russian Academy of Sciences before World War I, and before their restitution in 1947 the editors made fairly good photographs that are now an important part of the material basis of the edition. Each volume of the letter series (VIA contains Euler’s correspondence with one or more of his contemporaries, presented in a chronological order. Up to the present day, four volumes of the

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.

2015-09-30

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.

Linear theory of sound waves with evaporation and condensation

International Nuclear Information System (INIS)

Inaba, Masashi; Watanabe, Masao; Yano, Takeru

2012-01-01

An asymptotic analysis of a boundary-value problem of the Boltzmann equation for small Knudsen number is carried out for the case when an unsteady flow of polyatomic vapour induces reciprocal evaporation and condensation at the interface between the vapour and its liquid phase. The polyatomic version of the Boltzmann equation of the ellipsoidal statistical Bhatnagar–Gross–Krook (ES-BGK) model is used and the asymptotic expansions for small Knudsen numbers are applied on the assumptions that the Mach number is sufficiently small compared with the Knudsen number and the characteristic length scale divided by the characteristic time scale is comparable with the speed of sound in a reference state, as in the case of sound waves. In the leading order of approximation, we derive a set of the linearized Euler equations for the entire flow field and a set of the boundary-layer equations near the boundaries (the vapour–liquid interface and simple solid boundary). The boundary conditions for the Euler and boundary-layer equations are obtained at the same time when the solutions of the Knudsen layers on the boundaries are determined. The slip coefficients in the boundary conditions are evaluated for water vapour. A simple example of the standing sound wave in water vapour bounded by a liquid water film and an oscillating piston is demonstrated and the effect of evaporation and condensation on the sound wave is discussed. (paper)

Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

OpenAIRE

Zuidwijk, Rob

2005-01-01

textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...

Linear algebra and analytic geometry for physical sciences

CERN Document Server

Landi, Giovanni

2018-01-01

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers m...

Automatic interpretation of magnetic data using Euler deconvolution with nonlinear background

Digital Repository Service at National Institute of Oceanography (India)

Dewangan, P.; Ramprasad, T.; Ramana, M.V.; Desa, M.; Shailaja, B.

are close to each other. A possible solution to these problems is prposed by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization...

An addendum to the Heisenberg-Euler effective action beyond one loop

Energy Technology Data Exchange (ETDEWEB)

Gies, Holger; Karbstein, Felix [Helmholtz-Institut Jena,Fröbelstieg 3, 07743 Jena (Germany); Theoretisch-Physikalisches Institut, Abbe Center of Photonics,Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena (Germany)

2017-03-21

We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irreducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field approximation. One of our main findings is that at two-loop order there is a finite one-particle reducible contribution to the Heisenberg-Euler effective action in constant fields, which was previously assumed to vanish. In addition to their conceptual significance, our results are relevant for high-precision probes of quantum vacuum nonlinearity in strong electromagnetic fields.

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Directory of Open Access Journals (Sweden)

Ahmad Shahba

2011-01-01

Full Text Available Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finite element method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

Measure-valued solutions to the complete Euler system revisited

Czech Academy of Sciences Publication Activity Database

Březina, J.; Feireisl, Eduard

2018-01-01

Roč. 69, č. 3 (2018), č. článku 57. ISSN 0044-2275 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * measure-valued solution * vanishing dissipation limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.687, year: 2016 https://link.springer.com/article/10.1007/s00033-018-0951-8

Uniqueness of rarefaction waves in multidimensional compressible Euler system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Kreml, Ondřej

2015-01-01

Roč. 12, č. 3 (2015), s. 489-499 ISSN 0219-8916 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler system * uniqueness * rarefaction wave * Riemann problem Subject RIV: BA - General Mathematics Impact factor: 0.556, year: 2015 http://www.worldscientific.com/doi/abs/10.1142/S0219891615500149

A counterexample of the Euler condition: the Appell–Hamel dynamical system on a horizontally moving plate

International Nuclear Information System (INIS)

Shan-Shan, Xu; Shu-Min, Li; Jamal, Berakdar

2009-01-01

As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell–Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces. (general)

Discovering Euler Circuits and Paths through a Culturally Relevant Lesson

Science.gov (United States)

Robichaux, Rebecca R.; Rodrigue, Paulette R.

2006-01-01

This article describes a middle school discrete mathematics lesson that uses the context of catching crawfish to provide students with a hands-on experience related to Euler circuits and paths. The lesson promotes mathematical communication through the use of cooperative learning as well as connections between mathematics and the real world…

Maximal dissipation and well-posedness for the compressible Euler system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2014-01-01

Roč. 16, č. 3 (2014), s. 447-461 ISSN 1422-6928 EU Projects: European Commission(XE) 320078 - MATHEF Keywords : maximal dissipation * compressible Euler system * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2014 http://link.springer.com/article/10.1007/s00021-014-0163-8

On the estimation variance for the specific Euler-Poincaré characteristic of random networks.

Science.gov (United States)

Tscheschel, A; Stoyan, D

2003-07-01

The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.

Swimming holonomy principles, exemplified with a Euler fluid in two dimensions

International Nuclear Information System (INIS)

Hannay, J H

2012-01-01

The idealized problem of swimming—the self-propulsion phenomenon whereby a cyclic change of shape of a ‘swimmer’ produces a net movement—is well studied for the case of a very viscous incompressible liquid. The opposite limit of zero viscosity, the ideal or ‘Euler’ fluid, has also received some attention. There remain to be articulated and explored some points of principle, set here in the context of the Euler fluid in two dimensions, though partly common to both limits and to both two and three dimensions. (i) Perhaps surprisingly, both limits are purely geometric effects, ‘holonomies’, not dependent on any timings or rates, but only on the sequence of shapes adopted by the swimmer. (ii) A principle fully determining swimming in a Euler fluid is simply stated: the fluid moves at every moment so as to minimize the sum of its and the swimmer's kinetic energy. (iii) Euler swimming would be solvable explicitly were it not for the standard impasse of potential theory: to find the boundary normal derivative of a function obeying Laplace's equation given its value around the boundary (or vice versa). As usual more analytical progress is possible in two dimensions (by complexifying) than three, but full tractability still requires the extreme of slight, rapid swimming strokes, and a simple example is given. In both limits, for a non-symmetrical swimming stroke, a rotation or orientation holonomy accompanies the translational one—the swimmer has turned somewhat as well as translated. The whole holonomy is non-Abelian (the order of the shape sequence matters), but (iv) for two dimensions the rotation part is Abelian. A benefit (albeit cosmetic) is that the one-stroke displacement and turning can be written down as a complex line integral. (v) Another benefit is that while Stokes's theorem (in shape space) is normally sacrificed in non-Abelian holonomies, a partial recovery of the theorem is possible in two-dimensional swimming. To illustrate this last

On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

Science.gov (United States)

Kifonidis, K.; Müller, E.

2012-08-01

Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a

Convergence Analysis of Semi-Implicit Euler Methods for Solving Stochastic Age-Dependent Capital System with Variable Delays and Random Jump Magnitudes

Directory of Open Access Journals (Sweden)

Qinghui Du

2014-01-01

Full Text Available We consider semi-implicit Euler methods for stochastic age-dependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean-square sense under given conditions.

Stability of periodic steady-state solutions to a non-isentropic Euler-Poisson system

Science.gov (United States)

Liu, Cunming; Peng, Yue-Jun

2017-06-01

We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler-Poisson system without temperature damping term. The system arises in the theory of semiconductors for which the doping profile is a given smooth function. In this stability problem, there are no special restrictions on the size of the doping profile, but only on the size of the perturbation. We prove that small perturbations of periodic steady-states are exponentially stable for large time. For this purpose, we introduce new variables and choose a non-diagonal symmetrizer of the full Euler equations to recover dissipation estimates. This also allows to make the proof of the stability result very simple and concise.

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Directory of Open Access Journals (Sweden)

Zozulya V.V.

2017-01-01

Full Text Available New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

On the motion of incompressible inhomogeneous Euler-Korteweg fluids

Czech Academy of Sciences Publication Activity Database

Bulíček, M.; Feireisl, Eduard; Málek, J.; Shvydkoy, R.

2010-01-01

Roč. 3, č. 3 (2010), s. 497-515 ISSN 1937-1632 R&D Projects: GA MŠk LC06052; GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : Korteweg fluid * inhomogeneous Euler fluid * Korteweg stress * local-in-time well-posedness * smooth solution Subject RIV: BA - General Mathematics http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5226

Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method

International Nuclear Information System (INIS)

Suescun D, D.; Oviedo T, M.

2017-09-01

In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and

Evaluating of air flow movements and thermal comfort in a model room with Euler equation: Two dimensional study

Energy Technology Data Exchange (ETDEWEB)

Chafi, Fatima Zohra; Halle, Stephane [Mechanical engineering department, Ecole de technologie superieure, Quebec university, 1100 rue Notre-Dame Ouest, Montreal, Quebec H3C 1K3 (Canada)

2011-02-15

This paper presents the results of a study that consists of estimating the temperature distribution and air flow movement in a model room with a numerical model based on the Euler equations. Numerical results obtained for two scenarios of ventilation and heating are compared with the predictions of a Navier-Stokes model, as well as with experimental results. A comparison of the local thermal comfort indices PMV and PPD obtained experimentally and numerically is also presented. Results show that the Euler model is capable of properly estimating the temperature distribution, the air movement and the comfort indices in the room. Furthermore, the use of Euler equations allows a reduction of computational time in the order of 30% compared to the Navier-Stokes modeling. (author)

Derivation of the Euler equations in Thomas-Fermi theories of a hot nuclear system

International Nuclear Information System (INIS)

Wang, C.

1992-01-01

The variational extreme condition with respect to statistical distribution of nucleons in momentum space is applied to derive the Euler equation of the nuclear density profile. The resultant Euler equation of the nuclear density profile is proven to be identical with that obtained in the usual Thomas-Fermi theories of a hot nuclear system where the variation is made with respect to the nuclear density profile. A Fermi-Dirac-type distribution appears as a result of variation in the present approach, while it is used as a given expression in obtaining the variation of the nuclear density profile in the usual Thomas-Fermi theories

Nonlocal theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Directory of Open Access Journals (Sweden)

Zozulya V.V.

2017-09-01

Full Text Available New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Peer Jesper

2015-01-07

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.

Perturbation analysis of linear control problems

International Nuclear Information System (INIS)

Petkov, Petko; Konstantinov, Mihail

2017-01-01

The paper presents a brief overview of the technique of splitting operators, proposed by the authors and intended for perturbation analysis of control problems involving unitary and orthogonal matrices. Combined with the technique of Lyapunov majorants and the implementation of the Banach and Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the feedback synthesis problem and pole assignment problem in particular, as well as other important problems in control theory and linear algebra. Key words: perturbation analysis, canonical forms, feedback synthesis

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

Common pitfalls in statistical analysis: Linear regression analysis

Directory of Open Access Journals (Sweden)

Rakesh Aggarwal

2017-01-01

Full Text Available In a previous article in this series, we explained correlation analysis which describes the strength of relationship between two continuous variables. In this article, we deal with linear regression analysis which predicts the value of one continuous variable from another. We also discuss the assumptions and pitfalls associated with this analysis.

Orthogonal sparse linear discriminant analysis

Science.gov (United States)

Liu, Zhonghua; Liu, Gang; Pu, Jiexin; Wang, Xiaohong; Wang, Haijun

2018-03-01

Linear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.

Smooth values of the iterates of the Euler's Phi function

OpenAIRE

Lamzouri, Youness

2005-01-01

Let $\\phi(n)$ be the Euler-phi function, define $\\phi_0(n) = n$ and $\\phi_{k+1}(n)=\\phi(\\phi_{k}(n))$ for all $k\\geq 0$. We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $\\phi_k(n)$ is $y$-smooth, conditionally on a weak form of the Elliott-Halberstam conjecture.

Integration with respect to the Euler characteristic and its applications

Energy Technology Data Exchange (ETDEWEB)

Gusein-Zade, Sabir M [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2010-09-16

The notion of integration with respect to the Euler characteristic and its generalizations are discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic integration. The author describes applications of these notions to the computation of monodromy zeta functions, Poincare series of multi-index filtrations, generating series of classes of certain moduli spaces, and so on. Bibliography: 70 titles.

Further Generalization of Golden Mean in Relation to Euler Divine Equation

OpenAIRE

Rakocevic, Miloje M.

2006-01-01

In the paper a new generalization of the Golden mean, as a further generalization in relation to Stakhov (1989) and to Spinadel (1999), is presented. Also it is first observed that the Euler divine equation represents a possible generalization of Golden mean. In this second version the Section 6 is added.

The importance of Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov

Science.gov (United States)

Sharkov, N. A.; Sharkova, O. A.

2018-05-01

The paper identifies the importance of the Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov and for the modern knowledge in survivability and safety of ships. The works by Leonard Euler "Marine Science" and "The Moon Motion New Theory" are discussed.

Viscous Regularization of the Euler Equations and Entropy Principles

KAUST Repository

Guermond, Jean-Luc

2014-03-11

This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies, à la [Harten et al., SIAM J. Numer. Anal., 35 (1998), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

International Nuclear Information System (INIS)

Kaneko, Yuta; Yoshida, Zensho

2014-01-01

Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term −ΔQ, just representing the current density (Q is a Clebsch variable, and Δ is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

KAUST Repository

Karlsson, Peer Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2015-01-01

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system

Distributed adaptive asymptotically consensus tracking control of uncertain Euler-Lagrange systems under directed graph condition.

Science.gov (United States)

Wang, Wei; Wen, Changyun; Huang, Jiangshuai; Fan, Huijin

2017-11-01

In this paper, a backstepping based distributed adaptive control scheme is proposed for multiple uncertain Euler-Lagrange systems under directed graph condition. The common desired trajectory is allowed totally unknown by part of the subsystems and the linearly parameterized trajectory model assumed in currently available results is no longer needed. To compensate the effects due to unknown trajectory information, a smooth function of consensus errors and certain positive integrable functions are introduced in designing virtual control inputs. Besides, to overcome the difficulty of completely counteracting the coupling terms of distributed consensus errors and parameter estimation errors in the presence of asymmetric Laplacian matrix, extra information transmission of local parameter estimates are introduced among linked subsystem and adaptive gain technique is adopted to generate distributed torque inputs. It is shown that with the proposed distributed adaptive control scheme, global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

Science.gov (United States)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

Fluid-structure coupling in Lagrange-Lagrange and Euler-Lagrange descriptions

International Nuclear Information System (INIS)

Jones, A.V.

1981-01-01

Fluid-structure interaction problems are very common in the reactor safety field, examples being containment loading in LMFBR systems and the downcomer problem in LWRs. This article reviews the principal finite difference methodes employed for their solution. After a survey of the chief representations of the equations of motion of the fluid and structure and of their coupling, the Lagrange-Lagrange and Euler-Lagrange representations are examined in detail. The practical necessity of treating the structure in Lagrangian coordinates and the respective merits of the Lagrangian and Eulerian representations for the fluid are explained, both for coupling between continua and for coupling between a fluid and a thin shell. Detailed analyses of the stability and numerical dissipation of the Lagrange-Lagrange and Euler-Lagrange coupling techniques in a very simple one-dimensional problem are provided to supply indicators as to stability and dissipation in more complex multidimensional situations and to bring out the theoretical complexity of seemingly simple coupling algorithms. The article then presents some practical examples of coupled problems in which calculations can be compared with experiment, and concludes with a section on future trends in the field of fluid-structure coupling

AUTODYN - an interactive non-linear dynamic analysis program for microcomputers through supercomputers

International Nuclear Information System (INIS)

Birnbaum, N.K.; Cowler, M.S.; Itoh, M.; Katayama, M.; Obata, H.

1987-01-01

AUTODYN uses a two dimensional coupled finite difference approach similar to the one described by Cowler and Hancock (1979). Both translational and axial symmetry are treated. The scheme allows alternative numerical processors to be selectively used to model different components/regions of a problem. Finite difference grids operated on by these processors can be coupled together in space and time to efficiently compute structural (or fluid-structure) interactions. AUTODYN currently includes a Lagrange processor for modeling solid continua and structures, an Euler processor for modeling fluids and the large distortion of solids, an ALE (Arbitrary Lagrange Euler) processor for specialized flow models and a shell processor for modeling thin structures. At present, all four processors use explicit time integration but implicit options will be added to the Lagrange and ALE processors in the near future. Material models are included for solids, liquids and gases (including HE detonation products). (orig.)

Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

NARCIS (Netherlands)

R.A. Zuidwijk (Rob)

2005-01-01

textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an

Generalizations of Steffensen’s inequality via some Euler-type identities

Directory of Open Access Journals (Sweden)

Pečarić Josip

2016-08-01

Full Text Available Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Directory of Open Access Journals (Sweden)

Zozulya V.V.

2017-01-01

Full Text Available New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

Applied linear algebra and matrix analysis

CERN Document Server

Shores, Thomas S

2018-01-01

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series

Science.gov (United States)

Kushwaha, Jitendra Kumar

2013-01-01

Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction. PMID:24379744

A contribution for stress analysis in bend acessories of piping systems

International Nuclear Information System (INIS)

Melo, F.J.M.Q. de; Castro, P.M.S.T. de

1986-01-01

Analytical and numerical studies of the linear elastic behavior of bend pipes, with tangent pipes or flanged ends, such as used in nuclear power plants are presented. Two analytical techniques were developed; one is based on the integration of Euler equation and the other one is based on a Fourier analysis. The results obtained using these approaches are compared with results obtained by a finite element code for 'semiloof shells. (Author) [pt

The effect of non-uniform mass loading on the linear, temporal development of particle-laden shear layers

Energy Technology Data Exchange (ETDEWEB)

Senatore, Giacomo [Department of Aerospace Engineering, Universita di Pisa, Pisa 56122 (Italy); Davis, Sean; Jacobs, Gustaaf, E-mail: gjacobs@mail.sdsu.edu [Department of Aerospace Engineering and Engineering Mechanics, San Diego State University, San Diego, 92182 California (United States)

2015-03-15

The effect of non-uniformity in bulk particle mass loading on the linear development of a particle-laden shear layer is analyzed by means of a stochastic Eulerian-Eulerian model. From the set of governing equations of the two-fluid model, a modified Rayleigh equation is derived that governs the linear growth of a spatially periodic disturbance. Eigenvalues for this Rayleigh equation are determined numerically using proper conditions at the co-flowing gas and particle interface locations. For the first time, it is shown that non-uniform loading of small-inertia particles (Stokes number (St) <0.2) may destabilize the inviscid mixing layer development as compared to the pure-gas flow. The destabilization is triggered by an energy transfer rate that globally flows from the particle phase to the gas phase. For intermediate St (1 < St < 10), a maximum stabilizing effect is computed, while at larger St, two unstable modes may coexist. The growth rate computations from linear stability analysis are verified numerically through simulations based on an Eulerian-Lagrangian (EL) model based on the inviscid Euler equations and a point particle model. The growth rates found in numerical experiments using the EL method are in very good agreement with growth rates from the linear stability analysis and validate the destabilizing effect induced by the presence of particles with low St.

A further note on the force discrepancy for wing theory in Euler flow

Indian Academy of Sciences (India)

The Euler equations use the assumption that the fluid does not impart any resistance ... viscosity, the kinetic energy associated with these flow fields is now bounded, ..... Combining all the results together from Appendices B, C and D we get.

Euler principal component analysis

NARCIS (Netherlands)

Liwicki, Stephan; Tzimiropoulos, Georgios; Zafeiriou, Stefanos; Pantic, Maja

Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ℓ 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA,

Three Dimensional Steady Subsonic Euler Flows in Bounded Nozzles

OpenAIRE

Chen, Chao; Xie, Chunjing

2013-01-01

In this paper, we study the existence and uniqueness of three dimensional steady Euler flows in rectangular nozzles when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the exit are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal compon...

A-free rigidity and applications to the compressible Euler system

Czech Academy of Sciences Publication Activity Database

Chiodaroli, E.; Feireisl, Eduard; Kreml, Ondřej; Wiedemann, E.

2017-01-01

Roč. 196, č. 4 (2017), s. 1557-1572 ISSN 0373-3114 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : A-free condition * compressible Euler equations * measure-valued solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.864, year: 2016 https://link.springer.com/article/10.1007%2Fs10231-016-0629-9

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

Science.gov (United States)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

Science.gov (United States)

Loseille, A.; Dervieux, A.; Alauzet, F.

2010-04-01

This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows how to achieve this coupling in three steps. First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error. Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin finite element discretization. A goal-oriented error estimation is derived. It involves the interpolation error of the Euler fluxes weighted by the gradient of the adjoint state associated with the observed functional. Third, rewritten in the continuous mesh framework, the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations. The optimal continuous mesh is then derived analytically. Thus, it can be used as a metric tensor field to drive the mesh adaptation. From a numerical point of view, this method is completely automatic, intrinsically anisotropic, and does not depend on any a priori choice of variables to perform the adaptation. 3D examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency.

Parallel implementations of 2D explicit Euler solvers

International Nuclear Information System (INIS)

Giraud, L.; Manzini, G.

1996-01-01

In this work we present a subdomain partitioning strategy applied to an explicit high-resolution Euler solver. We describe the design of a portable parallel multi-domain code suitable for parallel environments. We present several implementations on a representative range of MlMD computers that include shared memory multiprocessors, distributed virtual shared memory computers, as well as networks of workstations. Computational results are given to illustrate the efficiency, the scalability, and the limitations of the different approaches. We discuss also the effect of the communication protocol on the optimal domain partitioning strategy for the distributed memory computers

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)

Linear discriminant analysis for welding fault detection

International Nuclear Information System (INIS)

Li, X.; Simpson, S.W.

2010-01-01

This work presents a new method for real time welding fault detection in industry based on Linear Discriminant Analysis (LDA). A set of parameters was calculated from one second blocks of electrical data recorded during welding and based on control data from reference welds under good conditions, as well as faulty welds. Optimised linear combinations of the parameters were determined with LDA and tested with independent data. Short arc welds in overlap joints were studied with various power sources, shielding gases, wire diameters, and process geometries. Out-of-position faults were investigated. Application of LDA fault detection to a broad range of welding procedures was investigated using a similarity measure based on Principal Component Analysis. The measure determines which reference data are most similar to a given industrial procedure and the appropriate LDA weights are then employed. Overall, results show that Linear Discriminant Analysis gives an effective and consistent performance in real-time welding fault detection.

Linearized FUN3D for Rapid Aeroelastic and Aeroservoelastic Design and Analysis, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — In Phase I, a prototypical FUN3D-based ZONA Euler Unsteady Solver (FunZEUS) was developed to generate the Generalized Aerodynamic Forces (GAFs) due to structural...

Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions

NARCIS (Netherlands)

J.L. López; N.M. Temme (Nico)

1998-01-01

textabstractBernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for $B_n(nz+1/2)$ and $E_n(nz+1/2)$ in powers of $n^{-1$, with coefficients being rational functions of $z$ and hyperbolic functions of argument $1/2z$. These expansions are

Well/ill posedness for the Euler-Korteweg-Poisson system and related problems

Czech Academy of Sciences Publication Activity Database

Donatelli, D.; Feireisl, Eduard; Marcati, P.

2015-01-01

Roč. 40, č. 7 (2015), s. 1314-1335 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : convex integration * Euler-Korteweg system * quantum hydrodynamics Subject RIV: BA - General Mathematics Impact factor: 1.444, year: 2015 http://www.tandfonline.com/doi/abs/10.1080/03605302.2014.972517

Euler: programa didáctico de elementos finitos

Directory of Open Access Journals (Sweden)

Dorian Luis Linero Segrera

2000-07-01

Full Text Available Este artículo muestra las características del programa Euler como herramienta para el aprendizaje del método de los elementos finitos, con énfasis en el análisis estructural. Euler puede resolver entre otros los siguientes problemas: análisis matricial estático de armaduras y pórticos planos, análisis de estabilidad, evaluación de frecuencias y modos de vibración en pórticos planos, deformaciones en vigas y en elementos sometidos a fuerza axial y otros problemas controlados por la ecuación diferencial de campo unidimensional indicada en este artículo. Además, se pueden solucionar problemas de torsión en secciones no circulares, flujo potencial, transferencia de calor y otros problemas controlados por la ecuación diferencial de campo bidimensional mostrada en este documento. También es posible resolver problemas de elasticidad bidimensional en condición plana de esfuerzos y en condición plana de deformaciones. Al operar el programa, el usuario debe escribir una de las instrucciones necesarias para obtener las cantidades de interés. Las instrucciones disponibles se clasifican así: edición de matrices, operaciones matriciales básicas, solución de sistemas de ecuaciones simultáneas, ensamblaje de matrices y vectores, numeración de grados de libertad, valores y vectores propios. Existen también instrucciones para la creación de matrices elementales como: funciones de forma, matriz gradiente, matriz de rigidez, vector de términos independientes, contribución interelemental, matriz de transformación y matriz de constantes elásticas.

Stochastic Optimal Prediction with Application to Averaged Euler Equations

Energy Technology Data Exchange (ETDEWEB)

Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2017-04-24

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

Lattice Boltzmann methods for global linear instability analysis

Science.gov (United States)

Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

2017-12-01

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

The Euler anomaly and scale factors in Liouville/Toda CFTs

Energy Technology Data Exchange (ETDEWEB)

Balasubramanian, Aswin [Theory Group, Department of Physics, University of Texas at Austin,2515 Speedway Stop C1608, Austin, TX 78712-1197 (United States)

2014-04-22

The role played by the Euler anomaly in the dictionary relating sphere partition functions of four dimensional theories of class S and two dimensional non rational CFTs is clarified. On the two dimensional side, this involves a careful treatment of scale factors in Liouville/Toda correlators. Using ideas from tinkertoy constructions for Gaiotto duality, a framework is proposed for evaluating these scale factors. The representation theory of Weyl groups plays a critical role in this framework.

Particular solutions of generalized Euler-Poisson-Darboux equation

Directory of Open Access Journals (Sweden)

Rakhila B. Seilkhanova

2015-01-01

Full Text Available In this article we consider the generalized Euler-Poisson-Darboux equation $$ {u}_{tt}+\\frac{2\\gamma }{t}{{u}_{t}}={u}_{xx}+{u}_{yy} +\\frac{2\\alpha }{x}{{u}_{x}}+\\frac{2\\beta }{y}{{u}_y},\\quad x>0,\\;y>0,\\;t>0. $$ We construct particular solutions in an explicit form expressed by the Lauricella hypergeometric function of three variables. Properties of each constructed solutions have been investigated in sections of surfaces of the characteristic cone. Precisely, we prove that found solutions have singularity $1/r$ at $r\\to 0$, where ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.

Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

Science.gov (United States)

Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

2018-04-01

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

Study of vortex breakdown of F-106B by Euler code

Science.gov (United States)

Pao, Jenn Louh

1990-01-01

The 'Three-dimensional Euler Aerodynamic Method' (TEAM) is presently applied to the F-106B at subsonic speed, in order to examine the relationship between off- and on-surface flow features at angles-of-attack sufficiently great for the occurrence of vortex breakdown. Although TEAM's flow separation is triggered by numerical dissipation, the general trend of vortex-breakdown effect on computed lift characteristics is similar to extant wind tunnel results.

Stability of the isentropic Riemann solutions of the full multidimensional Euler system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Kreml, Ondřej; Vasseur, A.

2015-01-01

Roč. 47, č. 3 (2015), s. 2416-2425 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * isentropic solutions * Riemann problem * rarefaction wave Subject RIV: BA - General Mathematics Impact factor: 1.486, year: 2015 http://epubs.siam.org/doi/abs/10.1137/140999827

Nuclear power history calculation for subcritical systems using Euler-MacLaurin formula

International Nuclear Information System (INIS)

Henrice Junior, Edson; Goncalves, Alessandro da Cruz

2013-01-01

This paper presents an efficient method for calculating the reactivity using inverse point kinetic equation for subcritical systems by applying the Euler-MacLaurin summation formula to calculate the nuclear power history. In accordance with the accuracy of the numerical results, this method does not require a large number of points for calculation, providing accurate results with low computational cost. (author)

Signals and transforms in linear systems analysis

CERN Document Server

Wasylkiwskyj, Wasyl

2013-01-01

Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7.  The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...

Design and Analysis of MEMS Linear Phased Array

Directory of Open Access Journals (Sweden)

Guoxiang Fan

2016-01-01

Full Text Available A structure of micro-electro-mechanical system (MEMS linear phased array based on “multi-cell” element is designed to increase radiation sound pressure of transducer working in bending vibration mode at high frequency. In order to more accurately predict the resonant frequency of an element, the theoretical analysis of the dynamic equation of a fixed rectangular composite plate and finite element method simulation are adopted. The effects of the parameters both in the lateral and elevation direction on the three-dimensional beam directivity characteristics are comprehensively analyzed. The key parameters in the analysis include the “cell” number of element, “cell” size, “inter-cell” spacing and the number of elements, element width. The simulation results show that optimizing the linear array parameters both in the lateral and elevation direction can greatly improve the three-dimensional beam focusing for MEMS linear phased array, which is obviously different from the traditional linear array.

Non linear stability analysis of parallel channels with natural circulation

Energy Technology Data Exchange (ETDEWEB)

Mishra, Ashish Mani; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in

2016-12-01

Highlights: • Nonlinear instabilities in natural circulation loop are studied. • Generalized Hopf points, Sub and Supercritical Hopf bifurcations are identified. • Bogdanov–Taken Point (BT Point) is observed by nonlinear stability analysis. • Effect of parameters on stability of system is studied. - Abstract: Linear stability analysis of two-phase flow in natural circulation loop is quite extensively studied by many researchers in past few years. It can be noted that linear stability analysis is limited to the small perturbations only. It is pointed out that such systems typically undergo Hopf bifurcation. If the Hopf bifurcation is subcritical, then for relatively large perturbation, the system has unstable limit cycles in the (linearly) stable region in the parameter space. Hence, linear stability analysis capturing only infinitesimally small perturbations is not sufficient. In this paper, bifurcation analysis is carried out to capture the non-linear instability of the dynamical system and both subcritical and supercritical bifurcations are observed. The regions in the parameter space for which subcritical and supercritical bifurcations exist are identified. These regions are verified by numerical simulation of the time-dependent, nonlinear ODEs for the selected points in the operating parameter space using MATLAB ODE solver.

Self-adjusting entropy-stable scheme for compressible Euler equations

Institute of Scientific and Technical Information of China (English)

程晓晗; 聂玉峰; 封建湖; LuoXiao-Yu; 蔡力

2015-01-01

In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, based on entropy variables, is employed to make the numerical diffusion term added around discontinuities automatically. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy.

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.

Analysis of Linear Hybrid Systems in CLP

DEFF Research Database (Denmark)

Banda, Gourinath; Gallagher, John Patrick

2009-01-01

In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive...

A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

Directory of Open Access Journals (Sweden)

J. Y. Kang

2013-01-01

Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.

Nonlocal multi-scale traffic flow models: analysis beyond vector spaces

Directory of Open Access Journals (Sweden)

Peter E. Kloeden

2016-08-01

Full Text Available Abstract Realistic models of traffic flow are nonlinear and involve nonlocal effects in balance laws. Flow characteristics of different types of vehicles, such as cars and trucks, need to be described differently. Two alternatives are used here, $$L^p$$ L p -valued Lebesgue measurable density functions and signed Radon measures. The resulting solution spaces are metric spaces that do not have a linear structure, so the usual convenient methods of functional analysis are no longer applicable. Instead ideas from mutational analysis will be used, in particular the method of Euler compactness will be applied to establish the well-posedness of the nonlocal balance laws. This involves the concatenation of solutions of piecewise linear systems on successive time subintervals obtained by freezing the nonlinear nonlocal coefficients to their values at the start of each subinterval. Various compactness criteria lead to a convergent subsequence. Careful estimates of the linear systems are needed to implement this program.

A new representation of rotational flow fields satisfying Euler's equation of an ideal compressible fluid

International Nuclear Information System (INIS)

Kambe, Tsutomu

2013-01-01

A new representation of the solution to Euler's equation of motion is presented by using a system of expressions for compressible rotational flows of an ideal fluid. This is regarded as a generalization of Bernoulli's theorem to compressible rotational flows. The present expressions are derived from the variational principle. The action functional for the principle consists of the main terms of the total kinetic, potential and internal energies, together with three additional terms yielding the equations of continuity, entropy and a third term that provides the rotational component of velocity field. The last term has the form of scalar product satisfying gauge symmetry with respect to both translation and rotation. This is a generalization of the Clebsch transformation from a physical point of view. It is verified that the system of new expressions, in fact, satisfies Euler's equation of motion. (paper)

A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

Czech Academy of Sciences Publication Activity Database

Bella, P.; Feireisl, Eduard; Lewicka, M.; Novotný, A.

2016-01-01

Roč. 48, č. 6 (2016), s. 3907-3930 ISSN 0036-1410 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : isentropic Navier-Stokes system * isentropic Euler system * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.648, year: 2016 http://epubs.siam.org/doi/10.1137/15M1048963

Some results on the well-posedness of Euler-Voigt and Navier-Stokes-Voigt models

OpenAIRE

Berselli, Luigi C.; Bisconti, Luca

2010-01-01

We consider the Euler-Voigt equations and the Navier-Stokes-Voigt equations, which are obtained by an inviscid alpha-regularization from the corresponding equations. The main result we show is the structural stability of the system in term of the variations of both viscosity of regularization parameters.

De la representación de sistemas Euler - Lagrange a la Hamiltoniana generalizada

Directory of Open Access Journals (Sweden)

L. H. Rodríguez - Alfaro

2015-01-01

Full Text Available La representación Hamiltoniana generalizada de sistemas brinda una estructura que puede ser utilizada con ventaja en muchas áreas, entre las cuales se puede mencionar el diseño de observadores y el diagnóstico de fallas basado en modelos. Muchos de los trabajos en estos te mas tienen como punto de partida al sistema en forma Hamiltoniana generalizada y, en general, se omite la explicación de cómo llegar a esta representación, por ejemplo, a partir de un modelo no lineal basado en las ecuaciones de Euler - Lagrange. En este tra bajo se presenta un análisis detallado de cómo es que se obtiene la representación Hamiltoniana generalizada de un sistema a partir de las n ecuaciones diferenciales de segundo orden obtenidas con el formalismo Euler - Lagrange. Con la finalidad de mostrar e n lo particular, después del caso general, cómo se obtiene la representación Hamiltoniana generalizada, se presentan algunos casos de estudio.

Manufactured solutions for the three-dimensional Euler equations with relevance to Inertial Confinement Fusion

International Nuclear Information System (INIS)

Waltz, J.; Canfield, T.R.; Morgan, N.R.; Risinger, L.D.; Wohlbier, J.G.

2014-01-01

We present a set of manufactured solutions for the three-dimensional (3D) Euler equations. The purpose of these solutions is to allow for code verification against true 3D flows with physical relevance, as opposed to 3D simulations of lower-dimensional problems or manufactured solutions that lack physical relevance. Of particular interest are solutions with relevance to Inertial Confinement Fusion (ICF) capsules. While ICF capsules are designed for spherical symmetry, they are hypothesized to become highly 3D at late time due to phenomena such as Rayleigh–Taylor instability, drive asymmetry, and vortex decay. ICF capsules also involve highly nonlinear coupling between the fluid dynamics and other physics, such as radiation transport and thermonuclear fusion. The manufactured solutions we present are specifically designed to test the terms and couplings in the Euler equations that are relevant to these phenomena. Example numerical results generated with a 3D Finite Element hydrodynamics code are presented, including mesh convergence studies

VennDiagramWeb: a web application for the generation of highly customizable Venn and Euler diagrams.

Science.gov (United States)

Lam, Felix; Lalansingh, Christopher M; Babaran, Holly E; Wang, Zhiyuan; Prokopec, Stephenie D; Fox, Natalie S; Boutros, Paul C

2016-10-03

Visualization of data generated by high-throughput, high-dimensionality experiments is rapidly becoming a rate-limiting step in computational biology. There is an ongoing need to quickly develop high-quality visualizations that can be easily customized or incorporated into automated pipelines. This often requires an interface for manual plot modification, rapid cycles of tweaking visualization parameters, and the generation of graphics code. To facilitate this process for the generation of highly-customizable, high-resolution Venn and Euler diagrams, we introduce VennDiagramWeb: a web application for the widely used VennDiagram R package. VennDiagramWeb is hosted at http://venndiagram.res.oicr.on.ca/ . VennDiagramWeb allows real-time modification of Venn and Euler diagrams, with parameter setting through a web interface and immediate visualization of results. It allows customization of essentially all aspects of figures, but also supports integration into computational pipelines via download of R code. Users can upload data and download figures in a range of formats, and there is exhaustive support documentation. VennDiagramWeb allows the easy creation of Venn and Euler diagrams for computational biologists, and indeed many other fields. Its ability to support real-time graphics changes that are linked to downloadable code that can be integrated into automated pipelines will greatly facilitate the improved visualization of complex datasets. For application support please contact Paul.Boutros@oicr.on.ca.

Self-adjusting entropy-stable scheme for compressible Euler equations

International Nuclear Information System (INIS)

Cheng Xiao-Han; Nie Yu-Feng; Cai Li; Feng Jian-Hu; Luo Xiao-Yu

2015-01-01

In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, which is based on entropy variables, is employed to make the numerical diffusion term be automatically added around discontinuities. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy. (paper)

The analysis and design of linear circuits

CERN Document Server

Thomas, Roland E; Toussaint, Gregory J

2009-01-01

The Analysis and Design of Linear Circuits, 6e gives the reader the opportunity to not only analyze, but also design and evaluate linear circuits as early as possible. The text's abundance of problems, applications, pedagogical tools, and realistic examples helps engineers develop the skills needed to solve problems, design practical alternatives, and choose the best design from several competing solutions. Engineers searching for an accessible introduction to resistance circuits will benefit from this book that emphasizes the early development of engineering judgment.

CFD analysis of linear compressors considering load conditions

Science.gov (United States)

Bae, Sanghyun; Oh, Wonsik

2017-08-01

This paper is a study on computational fluid dynamics (CFD) analysis of linear compressor considering load conditions. In the conventional CFD analysis of the linear compressor, the load condition was not considered in the behaviour of the piston. In some papers, behaviour of piston is assumed as sinusoidal motion provided by user defined function (UDF). In the reciprocating type compressor, the stroke of the piston is restrained by the rod, while the stroke of the linear compressor is not restrained, and the stroke changes depending on the load condition. The greater the pressure difference between the discharge refrigerant and the suction refrigerant, the more the centre point of the stroke is pushed backward. And the behaviour of the piston is not a complete sine wave. For this reason, when the load condition changes in the CFD analysis of the linear compressor, it may happen that the ANSYS code is changed or unfortunately the modelling is changed. In addition, a separate analysis or calculation is required to find a stroke that meets the load condition, which may contain errors. In this study, the coupled mechanical equations and electrical equations are solved using the UDF, and the behaviour of the piston is solved considering the pressure difference across the piston. Using the above method, the stroke of the piston with respect to the motor specification of the analytical model can be calculated according to the input voltage, and the piston behaviour can be realized considering the thrust amount due to the pressure difference.

On the stability of solutions, compacted to eleven dimensions, with the Euler invariants

International Nuclear Information System (INIS)

Fabris, J.C.

1991-01-01

The Supergravity Lagrangian at eleven dimensions has been modified by the inclusion of Euler invariants. Compact solutions have been obtained where the space-time is the Minkowski one, preserving, the internal space as a seven-sphere. The stability study of this configuration allows the restriction of the acceptable values for the coupling constants present in this model. (A.C.A.S.)

A Brief Historical Introduction to Euler's Formula for Polyhedra, Topology, Graph Theory and Networks

Science.gov (United States)

Debnath, Lokenath

2010-01-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…

Low-diffusion rotated upwind schemes, multigrid and defect correction for steady, multi-dimensional Euler flows

NARCIS (Netherlands)

Koren, B.; Hackbusch, W.; Trottenberg, U.

1991-01-01

Two simple, multi-dimensional upwind discretizations for the steady Euler equations are derived, with the emphasis Iying on bath a good accuracy and a good solvability. The multi-dimensional upwinding consists of applying a one-dimensional Riemann solver with a locally rotated left and right state,

A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

NARCIS (Netherlands)

Pesch, L.; van der Vegt, Jacobus J.W.

2008-01-01

Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The

Linear regression and sensitivity analysis in nuclear reactor design

International Nuclear Information System (INIS)

Kumar, Akansha; Tsvetkov, Pavel V.; McClarren, Ryan G.

2015-01-01

Highlights: • Presented a benchmark for the applicability of linear regression to complex systems. • Applied linear regression to a nuclear reactor power system. • Performed neutronics, thermal–hydraulics, and energy conversion using Brayton’s cycle for the design of a GCFBR. • Performed detailed sensitivity analysis to a set of parameters in a nuclear reactor power system. • Modeled and developed reactor design using MCNP, regression using R, and thermal–hydraulics in Java. - Abstract: The paper presents a general strategy applicable for sensitivity analysis (SA), and uncertainity quantification analysis (UA) of parameters related to a nuclear reactor design. This work also validates the use of linear regression (LR) for predictive analysis in a nuclear reactor design. The analysis helps to determine the parameters on which a LR model can be fit for predictive analysis. For those parameters, a regression surface is created based on trial data and predictions are made using this surface. A general strategy of SA to determine and identify the influential parameters those affect the operation of the reactor is mentioned. Identification of design parameters and validation of linearity assumption for the application of LR of reactor design based on a set of tests is performed. The testing methods used to determine the behavior of the parameters can be used as a general strategy for UA, and SA of nuclear reactor models, and thermal hydraulics calculations. A design of a gas cooled fast breeder reactor (GCFBR), with thermal–hydraulics, and energy transfer has been used for the demonstration of this method. MCNP6 is used to simulate the GCFBR design, and perform the necessary criticality calculations. Java is used to build and run input samples, and to extract data from the output files of MCNP6, and R is used to perform regression analysis and other multivariate variance, and analysis of the collinearity of data

N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1991-11-01

Gauge theory with a topological N=2 symmetry is discussed. This theory captures the de Rahm complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number χ (M) of M. Moduli spaces of instantons and of flat connections in 2 and 3 dimensions are explicitly dealt with. To motivate the constructions the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics are explained and a new kind of supersymmetric quantum mechanics is introduced, based on the Gauss-Codazzi equations. The gauge theory actions are interpreted from the Atiyah-Jeffrey point of view and related to super-symmetric quantum mechanics on spaces of connections. As a consequence of these considerations the Euler number χ (M) of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. The possibility of constructing a topological version of the Penner matrix model is also commented. (author). 63 refs

Large Scale Simulations of the Euler Equations on GPU Clusters

KAUST Repository

Liebmann, Manfred

2010-08-01

The paper investigates the scalability of a parallel Euler solver, using the Vijayasundaram method, on a GPU cluster with 32 Nvidia Geforce GTX 295 boards. The aim of this research is to enable large scale fluid dynamics simulations with up to one billion elements. We investigate communication protocols for the GPU cluster to compensate for the slow Gigabit Ethernet network between the GPU compute nodes and to maintain overall efficiency. A diesel engine intake-port and a nozzle, meshed in different resolutions, give good real world examples for the scalability tests on the GPU cluster. © 2010 IEEE.

Euler-Lagrange CFD modelling of unconfined gas mixing in anaerobic digestion.

Science.gov (United States)

Dapelo, Davide; Alberini, Federico; Bridgeman, John

2015-11-15

A novel Euler-Lagrangian (EL) computational fluid dynamics (CFD) finite volume-based model to simulate the gas mixing of sludge for anaerobic digestion is developed and described. Fluid motion is driven by momentum transfer from bubbles to liquid. Model validation is undertaken by assessing the flow field in a labscale model with particle image velocimetry (PIV). Conclusions are drawn about the upscaling and applicability of the model to full-scale problems, and recommendations are given for optimum application. Copyright © 2015 Elsevier Ltd. All rights reserved.

Comparison of equivalent linear and non linear methods on ground response analysis: case study at West Bangka site

International Nuclear Information System (INIS)

Eko Rudi Iswanto; Eric Yee

2016-01-01

Within the framework of identifying NPP sites, site surveys are performed in West Bangka (WB), Bangka-Belitung Island Province. Ground response analysis of a potential site has been carried out using peak strain profiles and peak ground acceleration. The objective of this research is to compare Equivalent Linear (EQL) and Non Linear (NL) methods of ground response analysis on the selected NPP site (West Bangka) using Deep Soil software. Equivalent linear method is widely used because requires soil data in simple way and short time of computational process. On the other hand, non linear method is capable of representing the actual soil behaviour by considering non linear soil parameter. The results showed that EQL method has similar trends to NL method. At surface layer, the acceleration values for EQL and NL methods are resulted as 0.425 g and 0.375 g respectively. NL method is more reliable in capturing higher frequencies of spectral acceleration compared to EQL method. (author)

Sonic boom predictions using a modified Euler code

Science.gov (United States)

Siclari, Michael J.

1992-04-01

The environmental impact of a next generation fleet of high-speed civil transports (HSCT) is of great concern in the evaluation of the commercial development of such a transport. One of the potential environmental impacts of a high speed civilian transport is the sonic boom generated by the aircraft and its effects on the population, wildlife, and structures in the vicinity of its flight path. If an HSCT aircraft is restricted from flying overland routes due to excessive booms, the commercial feasibility of such a venture may be questionable. NASA has taken the lead in evaluating and resolving the issues surrounding the development of a high speed civilian transport through its High-Speed Research Program (HSRP). The present paper discusses the usage of a Computational Fluid Dynamics (CFD) nonlinear code in predicting the pressure signature and ultimately the sonic boom generated by a high speed civilian transport. NASA had designed, built, and wind tunnel tested two low boom configurations for flight at Mach 2 and Mach 3. Experimental data was taken at several distances from these models up to a body length from the axis of the aircraft. The near field experimental data serves as a test bed for computational fluid dynamic codes in evaluating their accuracy and reliability for predicting the behavior of future HSCT designs. Sonic boom prediction methodology exists which is based on modified linear theory. These methods can be used reliably if near field signatures are available at distances from the aircraft where nonlinear and three dimensional effects have diminished in importance. Up to the present time, the only reliable method to obtain this data was via the wind tunnel with costly model construction and testing. It is the intent of the present paper to apply a modified three dimensional Euler code to predict the near field signatures of the two low boom configurations recently tested by NASA.

Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited

Science.gov (United States)

Cortissoz, Jean C.; Montero, Julio A.

2018-03-01

In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>5/2.

Error Analysis on Plane-to-Plane Linear Approximate Coordinate ...

Indian Academy of Sciences (India)

Abstract. In this paper, the error analysis has been done for the linear approximate transformation between two tangent planes in celestial sphere in a simple case. The results demonstrate that the error from the linear transformation does not meet the requirement of high-precision astrometry under some conditions, so the ...

Controllability analysis of decentralised linear controllers for polymeric fuel cells

Energy Technology Data Exchange (ETDEWEB)

Serra, Maria; Aguado, Joaquin; Ansede, Xavier; Riera, Jordi [Institut de Robotica i Informatica Industrial, Universitat Politecnica de Catalunya - Consejo Superior de Investigaciones Cientificas, C. Llorens i Artigas 4, 08028 Barcelona (Spain)

2005-10-10

This work deals with the control of polymeric fuel cells. It includes a linear analysis of the system at different operating points, the comparison and selection of different control structures, and the validation of the controlled system by simulation. The work is based on a complex non linear model which has been linearised at several operating points. The linear analysis tools used are the Morari resiliency index, the condition number, and the relative gain array. These techniques are employed to compare the controllability of the system with different control structures and at different operating conditions. According to the results, the most promising control structures are selected and their performance with PI based diagonal controllers is evaluated through simulations with the complete non linear model. The range of operability of the examined control structures is compared. Conclusions indicate good performance of several diagonal linear controllers. However, very few have a wide operability range. (author)

Linearized spectrum correlation analysis for line emission measurements.

Science.gov (United States)

Nishizawa, T; Nornberg, M D; Den Hartog, D J; Sarff, J S

2017-08-01

A new spectral analysis method, Linearized Spectrum Correlation Analysis (LSCA), for charge exchange and passive ion Doppler spectroscopy is introduced to provide a means of measuring fast spectral line shape changes associated with ion-scale micro-instabilities. This analysis method is designed to resolve the fluctuations in the emission line shape from a stationary ion-scale wave. The method linearizes the fluctuations around a time-averaged line shape (e.g., Gaussian) and subdivides the spectral output channels into two sets to reduce contributions from uncorrelated fluctuations without averaging over the fast time dynamics. In principle, small fluctuations in the parameters used for a line shape model can be measured by evaluating the cross spectrum between different channel groupings to isolate a particular fluctuating quantity. High-frequency ion velocity measurements (100-200 kHz) were made by using this method. We also conducted simulations to compare LSCA with a moment analysis technique under a low photon count condition. Both experimental and synthetic measurements demonstrate the effectiveness of LSCA.

Solution of Euler unsteady equations using a second order numerical scheme

International Nuclear Information System (INIS)

Devos, J.P.

1992-08-01

In thermal power plants, the steam circuits experience incidents due to the noise and vibration induced by trans-sonic flow. In these configurations, the compressible fluid can be considered the perfect ideal. Euler equations therefore constitute a good model. However, processing of the discontinuities induced by the shockwaves are a particular problem. We give a bibliographical synthesis of the work done on this subject. The research by Roe and Harten leads to TVD (Total Variation Decreasing) type schemes. These second order schemes generate no oscillation and converge towards physically acceptable weak solutions. (author). 12 refs

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.

Interpretation of high resolution airborne magnetic data (HRAMD of Ilesha and its environs, Southwest Nigeria, using Euler deconvolution method

Directory of Open Access Journals (Sweden)

Olurin Oluwaseun Tolutope

2017-12-01

Full Text Available Interpretation of high resolution aeromagnetic data of Ilesha and its environs within the basement complex of the geological setting of Southwestern Nigeria was carried out in the study. The study area is delimited by geographic latitudes 7°30′–8°00′N and longitudes 4°30′–5°00′E. This investigation was carried out using Euler deconvolution on filtered digitised total magnetic data (Sheet Number 243 to delineate geological structures within the area under consideration. The digitised airborne magnetic data acquired in 2009 were obtained from the archives of the Nigeria Geological Survey Agency (NGSA. The airborne magnetic data were filtered, processed and enhanced; the resultant data were subjected to qualitative and quantitative magnetic interpretation, geometry and depth weighting analyses across the study area using Euler deconvolution filter control file in Oasis Montag software. Total magnetic intensity distribution in the field ranged from –77.7 to 139.7 nT. Total magnetic field intensities reveal high-magnitude magnetic intensity values (high-amplitude anomaly and magnetic low intensities (low-amplitude magnetic anomaly in the area under consideration. The study area is characterised with high intensity correlated with lithological variation in the basement. The sharp contrast is enhanced due to the sharp contrast in magnetic intensity between the magnetic susceptibilities of the crystalline and sedimentary rocks. The reduced-to-equator (RTE map is characterised by high frequencies, short wavelengths, small size, weak intensity, sharp low amplitude and nearly irregular shaped anomalies, which may due to near-surface sources, such as shallow geologic units and cultural features. Euler deconvolution solution indicates a generally undulating basement, with a depth ranging from −500 to 1000 m. The Euler deconvolution results show that the basement relief is generally gentle and flat, lying within the basement terrain.

The Linear Time Frequency Analysis Toolbox

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel; Torrésani, Bruno; Balazs, Peter

2011-01-01

The Linear Time Frequency Analysis Toolbox is a Matlab/Octave toolbox for computational time-frequency analysis. It is intended both as an educational and computational tool. The toolbox provides the basic Gabor, Wilson and MDCT transform along with routines for constructing windows (lter...... prototypes) and routines for manipulating coe cients. It also provides a bunch of demo scripts devoted either to demonstrating the main functions of the toolbox, or to exemplify their use in specic signal processing applications. In this paper we describe the used algorithms, their mathematical background...

Application of linearized model to the stability analysis of the pressurized water reactor

International Nuclear Information System (INIS)

Li Haipeng; Huang Xiaojin; Zhang Liangju

2008-01-01

A Linear Time-Invariant model of the Pressurized Water Reactor is formulated through the linearization of the nonlinear model. The model simulation results show that the linearized model agrees well with the nonlinear model under small perturbation. Based upon the Lyapunov's First Method, the linearized model is applied to the stability analysis of the Pressurized Water Reactor. The calculation results show that the methodology of linearization to stability analysis is conveniently feasible. (authors)

Comparison of modal spectral and non-linear time history analysis of a piping system

International Nuclear Information System (INIS)

Gerard, R.; Aelbrecht, D.; Lafaille, J.P.

1987-01-01

A typical piping system of the discharge line of the chemical and volumetric control system, outside the containment, between the penetration and the heat exchanger, an operating power plant was analyzed using four different methods: Modal spectral analysis with 2% constant damping, modal spectral analysis using ASME Code Case N411 (PVRC damping), linear time history analysis, non-linear time history analysis. This paper presents an estimation of the conservatism of the linear methods compared to the non-linear analysis. (orig./HP)

Spatial Analysis of Linear Structures in the Exploration of Groundwater

Directory of Open Access Journals (Sweden)

Abdramane Dembele

2017-11-01

Full Text Available The analysis of linear structures on major geological formations plays a crucial role in resource exploration in the Inner Niger Delta. Highlighting and mapping of the large lithological units were carried out using image fusion, spectral bands (RGB coding, Principal Component Analysis (PCA, and band ratio methods. The automatic extraction method of linear structures has permitted the obtaining of a structural map with 82,659 linear structures, distributed on different stratigraphic stages. The intensity study shows an accentuation in density over 12.52% of the total area, containing 22.02% of the linear structures. The density and nodes (intersections of fractures formed by the linear structures on the different lithologies allowed to observe the behavior of the region’s aquifers in the exploration of subsoil resources. The central density, in relation to the hydrographic network of the lowlands, shows the conditioning of the flow and retention of groundwater in the region, and in-depth fluids. The node areas and high-density linear structures, have shown an ability to have rejections in deep (pores that favor the formation of structural traps for oil resources.

Generalized Linear Covariance Analysis

Science.gov (United States)

Carpenter, James R.; Markley, F. Landis

2014-01-01

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Acciones equivalentes y solución en desplazamientos interpolada en la viga de Bernouilli-Euler

OpenAIRE

Romero, J. L.; Ortega, M. A.

1998-01-01

Se propone un método para el cálculo de la viga de Bernoulli-Euler que permite optimizar los resultados obtenidos mediante los elementos finitos hermíticos tradicionales. La principal ventaja es que puede aproximar con gran bondad los desplazamientos y esfuerzos en el interior de los elementos, incluso para elementos de gran tamaño.

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

Science.gov (United States)

Shao, Zhiqiang

2018-04-01

The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

Modeling of Mixing Behavior in a Combined Blowing Steelmaking Converter with a Filter-Based Euler-Lagrange Model

Science.gov (United States)

Li, Mingming; Li, Lin; Li, Qiang; Zou, Zongshu

2018-05-01

A filter-based Euler-Lagrange multiphase flow model is used to study the mixing behavior in a combined blowing steelmaking converter. The Euler-based volume of fluid approach is employed to simulate the top blowing, while the Lagrange-based discrete phase model that embeds the local volume change of rising bubbles for the bottom blowing. A filter-based turbulence method based on the local meshing resolution is proposed aiming to improve the modeling of turbulent eddy viscosities. The model validity is verified through comparison with physical experiments in terms of mixing curves and mixing times. The effects of the bottom gas flow rate on bath flow and mixing behavior are investigated and the inherent reasons for the mixing result are clarified in terms of the characteristics of bottom-blowing plumes, the interaction between plumes and top-blowing jets, and the change of bath flow structure.

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.)

Implicit flux-split schemes for the Euler equations

Science.gov (United States)

Thomas, J. L.; Walters, R. W.; Van Leer, B.

1985-01-01

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

PART I – USUAL PROBLEMS OF OPTIMIZING THE ACTION SYSTEMS OFTHE BAND TRANSPORTERS

Directory of Open Access Journals (Sweden)

Nicoleta-Maria MIHUT

2012-05-01

Full Text Available Most of the systems of electric action are non-linear systems, including the continuous transportsystems with band, that could be brought by linearization and negligence at the linear system. The latest news inthe field of static convertors, of the new transfer schemes of electric energy, make possible the analysis of theaction systems of the continuous transport installations with band as linearisable systems. For the linearisableaction systems described by state equations, there are two consecrated calculation methods of the optimaltrajectory of the system, the variational calculation and the Euler-Lagrange algorithm, as the latter one isconsidered by the specialty literature as an optimum generator, and the first one as an extremum generator. Butthe two methods need conditions reviewed enough in the Euler-Lagrange conditions

Theoretical analysis of balanced truncation for linear switched systems

DEFF Research Database (Denmark)

Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef

2012-01-01

In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singu......In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians...... for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R....... Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009....

Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

Directory of Open Access Journals (Sweden)

Tunjo Perić

2017-01-01

Full Text Available This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1 Taylor’s polynomial linearization approximation, (2 the method of variable change, and (3 a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a using the optimal value of the objective functions as the decision makers’ aspirations, and (b the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.

Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis

Science.gov (United States)

Luo, Wen; Azen, Razia

2013-01-01

Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in…

Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model

International Nuclear Information System (INIS)

Peng Mingshu

2004-01-01

A discrete model with a simple cubic nonlinearity term is treated in the study the rich dynamics of a prototype delayed dynamical system under Euler discretization. The effect of breaking the symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

Science.gov (United States)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

Modelling non-linear effects of dark energy

Science.gov (United States)

Bose, Benjamin; Baldi, Marco; Pourtsidou, Alkistis

2018-04-01

We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving w models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter ξ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter σv. To quantify the importance of modelling the interaction, we create mock data sets for varying values of ξ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a ξ=0 modelling, ignoring the interaction. We find the fiducial growth parameter f is generally recovered even for very large values of ξ both at z=0.5 and z=1. The ξ=0 modelling is most biased in its estimation of f for the phantom w=‑1.1 case.

Linear and nonlinear stability analysis, associated to experimental fast reactors

International Nuclear Information System (INIS)

Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

1980-07-01

Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt

Advanced mechanics from Euler's determinism to Arnold's chaos

CERN Document Server

Rajeev, S G

2013-01-01

Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need to re-evaluate the purpose of learning mechanics and look at old material in the light of modern developments. Once you have learned basic mechanics (Newton's laws, the solution of the Kepler problem) and quantum mechanics (the Schrodinger equation, hydrogen atom) it is time to go back and relearn classical mechanics in greater depth. It is the intent of this book to take you through the ancient (the original meaning of "classical") parts of the subject quickly: the ideas started by Euler and ending roughly with Poincare. We then take up the developments of twentieth century physics that have largely to do with chaos and discrete time evolution (the basis of numerical solutions).

Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

International Nuclear Information System (INIS)

Fouxon, Itzhak; Oz, Yaron

2008-01-01

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

Science.gov (United States)

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

Science.gov (United States)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

Prediction of a Densely Loaded Particle-Laden Jet using a Euler-Lagrange Dense Spray Model

Science.gov (United States)

Pakseresht, Pedram; Apte, Sourabh V.

2017-11-01

Modeling of a dense spray regime using an Euler-Lagrange discrete-element approach is challenging because of local high volume loading. A subgrid cluster of droplets can lead to locally high void fractions for the disperse phase. Under these conditions, spatio-temporal changes in the carrier phase volume fractions, which are commonly neglected in spray simulations in an Euler-Lagrange two-way coupling model, could become important. Accounting for the carrier phase volume fraction variations, leads to zero-Mach number, variable density governing equations. Using pressure-based solvers, this gives rise to a source term in the pressure Poisson equation and a non-divergence free velocity field. To test the validity and predictive capability of such an approach, a round jet laden with solid particles is investigated using Direct Numerical Simulation and compared with available experimental data for different loadings. Various volume fractions spanning from dilute to dense regimes are investigated with and without taking into account the volume displacement effects. The predictions of the two approaches are compared and analyzed to investigate the effectiveness of the dense spray model. Financial support was provided by National Aeronautics and Space Administration (NASA).

Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics

Directory of Open Access Journals (Sweden)

Daniel W.F. Alves

2017-10-01

Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.

Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

Science.gov (United States)

Gonzalez-Vega, Laureano

1999-01-01

Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

Euler and Navier endash Stokes limits of the Uehling endash Uhlenbeck quantum kinetic equations

International Nuclear Information System (INIS)

Arlotti, L.; Lachowicz, M.

1997-01-01

The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics

Upwind MacCormack Euler solver with non-equilibrium chemistry

Science.gov (United States)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

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)

Robust Linear Models for Cis-eQTL Analysis.

Science.gov (United States)

Rantalainen, Mattias; Lindgren, Cecilia M; Holmes, Christopher C

2015-01-01

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.

Linear and Nonlinear Analysis of Brain Dynamics in Children with Cerebral Palsy

Science.gov (United States)

Sajedi, Firoozeh; Ahmadlou, Mehran; Vameghi, Roshanak; Gharib, Masoud; Hemmati, Sahel

2013-01-01

This study was carried out to determine linear and nonlinear changes of brain dynamics and their relationships with the motor dysfunctions in CP children. For this purpose power of EEG frequency bands (as a linear analysis) and EEG fractality (as a nonlinear analysis) were computed in eyes-closed resting state and statistically compared between 26…

An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes

International Nuclear Information System (INIS)

Almeida, Regina Celia Cerqueira de

1993-01-01

A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author)

Functional linear models for association analysis of quantitative traits.

Science.gov (United States)

Fan, Ruzong; Wang, Yifan; Mills, James L; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao

2013-11-01

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F-distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT-O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT-O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study. © 2013 WILEY

An analysis of the electromagnetic field in multi-polar linear induction system

International Nuclear Information System (INIS)

Chervenkova, Todorka; Chervenkov, Atanas

2002-01-01

In this paper a new method for determination of the electromagnetic field vectors in a multi-polar linear induction system (LIS) is described. The analysis of the electromagnetic field has been done by four dimensional electromagnetic potentials in conjunction with theory of the magnetic loops . The electromagnetic field vectors are determined in the Minkovski's space as elements of the Maxwell's tensor. The results obtained are compared with those got from the analysis made by the finite elements method (FEM).With the method represented in this paper one can determine the electromagnetic field vectors in the multi-polar linear induction system using four-dimensional potential. A priority of this method is the obtaining of analytical results for the electromagnetic field vectors. These results are also valid for linear media. The dependencies are valid also at high speeds of movement. The results of the investigated linear induction system are comparable to those got by the finite elements method. The investigations may be continued in the determination of other characteristics such as drag force, levitation force, etc. The method proposed in this paper for an analysis of linear induction system can be used for optimization calculations. (Author)

Stability Analysis for Multi-Parameter Linear Periodic Systems

DEFF Research Database (Denmark)

Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli

1999-01-01

This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...

Linearization effect in multifractal analysis: Insights from the Random Energy Model

Science.gov (United States)

Angeletti, Florian; Mézard, Marc; Bertin, Eric; Abry, Patrice

2011-08-01

The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of disordered systems, notably from the analysis of the so-called Random Energy Model. Considering a standard multifractal process (compound Poisson motion), chosen as a simple representative example, we show the following: (i) the existence of a critical order q∗ beyond which moments, though finite, cannot be estimated through empirical averages, irrespective of the sample size of the observation; (ii) multifractal exponents necessarily behave linearly in q, for q>q∗. Tailoring the analysis conducted for the Random Energy Model to that of Compound Poisson motion, we provide explicative and quantitative predictions for the values of q∗ and for the slope controlling the linear behavior of the multifractal exponents. These quantities are shown to be related only to the definition of the multifractal process and not to depend on the sample size of the observation. Monte Carlo simulations, conducted over a large number of large sample size realizations of compound Poisson motion, comfort and extend these analyses.

Effects of measurement errors on psychometric measurements in ergonomics studies: Implications for correlations, ANOVA, linear regression, factor analysis, and linear discriminant analysis.

Science.gov (United States)

Liu, Yan; Salvendy, Gavriel

2009-05-01

This paper aims to demonstrate the effects of measurement errors on psychometric measurements in ergonomics studies. A variety of sources can cause random measurement errors in ergonomics studies and these errors can distort virtually every statistic computed and lead investigators to erroneous conclusions. The effects of measurement errors on five most widely used statistical analysis tools have been discussed and illustrated: correlation; ANOVA; linear regression; factor analysis; linear discriminant analysis. It has been shown that measurement errors can greatly attenuate correlations between variables, reduce statistical power of ANOVA, distort (overestimate, underestimate or even change the sign of) regression coefficients, underrate the explanation contributions of the most important factors in factor analysis and depreciate the significance of discriminant function and discrimination abilities of individual variables in discrimination analysis. The discussions will be restricted to subjective scales and survey methods and their reliability estimates. Other methods applied in ergonomics research, such as physical and electrophysiological measurements and chemical and biomedical analysis methods, also have issues of measurement errors, but they are beyond the scope of this paper. As there has been increasing interest in the development and testing of theories in ergonomics research, it has become very important for ergonomics researchers to understand the effects of measurement errors on their experiment results, which the authors believe is very critical to research progress in theory development and cumulative knowledge in the ergonomics field.

High resolution solutions of the Euler equations for vortex flows

International Nuclear Information System (INIS)

Murman, E.M.; Powell, K.G.; Rizzi, A.; Tel Aviv Univ., Israel)

1985-01-01

Solutions of the Euler equations are presented for M = 1.5 flow past a 70-degree-swept delta wing. At an angle of attack of 10 degrees, strong leading-edge vortices are produced. Two computational approaches are taken, based upon fully three-dimensional and conical flow theory. Both methods utilize a finite-volume discretization solved by a pseudounsteady multistage scheme. Results from the two approaches are in good agreement. Computations have been done on a 16-million-word CYBER 205 using 196 x 56 x 96 and 128 x 128 cells for the two methods. A sizable data base is generated, and some of the practical aspects of manipulating it are mentioned. The results reveal many interesting physical features of the compressible vortical flow field and also suggest new areas needing research. 16 references

Linear stability analysis in a solid-propellant rocket motor

Energy Technology Data Exchange (ETDEWEB)

Kim, K.M.; Kang, K.T.; Yoon, J.K. [Agency for Defense Development, Taejon (Korea, Republic of)

1995-10-01

Combustion instability in solid-propellant rocket motors depends on the balance between acoustic energy gains and losses of the system. The objective of this paper is to demonstrate the capability of the program which predicts the standard longitudinal stability using acoustic modes based on linear stability analysis and T-burner test results of propellants. Commercial ANSYS 5.0A program can be used to calculate the acoustic characteristic of a rocket motor. The linear stability prediction was compared with the static firing test results of rocket motors. (author). 11 refs., 17 figs.

Linear stability analysis of collective neutrino oscillations without spurious modes

Science.gov (United States)

Morinaga, Taiki; Yamada, Shoichi

2018-01-01

Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system

Science.gov (United States)

Chen, Shuxing; Li, Dening

2014-09-01

We study the Cauchy problems for the isentropic 2-d Euler system with discontinuous initial data along a smooth curve. All three singularities are present in the solution: shock wave, rarefaction wave and contact discontinuity. We show that the usual restrictive high order compatibility conditions for the initial data are automatically satisfied. The local existence of piecewise smooth solution containing all three waves is established.

Use of linear discriminant function analysis in seed morphotype ...

African Journals Online (AJOL)

Use of linear discriminant function analysis in seed morphotype relationship study in 31 ... Data were collected on 100-seed weight, seed length and seed width. ... to the Mesoamerican gene pool, comprising the cultigroups Sieva-Big Lima, ...

Linear functional analysis for scientists and engineers

CERN Document Server

Limaye, Balmohan V

2016-01-01

This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance structure of a metric space, functional analysis is increasingly gaining the attention of not only mathematicians but also scientists and engineers. The purpose of the text is to present the basic aspects of functional analysis to this varied audience, keeping in mind the considerations of applicability. A novelty of this book is the inclusion of a result by Zabreiko, which states that every countably subadditive seminorm on a Banach space is continuous. Several major theorems in functional analysis are easy consequences of this result. The entire book can be used as a textbook for an introductory course in functional analysis without having to make any specific selection from the topics presented here. Basic notions in the setting of a metric space are defined in terms of sequences. These include total boundedness, c...

Non-linear analysis of skew thin plate by finite difference method

International Nuclear Information System (INIS)

Kim, Chi Kyung; Hwang, Myung Hwan

2012-01-01

This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed

On the efficacy of linear system analysis of renal autoregulation in rats

DEFF Research Database (Denmark)

Chon, K H; Chen, Y M; Holstein-Rathlou, N H

1993-01-01

In order to assess the linearity of the mechanisms subserving renal blood flow autoregulation, broad-band arterial pressure fluctuations at three different power levels were induced experimentally and the resulting renal blood flow responses were recorded. Linear system analysis methods were...

Linear and nonlinear analysis of high-power rf amplifiers

International Nuclear Information System (INIS)

Puglisi, M.

1983-01-01

After a survey of the state variable analysis method the final amplifier for the CBA is analyzed taking into account the real beam waveshape. An empirical method for checking the stability of a non-linear system is also considered

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

Sampling microcanonical measures of the 2D Euler equations through Creutz’s algorithm: a phase transition from disorder to order when energy is increased

International Nuclear Information System (INIS)

Potters, Max; Vaillant, Timothee; Bouchet, Freddy

2013-01-01

The 2D Euler equations are basic examples of fluid models for which a microcanonical measure can be constructed from first principles. This measure is defined through finite-dimensional approximations and a limiting procedure. Creutz’s algorithm is a microcanonical generalization of the Metropolis–Hastings algorithm (to sample Gibbs measures, in the canonical ensemble). We prove that Creutz’s algorithm can sample finite-dimensional approximations of the 2D Euler microcanonical measures (incorporating fixed energy and other invariants). This is essential as microcanonical and canonical measures are known to be inequivalent at some values of energy and vorticity distribution. Creutz’s algorithm is used to check predictions from the mean-field statistical mechanics theory of the 2D Euler equations (the Robert–Sommeria–Miller theory). We find full agreement with theory. Three different ways to compute the temperature give consistent results. Using Creutz’s algorithm, a first-order phase transition never observed previously and a situation of statistical ensemble inequivalence are found and studied. Strikingly, and in contrast to the usual statistical mechanics interpretations, this phase transition appears from a disordered phase to an ordered phase (with fewer symmetries) when the energy is increased. We explain this paradox. (paper)

Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren

2010-01-01

, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations...... and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...

Supersymmetric extension of the nine-dimensional continuation of the Euler density with N=2

International Nuclear Information System (INIS)

Hassaine, Mokhtar; Olea, Rodrigo; Troncoso, Ricardo

2004-01-01

A local supersymmetric extension with N=2 of the dimensional continuation of the Euler-Gauss-Bonnet density from eight to nine dimensions is constructed. The gravitational sector is invariant under local Poincare translations, and the full field content is given by the vielbein, the spin connection, a complex gravitino, and an Abelian one-form. The local symmetry group is shown to be super Poincare with N=2 and a U(1) central extension, and the full supersymmetric Lagrangian can be written as a Chern-Simons form

Supersymmetric extension of the nine-dimensional continuation of the Euler density with N=2

Energy Technology Data Exchange (ETDEWEB)

Hassaine, Mokhtar [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)]. E-mail: hassaine@blackhole.cecs.cl; Olea, Rodrigo [Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile); Troncoso, Ricardo [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)

2004-10-07

A local supersymmetric extension with N=2 of the dimensional continuation of the Euler-Gauss-Bonnet density from eight to nine dimensions is constructed. The gravitational sector is invariant under local Poincare translations, and the full field content is given by the vielbein, the spin connection, a complex gravitino, and an Abelian one-form. The local symmetry group is shown to be super Poincare with N=2 and a U(1) central extension, and the full supersymmetric Lagrangian can be written as a Chern-Simons form.

Sensitivity analysis of linear programming problem through a recurrent neural network

Science.gov (United States)

Das, Raja

2017-11-01

In this paper we study the recurrent neural network for solving linear programming problems. To achieve optimality in accuracy and also in computational effort, an algorithm is presented. We investigate the sensitivity analysis of linear programming problem through the neural network. A detailed example is also presented to demonstrate the performance of the recurrent neural network.

An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes; Uma formulacao de Petrov-Galerkin para a resolucao das equacoes de Euler e Navier-Stokes compressivel usando tecnicas adaptativas

Energy Technology Data Exchange (ETDEWEB)

Almeida, Regina Celia Cerqueira de

1993-12-31

A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.

An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes; Uma formulacao de Petrov-Galerkin para a resolucao das equacoes de Euler e Navier-Stokes compressivel usando tecnicas adaptativas

Energy Technology Data Exchange (ETDEWEB)

Almeida, Regina Celia Cerqueira de

1994-12-31

A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.

Robust linear discriminant analysis with distance based estimators

Science.gov (United States)

Lim, Yai-Fung; Yahaya, Sharipah Soaad Syed; Ali, Hazlina

2017-11-01

Linear discriminant analysis (LDA) is one of the supervised classification techniques concerning relationship between a categorical variable and a set of continuous variables. The main objective of LDA is to create a function to distinguish between populations and allocating future observations to previously defined populations. Under the assumptions of normality and homoscedasticity, the LDA yields optimal linear discriminant rule (LDR) between two or more groups. However, the optimality of LDA highly relies on the sample mean and pooled sample covariance matrix which are known to be sensitive to outliers. To alleviate these conflicts, a new robust LDA using distance based estimators known as minimum variance vector (MVV) has been proposed in this study. The MVV estimators were used to substitute the classical sample mean and classical sample covariance to form a robust linear discriminant rule (RLDR). Simulation and real data study were conducted to examine on the performance of the proposed RLDR measured in terms of misclassification error rates. The computational result showed that the proposed RLDR is better than the classical LDR and was comparable with the existing robust LDR.

Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis

Science.gov (United States)

Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel

2013-01-01

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007

An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations

Science.gov (United States)

Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan

2016-12-01

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function

Treating experimental data of inverse kinetic method by unitary linear regression analysis

International Nuclear Information System (INIS)

Zhao Yusen; Chen Xiaoliang

2009-01-01

The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)

Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow

Science.gov (United States)

Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr

2018-04-01

The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.

Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)

International Nuclear Information System (INIS)

Dubinskii, Yu A; Osipenko, A S

2000-01-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented

Describing three-class task performance: three-class linear discriminant analysis and three-class ROC analysis

Science.gov (United States)

He, Xin; Frey, Eric C.

2007-03-01

Binary ROC analysis has solid decision-theoretic foundations and a close relationship to linear discriminant analysis (LDA). In particular, for the case of Gaussian equal covariance input data, the area under the ROC curve (AUC) value has a direct relationship to the Hotelling trace. Many attempts have been made to extend binary classification methods to multi-class. For example, Fukunaga extended binary LDA to obtain multi-class LDA, which uses the multi-class Hotelling trace as a figure-of-merit, and we have previously developed a three-class ROC analysis method. This work explores the relationship between conventional multi-class LDA and three-class ROC analysis. First, we developed a linear observer, the three-class Hotelling observer (3-HO). For Gaussian equal covariance data, the 3- HO provides equivalent performance to the three-class ideal observer and, under less strict conditions, maximizes the signal to noise ratio for classification of all pairs of the three classes simultaneously. The 3-HO templates are not the eigenvectors obtained from multi-class LDA. Second, we show that the three-class Hotelling trace, which is the figureof- merit in the conventional three-class extension of LDA, has significant limitations. Third, we demonstrate that, under certain conditions, there is a linear relationship between the eigenvectors obtained from multi-class LDA and 3-HO templates. We conclude that the 3-HO based on decision theory has advantages both in its decision theoretic background and in the usefulness of its figure-of-merit. Additionally, there exists the possibility of interpreting the two linear features extracted by the conventional extension of LDA from a decision theoretic point of view.

Modos em vigas com secção transversal de variação linear

OpenAIRE

Jovita Rasch Bracht Juver

2002-01-01

O objetivo principal deste trabalho é a obtenção dos modos e as freqüências naturais de vigas de variação linear e em forma de cunha, com condições de contorno clássicas e não-clássicas, descritas pelo modelo estrutural de Euler-Bernoulli. A forma dos modos foi determinado com o uso das funções cilíndricas. No caso forçado se considera uma força harmônica e se resolve o problema pelo método espectral, utuilizando o software simbólico Maple V5. Realiza-se uma análise comparativa dos resultados...

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Energy Technology Data Exchange (ETDEWEB)

Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory; Morel, Jim E [TEXAS A& M UNIV

2008-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Science.gov (United States)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation

International Nuclear Information System (INIS)

Konopelchenko, B; Alonso, L MartInez; Medina, E

2010-01-01

It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock-type singularities are presented.

Linear Covariance Analysis for a Lunar Lander

Science.gov (United States)

Jang, Jiann-Woei; Bhatt, Sagar; Fritz, Matthew; Woffinden, David; May, Darryl; Braden, Ellen; Hannan, Michael

2017-01-01

A next-generation lunar lander Guidance, Navigation, and Control (GNC) system, which includes a state-of-the-art optical sensor suite, is proposed in a concept design cycle. The design goal is to allow the lander to softly land within the prescribed landing precision. The achievement of this precision landing requirement depends on proper selection of the sensor suite. In this paper, a robust sensor selection procedure is demonstrated using a Linear Covariance (LinCov) analysis tool developed by Draper.

Optimal choice of basis functions in the linear regression analysis

International Nuclear Information System (INIS)

Khotinskij, A.M.

1988-01-01

Problem of optimal choice of basis functions in the linear regression analysis is investigated. Step algorithm with estimation of its efficiency, which holds true at finite number of measurements, is suggested. Conditions, providing the probability of correct choice close to 1 are formulated. Application of the step algorithm to analysis of decay curves is substantiated. 8 refs

Monte Carlo Euler approximations of HJM term structure financial models

KAUST Repository

Björk, Tomas

2012-11-22

We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates. © 2012 Springer Science+Business Media Dordrecht.

Monte Carlo Euler approximations of HJM term structure financial models

KAUST Repository

Bjö rk, Tomas; Szepessy, Anders; Tempone, Raul; Zouraris, Georgios E.

2012-01-01

We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates. © 2012 Springer Science+Business Media Dordrecht.

Linearly Polarized IR Spectroscopy Theory and Applications for Structural Analysis

CERN Document Server

Kolev, Tsonko

2011-01-01

A technique that is useful in the study of pharmaceutical products and biological molecules, polarization IR spectroscopy has undergone continuous development since it first emerged almost 100 years ago. Capturing the state of the science as it exists today, "Linearly Polarized IR Spectroscopy: Theory and Applications for Structural Analysis" demonstrates how the technique can be properly utilized to obtain important information about the structure and spectral properties of oriented compounds. The book starts with the theoretical basis of linear-dichroic infrared (IR-LD) spectroscop

Generalized linear models with random effects unified analysis via H-likelihood

CERN Document Server

Lee, Youngjo; Pawitan, Yudi

2006-01-01

Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors.Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of...

Algorithm for Non-proportional Loading in Sequentially Linear Analysis

NARCIS (Netherlands)

Yu, C.; Hoogenboom, P.C.J.; Rots, J.G.; Saouma, V.; Bolander, J.; Landis, E.

2016-01-01

Sequentially linear analysis (SLA) is an alternative to the Newton-Raphson method for analyzing the nonlinear behavior of reinforced concrete and masonry structures. In this paper SLA is extended to load cases that are applied one after the other, for example first dead load and then wind load. It

Improved Methods for Pitch Synchronous Linear Prediction Analysis of Speech

OpenAIRE

劉, 麗清

2015-01-01

Linear prediction (LP) analysis has been applied to speech system over the last few decades. LP technique is well-suited for speech analysis due to its ability to model speech production process approximately. Hence LP analysis has been widely used for speech enhancement, low-bit-rate speech coding in cellular telephony, speech recognition, characteristic parameter extraction (vocal tract resonances frequencies, fundamental frequency called pitch) and so on. However, the performance of the co...

A Homotopy-Perturbation analysis of the non-linear contaminant ...

African Journals Online (AJOL)

In this research work, a Homotopy-perturbation analysis of a non –linear contaminant flow equation with an initial continuous point source is provided. The equation is characterized by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of ...

Linear discriminant analysis of structure within African eggplant 'Shum'

African Journals Online (AJOL)

A MANOVA preceded linear discriminant analysis, to model each of 61 variables, as predicted by clusters and experiment to filter out non-significant traits. Four distinct clusters emerged, with a cophenetic relation coefficient of 0.87 (P<0.01). Canonical variates that best predicted the observed clusters include petiole length, ...

On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model

International Nuclear Information System (INIS)

Unkel, Steffen; Belka, Claus; Lauber, Kirsten

2016-01-01

The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed

Comparative analysis of linear motor geometries for Stirling coolers

Science.gov (United States)

R, Rajesh V.; Kuzhiveli, Biju T.

2017-12-01

Compared to rotary motor driven Stirling coolers, linear motor coolers are characterized by small volume and long life, making them more suitable for space and military applications. The motor design and operational characteristics have a direct effect on the operation of the cooler. In this perspective, ample scope exists in understanding the behavioural description of linear motor systems. In the present work, the authors compare and analyze different moving magnet linear motor geometries to finalize the most favourable one for Stirling coolers. The required axial force in the linear motors is generated by the interaction of magnetic fields of a current carrying coil and that of a permanent magnet. The compact size, commercial availability of permanent magnets and low weight requirement of the system are quite a few constraints for the design. The finite element analysis performed using Maxwell software serves as the basic tool to analyze the magnet movement, flux distribution in the air gap and the magnetic saturation levels on the core. A number of material combinations are investigated for core before finalizing the design. The effect of varying the core geometry on the flux produced in the air gap is also analyzed. The electromagnetic analysis of the motor indicates that the permanent magnet height ought to be taken in such a way that it is under the influence of electromagnetic field of current carrying coil as well as the outer core in the balanced position. This is necessary so that sufficient amount of thrust force is developed by efficient utilisation of the air gap flux density. Also, the outer core ends need to be designed to facilitate enough room for the magnet movement under the operating conditions.

PISCES 3DELK - a coupled Euler/Lagrange program for computing dynamic fluid-structure interactions in three dimensions

International Nuclear Information System (INIS)

Chu, H.Y.; Cowler, M.S.; Hancock, H.

1983-01-01

This paper describes the main features of PISCES 3DELK, a computer code that is used to solve complex three-dimensional fluid-structure interaction problems in reactor safety. These features include: an Eulerian finite difference scheme for calculating fluid flow and large distortions of solid media; a Langrange finite element scheme for calculating the response of thin structures; coupling of the Euler and Langrange schemes at fluid-structure interfaces. The code has been well validated and applied to a number of reactor safety analyses including blowdown in reactor primary vessels and components, and loadings on the secondary containment caused by a breach in the primary containment. Details of two analyses are presented in this paper. The first analysis is of blowdown in a pressurized water reactor caused by a cold leg break (the HDR experiment). Results of the PISCES 3DELK calculation are compared with results obtained by the K-FIX code. Agreement between the two calculations is good. The second analysis is of the depressurization caused by a feedwater pipe break in a steam generator of the CANDU reactor. Calculations have been performed which show that flexibility of internal components in the heat exchanger mitigate structural loadings. (orig.)

[Comparison of application of Cochran-Armitage trend test and linear regression analysis for rate trend analysis in epidemiology study].

Science.gov (United States)

Wang, D Z; Wang, C; Shen, C F; Zhang, Y; Zhang, H; Song, G D; Xue, X D; Xu, Z L; Zhang, S; Jiang, G H

2017-05-10

We described the time trend of acute myocardial infarction (AMI) from 1999 to 2013 in Tianjin incidence rate with Cochran-Armitage trend (CAT) test and linear regression analysis, and the results were compared. Based on actual population, CAT test had much stronger statistical power than linear regression analysis for both overall incidence trend and age specific incidence trend (Cochran-Armitage trend P valuelinear regression P value). The statistical power of CAT test decreased, while the result of linear regression analysis remained the same when population size was reduced by 100 times and AMI incidence rate remained unchanged. The two statistical methods have their advantages and disadvantages. It is necessary to choose statistical method according the fitting degree of data, or comprehensively analyze the results of two methods.

Foundations of linear and generalized linear models

CERN Document Server

Agresti, Alan

2015-01-01

A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,

Linear Covariance Analysis and Epoch State Estimators

Science.gov (United States)

Markley, F. Landis; Carpenter, J. Russell

2014-01-01

This paper extends in two directions the results of prior work on generalized linear covariance analysis of both batch least-squares and sequential estimators. The first is an improved treatment of process noise in the batch, or epoch state, estimator with an epoch time that may be later than some or all of the measurements in the batch. The second is to account for process noise in specifying the gains in the epoch state estimator. We establish the conditions under which the latter estimator is equivalent to the Kalman filter.

The Application of Euler-Lagrange Method of Optimization for Electromechanical Motion Control

Directory of Open Access Journals (Sweden)

Cristian VASILACHE

2000-12-01

Full Text Available Industrial and non-industrial processes such as production plans, robots, pumps, compressors, home applications, transportation of people and goods etc., require some kinds of motion control. The main functions of electromechanical drives are to adjust these processes by controlling the torque, speed or position. The objective of this paper is to perform the control of motion while minimizing power losses, that is ∫Ri2dt, in process conversion of electrical energy to mechanical energy. The optimal control laws for our problem is find using the Euler - Lagrange principle. We consider three types of controlled drives: torque, speed and position. Each of them has different control laws. By implementation of these controls with Borland C++ and Matlab environment, substantial energy savings are obtained.

Linear discriminant analysis of character sequences using occurrences of words

KAUST Repository

Dutta, Subhajit; Chaudhuri, Probal; Ghosh, Anil

2014-01-01

Classification of character sequences, where the characters come from a finite set, arises in disciplines such as molecular biology and computer science. For discriminant analysis of such character sequences, the Bayes classifier based on Markov models turns out to have class boundaries defined by linear functions of occurrences of words in the sequences. It is shown that for such classifiers based on Markov models with unknown orders, if the orders are estimated from the data using cross-validation, the resulting classifier has Bayes risk consistency under suitable conditions. Even when Markov models are not valid for the data, we develop methods for constructing classifiers based on linear functions of occurrences of words, where the word length is chosen by cross-validation. Such linear classifiers are constructed using ideas of support vector machines, regression depth, and distance weighted discrimination. We show that classifiers with linear class boundaries have certain optimal properties in terms of their asymptotic misclassification probabilities. The performance of these classifiers is demonstrated in various simulated and benchmark data sets.

Linear discriminant analysis of character sequences using occurrences of words

KAUST Repository

Dutta, Subhajit

2014-02-01

Classification of character sequences, where the characters come from a finite set, arises in disciplines such as molecular biology and computer science. For discriminant analysis of such character sequences, the Bayes classifier based on Markov models turns out to have class boundaries defined by linear functions of occurrences of words in the sequences. It is shown that for such classifiers based on Markov models with unknown orders, if the orders are estimated from the data using cross-validation, the resulting classifier has Bayes risk consistency under suitable conditions. Even when Markov models are not valid for the data, we develop methods for constructing classifiers based on linear functions of occurrences of words, where the word length is chosen by cross-validation. Such linear classifiers are constructed using ideas of support vector machines, regression depth, and distance weighted discrimination. We show that classifiers with linear class boundaries have certain optimal properties in terms of their asymptotic misclassification probabilities. The performance of these classifiers is demonstrated in various simulated and benchmark data sets.

A spectral element-FCT method for the compressible Euler equations

International Nuclear Information System (INIS)

Giannakouros, J.; Karniadakis, G.E.

1994-01-01

A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements

Analysis of baseline, average, and longitudinally measured blood pressure data using linear mixed models.

Science.gov (United States)

Hossain, Ahmed; Beyene, Joseph

2014-01-01

This article compares baseline, average, and longitudinal data analysis methods for identifying genetic variants in genome-wide association study using the Genetic Analysis Workshop 18 data. We apply methods that include (a) linear mixed models with baseline measures, (b) random intercept linear mixed models with mean measures outcome, and (c) random intercept linear mixed models with longitudinal measurements. In the linear mixed models, covariates are included as fixed effects, whereas relatedness among individuals is incorporated as the variance-covariance structure of the random effect for the individuals. The overall strategy of applying linear mixed models decorrelate the data is based on Aulchenko et al.'s GRAMMAR. By analyzing systolic and diastolic blood pressure, which are used separately as outcomes, we compare the 3 methods in identifying a known genetic variant that is associated with blood pressure from chromosome 3 and simulated phenotype data. We also analyze the real phenotype data to illustrate the methods. We conclude that the linear mixed model with longitudinal measurements of diastolic blood pressure is the most accurate at identifying the known single-nucleotide polymorphism among the methods, but linear mixed models with baseline measures perform best with systolic blood pressure as the outcome.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

Science.gov (United States)

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

Linear Stability Analysis of an Acoustically Vaporized Droplet

Science.gov (United States)

Siddiqui, Junaid; Qamar, Adnan; Samtaney, Ravi

2015-11-01

Acoustic droplet vaporization (ADV) is a phase transition phenomena of a superheat liquid (Dodecafluoropentane, C5F12) droplet to a gaseous bubble, instigated by a high-intensity acoustic pulse. This approach was first studied in imaging applications, and applicable in several therapeutic areas such as gas embolotherapy, thrombus dissolution, and drug delivery. High-speed imaging and theoretical modeling of ADV has elucidated several physical aspects, ranging from bubble nucleation to its subsequent growth. Surface instabilities are known to exist and considered responsible for evolving bubble shapes (non-spherical growth, bubble splitting and bubble droplet encapsulation). We present a linear stability analysis of the dynamically evolving interfaces of an acoustically vaporized micro-droplet (liquid A) in an infinite pool of a second liquid (liquid B). We propose a thermal ADV model for the base state. The linear analysis utilizes spherical harmonics (Ynm, of degree m and order n) and under various physical assumptions results in a time-dependent ODE of the perturbed interface amplitudes (one at the vapor/liquid A interface and the other at the liquid A/liquid B interface). The perturbation amplitudes are found to grow exponentially and do not depend on m. Supported by KAUST Baseline Research Funds.

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

Science.gov (United States)

Anderson, Carl A; McRae, Allan F; Visscher, Peter M

2006-07-01

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

Science.gov (United States)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

Science.gov (United States)

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

Stability analysis and stabilization strategies for linear supply chains

Science.gov (United States)

Nagatani, Takashi; Helbing, Dirk

2004-04-01

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.

Linear and nonlinear analysis of fluid slosh dampers

Science.gov (United States)

Sayar, B. A.; Baumgarten, J. R.

1982-11-01

A vibrating structure and a container partially filled with fluid are considered coupled in a free vibration mode. To simplify the mathematical analysis, a pendulum model to duplicate the fluid motion and a mass-spring dashpot representing the vibrating structure are used. The equations of motion are derived by Lagrange's energy approach and expressed in parametric form. For a wide range of parametric values the logarithmic decrements of the main system are calculated from theoretical and experimental response curves in the linear analysis. However, for the nonlinear analysis the theoretical and experimental response curves of the main system are compared. Theoretical predictions are justified by experimental observations with excellent agreement. It is concluded finally that for a proper selection of design parameters, containers partially filled with viscous fluids serve as good vibration dampers.

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

Science.gov (United States)

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

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.)

Multi-cell vortices observed in fine-mesh solutions to the incompressible Euler equations

International Nuclear Information System (INIS)

Rizzi, A.

1986-01-01

Results are presented for a three dimensional flow, containing a vortex sheet shed from a delta wing. The numerical solution indicates that the shearing caused by the trailing edge of the wing set up a torsional wave on the vortex core and produces a structure with multiple cells of vorticity. Although observed in coarse grid solutions too, this effect becomes better resolved with mesh refinement to 614 000 grid volumes. In comparison with a potential solution in which the vortex sheet is fitted as a discontinuity, the results are analyzed for the position of the vortex features captured in the Euler flow field, the accuracy of the pressure field, and for the diffusion of the vortex sheets

Feature-space-based FMRI analysis using the optimal linear transformation.

Science.gov (United States)

Sun, Fengrong; Morris, Drew; Lee, Wayne; Taylor, Margot J; Mills, Travis; Babyn, Paul S

2010-09-01

The optimal linear transformation (OLT), an image analysis technique of feature space, was first presented in the field of MRI. This paper proposes a method of extending OLT from MRI to functional MRI (fMRI) to improve the activation-detection performance over conventional approaches of fMRI analysis. In this method, first, ideal hemodynamic response time series for different stimuli were generated by convolving the theoretical hemodynamic response model with the stimulus timing. Second, constructing hypothetical signature vectors for different activity patterns of interest by virtue of the ideal hemodynamic responses, OLT was used to extract features of fMRI data. The resultant feature space had particular geometric clustering properties. It was then classified into different groups, each pertaining to an activity pattern of interest; the applied signature vector for each group was obtained by averaging. Third, using the applied signature vectors, OLT was applied again to generate fMRI composite images with high SNRs for the desired activity patterns. Simulations and a blocked fMRI experiment were employed for the method to be verified and compared with the general linear model (GLM)-based analysis. The simulation studies and the experimental results indicated the superiority of the proposed method over the GLM-based analysis in detecting brain activities.

Flutter analysis of an airfoil with nonlinear damping using equivalent linearization

Directory of Open Access Journals (Sweden)

Chen Feixin

2014-02-01

Full Text Available The equivalent linearization method (ELM is modified to investigate the nonlinear flutter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flutter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation (LCO is chosen as an active increment to produce bifurcation charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.

Linear and nonlinear subspace analysis of hand movements during grasping.

Science.gov (United States)

Cui, Phil Hengjun; Visell, Yon

2014-01-01

This study investigated nonlinear patterns of coordination, or synergies, underlying whole-hand grasping kinematics. Prior research has shed considerable light on roles played by such coordinated degrees-of-freedom (DOF), illuminating how motor control is facilitated by structural and functional specializations in the brain, peripheral nervous system, and musculoskeletal system. However, existing analyses suppose that the patterns of coordination can be captured by means of linear analyses, as linear combinations of nominally independent DOF. In contrast, hand kinematics is itself highly nonlinear in nature. To address this discrepancy, we sought to to determine whether nonlinear synergies might serve to more accurately and efficiently explain human grasping kinematics than is possible with linear analyses. We analyzed motion capture data acquired from the hands of individuals as they grasped an array of common objects, using four of the most widely used linear and nonlinear dimensionality reduction algorithms. We compared the results using a recently developed algorithm-agnostic quality measure, which enabled us to assess the quality of the dimensional reductions that resulted by assessing the extent to which local neighborhood information in the data was preserved. Although qualitative inspection of this data suggested that nonlinear correlations between kinematic variables were present, we found that linear modeling, in the form of Principle Components Analysis, could perform better than any of the nonlinear techniques we applied.

Design and analysis approach for linear aerospike nozzle

International Nuclear Information System (INIS)

Khan, S.U.; Khan, A.A.; Munir, A.

2014-01-01

The paper presents an aerodynamic design of a simplified linear aerospike nozzle and its detailed exhaust flow analysis with no spike truncation. Analytical method with isentropic planar flow was used to generate the nozzle contour through MATLAB . The developed code produces a number of outputs comprising nozzle wall profile, flow properties along the nozzle wall, thrust coefficient, thrust, as well as amount of nozzle truncation. Results acquired from design code and numerical analyses are compared for observing differences. The numerical analysis adopted an inviscid model carried out through commercially available and reliable computational fluid dynamics (CFD) software. Use of the developed code would assist the readers to perform quick analysis of different aerodynamic design parameters for the aerospike nozzle that has tremendous scope of application in future launch vehicles. Keyword: Rocket propulsion, Aerospike Nozzle, Control Design, Computational Fluid Dynamics. (author)

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Science.gov (United States)

Chiodaroli, Elisabetta; Kreml, Ondřej

2018-04-01

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.

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)

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.,

Adjustment of Adaptive Gain with Bounded Linear Stability Analysis to Improve Time-Delay Margin for Metrics-Driven Adaptive Control

Science.gov (United States)

Bakhtiari-Nejad, Maryam; Nguyen, Nhan T.; Krishnakumar, Kalmanje Srinvas

2009-01-01

This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a linear damaged twin-engine generic transport model of aircraft. The analysis shows that the system with the adjusted adaptive gain becomes more robust to unmodeled dynamics or time delay.

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)

Design Analysis of Taper Width Variations in Magnetless Linear Machine for Traction Applications

Directory of Open Access Journals (Sweden)

Saadha Aminath

2018-01-01

Full Text Available Linear motors are being used in a different application with a huge popularity in the use of transport industry. With the invention of maglev trains and other high-speed trains, linear motors are being used for the translation and braking applications for these systems. However, a huge drawback of the linear motor design is the cogging force, low thrust values, and voltage ripples. This paper aims to study the force analysis with change in taper/teeth width of the motor stator and mover to understand the best teeth ratio to obtain a high flux density and a high thrust. The analysis is conducted through JMAG software and it is found that the optimum teeth ratio for both the stator and mover gives an increase of 94.4% increases compared to the 0.5mm stator and mover width.

Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force

OpenAIRE

Dias, Clenilda F; Carvalho-Santos, Vagson L

2012-01-01

The Euler-Lagrange equations (EL) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of EL to study one-dimensional motions under the action of a constant force. From using the definition of partial derivative, we have proposed two operators, here called \\textit{mean delta operators}, which may be used to solve the EL in a simplest way. We have applied this simplification to solve three simple mechanical problems under th...

Quantitative Approach to Failure Mode and Effect Analysis for Linear Accelerator Quality Assurance

Energy Technology Data Exchange (ETDEWEB)

O' Daniel, Jennifer C., E-mail: jennifer.odaniel@duke.edu; Yin, Fang-Fang

2017-05-01

Purpose: To determine clinic-specific linear accelerator quality assurance (QA) TG-142 test frequencies, to maximize physicist time efficiency and patient treatment quality. Methods and Materials: A novel quantitative approach to failure mode and effect analysis is proposed. Nine linear accelerator-years of QA records provided data on failure occurrence rates. The severity of test failure was modeled by introducing corresponding errors into head and neck intensity modulated radiation therapy treatment plans. The relative risk of daily linear accelerator QA was calculated as a function of frequency of test performance. Results: Although the failure severity was greatest for daily imaging QA (imaging vs treatment isocenter and imaging positioning/repositioning), the failure occurrence rate was greatest for output and laser testing. The composite ranking results suggest that performing output and lasers tests daily, imaging versus treatment isocenter and imaging positioning/repositioning tests weekly, and optical distance indicator and jaws versus light field tests biweekly would be acceptable for non-stereotactic radiosurgery/stereotactic body radiation therapy linear accelerators. Conclusions: Failure mode and effect analysis is a useful tool to determine the relative importance of QA tests from TG-142. Because there are practical time limitations on how many QA tests can be performed, this analysis highlights which tests are the most important and suggests the frequency of testing based on each test's risk priority number.

Quantitative Approach to Failure Mode and Effect Analysis for Linear Accelerator Quality Assurance.

Science.gov (United States)

O'Daniel, Jennifer C; Yin, Fang-Fang

2017-05-01

To determine clinic-specific linear accelerator quality assurance (QA) TG-142 test frequencies, to maximize physicist time efficiency and patient treatment quality. A novel quantitative approach to failure mode and effect analysis is proposed. Nine linear accelerator-years of QA records provided data on failure occurrence rates. The severity of test failure was modeled by introducing corresponding errors into head and neck intensity modulated radiation therapy treatment plans. The relative risk of daily linear accelerator QA was calculated as a function of frequency of test performance. Although the failure severity was greatest for daily imaging QA (imaging vs treatment isocenter and imaging positioning/repositioning), the failure occurrence rate was greatest for output and laser testing. The composite ranking results suggest that performing output and lasers tests daily, imaging versus treatment isocenter and imaging positioning/repositioning tests weekly, and optical distance indicator and jaws versus light field tests biweekly would be acceptable for non-stereotactic radiosurgery/stereotactic body radiation therapy linear accelerators. Failure mode and effect analysis is a useful tool to determine the relative importance of QA tests from TG-142. Because there are practical time limitations on how many QA tests can be performed, this analysis highlights which tests are the most important and suggests the frequency of testing based on each test's risk priority number. Copyright © 2017 Elsevier Inc. All rights reserved.

Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

International Nuclear Information System (INIS)

Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

2014-01-01

Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

Near-infrared reflectance analysis by Gauss-Jordan linear algebra

International Nuclear Information System (INIS)

Honigs, D.E.; Freelin, J.M.; Hieftje, G.M.; Hirschfeld, T.B.

1983-01-01

Near-infrared reflectance analysis is an analytical technique that uses the near-infrared diffuse reflectance of a sample at several discrete wavelengths to predict the concentration of one or more of the chemical species in that sample. However, because near-infrared bands from solid samples are both abundant and broad, the reflectance at a given wavelength usually contains contributions from several sample components, requiring extensive calculations on overlapped bands. In the present study, these calculations have been performed using an approach similar to that employed in multi-component spectrophotometry, but with Gauss-Jordan linear algebra serving as the computational vehicle. Using this approach, correlations for percent protein in wheat flour and percent benzene in hydrocarbons have been obtained and are evaluated. The advantages of a linear-algebra approach over the common one employing stepwise regression are explored

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.

Airfoil stall interpreted through linear stability analysis

Science.gov (United States)

Busquet, Denis; Juniper, Matthew; Richez, Francois; Marquet, Olivier; Sipp, Denis

2017-11-01

Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, M 0.2 and high Reynolds number, Re 1.8 ×106 . Steady RANS computation using a Spalart-Allmaras model is coupled with continuation methods (pseudo-arclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil.

Mathematical modelling and linear stability analysis of laser fusion cutting

International Nuclear Information System (INIS)

Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich

2016-01-01

A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.

Application of range-test in multiple linear regression analysis in ...

African Journals Online (AJOL)

Application of range-test in multiple linear regression analysis in the presence of outliers is studied in this paper. First, the plot of the explanatory variables (i.e. Administration, Social/Commercial, Economic services and Transfer) on the dependent variable (i.e. GDP) was done to identify the statistical trend over the years.

Mathematical modelling and linear stability analysis of laser fusion cutting

Energy Technology Data Exchange (ETDEWEB)

Hermanns, Torsten; Schulz, Wolfgang [RWTH Aachen University, Chair for Nonlinear Dynamics, Steinbachstr. 15, 52047 Aachen (Germany); Vossen, Georg [Niederrhein University of Applied Sciences, Chair for Applied Mathematics and Numerical Simulations, Reinarzstr.. 49, 47805 Krefeld (Germany); Thombansen, Ulrich [RWTH Aachen University, Chair for Laser Technology, Steinbachstr. 15, 52047 Aachen (Germany)

2016-06-08

A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.

Applications of the representation of the Heisenberg-Euler Lagrangian by means of special functions

International Nuclear Information System (INIS)

Valluri, S.R.; Lamm, D.R.; Mielniczuk, W.J.

1993-01-01

A convenient series representation for the real part of the Heisenberg-Euler Lagrangian density of quantum electrodynamics for arbitrary nonvanishing electric fields, E, and magnetic fields, B, has been previously provided by Mielniczuk. Using this representation, numerical information for the Lagrangian is presented for the range 0 cr ≤ 5 and 0 cr ≤ 10 (subscript cr stands for critical) with the electric and magnetic fields parallel and E cr ∼ 1.7 X 10 16 V cm -1 and B cr ∼ 4.4 X 10 13 G. It was found that for a fixed electric field, the Lagrangian is monotonically increasing with increasing magnetic field strength. However, for a fixed magnetic field, the Lagrangian exhibits a positively valued maximum before turning monotonically decreasing with increasing electric field strength. Further, the series representation is extended to the case of vanishing electric or magnetic field. Numerical results for these special cases are in very close agreement with previous results, which indicated a maximum value for the Lagrangian density for B = 0 at E/E cr ∼ 3. Also, the techniques developed for deriving the real part of the Heisenberg-Euler Lagrangian are applied to the imaginary part to deduce a similar, convenient series representation that agrees with the previous results derived by others for the special case of a vanishing magnetic field. Possible applications of this Lagrangian to quantum chromodynamics are discussed. This series representation will be of use in calculations of a quantum-electrodynamical field energy density in the absence of real charges, and for calculations of polarization and magnetization of the vacuum. More accurate calculations of the cross-section scattering of light by light in the presence of a constant, homogeneous magnetic and (or) electric field are possible with the aid of this series representation. (author)

Analysis of an inventory model for both linearly decreasing demand and holding cost

Science.gov (United States)

Malik, A. K.; Singh, Parth Raj; Tomar, Ajay; Kumar, Satish; Yadav, S. K.

2016-03-01

This study proposes the analysis of an inventory model for linearly decreasing demand and holding cost for non-instantaneous deteriorating items. The inventory model focuses on commodities having linearly decreasing demand without shortages. The holding cost doesn't remain uniform with time due to any form of variation in the time value of money. Here we consider that the holding cost decreases with respect to time. The optimal time interval for the total profit and the optimal order quantity are determined. The developed inventory model is pointed up through a numerical example. It also includes the sensitivity analysis.

A SOCIOLOGICAL ANALYSIS OF THE CHILDBEARING COEFFICIENT IN THE ALTAI REGION BASED ON METHOD OF FUZZY LINEAR REGRESSION

Directory of Open Access Journals (Sweden)

Sergei Vladimirovich Varaksin

2017-06-01

Full Text Available Purpose. Construction of a mathematical model of the dynamics of childbearing change in the Altai region in 2000–2016, analysis of the dynamics of changes in birth rates for multiple age categories of women of childbearing age. Methodology. A auxiliary analysis element is the construction of linear mathematical models of the dynamics of childbearing by using fuzzy linear regression method based on fuzzy numbers. Fuzzy linear regression is considered as an alternative to standard statistical linear regression for short time series and unknown distribution law. The parameters of fuzzy linear and standard statistical regressions for childbearing time series were defined with using the built in language MatLab algorithm. Method of fuzzy linear regression is not used in sociological researches yet. Results. There are made the conclusions about the socio-demographic changes in society, the high efficiency of the demographic policy of the leadership of the region and the country, and the applicability of the method of fuzzy linear regression for sociological analysis.

Stability analysis of linear switching systems with time delays

International Nuclear Information System (INIS)

Li Ping; Zhong Shouming; Cui Jinzhong

2009-01-01

The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.

Guidance for the utility of linear models in meta-analysis of genetic association studies of binary phenotypes.

Science.gov (United States)

Cook, James P; Mahajan, Anubha; Morris, Andrew P

2017-02-01

Linear mixed models are increasingly used for the analysis of genome-wide association studies (GWAS) of binary phenotypes because they can efficiently and robustly account for population stratification and relatedness through inclusion of random effects for a genetic relationship matrix. However, the utility of linear (mixed) models in the context of meta-analysis of GWAS of binary phenotypes has not been previously explored. In this investigation, we present simulations to compare the performance of linear and logistic regression models under alternative weighting schemes in a fixed-effects meta-analysis framework, considering designs that incorporate variable case-control imbalance, confounding factors and population stratification. Our results demonstrate that linear models can be used for meta-analysis of GWAS of binary phenotypes, without loss of power, even in the presence of extreme case-control imbalance, provided that one of the following schemes is used: (i) effective sample size weighting of Z-scores or (ii) inverse-variance weighting of allelic effect sizes after conversion onto the log-odds scale. Our conclusions thus provide essential recommendations for the development of robust protocols for meta-analysis of binary phenotypes with linear models.

Weighted functional linear regression models for gene-based association analysis.

Science.gov (United States)

Belonogova, Nadezhda M; Svishcheva, Gulnara R; Wilson, James F; Campbell, Harry; Axenovich, Tatiana I

2018-01-01

Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.

A linear programming manual

Science.gov (United States)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

A linear complementarity method for the solution of vertical vehicle-track interaction

Science.gov (United States)

Zhang, Jian; Gao, Qiang; Wu, Feng; Zhong, Wan-Xie

2018-02-01

A new method is proposed for the solution of the vertical vehicle-track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel-rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel-rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel-rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle-track interaction including a separation between wheel and rail.

A primer for biomedical scientists on how to execute model II linear regression analysis.

Science.gov (United States)

Ludbrook, John

2012-04-01

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.

Dynamic modeling of geometrically nonlinear electrostatically actuated microbeams (Corotational Finite Element formulation and analysis)

Energy Technology Data Exchange (ETDEWEB)

Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)

2006-04-01

In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.

On macroeconomic values investigation using fuzzy linear regression analysis

Directory of Open Access Journals (Sweden)

Richard Pospíšil

2017-06-01

Full Text Available The theoretical background for abstract formalization of the vague phenomenon of complex systems is the fuzzy set theory. In the paper, vague data is defined as specialized fuzzy sets - fuzzy numbers and there is described a fuzzy linear regression model as a fuzzy function with fuzzy numbers as vague parameters. To identify the fuzzy coefficients of the model, the genetic algorithm is used. The linear approximation of the vague function together with its possibility area is analytically and graphically expressed. A suitable application is performed in the tasks of the time series fuzzy regression analysis. The time-trend and seasonal cycles including their possibility areas are calculated and expressed. The examples are presented from the economy field, namely the time-development of unemployment, agricultural production and construction respectively between 2009 and 2011 in the Czech Republic. The results are shown in the form of the fuzzy regression models of variables of time series. For the period 2009-2011, the analysis assumptions about seasonal behaviour of variables and the relationship between them were confirmed; in 2010, the system behaved fuzzier and the relationships between the variables were vaguer, that has a lot of causes, from the different elasticity of demand, through state interventions to globalization and transnational impacts.

Linear regression analysis: part 14 of a series on evaluation of scientific publications.

Science.gov (United States)

Schneider, Astrid; Hommel, Gerhard; Blettner, Maria

2010-11-01

Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately. The performance and interpretation of linear regression analysis are subject to a variety of pitfalls, which are discussed here in detail. The reader is made aware of common errors of interpretation through practical examples. Both the opportunities for applying linear regression analysis and its limitations are presented.

Noise analysis of fluid-valve system in a linear compressor using CAE

International Nuclear Information System (INIS)

Lee, Jun Ho; Jeong, Weui Bong; Kim, Dang Ju

2009-01-01

A linear compressor in a refrigerator uses piston motion to transfer refrigerant so its efficiency is higher than a previous reciprocal compressor. Because of interaction between refrigerant and valves system in the linear compressor, however, noise has been a main issue. In spite of doing many experimental researches, there is no way to rightly predict the noise. In order to solve this limitation, the CAE analysis is applied. For giving credit to these computational data, all of the data are experimentally validated.

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

Science.gov (United States)

Tukhvatullina, R. R.; Frolov, S. M.

2018-03-01

A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh-Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005-0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.

Implementation of an Euler/Navier-Stokes finite element algorithm on the Connection Machine

International Nuclear Information System (INIS)

Shapiro, R.A.

1991-01-01

Massively parallel computers such as the Connection Machine (CM-2) have the potential to reduce significantly the computational cost for large problems of interest to the aerospace community. This paper examines the applicability of the CM-2 to an explicit, time-marching finite element solution method for the Euler and Navier-Stokes equations. The CM-2 architecture and the CM FORTRAN language are introduced. The paper points out some of the pitfalls involved in putting this code on the CM-2, with emphasis on interprocessor communications issues. The use of the FastGraph communication compiler and grid renumbering to reduce communication costs is discussed. Performance comparisons which indicate the approximate equivalence of a uniprocessor Cray and 1/8 of a CM-2 (8192 processors) for some typical problems are presented. 8 refs

The Euler equation with habits and measurement errors: Estimates on Russian micro data

Directory of Open Access Journals (Sweden)

Khvostova Irina

2016-01-01

Full Text Available This paper presents estimates of the consumption Euler equation for Russia. The estimation is based on micro-level panel data and accounts for the heterogeneity of agents’ preferences and measurement errors. The presence of multiplicative habits is checked using the Lagrange multiplier (LM test in a generalized method of moments (GMM framework. We obtain estimates of the elasticity of intertemporal substitution and of the subjective discount factor, which are consistent with the theoretical model and can be used for the calibration and the Bayesian estimation of dynamic stochastic general equilibrium (DSGE models for the Russian economy. We also show that the effects of habit formation are not significant. The hypotheses of multiplicative habits (external, internal, and both external and internal are not supported by the data.

Fourier two-level analysis for discontinuous Galerkin discretization with linear elements

NARCIS (Netherlands)

P.W. Hemker (Piet); W. Hoffmann; M.H. van Raalte (Marc)

2002-01-01

textabstractIn this paper we study the convergence of a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence fordifferent block-relaxation strategies. In addition to an

Econometrics analysis of consumer behaviour: a linear expenditure system applied to energy

International Nuclear Information System (INIS)

Giansante, C.; Ferrari, V.

1996-12-01

In economics literature the expenditure system specification is a well known subject. The problem is to define a coherent representation of consumer behaviour through functional forms easy to calculate. In this work it is used the Stone-Geary Linear Expenditure System and its multi-level decision process version. The Linear Expenditure system is characterized by an easy calculating estimation procedure, and its multi-level specification allows substitution and complementary relations between goods. Moreover, the utility function separability condition on which the Utility Tree Approach is based, justifies to use an estimation procedure in two or more steps. This allows to use an high degree of expenditure categories disaggregation, impossible to reach the Linear Expediture System. The analysis is applied to energy sectors

Linear stability analysis of the gas injection augmented natural circulation of STAR-LM

International Nuclear Information System (INIS)

Yeon-Jong Yoo; Qiao Wu; James J Sienicki

2005-01-01

Full text of publication follows: A linear stability analysis has been performed for the gas injection augmented natural circulation of the Secure Transportable Autonomous Reactor - Liquid Metal (STAR-LM). Natural circulation is of great interest for the development of Generation-IV nuclear energy systems due to its vital role in the area of passive safety and reliability. One of such systems is STAR-LM under development by Argonne National Laboratory. STAR-LM is a 400 MWt class modular, proliferation-resistant, and passively safe liquid metal-cooled fast reactor system that uses inert lead (Pb) coolant and the advanced power conversion system that consists of a gas turbine Brayton cycle utilizing supercritical carbon dioxide (CO 2 ) to obtain higher plant efficiency. The primary loop of STAR-LM relies only on the natural circulation to eliminate the use of circulation pumps for passive safety consideration. To enhance the natural circulation of the primary coolant, STAR-LM optionally incorporates the additional driving force provided by the injection of noncondensable gas into the primary coolant above the reactor core, which is effective in removing heat from the core and transferring it to the secondary working fluid without the attainment of excessive coolant temperature at nominal operating power. Therefore, it naturally raises the concern about the natural circulation instability due to the relatively high temperature change in the core and the two-phase flow condition in the hot leg above the core. For the ease of analysis, the flow path of the loop was partitioned into five thermal-hydraulically distinct sections, i.e., heated core, unheated core, hot leg, heat exchanger, and cold leg. The one-dimensional single-phase flow field equations governing the natural circulation, i.e., continuity, momentum, and energy equations, were used for each section except the hot leg. For the hot leg, the one-dimensional homogeneous equilibrium two-phase flow field

Generalized Stabilities of Euler-Lagrange-Jensen (a,b-Sextic Functional Equations in Quasi-β-Normed Spaces

Directory of Open Access Journals (Sweden)

John Michael Rassias

2017-07-01

Full Text Available The aim of this paper is to investigate generalized Ulam-Hyers stabilities of the following Euler-Lagrange-Jensen-$(a,b$-sextic functional equation $$ f(ax+by+f(bx+ay+(a-b^6\\left[f\\left(\\frac{ax-by}{a-b}\\right+f\\left(\\frac{bx-ay}{b-a}\\right\\right]\\\\ = 64(ab^2\\left(a^2+b^2\\right\\left[f\\left(\\frac{x+y}{2}\\right+f\\left(\\frac{x-y}{2}\\right\\right]\\\\ +2\\left(a^2-b^2\\right\\left(a^4-b^4\\right[f(x+f(y] $$ where $a\

Difference Discrete Variational Principles, Euler-Lagrange Cohomology and Symplectic, Multisymplectic Structures I: Difference Discrete Variational Principle

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun

2002-01-01

In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

Solution of the Euler and Navier-Stokes equations on MIMD distributed memory multiprocessors using cyclic reduction

International Nuclear Information System (INIS)

Curchitser, E.N.; Pelz, R.B.; Marconi, F.

1992-01-01

The Euler and Navier-Stokes equations are solved for the steady, two-dimensional flow over a NACA 0012 airfoil using a 1024 node nCUBE/2 multiprocessor. Second-order, upwind-discretized difference equations are solved implicitly using ADI factorization. Parallel cyclic reduction is employed to solve the block tridiagonal systems. For realistic problems, communication times are negligible compared to calculation times. The processors are tightly synchronized, and their loads are well balanced. When the flux Jacobians flux are frozen, the wall-clock time for one implicit timestep is about equal to that of a multistage explicit scheme. 10 refs

Simple estimating method of damages of concrete gravity dam based on linear dynamic analysis

Energy Technology Data Exchange (ETDEWEB)

Sasaki, T.; Kanenawa, K.; Yamaguchi, Y. [Public Works Research Institute, Tsukuba, Ibaraki (Japan). Hydraulic Engineering Research Group

2004-07-01

Due to the occurrence of large earthquakes like the Kobe Earthquake in 1995, there is a strong need to verify seismic resistance of dams against much larger earthquake motions than those considered in the present design standard in Japan. Problems exist in using nonlinear analysis to evaluate the safety of dams including: that the influence which the set material properties have on the results of nonlinear analysis is large, and that the results of nonlinear analysis differ greatly according to the damage estimation models or analysis programs. This paper reports the evaluation indices based on a linear dynamic analysis method and the characteristics of the progress of cracks in concrete gravity dams with different shapes using a nonlinear dynamic analysis method. The study concludes that if simple linear dynamic analysis is appropriately conducted to estimate tensile stress at potential locations of initiating cracks, the damage due to cracks would be predicted roughly. 4 refs., 1 tab., 13 figs.

International Space Station Centrifuge Rotor Models A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

Science.gov (United States)

Nguyen, Louis H.; Ramakrishnan, Jayant; Granda, Jose J.

2006-01-01

The assembly and operation of the International Space Station (ISS) require extensive testing and engineering analysis to verify that the Space Station system of systems would work together without any adverse interactions. Since the dynamic behavior of an entire Space Station cannot be tested on earth, math models of the Space Station structures and mechanical systems have to be built and integrated in computer simulations and analysis tools to analyze and predict what will happen in space. The ISS Centrifuge Rotor (CR) is one of many mechanical systems that need to be modeled and analyzed to verify the ISS integrated system performance on-orbit. This study investigates using Bond Graph modeling techniques as quick and simplified ways to generate models of the ISS Centrifuge Rotor. This paper outlines the steps used to generate simple and more complex models of the CR using Bond Graph Computer Aided Modeling Program with Graphical Input (CAMP-G). Comparisons of the Bond Graph CR models with those derived from Euler-Lagrange equations in MATLAB and those developed using multibody dynamic simulation at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) are presented to demonstrate the usefulness of the Bond Graph modeling approach for aeronautics and space applications.

Micosoft Excel Sensitivity Analysis for Linear and Stochastic Program Feed Formulation

Science.gov (United States)

Sensitivity analysis is a part of mathematical programming solutions and is used in making nutritional and economic decisions for a given feed formulation problem. The terms, shadow price and reduced cost, are familiar linear program (LP) terms to feed formulators. Because of the nonlinear nature of...

Painlevйe analysis and integrability of two-coupled non-linear ...

Indian Academy of Sciences (India)

the Painlevйe property. In this case the system is expected to be integrable. In recent years more attention is paid to the study of coupled non-linear oscilla- ... Painlevйe analysis. To be self-contained, in §2 we briefly outline the salient features.

On a nu-continuous famaly of strong solutions to the Euler or Navier-Stokes equations with the Navier-type boundary condition

Czech Academy of Sciences Publication Activity Database

Bellout, H.; Neustupa, Jiří; Penel, P.

2010-01-01

Roč. 27, č. 4 (2010), s. 1353-1373 ISSN 1078-0947 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euler equations * Navier-Stokes equations * zero viscosity limit Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5028

Z-score linear discriminant analysis for EEG based brain-computer interfaces.

Directory of Open Access Journals (Sweden)

Rui Zhang

Full Text Available Linear discriminant analysis (LDA is one of the most popular classification algorithms for brain-computer interfaces (BCI. LDA assumes Gaussian distribution of the data, with equal covariance matrices for the concerned classes, however, the assumption is not usually held in actual BCI applications, where the heteroscedastic class distributions are usually observed. This paper proposes an enhanced version of LDA, namely z-score linear discriminant analysis (Z-LDA, which introduces a new decision boundary definition strategy to handle with the heteroscedastic class distributions. Z-LDA defines decision boundary through z-score utilizing both mean and standard deviation information of the projected data, which can adaptively adjust the decision boundary to fit for heteroscedastic distribution situation. Results derived from both simulation dataset and two actual BCI datasets consistently show that Z-LDA achieves significantly higher average classification accuracies than conventional LDA, indicating the superiority of the new proposed decision boundary definition strategy.

[Relations between biomedical variables: mathematical analysis or linear algebra?].

Science.gov (United States)

Hucher, M; Berlie, J; Brunet, M

1977-01-01

The authors, after a short reminder of one pattern's structure, stress on the possible double approach of relations uniting the variables of this pattern: use of fonctions, what is within the mathematical analysis sphere, use of linear algebra profiting by matricial calculation's development and automatiosation. They precise the respective interests on these methods, their bounds and the imperatives for utilization, according to the kind of variables, of data, and the objective for work, understanding phenomenons or helping towards decision.

Simulation and sensitivity analysis for heavy linear paraffins production in LAB production Plant

Directory of Open Access Journals (Sweden)

Karimi Hajir

2014-12-01

Full Text Available Linear alkyl benzene (LAB is vastly utilized for the production of biodegradable detergents and emulsifiers. Predistillation unit is a part of LAB production plant in which that produced heavy linear paraffins (nC10-nC13. In this study, a mathematical model has been developed for heavy linear paraffins production in distillation columns, which has been solved using a commercial code. The models have been validated by the actual data. The effects of process parameters such as reflux rate, and reflux temperature using Gradient Search technique has been investigated. The sensitivity analysis shows that optimum reflux in columns are achieved.

Generalized Euler transformation for summing strongly divergent Rayleigh-Schroedinger perturbation series: the Zeeman effect

International Nuclear Information System (INIS)

Silverman, J.N.

1983-01-01

A generalized Euler transformation (GET) is introduced which provides a powerful alternative method of accurately summing strongly divergent Rayleigh-Schroedinger (RS) perturbation series when other summability methods fail or are difficult to apply. The GET is simple to implement and, unlike a number of other summation procedures, requires no a priori knowledge of the analytic properties of the function underlying the RS series. Application of the GET to the difficult problem of the RS weak-field ground-state eigenvalue series of the hydrogen atom in a magnetic field (quadratic Zeeman effect) yields sums of good accuracy over a very wide range of field strengths up to the most intense fields of 10 14 G. The GET results are compared with those obtained by other summing methods

On the dynamic analysis of piecewise-linear networks

OpenAIRE

Heemels, W.P.M.H.; Camlibel, M.K.; Schumacher, J.M.

2002-01-01

Piecewise-linear (PL) modeling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modeling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks. In this paper, the object of study will be dynamic electrical circuits that can be recast as linear complementarity systems, i.e., as interconnections of linear time-invariant differential equatio...

Stability, performance and sensitivity analysis of I.I.D. jump linear systems

Science.gov (United States)

Chávez Fuentes, Jorge R.; González, Oscar R.; Gray, W. Steven

2018-06-01

This paper presents a symmetric Kronecker product analysis of independent and identically distributed jump linear systems to develop new, lower dimensional equations for the stability and performance analysis of this type of systems than what is currently available. In addition, new closed form expressions characterising multi-parameter relative sensitivity functions for performance metrics are introduced. The analysis technique is illustrated with a distributed fault-tolerant flight control example where the communication links are allowed to fail randomly.

MetabR: an R script for linear model analysis of quantitative metabolomic data

Directory of Open Access Journals (Sweden)

Ernest Ben

2012-10-01

Full Text Available Abstract Background Metabolomics is an emerging high-throughput approach to systems biology, but data analysis tools are lacking compared to other systems level disciplines such as transcriptomics and proteomics. Metabolomic data analysis requires a normalization step to remove systematic effects of confounding variables on metabolite measurements. Current tools may not correctly normalize every metabolite when the relationships between each metabolite quantity and fixed-effect confounding variables are different, or for the effects of random-effect confounding variables. Linear mixed models, an established methodology in the microarray literature, offer a standardized and flexible approach for removing the effects of fixed- and random-effect confounding variables from metabolomic data. Findings Here we present a simple menu-driven program, “MetabR”, designed to aid researchers with no programming background in statistical analysis of metabolomic data. Written in the open-source statistical programming language R, MetabR implements linear mixed models to normalize metabolomic data and analysis of variance (ANOVA to test treatment differences. MetabR exports normalized data, checks statistical model assumptions, identifies differentially abundant metabolites, and produces output files to help with data interpretation. Example data are provided to illustrate normalization for common confounding variables and to demonstrate the utility of the MetabR program. Conclusions We developed MetabR as a simple and user-friendly tool for implementing linear mixed model-based normalization and statistical analysis of targeted metabolomic data, which helps to fill a lack of available data analysis tools in this field. The program, user guide, example data, and any future news or updates related to the program may be found at http://metabr.r-forge.r-project.org/.

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.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

Science.gov (United States)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Computational Tools for Probing Interactions in Multiple Linear Regression, Multilevel Modeling, and Latent Curve Analysis

Science.gov (United States)

Preacher, Kristopher J.; Curran, Patrick J.; Bauer, Daniel J.

2006-01-01

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

Steady state and linear stability analysis of a supercritical water natural circulation loop

International Nuclear Information System (INIS)

Sharma, Manish; Pilkhwal, D.S.; Vijayan, P.K.; Saha, D.; Sinha, R.K.

2010-01-01

Supercritical water (SCW) has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN using supercritical water properties has been developed to carry out the steady state and linear stability analysis of a SCW natural circulation loop. The conservation equations of mass, momentum and energy have been linearized by imposing small perturbation in flow rate, enthalpy, pressure and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been qualitatively assessed with published results and has been extensively used for studying the effect of diameter, height, heater inlet temperature, pressure and local loss coefficients on steady state and stability behavior of a Supercritical Water Natural Circulation Loop (SCWNCL). The present paper describes the linear stability analysis model and the results obtained in detail.

Advanced statistics: linear regression, part I: simple linear regression.

Science.gov (United States)

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Principal Component Analysis: Resources for an Essential Application of Linear Algebra

Science.gov (United States)

Pankavich, Stephen; Swanson, Rebecca

2015-01-01

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

The flow analysis of supercavitating cascade by linear theory

Energy Technology Data Exchange (ETDEWEB)

Park, E.T. [Sung Kyun Kwan Univ., Seoul (Korea, Republic of); Hwang, Y. [Seoul National Univ., Seoul (Korea, Republic of)

1996-06-01

In order to reduce damages due to cavitation effects and to improve performance of fluid machinery, supercavitation around the cascade and the hydraulic characteristics of supercavitating cascade must be analyzed accurately. And the study on the effects of cavitation on fluid machinery and analysis on the performances of supercavitating hydrofoil through various elements governing flow field are critically important. In this study comparison of experiment results with the computed results of linear theory using singularity method was obtainable. Specially singularity points like sources and vortexes on hydrofoil and freestreamline were distributed to analyze two dimensional flow field of supercavitating cascade, and governing equations of flow field were derived and hydraulic characteristics of cascade were calculated by numerical analysis of the governing equations. 7 refs., 6 figs.

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

Energy Technology Data Exchange (ETDEWEB)

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.

Development of a numerical model for vehicle-bridge interaction analysis of railway bridges

Science.gov (United States)

Kim, Hee Ju; Cho, Eun Sang; Ham, Jun Su; Park, Ki Tae; Kim, Tae Heon

2016-04-01

In the field of civil engineering, analyzing dynamic response was main concern for a long time. These analysis methods can be divided into moving load analysis method and moving mass analysis method, and formulating each an equation of motion has recently been studied after dividing vehicles and bridges. In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations for motion. Also, 3 dimensional accurate numerical models was developed by KTX-vehicle in order to analyze dynamic response characteristics. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 18 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by PSD functions of the Federal Railroad Administration (FRA).

Linear and Nonlinear Multiset Canonical Correlation Analysis (invited talk)

DEFF Research Database (Denmark)

Hilger, Klaus Baggesen; Nielsen, Allan Aasbjerg; Larsen, Rasmus

2002-01-01

This paper deals with decompositioning of multiset data. Friedman's alternating conditional expectations (ACE) algorithm is extended to handle multiple sets of variables of different mixtures. The new algorithm finds estimates of the optimal transformations of the involved variables that maximize...... the sum of the pair-wise correlations over all sets. The new algorithm is termed multi-set ACE (MACE) and can find multiple orthogonal eigensolutions. MACE is a generalization of the linear multiset correlations analysis (MCCA). It handles multivariate multisets of arbitrary mixtures of both continuous...

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

Science.gov (United States)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.

H{sub 2}/H{infinity} control of flexible structures through linear matrix inequalities with pole placement

Energy Technology Data Exchange (ETDEWEB)

Lopes, Jean C. [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil)

2009-07-01

The objective of this work is to apply the H2/H{infinity} control technique using linear matrix inequalities and pole placement constraints to the flexible structures control problem. The H2/H{infinity}control is a technique to design a controller with mixed features of the H2 and H{infinity} control formulations, such as, optimal dynamical performance and robust performance. The Linear Matrix Inequalities allow formulating the problem as a convex optimization problem, and additional constraints can be included such as the pole placement. The pole placement requirement comes from the necessity of adjusting the transient response of the plant and ensuring a specific behavior in terms of speed and damping responses. The mathematical model used for this study is related to a flexible beam, with an applied disturbance and an actuator in different positions. The state-space matrices of the structure were obtained using the finite element method with the Euler-Bernoulli formulation of beams. The results showed that the pole placement constraints can improve the performance of the controller H2/H{infinity}. The Matlab was used for the computational implementation. (author)

Linear and Generalized Linear Mixed Models and Their Applications

CERN Document Server

Jiang, Jiming

2007-01-01

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested

Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.

Science.gov (United States)

Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second

An improved multiple linear regression and data analysis computer program package

Science.gov (United States)

Sidik, S. M.

1972-01-01

NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.

Two-dimensional gauge dynamics and the topology of singular determinantal varieties

Energy Technology Data Exchange (ETDEWEB)

Wong, Kenny [Department of Applied Mathematics and Theoretical Physics,Centre for Mathematical Sciences, University of Cambridge,Cambridge, CB3 0WA (United Kingdom)

2017-03-27

We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices are related to the Euler characteristics of the singular skew-symmetric or symmetric determinantal varieties featuring in the analysis of their opposite phases, and we discuss the extent to which these relationships can be reconciled with standard Born-Oppenheimer arguments.

Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data.

Science.gov (United States)

Ying, Gui-Shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard

2017-04-01

To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field in the elderly. When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI -0.03 to 0.32D, p = 0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, p = 0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller p-values, while analysis of the worse eye provided larger p-values than mixed effects models and marginal models. In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision.

Numerical linear analysis of the effects of diamagnetic and shear flow on ballooning modes

Science.gov (United States)

Yanqing, HUANG; Tianyang, XIA; Bin, GUI

2018-04-01

The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvature-driving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition, through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.

Theoretical foundations of functional data analysis, with an introduction to linear operators

CERN Document Server

Hsing, Tailen

2015-01-01

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA).The self-contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self-adjoint and non self-adjoint operators. The probabilistic foundation for FDA is described from the

Frame sequences analysis technique of linear objects movement

Science.gov (United States)

Oshchepkova, V. Y.; Berg, I. A.; Shchepkin, D. V.; Kopylova, G. V.

2017-12-01

Obtaining data by noninvasive methods are often needed in many fields of science and engineering. This is achieved through video recording in various frame rate and light spectra. In doing so quantitative analysis of movement of the objects being studied becomes an important component of the research. This work discusses analysis of motion of linear objects on the two-dimensional plane. The complexity of this problem increases when the frame contains numerous objects whose images may overlap. This study uses a sequence containing 30 frames at the resolution of 62 × 62 pixels and frame rate of 2 Hz. It was required to determine the average velocity of objects motion. This velocity was found as an average velocity for 8-12 objects with the error of 15%. After processing dependencies of the average velocity vs. control parameters were found. The processing was performed in the software environment GMimPro with the subsequent approximation of the data obtained using the Hill equation.

A Laplace transform/potential-theoretic method for acoustic propagation in subsonic flows

CERN Document Server

Hariharan, S I

2003-01-01

This paper introduces a competitive computational approach for determining time-dependent far-field sound generated by subsonic flows around lifting airfoils. The procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil. It is assumed that the sound pressure on the boundary of this enclosed region (referred to as the Kirchhoff surface) is specified, possibly by another procedure such as solving the full Euler equations. Away from the Kirchhoff surface, the Euler equations are linearized about a uniform mean flow. It is well known that linearized Euler equations can be uncoupled into a scalar convective wave equation. However, due to the anisotropy present in the convective wave equation, it is difficult to compute solutions. In this context, direct numerical simulation of the convective wave equation requires proper numerical descriptions of far-field boundary conditions which is a non-trivial task. Moreover, if accurate far-field conditions can be formulated, the ...

Linear mixed-effects modeling approach to FMRI group analysis.

Science.gov (United States)

Chen, Gang; Saad, Ziad S; Britton, Jennifer C; Pine, Daniel S; Cox, Robert W

2013-06-01

Conventional group analysis is usually performed with Student-type t-test, regression, or standard AN(C)OVA in which the variance-covariance matrix is presumed to have a simple structure. Some correction approaches are adopted when assumptions about the covariance structure is violated. However, as experiments are designed with different degrees of sophistication, these traditional methods can become cumbersome, or even be unable to handle the situation at hand. For example, most current FMRI software packages have difficulty analyzing the following scenarios at group level: (1) taking within-subject variability into account when there are effect estimates from multiple runs or sessions; (2) continuous explanatory variables (covariates) modeling in the presence of a within-subject (repeated measures) factor, multiple subject-grouping (between-subjects) factors, or the mixture of both; (3) subject-specific adjustments in covariate modeling; (4) group analysis with estimation of hemodynamic response (HDR) function by multiple basis functions; (5) various cases of missing data in longitudinal studies; and (6) group studies involving family members or twins. Here we present a linear mixed-effects modeling (LME) methodology that extends the conventional group analysis approach to analyze many complicated cases, including the six prototypes delineated above, whose analyses would be otherwise either difficult or unfeasible under traditional frameworks such as AN(C)OVA and general linear model (GLM). In addition, the strength of the LME framework lies in its flexibility to model and estimate the variance-covariance structures for both random effects and residuals. The intraclass correlation (ICC) values can be easily obtained with an LME model with crossed random effects, even at the presence of confounding fixed effects. The simulations of one prototypical scenario indicate that the LME modeling keeps a balance between the control for false positives and the sensitivity

A Nutritional Analysis of the Food Basket in BIH: A Linear Programming Approach

Directory of Open Access Journals (Sweden)

Arnaut-Berilo Almira

2017-04-01

Full Text Available This paper presents linear and goal programming optimization models for determining and analyzing the food basket in Bosnia and Herzegovina (BiH in terms of adequate nutritional needs according to World Health Organization (WHO standards and World Bank (WB recommendations. A linear programming (LP model and goal linear programming model (GLP are adequate since price and nutrient contents are linearly related to food weight. The LP model provides information about the minimal value and the structure of the food basket for an average person in BiH based on nutrient needs. GLP models are designed to give us information on minimal deviations from nutrient needs if the budget is fixed. Based on these results, poverty analysis can be performed. The data used for the models consisted of 158 food items from the general consumption of the population of BiH according to COICOP classifications, with average prices in 2015 for these products.

A Linear Analysis of a Blended Wing Body (BWB Aircraft Model

Directory of Open Access Journals (Sweden)

Claudia Alice STATE

2011-09-01

Full Text Available In this article a linear analysis of a Blended Wing Body (BWB aircraft model is performed. The BWB concept is in the attention of both military and civil sectors for the fact that has reduced radar signature (in the absence of a conventional tail and the possibility to carry more people. The trim values are computed, also the eigenvalues and the Jacobian matrix evaluated into the trim point are analyzed. A linear simulation in the MatLab environment is presented in order to express numerically the symbolic computations presented. The initial system is corrected in the way of increasing the consistency and coherence of the modeled type of motion and, also, suggestions are made for future work.

Analysis of γ spectra in airborne radioactivity measurements using multiple linear regressions

International Nuclear Information System (INIS)

Bao Min; Shi Quanlin; Zhang Jiamei

2004-01-01

This paper describes the net peak counts calculating of nuclide 137 Cs at 662 keV of γ spectra in airborne radioactivity measurements using multiple linear regressions. Mathematic model is founded by analyzing every factor that has contribution to Cs peak counts in spectra, and multiple linear regression function is established. Calculating process adopts stepwise regression, and the indistinctive factors are eliminated by F check. The regression results and its uncertainty are calculated using Least Square Estimation, then the Cs peak net counts and its uncertainty can be gotten. The analysis results for experimental spectrum are displayed. The influence of energy shift and energy resolution on the analyzing result is discussed. In comparison with the stripping spectra method, multiple linear regression method needn't stripping radios, and the calculating result has relation with the counts in Cs peak only, and the calculating uncertainty is reduced. (authors)

The oscillatory behavior of heated channels: an analysis of the density effect. Part I. The mechanism (non linear analysis). Part II. The oscillations thresholds (linearized analysis)

International Nuclear Information System (INIS)

Boure, J.

1967-01-01

The problem of the oscillatory behavior of heated channels is presented in terms of delay-times and a density effect model is proposed to explain the behavior. The density effect is the consequence of the physical relationship between enthalpy and density of the fluid. In the first part non-linear equations are derived from the model in a dimensionless form. A description of the mechanism of oscillations is given, based on the analysis of the equations. An inventory of the governing parameters is established. At this point of the study, some facts in agreement with the experiments can be pointed out. In the second part the start of the oscillatory behavior of heated channels is studied in terms of the density effect. The threshold equations are derived, after linearization of the equations obtained in Part I. They can be solved rigorously by numerical methods to yield: -1) a relation between the describing parameters at the onset of oscillations, and -2) the frequency of the oscillations. By comparing the results predicted by the model to the experimental behavior of actual systems, the density effect is very often shown to be the actual cause of oscillatory behaviors. (author) [fr

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.

Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory

Directory of Open Access Journals (Sweden)

Qian Hong

2008-05-01

Full Text Available Abstract Background: Several approaches, including metabolic control analysis (MCA, flux balance analysis (FBA, correlation metric construction (CMC, and biochemical circuit theory (BCT, have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. Results: In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RT BS and ST BS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. Conclusion: One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA.

Classical linear-control analysis applied to business-cycle dynamics and stability

Science.gov (United States)

Wingrove, R. C.

1983-01-01

Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.

Global Existence and Large Time Behavior of Solutions to the Bipolar Nonisentropic Euler-Poisson Equations

Directory of Open Access Journals (Sweden)

Min Chen

2014-01-01

Full Text Available We study the one-dimensional bipolar nonisentropic Euler-Poisson equations which can model various physical phenomena, such as the propagation of electron and hole in submicron semiconductor devices, the propagation of positive ion and negative ion in plasmas, and the biological transport of ions for channel proteins. We show the existence and large time behavior of global smooth solutions for the initial value problem, when the difference of two particles’ initial mass is nonzero, and the far field of two particles’ initial temperatures is not the ambient device temperature. This result improves that of Y.-P. Li, for the case that the difference of two particles’ initial mass is zero, and the far field of the initial temperature is the ambient device temperature.

Introduction to generalized linear models

CERN Document Server

Dobson, Annette J

2008-01-01

Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...

MDCT linear and volumetric analysis of adrenal glands: Normative data and multiparametric assessment

International Nuclear Information System (INIS)

Carsin-Vu, Aline; Mule, Sebastien; Janvier, Annaelle; Hoeffel, Christine; Oubaya, Nadia; Delemer, Brigitte; Soyer, Philippe

2016-01-01

To study linear and volumetric adrenal measurements, their reproducibility, and correlations between total adrenal volume (TAV) and adrenal micronodularity, age, gender, body mass index (BMI), visceral (VAAT) and subcutaneous adipose tissue volume (SAAT), presence of diabetes, chronic alcoholic abuse and chronic inflammatory disease (CID). We included 154 patients (M/F, 65/89; mean age, 57 years) undergoing abdominal multidetector row computed tomography (MDCT). Two radiologists prospectively independently performed adrenal linear and volumetric measurements with semi-automatic software. Inter-observer reliability was studied using inter-observer correlation coefficient (ICC). Relationships between TAV and associated factors were studied using bivariate and multivariable analysis. Mean TAV was 8.4 ± 2.7 cm 3 (3.3-18.7 cm 3 ). ICC was excellent for TAV (0.97; 95 % CI: 0.96-0.98) and moderate to good for linear measurements. TAV was significantly greater in men (p < 0.0001), alcoholics (p = 0.04), diabetics (p = 0.0003) and those with micronodular glands (p = 0.001). TAV was lower in CID patients (p = 0.0001). TAV correlated positively with VAAT (r = 0.53, p < 0.0001), BMI (r = 0.42, p < 0.0001), SAAT (r = 0.29, p = 0.0003) and age (r = 0.23, p = 0.005). Multivariable analysis revealed gender, micronodularity, diabetes, age and BMI as independent factors influencing TAV. Adrenal gland MDCT-based volumetric measurements are more reproducible than linear measurements. Gender, micronodularity, age, BMI and diabetes independently influence TAV. (orig.)

Experimental and numerical analysis of behavior of electromagnetic annular linear induction pump

International Nuclear Information System (INIS)

Goldsteins, Linards

2015-01-01

The research explores the issue of magnetohydrodynamic (MHD) instability in electromagnetic induction pumps with focus on the regimes of high slip Reynolds magnetic number (Rm s ) in Annular Linear Induction Pumps (ALIP) operating with liquid sodium. The context of the thesis is French GEN IV Sodium Fast Reactor research and development program for ASTRID in a framework of which the use of high discharge ALIP in the secondary cooling loops is being studied. CEA has designed, realized and will exploit PEMDYN facility, able to represent MHD instability in high discharge ALIP. In the thesis stability of an ideal ALIP is elaborated theoretically using linear stability analysis. Analysis revealed that strong amplification of perturbation is expected after convective stability threshold is reached. Theory is supported with numerical results and experiments reported in literature. Stable operation and stabilization technique operating with two frequencies in case of an ideal ALIP is discussed and necessary conditions derived. Detailed numerical models of flat linear induction pump (FLIP) taking into account effects of a real pump are developed. New technique of magnetic field measurements has been introduced and experimental results demonstrate a qualitative agreement with numerical models capturing all principal phenomena such as oscillation of magnetic field and perturbed velocity profiles. These results give significantly more profound insight in the phenomenon of MHD instability and can be used as a reference in further studies. (author) [fr

Pleiotropy analysis of quantitative traits at gene level by multivariate functional linear models.

Science.gov (United States)

Wang, Yifan; Liu, Aiyi; Mills, James L; Boehnke, Michael; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao; Wu, Colin O; Fan, Ruzong

2015-05-01

In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F-distribution tests based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants in one genetic region. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and optimal sequence kernel association test (SKAT-O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F-distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and SKAT-O for the three biochemical traits. The approximate F-distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT-O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT-O in the univariate case. © 2015 WILEY PERIODICALS, INC.

Linear algebra

CERN Document Server

Said-Houari, Belkacem

2017-01-01

This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

International Nuclear Information System (INIS)

Yamamoto, K; Fujita, T; Kanda, K; Maenaka, K; Badel, A; Formosa, F

2014-01-01

In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator

Design and analysis of linear oscillatory single-phase permanent magnet generator for free-piston stirling engine systems

Science.gov (United States)

Kim, Jeong-Man; Choi, Jang-Young; Lee, Kyu-Seok; Lee, Sung-Ho

2017-05-01

This study focuses on the design and analysis of a linear oscillatory single-phase permanent magnet generator for free-piston stirling engine (FPSE) systems. In order to implement the design of linear oscillatory generator (LOG) for suitable FPSEs, we conducted electromagnetic analysis of LOGs with varying design parameters. Then, detent force analysis was conducted using assisted PM. Using the assisted PM gave us the advantage of using mechanical strength by detent force. To improve the efficiency, we conducted characteristic analysis of eddy-current loss with respect to the PM segment. Finally, the experimental result was analyzed to confirm the prediction of the FEA.

On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

Science.gov (United States)

Pomeau, Yves

2018-03-01

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply. xml:lang="fr"

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

International Nuclear Information System (INIS)

Wang, Y. B.; Zhu, X. W.; Dai, H. H.

2016-01-01

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

Energy Technology Data Exchange (ETDEWEB)

Wang, Y. B. [Department of Mathematics, ShaoXing University, No.900, ChengNan Avenue 312000, ShaoXing, Zhejiang (China); Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn [School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073 (China); Dai, H. H. [Department of Mathematics, City University of HongKong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong (China)

2016-08-15

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

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)

General form of the Euler-Poisson-Darboux equation and application of the transmutation method

Directory of Open Access Journals (Sweden)

Elina L. Shishkina

2017-07-01

Full Text Available In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations.

A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations

International Nuclear Information System (INIS)

Saurel, Richard; Franquet, Erwin; Daniel, Eric; Le Metayer, Olivier

2007-01-01

A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures

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

Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes.

Science.gov (United States)

Casellas, J; Bach, R

2012-06-01

Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.

Linear stability analysis of heated parallel channels

International Nuclear Information System (INIS)

Nourbakhsh, H.P.; Isbin, H.S.

1982-01-01

An analyis is presented of thermal hydraulic stability of flow in parallel channels covering the range from inlet subcooling to exit superheat. The model is based on a one-dimensional drift velocity formulation of the two phase flow conservation equations. The system of equations is linearized by assuming small disturbances about the steady state. The dynamic response of the system to an inlet flow perturbation is derived yielding the characteristic equation which predicts the onset of instabilities. A specific application is carried out for homogeneous and regional uniformly heated systems. The particular case of equal characteristic frequencies of two-phase and single phase vapor region is studied in detail. The D-partition method and the Mikhailov stability criterion are used for determining the marginal stability boundary. Stability predictions from the present analysis are compared with the experimental data from the solar test facility. 8 references

Comparison Between Polynomial, Euler Beta-Function and Expo-Rational B-Spline Bases

Science.gov (United States)

Kristoffersen, Arnt R.; Dechevsky, Lubomir T.; Laksa˚, Arne; Bang, Børre

2011-12-01

Euler Beta-function B-splines (BFBS) are the practically most important instance of generalized expo-rational B-splines (GERBS) which are not true expo-rational B-splines (ERBS). BFBS do not enjoy the full range of the superproperties of ERBS but, while ERBS are special functions computable by a very rapidly converging yet approximate numerical quadrature algorithms, BFBS are explicitly computable piecewise polynomial (for integer multiplicities), similar to classical Schoenberg B-splines. In the present communication we define, compute and visualize for the first time all possible BFBS of degree up to 3 which provide Hermite interpolation in three consecutive knots of multiplicity up to 3, i.e., the function is being interpolated together with its derivatives of order up to 2. We compare the BFBS obtained for different degrees and multiplicities among themselves and versus the classical Schoenberg polynomial B-splines and the true ERBS for the considered knots. The results of the graphical comparison are discussed from analytical point of view. For the numerical computation and visualization of the new B-splines we have used Maple 12.

Equivalent linearization method for limit cycle flutter analysis of plate-type structure in axial flow

International Nuclear Information System (INIS)

Lu Li; Yang Yiren

2009-01-01

The responses and limit cycle flutter of a plate-type structure with cubic stiffness in viscous flow were studied. The continuous system was dispersed by utilizing Galerkin Method. The equivalent linearization concept was performed to predict the ranges of limit cycle flutter velocities. The coupled map of flutter amplitude-equivalent linear stiffness-critical velocity was used to analyze the stability of limit cycle flutter. The theoretical results agree well with the results of numerical integration, which indicates that the equivalent linearization concept is available to the analysis of limit cycle flutter of plate-type structure. (authors)

Design and analysis of linear oscillatory single-phase permanent magnet generator for free-piston stirling engine systems

Directory of Open Access Journals (Sweden)

Jeong-Man Kim

2017-05-01

Full Text Available This study focuses on the design and analysis of a linear oscillatory single-phase permanent magnet generator for free-piston stirling engine (FPSE systems. In order to implement the design of linear oscillatory generator (LOG for suitable FPSEs, we conducted electromagnetic analysis of LOGs with varying design parameters. Then, detent force analysis was conducted using assisted PM. Using the assisted PM gave us the advantage of using mechanical strength by detent force. To improve the efficiency, we conducted characteristic analysis of eddy-current loss with respect to the PM segment. Finally, the experimental result was analyzed to confirm the prediction of the FEA.

Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures

International Nuclear Information System (INIS)

Bolisetti, Chandrakanth; Whittaker, Andrew S.; Mason, H. Benjamin; Almufti, Ibrahim; Willford, Michael

2014-01-01

Highlights: • Performed equivalent linear and nonlinear site response analyses using industry-standard numerical programs. • Considered a wide range of sites and input ground motions. • Noted the practical issues encountered while using these programs. • Examined differences between the responses calculated from different programs. • Results of biaxial and uniaxial analyses are compared. - Abstract: Site response analysis is a precursor to soil-structure interaction analysis, which is an essential component in the seismic analysis of safety-related nuclear structures. Output from site response analysis provides input to soil-structure interaction analysis. Current practice in calculating site response for safety-related nuclear applications mainly involves the equivalent linear method in the frequency-domain. Nonlinear time-domain methods are used by some for the assessment of buildings, bridges and petrochemical facilities. Several commercial programs have been developed for site response analysis but none of them have been formally validated for large strains and high frequencies, which are crucial for the performance assessment of safety-related nuclear structures. This study sheds light on the applicability of some industry-standard equivalent linear (SHAKE) and nonlinear (DEEPSOIL and LS-DYNA) programs across a broad range of frequencies, earthquake shaking intensities, and sites ranging from stiff sand to hard rock, all with a focus on application to safety-related nuclear structures. Results show that the equivalent linear method is unable to reproduce the high frequency acceleration response, resulting in almost constant spectral accelerations in the short period range. Analysis using LS-DYNA occasionally results in some unrealistic high frequency acceleration ‘noise’, which can be removed by smoothing the piece-wise linear backbone curve. Analysis using DEEPSOIL results in abrupt variations in the peak strains of consecutive soil layers

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

Science.gov (United States)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

Science.gov (United States)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Relation between nonlinear or 'not-linear' characteristics in nuclear kinetics and noise analysis of neutron flux

International Nuclear Information System (INIS)

Kataoka, H.

1975-01-01

The 'not-linear' or '2nd-class-nonlinear' characteristics in nuclear reactor kinetics with the feedback effect in the high-power operation and induce the increase in the amplitude of the neutron flux noise, specially in the very low frequency region. The fundamental behaviour of 'not-linear' characteristics and its effect for the reactor noise was investigated. Application of the reactor noise analysis technique to power reactors has not been successful because of unknown large disagreement between the result of the conventional theoretical analysis and the experimental facts. When the cause of this discrepancy is clear, reactor noise analysis techniques can be effectively applied to instrumentation, control, monitoring and diagnosis of power reactors. (author)

Focal spot motion of linear accelerators and its effect on portal image analysis

International Nuclear Information System (INIS)

Sonke, Jan-Jakob; Brand, Bob; Herk, Marcel van

2003-01-01

The focal spot of a linear accelerator is often considered to have a fully stable position. In practice, however, the beam control loop of a linear accelerator needs to stabilize after the beam is turned on. As a result, some motion of the focal spot might occur during the start-up phase of irradiation. When acquiring portal images, this motion will affect the projected position of anatomy and field edges, especially when low exposures are used. In this paper, the motion of the focal spot and the effect of this motion on portal image analysis are quantified. A slightly tilted narrow slit phantom was placed at the isocenter of several linear accelerators and images were acquired (3.5 frames per second) by means of an amorphous silicon flat panel imager positioned ∼0.7 m below the isocenter. The motion of the focal spot was determined by converting the tilted slit images to subpixel accurate line spread functions. The error in portal image analysis due to focal spot motion was estimated by a subtraction of the relative displacement of the projected slit from the relative displacement of the field edges. It was found that the motion of the focal spot depends on the control system and design of the accelerator. The shift of the focal spot at the start of irradiation ranges between 0.05-0.7 mm in the gun-target (GT) direction. In the left-right (AB) direction the shift is generally smaller. The resulting error in portal image analysis due to focal spot motion ranges between 0.05-1.1 mm for a dose corresponding to two monitor units (MUs). For 20 MUs, the effect of the focal spot motion reduces to 0.01-0.3 mm. The error in portal image analysis due to focal spot motion can be reduced by reducing the applied dose rate

Applied linear regression

CERN Document Server

Weisberg, Sanford

2013-01-01

Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus

Spectral analysis of linear relations and degenerate operator semigroups

International Nuclear Information System (INIS)

Baskakov, A G; Chernyshov, K I

2002-01-01

Several problems of the spectral theory of linear relations in Banach spaces are considered. Linear differential inclusions in a Banach space are studied. The construction of the phase space and solutions is carried out with the help of the spectral theory of linear relations, ergodic theorems, and degenerate operator semigroups

LINEAR AND NON-LINEAR ANALYSES OF CABLE-STAYED STEEL FRAME SUBJECTED TO SEISMIC ACTIONS

Directory of Open Access Journals (Sweden)

Marko Đuran

2017-01-01

Full Text Available In this study, linear and non-linear dynamic analyses of a cable-stayed steel frame subjected to seismic actions are performed. The analyzed cable-stayed frame is the main supporting structure of a wide-span sports hall. Since the complex dynamic behavior of cable-stayed structures results in significant geometric nonlinearity, a nonlinear time history analysis is conducted. As a reference, an analysis using the European standard approach, the so-called linear modal response spectrum method, is also performed. The analyses are conducted for different seismic actions considering dependence on the response spectrums for various ground types and the corresponding artificially generated accelerograms. Despite fundamental differences between the two analyses, results indicate that the modal response spectrum analysis is surprisingly consistent with the internal forces and bending moment distributions of the nonlinear time history analysis. However, significantly smaller values of bending moments, internal forces, and displacements are obtained with the response spectrum analysis.

Analysis of the linear induction motor in transient operation

Energy Technology Data Exchange (ETDEWEB)

Gentile, G; Rotondale, N; Scarano, M

1987-05-01

The paper deals with the analysis of a bilateral linear induction motor in transient operation. We have considered an impressed voltage one-dimensional model which takes into account end effects. The real winding distribution of the armature has been represented as a lumped parameters system. By using the space vectors methodology, the partial differential equation of the sheet is solved bythe variable separation method. Therefore it's possible to arrange a system of ordinary differential equations where the unknown quantities are the space vectors of the air-gap flux density and sheet currents. Finally, we have analyzed the characteristic quantities for a no-load starting of small power motors.

Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

Directory of Open Access Journals (Sweden)

Ram U. Verma

2009-01-01

Full Text Available Based on a notion of relatively maximal (m-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976 on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.

On the dynamic analysis of piecewise-linear networks

NARCIS (Netherlands)

Heemels, WPMH; Camlibel, MK; Schumacher, JM

Piecewise-linear (PL) modeling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modeling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks.

From linear to generalized linear mixed models: A case study in repeated measures

Science.gov (United States)

Compared to traditional linear mixed models, generalized linear mixed models (GLMMs) can offer better correspondence between response variables and explanatory models, yielding more efficient estimates and tests in the analysis of data from designed experiments. Using proportion data from a designed...

MTF measurement and analysis of linear array HgCdTe infrared detectors

Science.gov (United States)

Zhang, Tong; Lin, Chun; Chen, Honglei; Sun, Changhong; Lin, Jiamu; Wang, Xi

2018-01-01

The slanted-edge technique is the main method for measurement detectors MTF, however this method is commonly used on planar array detectors. In this paper the authors present a modified slanted-edge method to measure the MTF of linear array HgCdTe detectors. Crosstalk is one of the major factors that degrade the MTF value of such an infrared detector. This paper presents an ion implantation guard-ring structure which was designed to effectively absorb photo-carriers that may laterally defuse between adjacent pixels thereby suppressing crosstalk. Measurement and analysis of the MTF of the linear array detectors with and without a guard-ring were carried out. The experimental results indicated that the ion implantation guard-ring structure effectively suppresses crosstalk and increases MTF value.

Linear models with R

CERN Document Server

Faraway, Julian J

2014-01-01

A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition.New to the Second EditionReorganiz

Accurate electrostatic and van der Waals pull-in prediction for fully clamped nano/micro-beams using linear universal graphs of pull-in instability

Science.gov (United States)

Tahani, Masoud; Askari, Amir R.

2014-09-01

In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.

Materials analysis using x-ray linear attenuation coefficient measurements at four photon energies

International Nuclear Information System (INIS)

Midgley, S M

2005-01-01

The analytical properties of an accurate parameterization scheme for the x-ray linear attenuation coefficient are examined. The parameterization utilizes an additive combination of N compositional- and energy-dependent coefficients. The former were derived from a parameterization of elemental cross-sections using a polynomial in atomic number. The compositional-dependent coefficients are referred to as the mixture parameters, representing the electron density and higher order statistical moments describing elemental distribution. Additivity is an important property of the parameterization, allowing measured x-ray linear attenuation coefficients to be written as linear simultaneous equations, and then solved for the unknown coefficients. The energy-dependent coefficients can be determined by calibration from measurements with materials of known composition. The inverse problem may be utilized for materials analysis, whereby the simultaneous equations represent multi-energy linear attenuation coefficient measurements, and are solved for the mixture parameters. For in vivo studies, the choice of measurement energies is restricted to the diagnostic region (approximately 20 keV to 150 keV), where the parameterization requires N ≥ 4 energies. We identify a mathematical pathology that must be overcome in order to solve the inverse problem in this energy regime. An iterative inversion strategy is presented for materials analysis using four or more measurements, and then tested against real data obtained at energies 32 keV to 66 keV. The results demonstrate that it is possible to recover the electron density to within ±4% and fourth mixture parameter. It is also a key finding that the second and third mixture parameters cannot be recovered, as they are of minor importance in the parameterization at diagnostic x-ray energies

Simplified non-linear time-history analysis based on the Theory of Plasticity

DEFF Research Database (Denmark)

Costa, Joao Domingues

2005-01-01

This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...... is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation...

voom: Precision weights unlock linear model analysis tools for RNA-seq read counts.

Science.gov (United States)

Law, Charity W; Chen, Yunshun; Shi, Wei; Smyth, Gordon K

2014-02-03

New normal linear modeling strategies are presented for analyzing read counts from RNA-seq experiments. The voom method estimates the mean-variance relationship of the log-counts, generates a precision weight for each observation and enters these into the limma empirical Bayes analysis pipeline. This opens access for RNA-seq analysts to a large body of methodology developed for microarrays. Simulation studies show that voom performs as well or better than count-based RNA-seq methods even when the data are generated according to the assumptions of the earlier methods. Two case studies illustrate the use of linear modeling and gene set testing methods.

Similarity Analysis for Reactor Flow Distribution Test and Its Validation

Energy Technology Data Exchange (ETDEWEB)

Hong, Soon Joon; Ha, Jung Hui [Heungdeok IT Valley, Yongin (Korea, Republic of); Lee, Taehoo; Han, Ji Woong [KAERI, Daejeon (Korea, Republic of)

2015-05-15

The newly derived dimensionless groups are slightly different from Hetsroni's. Reynolds number, relative wall roughness, and Euler don't appear, instead, friction factor appears newly. In order to conserve friction factor Reynolds number and relative wall roughness should be conserved. Since the effect of Reynolds number in high range is small, and since the scaled model is far smaller than prototype the conservation of friction factor is easily obtained by making the model wall just smooth. It is much easier to implement the test design than Hetsroni's because the Reynolds number and relative wall roughness do not appear explicitly. In case that there is no free surface within the interested domain of the reactor, the gravity is of second importance, and in this case the pressure drops should be compensated for in order to compare them between prototype and model. The gravity head compensated pressure drop is directly same to the measured value by a differential pressure transmitter. In order to conserve the gravity effect Froude number should be conserved. In pool type SFR (Sodium Cooled Fast Reactor) there exists liquid level difference, and if the level difference is desired to be conserved, the Froude number should be conserved. Euler number, which represents pressure terms in momentum equation, should be well conserved according to Hetsroni's approach. It is not a wrong statement, but it should be noted that Euler number is NOT an independent variable BUT a dependent variable according to Hong et al. It means that if all the geometrical similarity and the dimensionless numbers are conserved, Euler number is automatically conserved. So Euler number need not be considered in case that the perfect geometrical similarity is kept. However, even in case that the geometrical similarity is not conserved, it possible to conserved the velocity field similarity by just conserve Euler number. It gives tolerance to the engineer who designs the test

Non-linear singular problems in p-adic analysis: associative algebras of p-adic distributions

International Nuclear Information System (INIS)

Albeverio, S; Khrennikov, A Yu; Shelkovich, V M

2005-01-01

We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of p-adic analysis related to p-adic distributions (generalized functions). We construct the p-adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous p-adic distributions. This algebra is embedded in the Colombeau-Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed

Positivity-preserving CE/SE schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes

KAUST Repository

Shen, Hua

2018-05-28

We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

Energy Technology Data Exchange (ETDEWEB)

Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)

2013-07-01

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

International Nuclear Information System (INIS)

Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.

2013-01-01

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)